Technical Report No. 226 004860-4-T INVESTIGATION OF THE PROPAGATION STABILITY OF A TIME SPREAD UNDERWATER ACOUSTIC CHANNEL by Raymond L. Veenkant Approved I. Theodore G. Birdsall COOLEY ELECTRONICS LABORATORY Department of Electrical and Computer Engineering The University of Michigan Ann Arbor, Michigan for Contract No. N0014-67-A-0181-0035 Office of Naval Research Department of the Navy Arlington, Va. 22217 May 1974 Approved for public release; distribution unlimited.

ABSTRACT An experimental investigation of analysis and display techniques for extracting stability information from underwater acoustic propagation data has shown the feasibility and usefulness of a specific display format, called the Channel Digit Response. All of the complex nature of the channel reception is retained in the display, but the format compresses the data and enhances the extraction of qualitative stability information. The investigation and conclusions are limited to propagation tests using periodic transmissions, as periodic transmissions are the usual type used for studying varying multipath propagation. The investigation data base spanned 133 hours, from a 43 n. mile range across the Straits of Florida. The effective time resolution of the data was. 02 seconds. Crosscorrelation, autocorrelation, and power spectrum analysis, and several threshold techniques based on time-lag crosscorrelation were investigated, and their effectiveness compared to the Channel Digit Response. iii

ACKNOWLED GMENTS The author wishes to thank the members of his committee, especially Professor Birdsall for his aid, encouragement and inspiration over several exciting years of graduate study, and Professor Root for several discussions on basic notions of system identification. Special thanks are due to Texas Instruments Incorporated, P. Lorraine and T. W. Ellis for their generous cooperation and the use of computer facilities for this thesis. The author is indebted to the entire Project MIMI and the United States Navy Office of Naval Research for continuing support of MIMI and a part of this thesis. iv

TABLE OF CONTENTS Page ABSTRACT iii ACKNOWLEDGMENTS iv LIST OF ILLUSTRATIONS vii LIST OF SYMBOLS AND ABBREVIATIONS ix CHAPTER 1: INTRODUCTION 1 CHAPTER 2: MIMI: THE EXPERIMENT AND THE CHANNEL 6 2. 1 Introduction 6 2. 1. 1 Signal and Receiver Designs 10 2.1. 2 Low-Pass Processing of Bandpass Signal 13 2.1. 3 Independent Variables - Discrete Notation 14 2. 2 Characterization and Measurement of the MIMI Channel 16 2. 2. 1 General Characterization 16 2. 2. 2 Noise-Free Measurements of a Doubly Spread Channel 19 2. 2.3 Instantaneous h(t, X) Measurement of the UWAP Channel in Noise, 20 2. 2. 4 Decomposition of the Doubly Spread Channel into Two Singly Spread Channels 21 2. 3 The DUAL Experiment 23 2. 3. 1 The CW Experiment 25 2. 3. 2 The Multipath Experiment 25 2. 3. 3 Noise Measurement 27 2. 3. 4 The CANDOR Experiment 27 2. 3. 5 BL Effects on h(t, X) Measurements 33 2.4 Summary V

TABLE OF CONTENTS (Cont.) Page CHAPTER 3: PRESENTATION AND DISCUSSION OF DUAL RESULTS 40 3.1 Results 40 3. 2 Time Base Artifact of Data Files 9, 10, 11, and 12 67 3. 3 Summary - A Preliminary Channel Model 68 CHAPTER4: THE CDR GRAM DISPLAY 70 4. 1 Introduction 70 4.2 Description of Display 71 4. 2. 1 Display Format 71 4. 2. 2 Amplitude and Phase Information 75 4. 2. 3 Thresholding for Clutter Suppression 77 4. 3 Experimental Results 78 4. 3. 1 CDR Data Presentation 78 4. 3. 2 Parameter Extraction 79 4.3.3 Time-Invariance, Correlatedness and Stationarity of h(t, X) 105 4. 3. 4 Identification of Two Physical Propagation Modes 114 4.4 Summary 119 CHAPTER 5: OTHER CHANNEL REPRESENTATIONS 122 5.1 Channel Digit Spectrum 122 5. 2 Channel Autocovariance 135 CHAPTER 6: CONCLUSIONS 148 APPENDIX A: SCAN PLOTS WITH THE 731 RECORDER 150 APPENDIX B: CHIRP-Z-TRANSFORM 153 REFERENCES 160 DISTRIBUTION LIST 164 vi

LIST OF ILLUSTRATIONS Figure Title Page 2. 1 The Miami-Bimini Range: (a) The Straits 7 of Florida, (b) Bottom Profile 2.2 Sound Speed vs. Depth 8 2.3 Sound Ray Paths 9 2. 4 Magnitude Spectrum of the MIMI CM Signal 11 2. 5 The Linear, Quasi-Stationary UWAP Chan- 16 nel, An Impulse Response Representation 2. 6 Frequency Spreading of the UWAP Channel, 17 Observed Using a CW Transmission 2. 7 The Multipath Structure Delay Spread of the 19 Channel 2. 8 The Frequency Responses of the DUAL Pro- 24 cessing Filters 2.9 The Phase-Only Matched Filter 26 2. 10 CW Reception Magnitude Spectrum 34 2. 11 The Multipath Measurement Signal Spectrum 35 2. 12 The Periodic Pulse Signal 36 2. 13 Received Frequency Spread Line Spectrum 36 2. 14 Typical Multipath Reception 38 3. 1 Chronology of November 1970 DUAL Exper- 43 iment 3.2 ) 48DUAL Graphs 1 to 19 66 3.20 J vii

Figure 4. 1 4.2 4. 3 4. 12 4. 13 4.22 J 5.1 5. 10 5.11 ) 5.20 LIST OF ILLUSTRATIONS (Cont.) Title Fundamental Display The Ordered Pair Gram Display CDR Grams 1 to 19 CDR Grams 1 to 19 with Clutter Suppression CDS Grams 1 to 19 COVH Grams 1 to 19 Page 72 74 8089 9099 126135 138147 viii

LIST OF SYMBOLS AND ABBREVIATIONS A(t) B BL C(t) cdr(t, X) CDR CDS CM COVH Covht(/L) CW CZT FFT f, Af gi Hc(f) HN(f) HR(f) The received carrier signal phase angle The channel frequency spread extent Kailath's doubly spread channel factor The received carrier signal power The time spread channel digit response, also h(t, X), ht(X) Channel digit response Channel digit spectrum Complementary-phase modulation Covariance of ht(X) The covariance of ht(X) at time t Carrier wave The Chirp- Z- Transform The fast Fourier transform algorithm The discrete frequency index and discrete frequency increment Processing gaps in the data The carrier processing filter transfer function The noise process filter transfer function The reverberation filter transfer function ix

LIST OF SYMBOLS AND ABBREVIATIONS (Cont.) Hs(f) h(t, X), ht(X) hst(X ) L mt N(t) n(t, X) pof(X ) R(t) RBR S(t) St(f) SRS s(t)bp s(t) T d T p T (t) t, At The pulse signal filter transfer function The channel digit response (complex envelope) The channel sequence response The channel time spread extent The binary signal sequence The measured noise power process The instantaneous noise process of the time spread channel The phase-only matched filter for hst(X) The measured reverberation power process Refracted- Bottom-Refracted propagation The measured pulse power process The channel digit magnitude spectrum Surface-Reflected-Surface propagation The bandpass signal reception The complex envelope of s(t)bp The signal (sequence) digit duration The signal (sequence) period The measured forward decorrelation time of the channel's normalized cross-correlation coefficient, measured with respect to criterion The discrete time index and the discrete time increment x

LIST OF SYMBOLS AND ABBREVIATIONS (Cont.) t. The starting time of data file i 1 UWAP Underwater acoustic propagation X, AX The discrete time-delay index and the timedelay increment Pt t The channel's normalized cross-correlation 1 2 coefficient xi

CHAPTER I INTRODUCTION The goal of this thesis is to discover signal processing concepts and methods that can be used in channel modeling and measurements of underwater acoustic propagation. This work is based on a firm foundation. There are two major aspects of this foundation: first are the theoretical materials of various authors on characterization, modeling and measurement of channels, and, second is the very well planned MIMI propagation experiment which has existed for approximately ten years, and which has been conducting virtually continuous field measurements since 1970. The theoretical efforts mentioned provide a basis for this work for several reasons. Although many ideas come from intuition, it is always reassuring to be able to put the intuitive situation in theoretical context, adding legitimacy to the results. The particular case is described in theoretical terminology of a general case and makes possible ready communication and education of ideas and results to others. Finally, intuition gets the credit for many ideas but it is the theory that breeds, extends and perpetuates that intuition for other and later co-workers. The MIMI design consists of three very interactive and interdependent parts: (1) signal design, (2) receiver design and 1

2 (3) transmitter and receiver implementation. The MIMI experiment has most recently consisted of a processing program called DUAL together with all the required support. DUAL has been collecting and measuring propagation data in many sites for several years. Very briefly, DUAL is an experiment to continuously measure and record for long periods of time, several propagation parameters: 1. Broadband noise power, 2. Broadband signal power, 3. Narrowband signal power and phase angle, and 4. Forward scattered surface reverberation power. DUAL also obtains an approximate instantaneous measurement of the channel impulse response, most accurately called the channel pulse or digit response, but often simply referred to as the channel multipath response. All of these data, which represent a tremendous reduction of information from the raw unprocessed propagation data, are the input data for this thesis. More specifically, the data used in this thesis is from a DUAL experiment conducted in November 1970 in the Straits of Florida and reported by Dr. R. H. Heitmeyer [ 1 ]. Therefore, in the context of the MIMI experiment, this thesis is to be an extension of DUAL. In particular, the channel digit response, CDR, will be concentrated on as the starting

3 point for developing methods to extract more information from the channel. The UWAP channel is clearly stochastic so that the basic questions that immediately arise are: 1. Is a stationary model satisfactory, 2. Can an uncorrelated model be used, 3. To what extent is the channel spread, 4. What are the channel's statistics (can it be modeled as Gaussian)? The answers to these questions are a major objective of this thesis; or at least to obtain methods which may be used to answer such questions. Conclusive answers to each of the above general questions concerning characterization of the UWAP channels may be hard to come by, that is, conclusions drawn here may be somewhat on the subjective side, however, the methods used will be objective. Thus, if the reader and later experimenters disagree with the conclusions here, they will certainly be free and able to draw their own conclusions from the results presented here or obtained later using methods presented here. Considerable literature concerning the theoretical aspects of channel modeling and measurements exists. VanTree's Detection, Estimation, and Modulation, Part II is a comprehensive, easily read text largely concerned with detection and estimation

4 (and, therefore, modeling) in singly and doubly spread stochastic channels [ 25 ]. This text also contains a very extensive and recent bibliography of theoretical and empirical work in this area. A classic article by Kailath addresses the problems of noise-free measurements in doubly spread channels [ 3 ]. The important result of this work is that if the channel spreading area (BL product) is less than 1, the channel is called underspread, and instantaneous (impulse response) channel measurements are meaningful. Otherwise, (BL > 1) the channel is overspread and average (e. g., autocorrelation of the impulse response) measurements must be relied on to obtain unambiguous measurements. Bello [ 32] discusses at length variations of fundamental models of spread random channels. Although the UWAP channel turns out to be an underspread channel, so that Kailath's results guarantee that instantaneous measurements are meaningful here, our measurement techniques will be more physically motivated and are complicated by the presence of noise. The UWAP channel is well known to be a doubly spread channel, where frequency or Doppler spreading is largely attributed to interaction of the random moving surface with propagation (the formal terminology for the frequency spreading phenomenon is "forward scattered surface reverberation") and the time spreading (usually referred to as "'multipath") is due to the transmission

5 of sound between two points via multiple paths. The primary emphasis of this thesis will be the study and characterization of the time-spread channel. The limitation of noise contaminated measurements and the impracticality of twodimensional processing preclude the use of instantaneous measurements of the doubly spread channel. However, because the channel is underspread, proper signal design provides a decomposition of the general doubly spread UWAP channel into two singly spread channels, which can readily be investigated either simultaneously or separately. Although the multipath channel is emphasized, the frequency spread channel is still of interest. As this thesis proceeds, another very natural and convenient decomposition results in the identification of two UWAP channels which may each be considered as a general channel to be characterized. Indeed, these two channels are quite different and therefore, each is interesting in its own right.

CHAPTER 2 IMMI: THE EXPERIMENT AND THE CHANNEL 2. 1 Introduction Since the early 1960's cooperative efforts to study underwater acoustic propagation (UWAP) have been conducted by The University of Michigan and the University of Miami. The primary site of these studies has been the 43-mile range in the Straits of Florida from a fixed transmitter off the Miami shore to various hydrophones in the waters of Bimini Island in the Bahamas. The major features of the MIMI experiments are: (1) fixed transmitters and receivers and (2) the interest in very long time series of data. The fixed sites greatly simplify the experimental setup, provide a relatively permanent facility necessary for long time operation, and avoid the introductionofDoppler effects due to moving platforms. Long time series data are believed necessary for understanding UWAP and for developing and testing UWAP models. The Miami-Bimini range is illustrated in Figure 2. l(a) together with a bottom profile in Figure 2. l(b). A velocity profile, obtained in November 1961, of the straits is illustrated in Figure 2. 2. Although the velocity profile changes continuously, this example can be considered reasonably typical for this time of year. 6

7 (a) 800o' 79*4' 79'30 79'20' uJ'I: aJ 0. UJ:l = 600 I VERTICAL SCALE ~ 37 tHORIZONTAL) 0 10 20 30 a, I I. I, I 40 N. MILES i -— 7'1 —,-~~~~~~~~i —---- - -- - r — 1 - ~ 1 (ONE 10 ONE SCALE) (b) Fig. 2. 1. The Miami-Bimini Range: (a) The Straits of Florida, (b) Bottom Profile

8 h'AUTCAL MILES O 1 20 30 40 I I i I I 4 i I. * l i -200 a 1540'C. - 1. ii0;20 SOUND SPEED SCALE - /SEC. / ^~/ / 1~i0, Fig. 2.2. Sound Speed vs. Depth The point of interest is the velocity gradient, which is a function of time and space. The velocity gradient, even as a function of depth, leads to a very complex propagation structure. The propagation ray trace corresponding to this velocity profile is presented in Figure 2. 3. In this figure there are illustrated two basic types of propagation. There are sound paths traveling along the surface boundary undergoing reflection and refraction. This is called SRS

200- > 400800Fig. 2. 3. Sound Ray Paths Along 25~ 44' on 28-29 Nov. 1961

10 propagation. Sound paths are similarly traveling along the bottom by reflection and refraction. This is called RBR propagation. The data for the research in this thesis are selected from a two-week experiment conducted at this site in November of 1970. The data were conveniently available, are of good quality, and are representative of the Straits of Florida at this time of year. The data were organized into 19 files. File 1 to 8 are continuously recorded from the deep (1200 feet) bottom mounted hydrophone located at point 3 in Fig. 2. l(a), starting at 17:16 hours on November 11, 1970, until 18:46 hours on November 17, 1970. Files 9 to 19 are from 10:20 hours on November 23 to 9:05 hours on November 29, 1970, and were recorded from the bottom mounted shallow (100 feet) hydrophone also located near point 3 in Fig. 2. l(a). For more details of the experiment refer to Reference [ 1], a preliminary report on that experiment. 2. 1. 1 Signal and Receiver Designs. The signal and receiver designs of the MIMI experiment have evolved over a period of time, and are largely due to the efforts of Dr. T. G. Birdsall. Detailed discussions and analyses of the signals and receivers may be found in References [ 1 ], [ 15 ], and [16]. A brief discussion of the more important properties of the signals and the receivers is useful. The signal consists of a 63-digit binary maximal pseudo-random sequence complementary-phase modulated (CM) onto an ultra-stable 420 Hz

11 carrier wave (CW). The signal is transmitted continuously. Each digit of the sequence corresponds to 8 carrier cycles (approximately 20 msec) and the period of the sequence is 1.2 seconds. The signal may be expressed s(tbp = A cos (2f 420t + mt v/4) where mt = ~ 1 the binary values of the sequence. Thus, the transmitted signal is a continuously transmitted 420 Hz sinusoid with ~ 45 degree phase shifts occurring at integer multiples of 20 milliseconds with resulting spectrum sketched in Fig. 2. 4. (There are actually 62 lines on each side of the carrier to the first nulls.) CW LINE Af /T Hz,If A-t f Hz I | | - - - - - I ] - f Hz 7^*-9f\ ow\/\ n'o AIn jlU Ki-/Td - d Fig. 2. 4. Magnitude Spectrum of the MIMI CM Signal

12 The carrier contains approximately half the total power. The remainder of the signal magnitude spectrum is a line spectrum with a sin7Td envelope. Theline spacing is determined by the rf Td signal period, T, so that Af = 1/T. The zeros of the envelope are determined by the duration, Td = 20 msec, of the sequence digits. The phase spectrum of the CM signal is a pseudo-random function of frequency. It should be clear that since this phase spectrum is known, by simple phase correction and adjustment of the carrier line, multiply by 1/63, the signal spectrum becomes sin 7rf T nf T d with constant phase. This transformation can be accomd plished by multiplying the complex signal spectrum by a spectrum of the transmitted signal. The transformation can also be performed in the time domain by cross-correlating the signal with the original 63-digit sequence of 1 and -l's. This technique has become known as phase-only matched filtering. Obviously, the resulting spectrum is that of a T second periodic pulse with duration, Td. Thus, the CM-CW signal provides continuous and simultaneous CW and pulse experiments with high average power in both experiments at low peak transmitted power. Although simultaneous CW and pulse experiments are performed, they will be treated separately through the remainder of this work.

13 2.1. 2 Low-Pass Processing of Bandpass Signals. In all MIMI processing the received bandpass (100 Hz) signal centered at 420 Hz is translated to DC (zero Hz). The result is that the original real-valued bandpass signals become complex-valued lowpass signals. The following relations between the bandpass and low-pass signals are valid. * s(t)b = Is(t)l cos (wt+ 0) = Re{s(t) eiwt} where s(t) is the complex-valued envelope of s(t)bp s(t) - ls(t)l e0 Hereafter, all discussions will be in terms of the process complex envelopes and complex low-pass filters. Therefore, the CW experiment becomes, in the receiver, a DC experiment. And, although the multipath structure is denoted by ht(X) a low-pass process, the real measurement is at 420 Hz. That is, the ht(X) discussed and presented is the complex envelope of the bandpass channel See Reference [ 15 ] for the MIMI implementation and Reference [ 25 ] for the proofs of these relations for both deterministic and stochastic signals.

14 i27r420t ht(X )bp = Rel{ht(X )e e 2. 1.3 Independent Variables - Discrete Notation. Since all of the signal processing discussed here is performed on a digital computer following antialias filtering, sampling and analog-todigital conversion, the independent variables are integer-valued discrete indices rather than continuous variables. The purpose of this discussion is to eliminate subsequent questions about notation or interpretation. The three independent variables of interest are: 1. time = t * At 2. frequency= f A f 3. time-delay =X ~ AX where f is the discrete Fourier transform index corresponding to the X index. This frequency index is not the frequency spread variable corresponding to the Fourier transform with respect to the time variable, t. This is a possible source of confusion, but with this warning the distinction should be clear in the context. The independent variables incremental values are fixed throughout: 1. At = 102 seconds 2. AX =5 milliseconds 3. Af -.833Hz

15 where A f is determined by the transmission signal period, A f = 1/T, T = 1.2 seconds and AX is a more than adequate sampling interval for the 100 Hz transmission bandwidth. The range of the indices are: 1. t =0, 1,... 2. f = -63,..., 0,..., 62 covering the ~ 50 Hz transmis sion band 3. XeA where A = {0,..., 251} and the signal period, T = 252AX and the signal pulse Td = 4AX. The major functions involving these independent are: duration, indices 1. The channel digit response, cdr(t, X) = h(t, 2. Various DUAL scalar processes; e. g., C(t) 3. The channel digit spectrum, X) = ht(X) A /~ v "/ i27if) /252 St(f) = Z ht(X) e /2 XcA A familiarity with discrete parameter representation has been assumed. Reference [28 ] is directed at the fundamentals of digital signal processing.

16 2. 2 Characterization and Measurement of the MIMI Channel 2.2. 1 General Characterization of the MIMI Channel. In general, the UWAP channel can be viewed as a linear, quasi-stationary doubly spread filter with an impulse response, h(t, ) - ht(X ). The assumption of quasi-stationarityappears to be quite valid and will be justified in later development. This description of the UWAP channel is summarized in Figure 2. 5. n(t) x(t)> h(t y(t) a yt) y(t) =h (x,t) x(t-X)dX+n(t) 0 Fig. 2. 5. The Linear, Quasi-Stationary UWAP Channel, An Impulse Response Representation The doubly spread description of the channel includes both frequency (or Doppler) spreading, which is caused by "short term" time fluctuation in the channel, and time-delay spreading, which in the UWAP channel is due to multiple path propagation. The concept

17 of spreading involves the influence of the channel upon a transmitted signal, whereby the received signal is of greater bandwidth or time duration than the transmitted signal [25 ]. Obviously, a channel may be only time-delay spread, or only frequency spread in which case the channel is called singly spread. Frequency spreading is most clearly observed using a constant amplitude continuous sinusoidal wave, CW, transmission. In the UWAP channel the frequency spread phenomenon results in a slight (on the order of tenths of millihertz) spreading in the CW line and the introduction of sidebands of incoherent energy in the approximate region from 0. 1 to 0. 3 Hz each side of the CW. This is illustrated in Fig. 2. 6. The slight spreading of the CW is attributed to such long term phenomena as tides (12 and 24-hour periods) and internal waves (1 to several hour periods) and is so insignificant that it is not considered in subsequent frequency spreading discussion. A S oHz -.3 -.1 0.1.3 Fig. 2. 6. Frequency Spreading of the UWAP Channel, Observed Using a CW Transmission

18 The major frequency spreading has been adequately modeled to date as an amplitude modulation process of the CW transmission by a narrow band, 0. 2 Hz, random process. Due to the high correlation of frequency spreading activity with the ocean's surface conditions and the modulation frequencies, 0. 1 to 0. 3 Hz, correspondence to common surface wave periods, 3 to 10 seconds, the frequency spreading in the UWAP channel is largely attributed to direct interaction of sound rays (or paths) with the randomly moving surface waves. This frequency spread energy is called forward scattered surface reverberation or just reverberation. Clearly, reverberation energy is dependent upon the presence of a surface mode of propagation as well as the surface conditions. However, given a surface propagation mode, the relation between the surface conditions and the reverberation energy is not known; however, total reverberation energy approaching 50 percent of the received CW energy is not uncommon. The time-delay spread feature of the UWAP channel is often called multipath because the delay spreading is a result of the multiple propagation paths, each with its own attenuation, arrival (delay) time, etc. The multipath structure of the channel is best observed using a short pulse (approximate impulse) transmission. Figure 2.7 illustrates the delay spread created by an all pass, three path structure. The delay spread of the MIMI channel can

19 vary from approximately 20 milliseconds (msec) to 500 or 600 msec. to t t2 t3 TIME ~0 1 2 3 DELAY SPREAD Fig. 2. 7. Arrivals at t, t2, and t3 from a Single Pulse Transmission at to Illustrate the Multipath Structure (Delay Spread) of the Channel 2. 2. 2. Noise Free Measurements of a Doubly Spread Channel. Kailath [3 ] shows that, even in the noise free case, unambiguous measurements of a doubly spread channel are only possible under certain restrictions. A doubly spread channel based upon the severity of spread is classified as either underspread or overspread. The severity of channel spread is measured by the channel spread factor, BL, where B is a measure of the channel frequency spread and L is a measure of the channel's delay spread. The parameters B and L are defined in terms of the channel's impulse response, h(t,X ). B = max Bandwidth of h(t, X)} mwx {smallest f0 9 H(f, X) = 0, f > f0} and max L = m {Duration of h(t, A) max - t {smallest A0 h(t, A) = 0, X > A0 }

20 where bandwidth is measured in terms of frequency variable in the Fourier transform of h(t, X) with respect to the time variable, t, and the duration of h(t, X) is measured with respect to the delay variable, A. For practical reasons, looser definitions of bandwidth and duration are assumed in the data interpretation of this thesis. If BL > 1, the channel is called overspread and only unambiguous average, e. g., mean and auto-correlation, measurements are possible. Kailath [3] and Bello [19], and [20], discuss in length measurement techniques for the overspread, noise-free channel. These techniques generally made statistical assumptions about the channel and often are limited to the case BL < 2. For BL < 1, the underspread channel, unambiguous instantaneous measurements of h(t, X) can be made. From previous discussion B a 0. 6 and L 0. 6 in the MIMI channel so that BL - 0. 36 and the channel is clearly underspread [ 15 ], [16], and [ 17]. Thus, "instantaneous" h(t, X) measurements can be made on the MIMI channel. In general, the UWAP channel will be less complex than the MIMI channel so that it may be safely generalized that the UWAP channel is underspread. 2. 2. 3. "Instantaneous" h(t, X) Measurements of the UWAP Channel in the Presence of Noise. Since the ocean contains considerable environmental (ambient, biological, surface, etc. ) and

21 man-made (shipping) noise, measurements of h(t, X) must include signalling and filtering techniques designed to obtain reliable, high signal-to-noise ratio measurements of h(t, X) which can still be considered instantaneous. Fortunately, the UWAP channel is "time-invariant" for intervals of 5 to 15 or more minutes, so that by using periodic, low peak power but high average power, signal transmission techniques and long term, approximately one minute, coherent "matched" filtering techniques high signal- to- noise ratio, instantaneous channel measurements are obtained. 2. 2. 4. Decomposition of the Doubly Spread Channel Into Two Singly Spread Channels. A practical solution to the measurement of a doubly spread channel under the constraint of additive channel noise is to decompose the problem into the measurement of two singly spread channels. In general, this would be a compromise forced by the measurement noise. However, due to the nature of the UWAP channel, this approach is a natural decomposition of the coherent component(delay spread) from the incoherent (frequencyspread) component, which is very simply accomplished, because these components are orthogonal (occupy disjoint regions of the * Coherent processing is obtained by use of very coherent frequency and phase references at the transmitter and receiver, and filtering is implemented digitally in a computer [ 15 ].

22 frequency axis), by appropriate signal design and linear filtering. Whenever, due to the lack of a surface mode, reverberation is not present, the channel is naturally and conveniently singly spread. The means of this decomposition is quite simple and is briefly described. The basic idea is to transmit periodic signals with spectral lines spaced far enough apart so that the reverberation sidebands fall between these lines. In the noise free case h(t, X) can be measured using an impulse input x(t) = 6 (t) so that the output y(t, X) = h(t, X). With additive noise this measurement becomes a highly contaminated one, y(t, X) = h(t, X) + n(t, X). The peak signal-to-noise ratio of this measurement is estimated at approximately - 10 to 0 dB in the MIMI channel. By making x(t) a periodic train of impulses, M- 1 x(t) =- 6 (t - mT ) and using the time invariance of the channel m=0 P over te[0, MT ], the multipath structure (delay spread) of h(t, X) is estimated by M-1 ht(X) - h(t- mT X) + n(t- mTp, X) m=0 pp In practice for values of M = 85 and MT 102 seconds p high (+10 to 20 dB) signal-to-noise ratio estimates of ht(X) are obtained. Note that MT = 102 seconds is well within the time invarip ance limit of 5 to 15 minutes and that for M > 8 with T = 1. 2 - p

23 seconds the frequency spread energy is filtered out of the ht( ) measurement. A description of the reverberation measurement is included in the next section which briefly describes the DUAL experiment. 2. 3 The DUAL Experiment With minor variations, DUAL is the basic MIMI experiment currently in the field obtaining long time series acoustical data on the UWAP channel at various locations. The DUAL experiment consists of three subexperiments simultaneously measuring various aspects of the channel behavior. The first of these is the CW experiment, which measures the CW power, C(t), phase angle, A(t) and the reverberation power in the CW reception, R(t). The magnitude spectrum of the filters, HC(f) and HR(f), used to measure CW and reverberation parameters, respectively, are illustrated in Fig. 2. 8. Second, the multipath experiment obtains an estimate of the channel digit response, ht(X), measures the total received broadband-signal power, S(t), and measures the decorrelation time, T+ (t), of the channel's normalized cross-correlation coefficient. Third, a total noise power measurement, N(t), in the transmission band is made. The filters HS(f) and HN(f) for the multipath and noise measurements, respectively, are illustrated in Fig. 2. 8. Each of these three experiments are discussed in

-H I- 13.24 MHz Hc(f) f = 420 Hz c f (a) HS(f) +-e 13.24 MHz - g.of - 1.69Hz T - 1 1 11 1 LI I 11 1.1 1 1 1. 1 1 1 1 f (b) c f f HN(f) H - 13. 24 MHz Af = 1. 69Hz = T -,1,1. 1,1 f1,1t 1,1 1,1 1,1 1,1, 1 1, 1,1 1..1 it 11 HIR(f - e-.848 f + C Fig. 2. 8. The Frequency Responses of the DUAL Processing Filters

25 brief detail. 2. 3. 1. The CW Experiment. The CW experiment is used to obtain continuous narrowband power and phase angle measurements as well as the reverberation measurements. The CW power process is denoted by C(t) and the CW phase process is A(t). The reverberation measurement is a total power measurement, R(t). The R(t) measurement is only made on the CW sidebands because it is the only line in the signal spectrum providing sufficient reverberation to noise power ratio for meaningful R(t) measurements. The CW and reverberation filters, Hc(f) and HR(f), respectively, are illustrated in Fig. 2. 8. 2. 3. 2. The Multipath Experiment. In the multipath experiment ht(X) is measured using M-1 ht(X) = h(t - kTp X) + n(t- kT, X ) k=0 Pp where T = 1.2 seconds and M = 85 so that each ht( ) represents the multipath structure of the channel for 102 seconds. Every 102 seconds a new ht(X) is measured. DUAL measures ht(), computes some parameters of physical significance and saves ht(X ) on digital tape, but does not display ht(X). The physical parameters computed are: (1) the total received broadband (pulse) power, S(t), and (2) TW(t), the decorrelation time of the

26 normalized cross-correlation coefficient of ht(X). The T (t) analysis is discussed later in this section in the CANDOR experiment. S(t) is related to ht(X) by S(t) = L Iht(X) = j Ihst(X)12 X6A XeA where ht(X ) is the phase-only match filtered form of hst(X ) This relationship is illustrated in Fig. 2. 9. t hst(x) t( x) j, -- r pof(x) Fig. 2. 9. The Phase-Only Matched Filter This is the transformation in the receiver which provides the channel equivalent pulse response ht(X) from the binary sequence response hst(X). For this reason, the multipath structure representation ht(X) is also called the channel digit response, CDR. As pointed out earlier, the phase-only matched filter has no effect on the magnitude spectrum of hst(X ) so that S(t) can be computed from hst(X) or ht(X). The transfer function, * The CW signal is filtered out of hst( ) before the phaseonly filtering.

27 H (f), of the multipath measurement filter, a comb filter on the s signal lines, is illustrated in Fig. 2.8. For more details on the computation of hst(X ) and ht(X) see References [15] and [ 16]. 2. 3. 3. Noise Measurement. By placing a comb filter, HN(f), between the passbands of H (f) a total noise power measurement in the transmission band, 420 ~ 50 Hz, is obtained. The noise power measurement is denoted N(t). HN(f) is illustrated in Fig. 2. 8. 2. 3. 4. The CANDOR Experiment. CANDOR is presented here as an extension and continuation of the experiment designed by T. G. Birdsall and performed in the MIMI experiments of July 1970. Results of that experiment are documented in Reference [ 2]. CANDOR is an acronym for Continuous Analysis with Decision Oriented Recording. As implied in the full title, the major goal of CANDOR is to represent the UWAP channel with a minimum, or at least reduced, quantity of recorded data. That is, the objective is to retain sufficient information about the channel while avoiding excessive redundancy in the data. The motivation for this attempt at data reduction is the overwhelming task of data digestion necessary for understanding the UWAP channel. The storage of all the data from a continuous DUAL experiment is alone a great practical problem. An effective means for displaying and interpreting long time series of ht(X )

28 is the major contribution of this thesis. But, off-line analysis of propagation experiments is necessary in developing new ideas and techniques, and the cost of such analysis in dollars, human resources, computer resources and simply time is at least proportional to the quantity of data involved. Thus, an order of magnitude reduction of data necessaryfor an adequate representation of the channel can be the difference that makes a post-processing task practical. That is, unless considerable data reduction techniques are developed, many post-processing efforts will never be started, which will greatly stunt the development of new MIMI experiments. The premise of CANDOR is that a single ht(X ) from each interval of channel time-invariance is a sufficient representation of the channel. Since a new ht(X) is measured every 102 seconds and the channel is time-invaiant for durations of typically five to fifteen minutes, an approximate order of magnitude reduction in data quantities is expected. The criteria used to evaluate a representative ht(X) are all based upon the normalized cross-correlation coefficient of ht(X ) Pt t defined by 1 2 251 ht ()ht (X) A X=0 1 2 tt' t 1 2 11 ht (X)il 21 h (X 1 2

29 where 11h( )11 - oht( ) ht (X) ]lht(X)]z 251 ~ ~. X =0 Pt t is the normalized cross-correlation function of 12 ht(X) evaluated at zero delay. As will be seen in the CDR grams in Chapter 4 and as documented in Reference [2 ], the changes in the channel multipath structure are not manifested in arrival time changes, that is, the average propagation time of the multipaths are constant for hours, so that t t is as effective a measure 1,2 of the similarity or dissimilarity of ht(X) as the entire crosscorrelation function and there is no reason to compute that function for these purposes. The forward interval of time for which ht (X) is repre1 sentative is the interval t2 - t1 = T (t1) of time such that pt t 2z ~ s 1~ t ~1 2 "satisfies E ". Expressed in polar coordinates iot t2 1 2 Pt' t = pt' t I e t 2 12 where 0 < pt _ t I < 1 and -Il< t2 < 1 12 12

30 where Pt t \ i= 1 The three criteria investigated here are: (1) - 3 dB = Pt t2 iPt' t2 1 2 (2) (-6dB = Pt t t I lt t2 i 2i t2 2 (3) 45 = Ptt 1-45~ <0 t < 45~ ~ 450 t 1 2 tl 2 The corresponding forward decorrelation times are T 3 dB + + T+ A T6 dB and T450 respectively, where T+ (t) -= nmx{t2 - t pt. t2 satisfies C for all t2 in {t, T (t)} Thus, CANDOR reduces the data set ht(X), t1 < t < T (tl) representing the channel from t1 to T (t) to just ht (). The purpose in this thesis is not actual data reduction but investigation of this technique. This is done by studying the parameter T+ (t) throughout the data set as a function of t and ~. Therefore, T (t) is computed and plotted with the DUAL parameters for each ht(A) in the available data. Due to computer memory limitations, values of T+ greater than 48 minutes were not computed so that whenever T > 48, T - 48.

31 T+ (t) as defined here is an arbitrary but reasonable measure of the duration of the channel's quasi-time-invariance at each t. A detailed discussion of the results of this analysis is in Chapter 3, Presentation and Discussion of DUAL Results. In general, the T (t) measurements reflect quite agreeably with the general rule that the MIMI channel is quasi-time-invariant for five to fifteen minutes. One approach to data reduction has been investigated which promises to reduce recorded data in DUAL experiments by an order of magnitude. However, the approach is very strict in that the channel is essentially treated as deterministic and time-invariant, i. e., microscopic changes in the channel structure are retained even in the reduced data representation. Yet, the channel is admittedly stochastic and quasi-stationary. At this level, significant changes in the channel are much more macroscopic, e. g., the average propagation time of the channel changes significantly, a mode fades away or a new mode becomes apparent in the reception. This more general (statistical) viewpoint of data reduction appears feasible based upon observations of the CDR grams in Chapter 4, where the main structure of the multipath is "constant" for long periods of time, hours, while the microstructure is very complex, random and vague. Certainly this approach will not retain as much about the channel, but it will still represent the most significant

32 characteristics and will result in another order of magnitude of data reduction. Candidates for statistical channel representations and evaluation criteria for those representations are not investigated or even proposed here. Obvious representation candidates include the autocorrelation function. However, later data analyses presented in Chapter 5, indicates that such a statistically classical representation of the channel misses much of the channel's structure. The two approaches, deterministic and statistical, discussed here are extremes on opposite ends of the spectrum. Hopefully, study of the channel through the CDR gram presented in Chapter 4 will lead to a middle solution that sufficiently represents the channel and provides more data reduction. A DUAL experiment as has been described, performed in November 1970 in the Straits of Florida is the source of data for this thesis. Preliminary results on that experiment are reported in Reference [ 1. However, no satisfactory means for displaying, interpreting or otherwise using ht(X) has previously existed. The solution to this problem of using ht(X ) to understand and characterize the UWAP channel is the major contribution of this thesis. Many of the DUAL measurements from the November 1970 experiment will be presented here to assist in the interpretation of the UWAP channel developed. Before proceeding with the presentation

33 and interpretation of experimental results, the limitations of the MIMI measurement techniques imposed by the channel's BL factor and a comparison with the theoretical limitations discovered by Kailath are investigated. 2. 3. 5. BL Effects on h(t, X) Measurements. Within the constraints of the signal and receiver designs in the MIMI measurements, there are limits on the ranges of B, L and BL for which the measurements are undistorted. Kailath's results state that distortionless measurements of h(t, X) are possible if and only if, BL < 1. However, it should be interesting and informative to study in some detail the direct effects of B and L on the MIMI techniques. It should be noted that Kailath's discussion was for noisefree measurements which are not available in the MIMI experiments. The periodic nature of all MIMI signals, whether carrier (CW) or pulse, and the matched processing of those signals are the fundamental properties of the MIMI signal and receiver designs. Although the CW and pulse transmissions and measurements are simultaneous, they may be discussed separately. Consider the CW experiment first. The signal is a continuous 420 Hz sinusoid. Thus, its spectrum is essentially a line at 420 Hz. However, the reception reflects much propagation phenomena. The received signal is essentially

34,/i // // // ///ILX —MHz// /N/ / // HZ -.3 -.1 0.1.3 Fig. 2. 10. CW Reception Magnitude Spectrum Demodulated From 420 Hz to DC a very narrowband process at 420 Hz with two significant sidebands of incoherent energy. The narrowband carrier process has slight frequency spreading due to long term (hours) effects such as tides and internal waves. The two incoherent sidebands are attributed to amplitude modulating effects of the surface upon the carrier. Since the CW measurement is an average measurement over timedelay (multipath), frequency selective fading of the carrier reception can occur relatively frequently. Typically, the fade is very short (a minute or so) and fading often occurs at half-hour or hour intervals. Values of B and L have little direct effect upon the CW experiment design except in the choice of filter bandwidths. However, a large L implies excessive multipath presence setting the stage for multipath interference effects, which are reflected as frequency selective fading. That is, the rate of occurrence of carrier fading

35 is highly correlated with multipath activity. The multipath measurements, h(t, X) are based upon a periodic pulse signal, which has a line spectrum rather than a continuous spectrum. The channel impulse response is measured approximately by a train of short duration pulses rather than imsinfT d with zeros determined by the pulse duration, Td, and line spacing determined the signal period, T. The signal spectrum is illustrated in Fig. 2. 11, The Multipath Measurement Signal Spectrum. *1 -- Af-= Tp HZ I I- I-I I I I l —— l- - H H 0H -50 0 50 K- 1'IT. Fig. 2. 11. The Multipath Measurement Signal Spectrum

36 The parameters of the pulse train are illustrated in Fig. 2. 12. -ITd - H HTIME Fig 2 2. Fig. 2. 12. Periodic Pulse Signal The CW reception illustrated the frequency spreading effects on a line so that the spreading effects on the line spectrum of the pulse train signal are immediately clear. That is, each line undergoes a slight spreading and a pair of incoherent sidebands are associated with each line in the signal spectrum. This reception spectrum is illustrated in Fig. 2. 13. Hz P Fig. 2. 13. Received Frequency Spread Line Spectrum

37 As can be seen from Fig. 2. 13, to prevent distortion 1/T must place signal lines enough apart so that the frequency spread sidebands fall between these lines rather than on the signal lines. Thus, 1/T must be greater than.3 Hz. For the range of values of 1/T between.3 and.6 Hz sidebands from adjacent lines will p overlap. Since these sidebands are filtered out for the h(t, ) measurements, the overlap is of no importance in h(t, X ) meassurements. Thus, an upper limit on the pulse train period of 1/T >. 3 Hz has been established based on the frequency spread characteristics of the channel. A lower limit on T is determined by L, the delayspread parameter of the channel. The delay spread results from the propagation of the transmitted signal over several routes (multiple paths) each having a different distance. The result is analogous to the reception of a pulse from a tapped delay line. Each path corresponding to a tap on the delay with its own attenuation, phase and propagation delay time. Figure 2. 14 illustrates a typical multipath reception of delay-spread L, where a pulse period of T seconds was used. P

38 -A. s *.. ~.' ~ r.,rtrftotyjj; Vir ~:YY ~:t,.'~.A'?; o. ^'. ~ ~ii (N-)Tp NTp (N+1)Tp Fig. 2. 14. Typical Multipath (Or Delay Spread) Reception Clearly, the channel's maximum delay spread, L, must be less than T. Otherwise, receptions from neighboring pulses will overlap and the h(t, X ) measurement will be distorted. Therefore, the channel delay spread factor, L, places a lower limit on T in the signal design. P Summarizing, for distortionless h(t, X) measurements B 1 the relationships shown are - < 1 (sideband distortion allowed) t ri p and T > L. Combining these two equalities gives BT -2 < 1 or BL< 2 If sideband distortion is not allowed, then B <, T > L and BL < 1 T p P

39 Therefore, the MIMI measurement techniques for the doubly spread UWAP channel are effective in that they are limited only by the general theoretical limitations for instantaneous measurements of doubly spread channels. Although noise considerations have been ignored in the discussion, all MIMI processing of transmitted signals is a modified form of matched filtering (with respect to the transmitted signals) that trades improved time resolution for snr. Generally, due to long coherent integration times and medium stability, high snr measurements are obtained.

CHAPTER 3 PRESENTATION AND DISCUSSION OF DUAL RESULTS 3. 1 Results The results presented here are the scalar parameter measurements of the MIMI channel from the November 1970 experiment. This data consists of a modified DUAL experiment. Some additional parameters are included, no spectral analysis of the surface rever* beration is performed, and the display of ht(X) is presented separately in Chapter 4, The CDR Gram. The entire data set is organized into 19 files in chronological order, but not necessarily contiguous in time. Time and date information is summarized in Figure 3. 1 and Table 3. 1. The DUAL results of each data file are presented together in 5 different plots. In each of these plots the abscissa is the independent variable, time. Each parameter is measured and plotted every 102 seconds. Two hour intervals are marked on the abscissa. The plots were generated on a Hathaway Electronics 731 recorder, a raster scanning fiber optics device. The display format of a dependent variable plotted versus an independent variable is commonly known as an A-scan format. Such plots are most commonly generated on an X-Y device. However, Appendix A outlines a very For those results see Reference [ 1]. 40

41 TABLE 3.1 DATA CHRONOLOGY TABLE 3. la. (DEEP HYDROPHONE) L - File. extends from t. through ti. with data obtained from the shaded intervals of time in Figure 3. 1. During the nonshaded intervals, gk the time base was lost and data was either not recorded or not processed. i t. 1 tI t2 t3 t4 t5 t6 t7 t8 - Day (Hr:Min) = 11(17:16) = 12(5:18) = 14(1:36) - 14(16:18) = 15(7:17) 16(4:45) 16(19:05) =17(7:32).L k = Day(Hr:Min) to Day(Hr:Min) = 12(9:27) to 13(16:53) g2 14(9:29) to 14(10:55) g3 14(15:29) to 14(16:18) g = 15(3:06) to 15(5:38) i g5 = 15(10:13) to 15(19:13) gg =16(10:55) to 16(12:52) g = 17(12:06) to 17(12:33) g8 = 17(18:46) to 23(10:20) g8 t = 23(10:20) 9

42 TABLE 3. lb. (SHALLOW HYDROPHONE) t. = Day(Hr:Min) g= Day(Hr:Min) to Day(Hr:Min) t9 = 23(10:20) t1 = 23(22:47) gg = 24(10:49) to 24(18:42) tl = 24(18:42) t12 = 25(7:09) g 10= 25(11:18:00) to 25(11:18:05) t13 = 25(19:11) t14 = 26(7:38) t15 = 26(19:40) t16 = 27(8:07) t17 = 27(20:09) t1 = 28(8:36) 18 t = 28(20:38) t2 = 29(9:05) simple procedure for generating on-line A scans with a raster scanning device. The first plot contains the four power variables C(t), S(t), R(t), and N(t) in decibels (db) where unity is the arbitrary reference level. C, S, R, and N are plotted on a constant gain x band

43 C) C) (7,....,,.. c: C:) (.,,.,.. C) -) (:5 C) C) d: C) LC CD C:) 0 CD C: C C) 00 t I t t t2 1 2 91 9 g 9 3 Ig4 9 6 I g7 t3 4 5 g 6 7 t8 //77//A - RECORDED, PROCESSED AND DISPLAYED DATA 0 cJ I I — C) CD 6> q — C-. * ] CO Cs CD C) 6 O I 0 C\ 8 C5 C\1 * cr 7I I f'll//,/l/,I ~~~~I 77 7 77 7 7 Z 7.I 0 - t t9'1 g8 9 10 g9 II tl2g10t13 t14 t15 tl6 t17 t18 t19 t20 RECORDED, PROCESSED AND DISPLAYED DATA Fig. 3. 1. Chronology of November 1970 DUAL Experiment

44 width product basis so that signal-to-noise ratio is easily computed from the plot by simply subtracting the indicated power levels. The power ordinate is marked in 12 dB increments. Although the DUAL power measurements are time-spread averaged measurements, C(t) = I L ht(X)I XeA S(t) = Iht(X)1 XcA 2 R(t) =' h(t', X) Tt = (t, t+MT ) N(t) = h)12 XeA they reveal much about the behavior of the UWAP channel. Most of the time in the data here and typically in the past, a normal behavior of these parameters has beenobserved. C(t) is generally fluctuating with rapid fading attributed to the narrowband frequency selective fading due to highly interactive and interferring multipath structure. S(t) is normally steady in level indicating that the frequency selective fading is narrowband. S(t) and C(t) are only slightly correlated. R(t) is low level, 3 to 6 dB above N(t), and is usually correlated with N(t) rather than S(t) or C(t). Thus, R(t) * For unity gain plots see Reference [ 1] where total power measurement is readily available.

45 is generally noise driven indicating surface effects are definitely secondary phenomena under normal conditions in the 43 mile Straits of Florida channel. N(t) is steady except for irregular increases due to shipping. A second, more interesting channel behavior is exhibited when the channel surface effects become evident. C(t) does not fade, S(t) fluctuates, R(t) drastically increases and C(t), S(t), and R(t) are all highly correlated. This type of behavior is illustrated here in files 11, 12, 13, 14, and 15. In the second plot an estimate of the phase-only matched filter gain is presented in decibels relative to 1. This matched filter gain measurement, denoted MFG is estimated by MFG(t) ~ peak SNR(t)/average SNR(t) - EAK(t)/S (t) where SpEAK(t) is measured from the threshold processed ht(X) The threshold processing is discussed in Section 4. 2. 3. The theoretical value of MFG, where no decorrelation loss due to multipath is incurred and additive white Gaussian noise is assumed, is MFG 10 log10 2WT 10 log10 63 _ 18 dB

46 A high MFG value indicates low decorrelation loss which in turn indicates relatively little multipath. Whereas low MFG implies high decorrelation loss and therefore high multipath activity. In this experiment, these observations are reflected where during the simplest multipath structure, files 11 and 13, MFG takes its highest values, +9 to +15 dB and MFG takes its lowest values, 3 to 6 dB, during periods of extensive multipath reception. The CW phase angle in degrees, A(t), is presented in the fourth plot. This plot substantiates the well-behaved nature of the CW phase, reveals any discontinuities in the phase and displays the short-term small variations. The fourth and fifth plots are the channel's forward decorrelation times from the CANDOR analysis. T (t) and T (t) are in the fifth plot with T_3(t) < T 6(t) for all t. T450(t) is in the last plot. Limited computer memory forced limiting values of T+ (t) > 48 minutes to T+ (t) = 48 minutes. The ordinates are marked in 10 minute intervals from 0 to 50 minutes. The T, (t) plots allow study of the channel's rate of time variation and evaluation of the data reduction potential of the deterministic, quasi-time-invariant CANDOR technique. T+ values are large and often limited at 48 minutes during * + files 10 through 13. That is, large T coincides with the occurrence T45o (t) was inoperative in files 9, 10, 11, and 12 due to the Time Base Artifact, Section 3. 2.

47 of high R(t), smooth C(t) and high S(t) correlation with C(t). The channel structure is surmised to be dominated by a surface mode, due to the high R(t); and based upon past observations and reasoning the smooth C(t) and high correlation of the three signal powers (C, S, and R) a very simple (non-interferring) multipath structure again * dominated by a surface mode is strongly implied. Otherwise, T values are between 5 and 15 minutes most of the time, reflecting the normal quasi-time-invariant behavior of the MIMI channel. During these times, the signal power measurements, C, S, R are behaving normally. C(t) displays considerable rapid fading, caused by high multipath activity and interference. In contrast, S(t) is very steady and only mildly correlated with C(t). R(t) is rather low, 3 to 6 dB above N(t) and is generally correlated with N(t) rather than C(t) or S(t). Thus, normal conditions definitely do not reflect any surface interaction and generally the narrowband frequency selective fading of complex multipath structure is clearly present. Under normal conditions T+ T+ indicating that -6 -3 Ipt t2 falls sharply so that the exact threshold value on IPt t21 1' 2 1 2 is not critical. T45o(t) and A(t) measure change in the multipath average These conclusions are supported further in the CDR gram presentations of ht(t).

48 156, 1 108' 18 dB MFG(t) n,,,,,- I. I. —-,, -. -,"' I A(t) 1' J ---- t A ( | ) X.I I 71T 0 l. r r -.. / * 1 4' P 0. / I' A A % ~ "* Nt.,. ff,: _ % v r ^\l. v...6 - V * *'* -7T 50' T+ (t) > T+ (t) 50' I!l I I"' T (t)',IV' %'I I - - 0o i p _ 11(17:16) 12(05:18) Fig. 3. 2. Dual Graph 1

49 156 dB 156 C(t) S(t) 32 e-l,~~ ~,.,t,*d, ~.~,,.W^,', 132 2h' 2'-' 108 RF(t) 84 -"''-~ -'.-'"' ". ":- i,.. 84+..'..VN(t) 60 36 b.....'........ -, -.......-. i;-... dB 18 MFG(t) ~ ~~ A(t) ~, ~ ~~, -, ~,.-. *\ *- - * v..',...;\ *\: O% Tr A- - -. 12(05:18) (14(036(t) 0..'I, % ~ %~~~~~, 1205 18 11(0'6 Fig. 3.3. Dual Graph 2

50 156 132 108 84 60 36 18 dB MFG(t) 1~..........-r ~ -V., _' A L ~. _... *......... n~~~~r c Fl i- - A___ ~ r v.,( _. *. A(t) / 1 *.. /7 ['-~ ~ -; ~ r ~~~~~L~~~. ~..-. 0.. I.. * V\'! *./"-..:.9/**:v 0%. I.', -7T' 50' 0' ~ ~ T (t) > T I(t) -.O - A E t',~s^^ V ~ IL %,~ A Al-, a -MEL & JL 4L - *4L A -' I I I 50' 0' 14(01:36) 14(15:29) Fig. 3. 4. Dual Graph 3

dB 156 j C(t) ^-S(t) 132: V^C. V^ 108':' R(t) 84. 60 36 -, -- 1. 18.F 18 ldB MFG(t) O.:... - - 0 f i A(t) *". ~' r * *,. *. II; *\ *< -.*...1 50'1 T+ (t) > (t),- -Y -w \ 0' (1\ 6: T+ ( t) o. L,v^,, -........ \. 14( 16: 18) g4 15(07:17)! Fig. 3.5. Dual Graph 4

52 60 36 -— *-.-. 18 dB MFG(t) t 50] AT +6(t) >T+3(t) 584 Tt+45(t) Z^y.' * K.'-' 0 5 95 16045A(t) 15(07:17) g 16(04:45) Fig. 3.6. Dual Graph 5

53 RD 156 uv C(t) S(t)7 132 ~,.. A; _,,,,, 108,.- 84 R(t)-/ N(t) 60 36 -- _, _ l - l-. 18 dB 18 3 dB MFG(t) Jn... =.t.,.=.'.. r... *~-. -. u A(t) 3- *.i. f, 71 0 -1T *; 7' ~, 1 a ~~ I ~ v,? I 0 0J * 4 I V A,.V I I T+ (t), T+ (t) 50' 0' T 45(t) +t45 0%,' I' **' * \O V * i, \...I'" V C'k ~ u. - "~'~ "A 0 0 0 1 N I - -- - I 16(04:45) 96 16(19:05) Fig. 3.7. Dual Graph 6

54 dB 156 dB 156 C(t) S(t) 132 m, 108' Rt. 84' N(t) 60 36 18 dB MFG(t). A'A(t)*..,,. *,,. 1 - -; ~........ ~: -,-'.' -,,... %. 3 A(t)', o rY 50' 50 TT+6(t) > T+3(t) t^ ^tp fa6 3 O' 50 0 VA9 T (t) a ~T+45 VI.' ~),."- ~, ^ ^., 16(19:05) 17(07:32) Fig. 3. 8. Dual Graph 7

55 dB 156 132 108 84 60 C(t) S(t) "~;R ^^^^^N, _t ~=^^^^^^^^^^~~1 ww I 36 18 0 0 50's4 10 0 1: I A(t) I,s.. s-. 0 A. 1: %. A k. I t. - toj.t~/':' a v [ I T+ (t) > T+ M -6 -3 ~~LJPL~~*bih~~i~j~~g~=&~~gk~~ 50' 0' 17(07:32) 97 17(18:46) Fig. 3.9. Dual Graph 8

56 dB 156 132 108 84 60 36 18 0 7T. 0. 50 50' A(t):......,-.-... ~.: ~' ~ ~,11.. * I 1.. -- - * ~. * ~. %, 7. *.' ~ ~ a. ~ *. I.. * * * *'.. L. %.'. 1t~- - J6 —... Il - ~l -A I 0.. 0 - -, 0 ~ 0 - - -... -- --.~...: I * * * * ** l:@ *::,.; ---,.,.... I...* * * * I *: *'*%*e ~. * * I T+ (t) > T+ Mt 501 T+45(t) C O' I _~~~~~~~~~~ 23(10:20) 23(22:47) Fig. 3.10. Dual Graph 9

57 156 tdB C(t) S( 132 108'' 7" 84'" 60 N(t) 36..1 18 tdB MFG(t) 0......... Ii''' ~:,,'." l' 1t':' ",:' A(t)' -6 - -3 50', ).........: T:45 t), O''; _ - I ~ ~ I'''~ - I'$ -1, 23(22:47) 24(10:49) Fig.. 11. Dual Graph 10 ]Fig. 2. 11. Dual Graph 10

58 156 132 108 84 60 36 18 dB MFG(t) ^ 1 I I I I I r'r'pejL, 7(T- 1 U A(t),~ ~~'..... ~. % ~ -.. ~ ~ ~...''...~ ~ ~..~. ~ qb ~.~ ~' ~ ~,. ~.~ ~~''. ~ ~... ~..~ ~~~~~~~~~~~~~~~~~~ ~ ~ ~ ~l,~'.' ~''~'' ~'' "'''' ~ "~' ~''~ ~.... ~ ~~~~~~~~~~''.~ ~.''~'~[ ~ ~.i ed ~. 7T 0 -T7'I, b *: - e"' *. ~ - " ~'. v ~: ~'.; ~'. ~...... ~........ ~(t ~%~... ~. ~..-. * ***.**.. *...... ~, ~ \ 50 50 45(t) I-..- ---' ~ 3 24(18:42) 25(07:09) Fig. 3. 12. Dual Graph 11

59 JAD 156 a I 132 108 84 a I J * dl dl OU c(t) S(t) N(t) 60 36 18 dB MFG(t) F,,'ZrT ~L. ~ _. - w ~~M~Lyl wf~r 0 A(t) *.*. ^,,, ^i.. f 0T 0 1,I &.... o, -. o.. 0 0,,, -. * *. *: *..* * o ~ I VI I:aaW -aTf l T+ (t) > T'gt 50' 0' 50' 0' ) Fig. 3. 13. Dual Graph 12

60 dB 156 132 108 84 60 36 18 0 7T 0 a a a dB MFG(t)r IA -. " r i'.-. * i I * 1 _ I A(t) \ \.........i.. _.... - I 1 T+6(t) > 3(t) _6 -3 * * a *: %. I " 1 114 50' 0' 50' 0' 25(19:11) 26(07:38) Fig. 3. 14. Dual Graph 13

61 156 dB S(t) S(t) 132.. / 108 84 ^.^ I N(t) 60 36, --. 18 d MFG(t) n',, _. 0 ". -' —-----------, 1 - o::./. 1 Jv T ] A(t). 0 + 9'' T+ t> T+ (t J V- [^^^ O' 26(07:38) 26(19:40) Fig. 3. 15. Dual Graph 14

62 dB 156 C(t) S(t) 132 j ".,,, /,,',,,/ 108 tuo - By;-L *^*>__* *.-r"11_1;",: > 60 N(t) 36 —- i 18 dB MFG(t) 7 A A(t) - r W 50' T+ (t) T+(t) p1 <' ~: i 26(19140)T27(08:0: u50' h T > T445(t)_' 26(19:40) 27(08:0; 7) Fig. 3. 16. Dual Graph 15

63 dB 156 132 j C(t) Y s(t) 132:,W *,,.. 84 " "...W....* MA: ^"~ 60 N ( t) 360 18 dB MFG(t) 1 —-:. -, ~.'; —:',,,. [ *............... -.'...w * * \'w 60 *'s -; -' - - ~. A( t) % r 50' o' T 6(t) > T, 3; ^d T45(t), t 50' E i E O 2(09. 27(08:07) 27(20:09) Fig. 3. 17. Dual Graph 16

156 132 108 84 60 64 dB C(t) S(t) N(t)!! i i m* D l P II I I 36 18 I dB MFG(t) F 1^A*~'*-^-^'-*.1~t ~ I lf;"i. I T-^hj. U A(t) V,.- \, ~...' "'t' -. **: ado. 0 - ^.'lb. * N r 1T 0 -1T 50' 0' 50' 0' 4 1 *0 %... #*4 S'.\ a' ~~ tL~~~ ~ ee ~ 0, l T+ (t) > T' M -6 -3 4'"w, 27(20:09) 28(08:36) Fig. 3. 18. Dual Graph 17

65 OR 156 uu 156 6: C(t) S(t) 1 3 2:. 108 84 >. i t M O>/^ -t._Vlo'**o o N(t) 60 36. i 18 dB MFG(t). \ -.. 280 3 A(t). -T 0 3 - T - 6I (/ t ) _1 -3-(), - "' O' l.' *; ~... 28(08:36) 28(20:38) Fig. 3. 19. Dual Graph 18

66 156 dB 156 d C(t) S(t) 132 /:,.',: A A/ " 108 i 84 = N(t) 60 36~ i i -... 18 0 dB MFG(t), *~T ^.' N'.'.''1 \ ^ ^:... i i.'..';, -..., A (t).' T. t) - 7T+ T+ T (t) > T (t) L-6 -3 50' 80 29(09:05) 0' IT45(t):,. v \\ v, E 28(20:38) 29(09:05) - - % - - - - f Fig. 3. 20. Dual Graph 19

67 arrival time providing a verification of the assumption that pt t 1' 2 only needs to be evaluated at AX = 0. The experimental results of DUAL processing are all relatively simple to compute and display. They are important because they reveal a wealth of information about the time-spread averaged channel and because they provide quantitative measurements of parameters that are very qualitative or not available in the ht(X) display of Chapter 4. 3. 2 The Time Base Artifact of Data Files 9, 10, 11, and 12 From 18:46 hours on November 17 until 11:18 hours on November 25, the time base references at the transmitter and receiver were out of synchronism by approximately 1. 7 millihertz. Data files 9, 10, 11, and part of 12 are during this time. Although the time base error was too small to have noticeable effects on power measurements, the artifact is reflected in the CDR grams, the carrier phase angle measurement, etc., as a constant rate of change in the propagation time of the channel. This rate measured from the CDR grams is approximately 14. 3 milliseconds per hour or from the corresponding A(t) approximately 6 cycles of carrier phase per hour. These two measurements agree with each other and correspond to a 1. 7 mHz reference offset. Although this artifact is very noticeable in the phase striping patterns of CDR grams 9, 10, 11, and 12, the basic multipath

68 structure is not lost. Thus, these grams are still useful and, therefore, retained. 3. 3 Summary - A Preliminary Channel Model A simple model of the UWAP channel in the Straits of Florida that reflects current knowledge and is consistent with MIMI measurement results and techniques provides a preliminary basis for more detailed modeling discussion later. To date, the surface effects have been modeled as a simple amplitude modulation. A simple model for the channel, which allowed for some reception unaffected by the surface, can be expressed as h(t, X) = a(t) hl (A) + h2 () t t The surface modulation is represented by a(t), a narrow bandpass, 0. 2 Hz bandwidth centered at 0. 2 Hz, random process. The reverberation measurement, R(t), is nominally a measurement of the power of a(t). The two components hl (X) and h2 (A), of multit t path structure are quasi-time-invariant linear time-spread channels. The time dependence of ht (X) and h2 (X) is implicit in the notation. t t The component of the multipath structure undergoing surface modulation is h1 (X). In some sense h1 (X) must therefore be a surface t t channel. The unmodulated component of the channel is h2 (A). Gent erally, in MIMI measurements of ht(X) these two components are

69 not separated so that ht(A) h1 (A) + h2 (X). The time variation re1t t maining in h1 (X) and h2 (X) is due to slowly varying phenomena t t such as tides, internal waves, heating and cooling, currents, meanders, etc. This model will be expanded in more detail later.

CHAPTER 4 THE CDR GRAM DISPLAY 4. 1 Introduction In the discipline of signal processing, optimum filters receive extensive and intensive investigation with regard to theoretical, computational and implementation aspects. However, the weakest aspect of signal processing system is displays. Displays are also probably the most ignored aspect of signal processing systems. This is unfortunate because in problems of practical interest displays are as important as the receiver. This is because in practice many parameters of the signals and noise are unknown so that decision regions are difficult to determine. Therefore, when the situation allows, displays are often used. Because the human eye and brain provide a very adaptive or versatile pattern recognizer, the display-observer decision making mechanism usually provides better performance and much simpler system implementation than is otherwise practical. Thus, the display and observer often become an integral part of the signal processor, so that an optimum system implies optimum display as well as optimum filtering. A good display should be simple to generate, simple to interpret, and it should provide a maximum of information that is relevant to the objective at hand. In signal processing research, displays provide an additional 70

71 vital function, namely information obtained from the display provides qualitative data about the signals. This type of preliminary information provides the basis for the design of feasible decision-making equipment. That is, even when a display is not included in the final system, it can be an invaluable design tool. Although this thesis is strongly supported by theoretical channel characterization and the well designed and implemented MIMI experiment, the new element of this thesis are the results obtained by the use of a unique display technique for channel propagation studies. Although the application is original, the display technique (or format) is due to a very creative individual, Charles I. Black of Texas Instruments Incorporated. 4. 2 Description of Display 4. 2. 1 Display Format. The major objective of the display is to very compactly illustrate a complex function of two independent discrete variables, h(t, ), where t is time and the second variable may be X, time delay, or f, frequency or another independent variable. For the cdr (t, X) the second independent variable is time delay. Figure 4. 1 illustrates the basic format of the display, where the independent variables are the usual displacements in the plane (paper, CRT screen, etc. ) and the display intensity, shade, or color at coordinate t, X is a memoryless mapping of h(t, X). The display device used in this work, a Hathaway 731 recorder, has intensity

72 x I I I I W —-m vwm Wmmm I Ql V )=g[ h(t'p V )l 0 tI t + Fig. 4. 1. Fundamental Display modulation on white paper, where writing intensity may vary from white through gray to black. If g is the norm operator (or a variation), then the display format is a very conventional one commonly used in oceanography, seismology, sonar, speech research, etc. In these areas h(t, *) is often a spectrum h(t, -) = S(t, f). Table 4-1 lists some conventional mapping functions, g(t, ). Table 4-1. Conventional Display Mappings I1(t, ) = I2(t, ) = I3(t, *) lh(t,.)I I lh(t,.)I 12 log lh(t, )I

73 Conventional displays have always mapped the complex function h(t, ) into the positive reals. This display has been very valuable in many areas of application; however, it has the disadvantage of eliminating all the phase information in the generally complex-valued h(t, -). The inclusion of phase as well as magnitude into the display is a new technique providing very valuable, additional information. The display mapping function used is I(t, X) = (h(t, X), hy(t, X)) + (b, b) where h and h denote the real and imaginary parts of h x y and b is a constant gray scale bias. That is, the display intensity function is now an ordered pair of real values with h = (0, 0) - gray display, whereas in the conventional display I(t, X) was a positive real value with h (0, 0) - a white display. Finally, the ordered pair (I = h + b, I = h + b) are plotted side by side on the X axis. x x y y Figure 4. 2 illustrates the mapping g(h[ t, X]) used in this thesis which encodes both amplitude and phase information of the complexvalued function h(t, X) into the otherwise conventional display. Let us refer to this display as the OP (Ordered Pair) gram and the conventional display will be called the PR (Positive Real) gram. Since the intensity perception of the eye is approximately logarithmic (that is, relatively insensitive to small changes in light intensity) the dynamic range (with respect to intensity amplitude) of the display is rather limited. In the conventional display the many

74 I x tt t I Fig. 4. 2. The Ordered Pair Gram Display variations of g(t, ) around the norm operator (e.g., the logarithm of the norm) are an attempt to map the dynamic range of the information function into the natural dynamic range of the display. Obviously, similar variations of the OP gram could be of interest for the same reasons, e.g. ( /h-loglh h loglh I I(t, X) = (t, X), Iy(t, )) = hy log^h + (b, b) would preserve the information phase while compressing the range of the information amplitude. Such dynamic range compression techniques are not used in this thesis. A display technique incorporating amplitude and phase

75 information as opposed to the conventional amplitude-only display has been described. The value of this added dimension in the display is great and its value in channel propagation studies will become clear in the subsequent material. 4.2.2 Amplitude and Phase Information in the CDR Gram. The value of the OP gram in displaying cdr (t, X) is in the tremendous quantity of qualitative and gross quantitative information available in a compact space. Typically, a gram of 6 to 12 hours of cdr (t, A) is plotted onto an area less than 8-1/2 by 11 inches. Although quantitative amplitude measurements cannot be made from the CDR gram, relative amplitudes can be observed so that high-energy reception is distinguishable from low-energy reception, thus, primary multipath can be identified on the gram. (To relieve the observer of the task of this discrimination, thresholding based upon measured SNR is used, thus, allowing the observer to concentrate on the extraction of information and features from the primary multipath. ) Likewise, at best, phase can only be measured to the nearest quadrant. However, trends of constant phase (in t or A or both) can easily be observed as well as phase rates of change. This phase information tells much about the time invariance, randomness, stationarity, and correlatedness of the channel (reception). In one glance at a typical gram with its myriad of random patterns in t and A the channel CDR is clearly stochastic. In addition, the majority of

76 primary multipath will have constant "phase patterns" of at least 5 to 15 minutes duration (i. e., on the t axis) indicating that the stochastic channel process is very narrowband (remember the channel being studied is over 50 Hz wide so that the channel random process could change much faster than it does). If cdr (t, X) = r(t, X) cdr'(A) where cdr'(X) is time invariant and r(t, A) is a class of very narrowband random processes the channel could be modeled as quasi-time-invariant. In other words, the 100 second comb filter used to obtain a high SNR representative CDR could easily be extended to 5 to 15 minutes without degrading the instantaneous CDR measurement. Although the amplitude and phase of cdr (t, 7) are grossly quantified in the gram display, the basic nature of the reception is retained. And, although the gram greatly compresses a large quantity of information into a small region, much of the adaptive recognition potential of a human observer is retained. This is very important because, due to the unknown and complex nature of the channel, rote application of electronic averaging, whether coherent or incoherent, while greatly compressing the quantity of information, will also mask much of the information unless the averaging process is "matched" to the information process. (Even if matched electronic averaging was used to remove excessive redundancy the quantity of data remaining would still be enormous and again a gram display may be the best available means of displaying the averaged

77 information. ) 4. 2. 3 Thresholding for Clutter Suppression. Often very lowenergy multipath reception is readily detectable in the CDR gram by distinctive phase patterns. Although there is enough dynamic range in the gram to distinguish high-energy (primary) multipath reception from low-energy (secondary) reception, to do so requires considerable concentration. Thresholding of cdr (t, X) based upon measured broadband signal and noise power, cleans up the gram, thus, relieving the observer of the distracting task of discriminating significant reception from insignificant reception. The result is that the general characteristics of the significant reception can be observed in a glance. In some cases, such as file 7, it greatly enhances the presence of a high strength reception that was not nearly so distinct in the unprocessed gram due to very strong phase patterns of the low-energy reception. The thresholding introduces a quantitative energy measure into the gram which allows ready measurement and observation of the channel time-delay spread factor, L. If L was judged from the unprocessed gram it would be two to three times its values as estimated from the distinctive phase patterns and the large extent of very low level but coherent reception. The threshold operation is based upon the broadband signal and noise measurements as expressed by

78 if 20 log 10cdr(t, X) I > max IS(t)- 6dB, N(t)+ 6dB}, then cdr(t, A) = cdr(t, A) otherwise cdr(t, A) = (0, 0). That is, the instantaneous power of cdr(t, A) must exceed S(t)- 6dB and N(t)+ 6dB to be considered primary reception. Although the threshold processing is not always necessary, in much of the data it considerably enhanced the significant multipath reception and made possible valid interpretation of the cdr(t, X) gram. 4. 3 Experimental Results This section, consisting of the presentation and subsequent discussion of approximately 133 hours of cdr(t, A) data, is divided into four parts: 1. The CDR and threshold processed CDR gram displays, and discussions of 2. Parameter extraction from the CDR gram 3. Time invariance, correlatedness, and stationarity of ht(X) 4. Identification of two physical propagation modes. 4. 3. 1 CDR Data Presentation. There are 19 data files each containing approximately 12 hours of CDR data. Table 3.1 and Figure 3.1 summarize the chronology of the data. Each data file is presented in a CDR gram and in a threshold processed CDR gram. The unprocessed grams are presented first, followed by the threshold

79 processed grams. The CDR grams begin and end with a series of alternating black and while bars along the time spread axis, X. There are 63 bars, 32 black and 31 white, each representing the 20 millisecond duration of the transmitted digit. Due to display device blooming, the black bars over extend into the white regions. Nevertheless, the time spread of the channel can readily be measured in units of 20 msec. Every 120 minutes a scan of this alternating black and white bar pattern is imposed. Along the time, t, axis in the margin the times, ti, and time gaps, gk, are annotated corresponding to the chronology summarized in Table 3. 1, to provide a time element. Note that although the data is displayed in chronological order, events, gk, denote the occurrence of time intervals where data was not obtained due to experiment down times. Although the threshold processed CDR gram is the point of reference in subsequent discussion, both grams are presented in order to: 1. Provide a complete and unretouched representation of the channel. 2. Allow the reader to evaluate the threshold processing effects. 4. 3. 2 Parameter Extraction. Using a threshold processed CDR gram, several valuable parameters of the channel can be

80 I, I I I I I 12(05:18) | 12(0o9:27) 3 13(16::3) B 14(01:36) u COR GRAMS 1 & 2 Fig. 4.3

81 14(01:36) 14(09: 29) 14(10:55) 14(15:29) 14(16:18) 15(03:06) 15(05:38) 15(07:17)... -0 E Fig. 4.4

82 OF: i ii''7777 ~ ~' *~:2~,.i:1......... DF, Dam.: i..:' t.......... I.:;.g: mu:: s k<.;.. t......... All' r~A 12 CDR GRAMS 5 & 6 15(07:17) 15(10:13) 15(19:13) 16(04:45) 16(10:55) 16(12:52) 16(19:05) Fig. 4. 5

83,4 16(19:05) 1.2 17(07:32) H| 17(12:06) ~! 17(12:33) Rifii 17(18:46) 1.2 0 CDR GRAMS 7 & 8 Fig. 4. 6

84 23(10:20) - -- --- -- --. - -..- - - -: 23(22:47) a a a a a a a a a a a a a a a a a a a a a a - a a - a @w* 24(10:49) 0 1.2 CDR GRAMS 9 & 10 Fig. 4. 7

85 24(18:42) 25(07:09) 25(11: 18) 1 25(11'18) 25(19:11) 1.2 0 CDR GRAMS 11 & 12 Fig. 4. 8

86 25(19:11) 26(07:38) 26(19:40) 0 CDR GRAMS 13 & 14 Fig. 4.9

87;Id''i iI'1fUEw flE EE"E'D1E" E.."U.' UE-U "1" - UII' w' I * a a a a a s a a as U a a a l a IIa a a a a u l.... Z. i u * 26(191:40) 1r' 27(08:07) | 27(20:09) 1.2 0 CDR GRAMS 15 & 16 Fig. 4. 10

88 2(20:0:9)' 28(08:36) 28(20:38) 0 1.2 CDR GRAMS 17 & 18 Fig. 4.11

89 8 t(2 38) 29(09:05) 1.2 0 CDR GRAM 19 Fig. 4. 12

90 (0:1 8::: 12(009 32) 13(16:1W-53) 14(01: 36) 0 -- - - 1.2 CDR GRAMS 1 & 2 CLUTTER SUPPRESSED Fig. 4. 13

a3SS3Uddns H3iLn1 (E:SO)St (::9 I:t 16

92 16(04:45) 16(1055) 16(12:52) 16(19:05) 0 1.2 CDR GRAMS 5 & 6 CLUTTER SUPPRESSED Fig. 4. 15

i:~.-~~~t t'o....~:O A:~~~-4 -4 r C. co cm,on l_ICO L4 0i - w C.~ CO or., *,l 0

94 23( 1020o) EiUUUUUUUWU U E 353 35 351 ill m mlm m m m'm m B ww wwm, wwww I I23(22:47) ~m,~~ ~ m~ m m - m m m.............. m: 24(10:49) 0 1.2 CDR GRAMS 9 & 10 CLUTTER SUPPRESSED Fig. 4. 17

81 *t *kLd O3SS3SiddOS M3IniD:ZTI T 1T SWVW9 Ba 0 (8,tl *I I)6 0- IT)S4 z (6to.o)sz

96 26(7:t38l) 26(19: 40): 0 CDR GRAMS 13 & 14 CLUTTER SUPPRESSED Fig. 4. 19

97 26(19:40) i 27(08:07) i 2 a i j 27 (20:0-9) CDR GRAMS 15 & 16 CLUTTER SUPPRESSED Fig. 4. 20

98 28(08:360) 0 28(20* 38) 1.2 CDR GRAMS 17 & 18 CLUTTER SUPPRESSED Fig. 4.21

99 1.2 CRD GRAM 19 CLUTTER SUPPRESSED Fig. 4.22

100 measured, some rather quantitatively, others qualitatively. Some illustrative examples follow. L A very important channel parameter is the time-delay spread coefficient (or multipath extent), L. In the data here, L is clearly less than T, the signal period. This condition, T > L, is required to avoid distorted measurements of the channel. From the threshold processed grams, the channel has an L value of approximately 600 msec. If unprocessed grams are used, then L measurements are significantly affected by the preponderance of very low energy, but coherent, reception that is very detectable in the CDR gram. This unprocessed gram would imply L estimates more like 1200 msec. Since this insignificant (with respect to energy content) reception can influence L measurements so greatly, CDR grams must be threshold processed to obtain reliable L estimates. Arrival Time Tracking, Path, or Mode Fading, and Multipath Resolution Before this work, no information about the long-term time behavior of path propagation times has been ever measured. The behavior of path (or path group) arrival times is readily observable in the CDR gram (particularly if threshold processed). When paths are time resolvable on the gram, the individual arrival time of each Section 2.5. BL Effects on h (t, ) Measurements Section 2. 3. 5. BL Effects on h (t, X) Measurements.

101 path is easily observed. As illustrated in the CDR grams such paths have essentially constant arrival times for several hours. Typically, the arrival (or travel) time may change 10 milliseconds in 6 hours. The reception in files 9, 10, 11, and 12 appear to be moving more rapidly (and steadily). The time base in these files contains equip* ment induced accumulative error. It can be seen that two-path arrivals butted side to side as in file 12 can be resolved and identified as two distinct paths in the CDR grams due to the phase discontinuity at the interface of the two arrivals. In previous CDR displays the resolution of such paths is observable on the basis of phase discontinuity and often an amplitude notch at the interface. However, previous presentations spanned very short periods of time, 5 to 15 minutes. It is important that the ability to resolve mildly interferring paths has not been lost in the CDR gram. In high-interference reception, paths can be individually identified for only very short intervals (minutes), tracking of individual path arrivals is very difficult and probably pointless. The approach here is to be only concerned with the average arrival time of the very complex-looking gob of reception. This type of reception will be called clustered mode reception. Only the trend of this clustered mode travel time is of interest, since small random perturbations in a short-time average-travel-time measurement are simply See Section 3. 2.

102 reflections of the highly interactive behavior of individual paths in the cluster. Generally the average arrival times of the cluster modes in the data here are constant for very long periods (hours). This observation is consistent with the previously observed behavior of individual paths. However, it cannot be concluded, only surmised, that the individual paths within the cluster have constant travel times. As a group of paths, they have a constant travel time, but as individual paths, they may be moving around within the cluster. Thus, for the first time, based upon the CDR gram, statements can be made about the long term behavior of propagation path (or mode) travel times. It could be interesting to pursue this question in more detail. For example, individual path travel times could be correlated with each other and with large driving forces such as the tide, etc. The CDR grams of data files 16, 17, 18, and 19 illustrate the ability of the observer to identify the superimposed reception of several distinct simple paths on a background of a cluster mode arrival. In addition, the individual path arrivals can actually be tracked (visually) in time through the cluster mode arrival. This type of reception, simple paths superimposed on cluster mode, has not been previously recognized or identified, and to do so with previous techniques would be virtually impossible. Thresholding introduces enough quantitative amplitude measure into the CDR grams to provide observation of path and, even,

103 cluster mode fading in the CDR gram. This phenomenon has been surmised in the past from DUAL measurements but never observed before. Narrowband frequency selective fading of the CW signal has been observed for a long time. This is a phenomenon associated with multipath interference. However, path fading is a broadband phenomenon rather than narrowband and cannot be generally associated with multipath interference. Although extensive quantitative measurements have not been made of the total broadband power in a single path, broadband energy fading does not appear to be nearly as extreme as in the CW case so that in the broadband case energy fluctuation is a better term than fading. Although the CDR gram represents the UWAP channel more comprehensively thanDUAL measurements, DUAL does provide quantitative data and the CDR gram is used now to note correlation between DUAL process behavior and channel structure observable in the CDR gram. In gram 13 the reception consists only of two distinct time resolved paths. The C(t) and S(t) curves in the associated DUAL plots indicate significant broadband power variation. The high correlation of C(t) and S(t) here is rather unusual and is a reflection of the lack of multipath interference, i. e., cluster mode reception is not present. Furthermore, the distinct absence of CW fading during this time is also a reflection of the absence of multipath interference. In other words, high correlation of C(t) and S(t) together with wide S(t) fluctuation and the absence of

104 CW fading are strong indications that the reception is of the simple type. The art of extending DUAL measurements to hypothetical channel structure is subtle and is subject to complications. This is only an introduction to the concept which is implicitly developed throughout much of the remainder of this thesis. The number of paths in simple reception is generally small, typically one to three paths. While cluster mode reception consists of many paths in a bundle or group, which may be spread over as much as 600 milliseconds of time delay, resulting in highly interactive and random multipath interference. This is reflected in DUAL measurements by CW fading and constant S(t) measurements. Usually, reception consists of combined simple reception plus cluster mode reception, for example, grams 1, 2, 3, 9, 10, 14, 16, 17, 18, and 19. Let us call this complex type reception. Grams 4, 5, 6, 16, 17, and 18 also illustrate two simultaneous cluster modes. Simple type reception is reflected in the distinctive behavior of the DUAL measurements C(t) and S(t). However, in complex reception, the cluster mode component dominates the S(t) and C(t) measurements so that the presence of the simple component is not detectable in the DUAL measurements. CDR gram 1 is a particularly interesting example of complex reception where the two paths in the simple component are strongly fluctuating. The two paths are fading and building completely out of phase with each other. This

105 dramatic behavior so clearly represented in the CDR gram is not reflected in the DUAL measurements due to: (1) cluster mode masking and (2) the out of phase fluctuations average each other out. Averaging and masking effects on DUAL parameters could be avoided by making measurements on individual paths or modes. Possibilities of such measurements are discussed in Section 6. 3. The application of CDR grams for arrival time tracking, multipath resolution and path or mode fading has brought exciting new observations and aspects to UWAP channel studies. 4. 3. 3 Time Invariance, Correlatedness, and Stationarity of h (t, A). The general UWAP channel has been modeled as a linear, stochastic, doubly spread system with a channel digit response h(t, A) where X is the time delay parameter. MIMI measurements filter out the frequency spread component of h(t, A) = a(t) h1(t, A) + h2(t, A). Thus, the MIMI measurements provide a singly (delay) spread system for study. This system is denoted by h(t, X) = h1(t, ) + h2(t, X). In abstract channel modeling or characterization, additional assumptions of uncorrelatedness and wide-sense stationarity of the channel are highly desirable for mathematical convenience. Verification of such assumptions is no mean task. An in-depth study of these questions for the UWAP channel is not the objective of this work, but some preliminary efforts have been made. The purpose here will be only to show that these assumptions are reasonable.

106 Time Invariance At normal transmission levels h(t, X) measurements using one minute integration provide reliable (high SNR) estimates. Continuous measurements show that h(t, A) - ht (X), t1 < t < t2 with 1 t2 - t1 approximately 5 to 15 minutes, i. e., for time intervals of 5 to 15 minutes the UWAP is a time invariant channel. This has been reported in MIMI references spanning several experiments [2], [15], 1 16], [ 17]. Using previous display techniques to determine time invariance durations was feasible but somewhat awkward. Therefore, the measurement technique CANDOR presented in 2. 3. 4 was implemented. However, the CDR gram provides a less quantitative but comprehensive means to judge not only durations of total channel time invariance, but durations of time invariance of individual components (paths and modes) of the CDR. That is, simple reception time invariance durations are significantly greater than for cluster modes or the components of the cluster mode microstructure. This behavior is apparent in CANDOR measurements only during simple mode reception. During complex reception such behavior is quite observable in the CDR gram, although not so in CANDOR measurements. In all measurements and discussions of time invariance, the structure of interest is in the CDR phase while pure gain variation is normalized out. Besides general curiosity, the great interest in channel time invariance is motivated by the tremendous practical need to minimize data quantities for meaningful channel representation.

107 For example, by using S(t) and a single normalized cdr (t, X) from each time invariant interval, the quantity of data required to represent h(t, X) is reduced by an order of magnitude. This translates into an order of magnitude savings on data storage requirements and post-processing times. Thus, studies that would be a practical impossibility become feasible. Correlatedness The cdr (t, A) = h(t, X) is a family of random processes with indices t and A. In this section properties of the channel with respect to the A parameter are of major interest. The time parameter will be demoted to the role of subscript in the notation to emphasize X, h(t, X) A ht(). Since ensemble averages are not available, ergodicity and stationarity assumptions on ht(X) allow the correlation properties of ht(X) to be studied using time averages. Since ht(A) are zero mean, the normalized auto-covariance of the CDR is estimated by C h (A) h X-A) AX A 11 ht(X) 1 The auto-covariance analysis fulfills two purposes: to study the X-correlatedness of the channel and to investigate an alternative The mean of ht(A) is estimated Mh = C ht(X) and subtracted to assure zero mean ht (X). X

108 statistical representation of the channel. Here only X-correlatedness is the topic. The complete Covht(,) analysis of the CDR data is presented in gram format with a discussion of Covht(j,) as a representation of the channel in Chapter 5. The gram display of Covht(L) is inadequate for highly quantitative measurements. However, two preliminary observations are immediately obvious: * Covht(,() is nominally "constant" for several hours at a time * ht(A) is approximately uncorrelated most of the time Covht(AI) is nominally "constant" means the width of the significant portion of Covht(/i) is "constant" and no significant changes in Covht (/I) are apparent for large durations of t. This condition implies that time averaging of Covht(I) is a reasonable method of obtaining better statistical estimates of Covht(L). Under normal conditions, cluster mode reception, Covht(pL) quickly falls well down from Covht(o) withing two digit durations, i.e., Covht(4) - 0. 1 Covht(o). To be considered completely uncorrelated Covht(ji) should fall within one digit duration. However, considering L _ 300 to 600 msec, or 15 to 30 digits, ht(X) is approximately uncorrelated under normal conditions. The paths in simple mode reception often appear to be well correlated. In files 9, 10, and 11 several resolved paths are present and spread widely in time delay. The Covht(Li) grams of this reception

109 indicate considerable correlation between paths. However, based on past experience, this type of reception is rather anamolous and has only been observed in November and December. Although more detailed and quantitative investigation are desirable, those efforts have been left for later work. The preliminary conclusion here is that the MIMI channel under normal conditions is approximately uncorrelated. Stationarity The concept of wide-sense stationarity involves 1st and 2nd moment statistical properties of the channel. In our notation the UWAP channel is WSS with respect to t, if and only if Eh(t, X) - M(X) and Eh(t, A) h*(s, A) = R(t-s, X) These conditions are impractical to verify. The assumption that the UWAP channel is quasi-stationary appears very reasonable for intervals of time necessary for DUAL and h (t, X) measurements as indicated by experimental results showing channel durations of time invariance on the order of 5 to 15 minutes. For these orders of time, physical arguments that the ocean is a very high inertia system must further support such an assumption. However, for longer periods of times the UWAP is generally assumed to be non-stationary. The attitude prevails that one minute

110 of stationarity was all that was needed to make measurements, why push it further? However, the question of what is the full extent of the quasistationary behavior of the UWAP channel is important. Although answering this question is not the purpose of this work, preliminary bases for extending the quasi-stationarity assumption to several hours are presented in the hope of motivating further thought on this subject because an answer to this question could have tremendous effects on future propagation experiments and models. With a little thought, it should be clear that simply because C(t), S(t), and other DUAL parameters are not constants does not mean the channel is non-stationary. Moreover, the channel could be stationary to within a pure (broadband) time-varying gain. Or some modes or parameters, rather than the total process, may be stationary in some sense. For example, possibly the cluster mode reception is stationary but the simple mode reception is not. Or perhaps, just a parameter such as arrival times of either modes or paths are stationary. The point is that many possibilities exist and just because one approach hits a dead end, the search should not be given up. The following discussion presents, possibly disconnectedly, several preliminary results supporting the possibilities of some long term quasistationarity in the channel.

1ll Quasi-Stationarity of Structure Given the channel structure at any particular time, say complex with a single cluster mode and two simple paths, the most fundamental notion of quasi-stationarity must include "constant" structure for long periods. More specifically, if the complex structure of a cluster mode and two paths remains, and parameters, such as arrival times and delay spread, are constant, some underlying notion of quasi-stationarity must be present, if not in the structure process, then at least in some of the key parameters of the structure. The "constant" structure of the channel is also illustrated in the auto-covariance grams by the long periods of "constant" decorrelation time. It is intuitively agreeable that the basic nature of a high-inertial system, such as the ocean where the most significant driving force, the tide, has a 12 hour period, has been observed to be very slowly changing. The most obvious mechanisms disrupting the structure of the channel are the variability (coming and going, and S(t) variation) of the simple paths. Quasi-Stationary and Some Average Channel Parameters Practical considerations of storage, display, and computation often dictate averaging of the time delay, X, aspects of the channel. The discussion here centers on speculation about the stationary nature of the channel based upon A-averaged measurements. The preliminary report [ 1] on the experiment from which the

112 data in this thesis was obtained, contained sample mean and standard deviation analyses of the DUAL parameters C(t), S(t), R(t), and N(t). The samples used to compute these statistics represented 102 second coherent measurements of the channel and they were taken continuously from contiguous 102 second intervals. Then, the sample statistics were computed using three hour sliding averages on the mean and 25-minute sliding averages for the standard deviations. Generally, the mean statistics are constant over periods of several hours. During those exceptions to this statement the channel structure consisted of the simple type where variations are wide and C(t), S(t), and R(t) are highly correlated. The standard deviation measurements are discussed individually. The C(t) standard deviation, ac, displayed considerable fluctuation about a constant average level. This fluctuation rate was driven by the deep CW fades, which occur throught the experiment except during conditions of simple type channel structure. The S(t) standard deviation, as, was quite constant throughout, R(t) and N(t) standard deviation measurements, aR and aN, were relatively constant throughout, except for shipping noise spikes. More details and a presentation of this statistical data is available in Reference [ 1]. Except for shipping interference and during simple type structure these results support hypotheses of long term (several hours) quasi-stationarity of the channel. Another X-averaged channel measurement, which supports the

113 quasi-stationary hypothesis, is the CANDOR measurement. CANDOR involves the computation of the normalized cross-correlation coefficient of h (t, X), h (t, X) h*(t-s, X) AX p(t, t-s) = I I ht ( I 2 htS ) I where Ilht(X)ll= th(X)12 AX. In an average-X-sense p(t, t-s) = p(s) implies WSS of h(t, A) where any pure (broadband) time varying gain is normalized out. Although p(t, t-s) was computed for all t with At = 102 seconds and all s-t in [0, 48 minutes] with A(s-t) = 102 seconds, the condition p(t, t-s) = p(s) was not fully tested. However, the -3 db and -6 dB decorrelation times, T+ and T+, were plotted for all t, At = 102 seconds in Section 3. 1. The parameters display constant values of 5 to 15 minutes most of the time, corresponding to the channel's nominal duration of time invariance. Thus, preliminary indications are that the X-average WSS test of hX(t), p(t, t-s) = p(s) may be successful. Finally, the normalized cross-correlation statistics of h (t) appear to be time invariant for much greater lengths of time than ht(X) itself is time invariant. Although this discussion on quasi-stationarity has been highly speculative, the data base relatively small and the measurement

114 techniques compromised, the discussion is constructive because the results presented were obtained using practical measurement techniques and they provide an early intuitive basis for serious efforts in determining the quasi-stationary properties of the UWAP channel. 4. 3. 4 Identification of Two Physical Propagation Modes. As pointed out earlier, there often appear to be two kinds of received multipath structure present in the CDR grams. First, a group of closely packed paths with very random appearing structure but a relatively constant average time of arrival has been denoted as cluster mode reception or structure. Although the delay spread of this cluster mode type structure is relatively constant for several hours at a time, during various periods of the experiment this spread can vary considerably. For example, in file 9 and 10 the cluster mode spread is approximately 300 milliseconds, while in file 4 the spread is approximately 150 milliseconds. In addition, on some occasions, see data files 4 and 5, two cluster modes appear in the channel's structure. The second type of structure identified in the CDR gram consists of a small set of clearly resolved paths. Usually one to three paths are present and, although definitely resolvable, all within 120 milliseconds of delay spread. The paths are generally well correlated. Trace these two basic modes of propagation throughout the two weeks of data. Often the two modes are separated so that they can easily be studied individually. However, they can be superimposed as in files 16, 17, 18, and 19, so that, although they are being

115 visually identified, individual study would be difficult since simple delay gating would no longer isolate the modes. These two modes appear independent and are clearly contrasting in nature. The natural conclusion is that two distinct physical mechanisms or modes of propagation are operating. Physical reasoning together with some simplified propagation analysis of the Straits of Florida provide a convincing argument that the cluster mode and simple mode structures are bottom, RBR, and surface RSR, SRBR, or surface duct propagation modes, respectively. The reasoning for these conclusions is expressed in the following paragraphs. Since significant Doppler spread energy has been noted and attributed to surface wave interaction with propagation, there certainly must be a surface mode of propagation in order for this interaction to occur. Furthermore, since Doppler spread activity correlates well with the presence of simple mode structure, the conclusion is that the simple structure is a surface mode of propagation. Other information further substantiates this conclusion. Greater variability in propagation (loss, speed, etc. ) is anticipated in a surface mode because of the relatively unstable water column. This fluctuating water column is driven by the sun (heating), clouds (cooling), winds, currents, etc., which produce a fairly dynamic propagation media (i. e., unstable water column). This expected variability in the surface mode is reflected in the S(t) variation in files 11, 12, and 13 where only simple type reception is present. This amplitude

116 variation in the simple paths is also evident in file 1. During simple mode reception S(t) is typically higher than during complex or cluster mode reception. Because greater losses are associated with surface reflections than bottom reflections there may be some question as to whether the surface mode is a channel, near the surface but not reflecting from it, or a refracted, surface reflected (RSR) mode. However, direct surface interaction appears to be the only significant spreading mechanism so that RSR is the more logical choice. Indirect frequency spreading surface mechanisms include modulation of the sound velocity due to pressure variations caused by waves or direct modulation of the acoustic signal, a pressure wave, by induced pressure waves from the surface waves. However, these are rather implausible explanations because the velocity is rather insensitive to such small pressure perturbations, and nonlinear phenomenon from pressure wave interaction is a negligible higher order effect. The cluster mode reception is identified as refraction-bottomreflected (RBR) propagation. In shallow depth water temperature is continually decreasing and pressure increases; if the temperature gradient is high sound velocity decreases with depth. Thus, a sound ray is refracted downward until it is reflected from the bottom upward only to be refracted downward again. Figure 2. 3 is a ray trace of the Straits of Florida illustrating several RBR paths as well as RSR propagation. In contrast to the surface the deep water

117 column is very stable due to the lack of many of the dynamic driving (200 meters and deeper) forces at the surface. Therefore, propagation variability with time will be much less for RBR. However, simplified RBR ray theory in the Straits of Florida predicts many closely stacked up arrivals [ 11], providing excellent support for a quasi-stationary uncorrelated Gaussian process due to many small scale variations and interactions in the received RBR propagation. CDR grams 9 and 10 contain two apparent surface paths (along the right hand margin and continuing through CDR gram 14) and what appears to be basically RBR (i. e., many paths) but displaying the noncharacteristic feature of resolved individual arrivals. It is not clear what drives this variation in RBR propagation, possibly deep internal waves, or a changing surface layer depth. Thus, although some very complicated results can be obtained and uncertainty exists, two contrasting propagation modes identified in the CDR gram, have been logically associated with the two major modes of propagation. Decomposition of the Delay Spread UWAP Channel The CDR gram and the DUAL measurements suggest and provide the means for further measurements and experiments to substantiate the identification and to better study and understand these two modes. The CDR gram illustrates the possibility for a decomposition of the UWAP channel into two natural subchannels by very simple time-delay gating. Previously, measurements such as DUAL,

118 CANDOR, etc., have been measurements on the total channel, which is constructed of two very different and interesting subchannels. Such measurements can be made individually on the two channels whenever they are noninterfering. Such analysis has already proved interesting when simple mode is present alone, files 11, 12, and 13. Here DUAL and CANDOR results are quite different than the normal measurements dominated by cluster mode. S(t) and R(t) measurements of the decomposed channels can be particularly interesting. Since cluster mode is almost always present, previously little opportunity has been presented to extensively correlate variable S(t) with individual paths or even simple mode structure, or to correlate R(t) activity with simple mode S(t) activity. However, individual CW measurements are impossible with single hydrophones and individual R(t) measurements may be impractical. Thus, individual S(t) measurements will be compared with total channel C(t) and R(t) measurements. Nevertheless, such studies should be very interesting, informative, and simple to implement. Subchannel Modeling Two very distinct types of propagation, which can often be isolated, have been identified in the CDR gram and individual study has been suggested. Since the subchannels are so contrasting in nature, the appropriate models and modeling techniques will be quite different. The cluster mode structure appears to be a perfect candidate for stochastic, quasi-stationary, uncorrelated Gaussian modeling where statis tical methods appear most useful.

119 The simple mode structure seems best suited for non-random parameter tracking techniques. Each path of the mode can be resolved and its parameters, amplitude, phase, duration, and arrival time may be individually tracked and studied. The paths and their respective parameters can be correlated with each other, environmental measurements, etc. 4.4 Summary The author feels that the ordered pair gram display of the channel digit response, cdr(t, X) is a breakthrough for MIMI signal processing and will provide new insight in underwater acoustic propagation study. The display presents a more complete picture of the multipath structure of the UWAP channel, its complexity and simplicity, and its variability, for much longer durations than has been possible previously. For the first time, the whole of the channel can be simply presented and comprehended. In general, the value of the CDR gram is the compact and useful presentation of the tremendous quantity of qualitative and gross quantitative information inherent in the cdr (t, A) data. For example, a CDR gram spanning several hours of time is easily displayed on an 8-1/2 by 11 inch area. Multipath structure can be readily detected and identified as simple or complex, the duration (hours, days, etc.) of each general structure is easily observed. The simultaneous reception of a simple and complex structure, whether non-overlapping

120 or superimposed in time delay, is readily identified. Visual correlation of the general channel structure with key scalar functions (e.g., DUAL parameters) representing the channel are simply achieved by observing side-by-side plots of such parameters and the corresponding CDR grams. The CDR gram is equally as important as a springboard or testing ground for new post-processing ideas of UWAP data as it is for the direct extraction of information from the display. A significant attribute of the CDR gram is that without any processing, several parameters can be at least semi-quantitatively estimated. This means the computing time of several special post-processing algorithms can be avoided. Even more importantly, the gram provides preliminary information on parameters and their behavior so that the probability of success and the basic nature of the algorithm can be intelligently surmised without the time consuming task of blindly defining, implementing, and evaluating an algorithm. The value of this ability to rather effortlessly obtain preliminary algorithm design and evaluation can not be over emphasized. The simple and complex types of structure are so contrasting in nature that an observer immediately wants to classify them. Based upon propagation theory, these two types of structure are readily hypothesized to be very distinct physical propagation modes. The simple reception is apparently a surface related mode and the complex reception must be a bottom mode. Immediately, several ideas

121 are generated. When the two modes are non-interferring in time delay or only one mode is present, they may be studied separately. For example, S(t) or CANDOR analyses can be independently performed on the modes. Surface reverberation measurements from DUAL can easily be correlated with the presence of the surface mode. Since the two modes are so different in nature, measurement and modeling approaches most suitable for each mode are likely to be quite different. Observations of the CDR grams clearly indicate tremendous data reduction may be possible without significantly compromising the quality of the data base or the representation of the channel which the data base provides. The possibilities are indeed vast and exciting. But most importantly, new ideas using or generated from the CDR gram will provide a greater understanding of the UWAP channel and piece by piece useful and reliable models and experimental methods will be developed.

CHAPTER 5 OTHER CHANNEL REPRESENTATIONS Although the CDR, ht(X), appears to be a useful representation of the UWAP channel, other likely candidates are briefly presented and discussed. The alternatives investigated, the channel digit spectrum, St(f) and the channel covariance function, Covht(ji), provide some informationabout the MIMI channel, but they appear considerably less interesting than the cdr (t, X) 5. 1 Channel Digit Spectrum, St(f) The channel digit spectrum is a logical alternative representation of the UWAP channel. The CDS denoted by St(f) is the Fourier transform of the time spread channel digit response, ht(X ), taken with respect to the time spread variable, St(f) = ht( ) e2 where f [-63, 62], A' = 252 AX _ 5 msec and Af T 0.833 Hz P 122

123 Since 252 is not an integer power of two, the usual fast Fourier transform algorithm could not be used to compute St(f) here [27]. However, 252 is a high composite number, 252 = 3 - 3 * 7 2 2, so that an efficient but very specialized FFT algorithm could have been used [30]. However, a more general computational algorithm called the Chirp Z-Transform, CZT, was used here [29], [31]. The advantages of the CZT, obtained at the expense of increased computer memory requirements, are: ~ The CZT expresses the Fourier transform as a convolution. Thus, fast convolution techniques using the conventional FFT algorithm may be used to obtain computation efficiency. * A' is an arbitrary integer variable in the CZT. In the conventional FFT A' is restricted to integer powers of 2. This discussion is not intended as a detailed development of computational techniques such as the FFT, CZT, or fast convolution. * These techniques are well documented in the open literature. This is simply a straightforward application of an algorithm that does not contain the restriction of conventional FFT analysis. References [26 31 References [26 ].- 31].

124 This added flexibility is important because varied MIMI experimental conditions and objectives dictate different signal periods. That is, A varies and is never an integer power of two since maximal length binary sequences are always one less than a power of two, so that A = Integer ~ 2 - 1. Thus, the CZT algorithm provides efficient and versatile signal processing, spectral analysis, correlation and convolution, of MIMI signals. Another approach to this same problem is currently being studied from the signal design aspect of the problem [14 ]. The major equations and a Fortran listing of the CZT are in Appendix B. Since St(f) is positive real valued, the positive real (PR) gram format discussed in Section 4. 2 is the natural technique for displaying it. These CDS grams are organized by files as summarized in Table 3. 1. The time variable, t, runs down the gram and frequency is across the gram. Since the transmitted signal main lobe has a ~50 Hz main lobe sin rfT 7rfT p and the reception is filtered sharply at ~ 50 Hz, only the ~ 50 Hz region of St(f) is displayed. However, St(f) was computed from -100 Hz to +100 Hz and the power in the main lobe -50 to +50 Hz

125 was computed 63 MLP = ISt(f) I f= -63 The ratio of MLPt to S(t) is an indicator of the analog prefiltering integrity and, likewise, it is a measure of the over sampling of the current MIMI sampling rates. This ratio expressed in decibels, 10 Log10 MLPt/S(t) was nominally -0.1 ~ 0. 075 dB for all the data presented, or -0. 01 MLPt = 10 S(t) = 0. 975 S(t). That is, approximately 97. 5 percent of the total reception energy is within the ~ 50 Hz band. Thus, for practical purposes, including sampling rate aliasing concern, the sidelobes are negligible. The CDS grams do not appear to reveal the basic nature of the channel as the CDR grams. The first impression of the CDS grams is sameness; they are all alike. However, there is some information unavailable in the CDR grams. Most of the received energy is nominally in the ~ 30 Hz band around center. However, the band from -30 to 0 Hz generally has more energy than the corresponding 0 to 30 Hz band. This phenomenon is particularly emphasized during simple mode propagation, e. g., file 9. Although there are probably more informative ways to display or otherwise

fr" a t - i —r~ 0 X 0,........................................

-. > oi~q S C7~2 4%);

*9 * JSc 9 1 9 Swvo9 Sao 09 2S a ZH 0 a SZ* O (SO:61)9T (ZS*Z0)9T (Sw 0o)91::tI.)S i 4rC. T )4T"~3z ~::::-:::~-~~::::: i::::~: -.~~Y*:: C: I sallpl::;:;::::::':a-~:::'i:.3::::::2~:::: I::':I::::_~i~:r 1:::~~' ~p(i —:::,4 un: ~~~i; I

129 -751 17(07:32 17(12:33.) 17(18:46) 50: -25 0 Hz 25 s50 CDS GRAMS 7 & 8 Fig. 5. 4

130 23(22t:47 241:49) ~'::: 5 0! CDS GRAMS 9 & 10 Fig. 5. 5

9 *''2Ij ZT I It SWV9 Sa3 0S9 ZH 0 a 09S (t *:61)9 E (81:1t1). ~ (6-0: Lo0)s

L9 "Ol VT I CT SWVn S03 ZH 0 a U

133 I 2(t9 40 ft I I ~-~ i:, ":::: -:~::i::,:~~:~:;::::::::i:::::':::i:: ::i~:::::- r i:: 1:.:-:::j::::'-: 3 27(08:07) 27(20:09) -50 -25w w 2 -50 -25 0 Hz 25 50 CDS GRAMS 15 & 16 Fig. 5. 8

134 272:9 280836 282: 8 t-50 -25 0 Hz 25 5 CDS GRAMS 17 & 18 Fig. 5. 9

J3 5 CDS:: Hzt: CDS GRAM 19 Fig. 5. 10 process St(f), the CDS does not appear nearly as revealing a representation of the UWAP channel as the CDR. 5. 2 The Channel Auto Covariance Under normal conditions, cluster mode reception, arguments have been made of quasi-stationarity. G'aussianness of ct(X) can be argued on the basis of th-e cluster mode reception consis ting of tihe relatively llare numbe of closely spaced r.anldoml multith arr ivl s. Assutlming ergodicity, time averages are used to estimnat-e the mean and auto covariance functions of hit().

136 * Since ht(X) is zero mean, the normalized auto covariance of the CDR is estimated by ht () h X) AX Covht(() = A I ht(X)ll Covht( /) is complex-valued conjugate symmetric function. The computations were performed using fast convolution techniques and the results of this analysis on all of the CDR data are presented in ordered pair format. A tremendous amount of information appears to be lost in going from the CDR gram to the COVH gram. As with the CDS, the COVH grams generally leave an impression of "sameness" and certainly do not convey the physical characteristics so vividly illustrated in the CDR gram. Possibly Covht (,) is a very incomplete statistical representation of the channel. However, any statistical representation is likely to wash out the physically distinctive features of the channel. The preliminary conclusion drawn here is that Covht (Li) is probably an inadequate representation of the UWAP channel. However, the CDR gram and ht (X) are very rich in physical information about the UWAP channel The mean is estimated Mh = ht(X) and subtracted to t t assure zero mean ht(X).

137 and clearly should be the primary base for MIMI experiments at this time. The Covht(AL) grams are presented on a one-to-one basis corresponding to the CDR grams. The Covht(j) grams are OP grams as are the CDR grams. The general format of the COVH grams are otherwise similar to the CDR grams. Alternating black and white bar patterns are plotted every 100 minutes and the black and white bar durations in Ai correspond to the 40 msec width of the correlation triangle resulting from an ideal 20 msec pulse in the CDR. The significant extent of Covht(ji) appears to be approximately 40 to 60 or 80 msec in the gram. That is, the channel appears to be uncorrelated within one to two transmission digits. In files completely consisting of simple mode reception, more correlation is present. In general, Covht(() gives a strong impression of "sameness" which supports contentions of stationarity and indicates that time averaging should be a valid means for obtaining better estimates of Covht(,I).

138 1205 18 144X0+:7 13(1:53::::::~~ 140136 -310 0 MSEC 310 C0VH GRAMS I & 2 Fig. 5. 11

Z T *;'2Hd a I E SWVO9 HAO3 OIC1 33SW 0 OIE 0.?:6*01 ) T,,'. I: WI:~::is:~.,: ~:e! 691

,i >u........... A~~~~~~~ ".j~~~~~~~~~~~~~~~~~~~~~~~I m Joint. sir.:. I a'.::""..' at 1''fP *.:" *Ai~:"'t~:~::!::':' I.................. r:? ~ i:in' I 4 9 j 1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ —-?~'!~.-.~.~i?...-.-~~ ~..._,~~i~~~., -..: X::,,::::, 7,,,.. '',, l I I

141 17(73 17(1:6 1i( 12::::: 33 171:46):.-310 ~ 0 MSEC COVH GRAMS 7 & 8 Fig. 5. 14

/::::: I::j::::: i? =::~!ii:~::.z::i~""~:~'i~':I:r".:.-v: W.r ~~~~~~~~~~~~~~~~~~~~~~~~~~~~...............Ii~ i os~~~~~~~~~~~~~~~~~~~~~~~~~~~~ VIC~~~~~~~~~~~~~~~~~~ ~~~~~~ V~~~~~~~u~vp~t it'Il 1 1 IW4:~~~~~~~~~~~~~~~~~~~~~~~~I ~~iii:ili::~il:?ji::~iii i~j to 11M 77,bt~ Eric~~~~~~~~~~~~~~~ II 1-:. p.. ~ W*.4r.!~4. ~ O' I.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~K i i~-J~ crt Kw "~::i Ii..0 47 t /'.t

flrazii ~I ~ ~~~~~~~~~~~~~~0.4 i~~~~~~~~~~~~~g~~~~~~~~~~~l (4'I4''.4' * *4. at.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...... U..' i. or C. to.tot0 N~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~g~ N ~ ~ ~ %4~~4~~ 47' ~~~~c~tt~~~'~~t4&4, C'S CV "'~~~~~~ I.~~~~~~~~~~~~~~~~~~,.,# ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~g~~~~~~~~~~~~~~~i gci my~~~~~~~~~~~~~~~~~~~~L' II U I ~ ~ ~ ~ ij I iJ I U E.~:~" I I'I I* 14 *II.4......r....j *I*~~~~~~~~~~~~~~~~~~~~~~~~P!ig;:' - ~ ~ ~ ~ ~ * ~~~~~~~~ %4fft ~~~~~~~~~~~~~~,~~I

144 26(07;38 026(1940) -310: 0 MSEC 3.0 o0 H GRAMS 13 &:14 Fig. 5. 17

145 2 6ii."'{i?!iii,:i~!i "i~'ii~;i:.........i~~~ -i310.: 0a:O:MSEC:31.U iiv GRAMS:i5 & S 16 Fig. 5. 18

146 28f08:.. 36fi. 2 8 ( i ii.:: i:::. i:E: 3 8)i:S l i.i-i n if i S i.. EREd i E! E in...... -310 0 MSEC 310 COVH GRAMS 17 & 18 Fig. 5. 19

OZ' g ~gS 33SW: oftt LV[

CHAPTER 6 CONCLUSIONS The contribution of this work is the presentation, application, and interpretation of a simple display of long time-series of the underwater acoustic channel digit response, or multipath structure, for the first time. The display has been demonstrated to be particularly useful in three areas: 1. elementary information extraction, which includes: 1. 1 measurement of arrival times, delay spread, timeinvariance durations, and structure duration 1. 2 classification of structure into simple, cluster, and complex modes 1. 3 path and mode resolution 2. correlation of multipath reception characteristics with power measurements 3. association between observed multipath structure and physical propagation modes. The simple mode structure is recognized as a surface interacting mode and cluster mode is, most likely, refracted, bottom-reflected propagation. The conclusion is that the channel digit response display is a promising research tool for acoustic propagation studies. However, 148

149 much work remains to gather more propagation data and to obtain experience with the display. These efforts should provide new and useful inputs for physical and abstract underwater acoustic propagation modelling.

Appendix A GENERATING A-SCAN PLOTS WITH THE 731 RECORDER The DUAL plots in Chapter 3 illustrate the capability of a raster-scanning recorder for presenting data in an A-scan format. The Hathaway 731 recorder was the particular device used in this thesis. Many other similar and inexpensive commercial devices are available. In general, this type of device has several advantages over an X-Y plotter including speed, silence and reliability. At times, the disadvantage of data formatting may exist; however, this is not true in many cases. If the paper motion direction is selected as the axis for the independent variable, the formatting task is trivial. This is illustrated below by outlining the formatting task using Fortran-like statements. Outline of Formatting Task 1. Declare a dependent variable plotting array of N variables Dimension Depvar (N) Integer Depvar 2. Clear Depvar (I) (I=1, N, 1) i. e., intensity off 3. "Format" the integer variable X a. Scale X, assume X is positive X' = X*N/XMAX 150

151 15 XMAX is generally 2 since variables are single precision (16 bit) integer variables Typical values of N are 500 or 1000 providing 9 to 10 bits of dynamic range in the plotting variable, i. e., 54 to 60 dB of amplitude (voltage) dynamic range. b. Depvar (X') = Intensity ON 4. Trigger the scan Call plot 731 (Depvar, N) 5. Wait for scan completion 6. Clear those "Intensity ON" elements of Depvar(I) Depvar(X') = 0 (Intensity Off) 7. Return to 3. to format and plot next scan (each scan corresponds to an increment on the independent variables, i. e., t = t + At). This outline is for the plotting of a single dependent variable. The DUAL plots are multiple dependent variables which are a simple extension of the above outlined procedure. A procedure similar to the above was programmed in Fortran in about two hours. The procedure ran quickly. Each plot scan was formatted and plotted in the 50 msec sweep time of the 731. The paper speed was approximately an inch per second.

152 The 731 is very suitable for producing A-scan plots at speeds, silence and reliability not available in X-Y plotters with a very simple and fast formatting algorithm. Such devices can be used effectively for nonimpact alpha-numeric printing, too.

Appendix B CHIRP- Z- TRANSFORM This is a brief presentation of the basic equations and Fortran listings of the CZT algorithm used in this thesis for computing the channel digit spectrum. Denote the finite, discrete Fourier transform of f(t) by F(co) where = 0,..., N - 1 and t = O..., N- 1 Then F(c) A 2 N f(t) e t/ (B. 1) N t=O Using the identity (a - t) = ta - 2wt + c or -wt = (o - t)2/2 - t2 /2 - Wa/2, Equation B. 1 becomes F(L) = e-1idw/2 N- f(t) ei( /2 (B. 2) t=0 where f'(t) = f(t) e-it /2 But N-1 LN-1 f'(t) ei(t)/2 t=0 153

154 itz /2 is just the convolution of f'(t) with e Thus Equation B. 2 can be evaluated using the fast convolution (FFT) technique. The only significant practical difficulty is obtaining the results of an aperiodic convolution from periodic representations. This result is achieved by simply augmenting f(t) with enough zeros so that for the region of interest, = 0,..., N - 1, the aperiodic and periodic results are the same. This may seem to be a hard way to evaluate Equation B. 1. Why not evaluate Equation B. 1 with an FFT in the first place? For values of N not equal the a power of two a versatile and efficient FFT algorithm does not exist. The fast convolution technique was also used to compute the channel auto covariance Covht(i). The major subroutines in the CZT are: 1. CZT - the basic algorithm 2. CZT0 - initialization 3. FXCV - fast convolution 4. FXCTC - an in-place Cooley-Tukey FFT All arithmetic is 16 bit block floating point. The arrays IX1 and IY1 are the real and imaginary parts of the data vectors. (IX1, IY1) is both the input vector, f(t), and the output vector, F(w). Similarly, (ICX, ICY) is the e-i /2 vector IEZ is the

155 FFT coefficient vector, eiwt/N and (IFX IFY) is the e-it /2 transform vector. ICHAR is the block floating point characteristic.

156 SUBROUTINE CZT (IX1, IY1, ICX, ICY, IEZ, IFX, IFY, NL, N, ICHAR) DIMENSION IX1(1), IY1(1), ICX(1), ICY(l), IEZ(1), IFX(1), IFY (1) C IZ1 - I/O DATA BUFFER C ICZ = CZT COEF C IFZ = FFT(CZT COEF) C IEZ = FFT COEF LOGICAL ISW, ISW2 DATA ISW/. FALSE. /, ISW2/. FALSE./ IC0=0 IC1=0 IF (ISW) GO TO 10 CALL CZTO (ICX, ICY, IFX, IFY, IFC, IEZ, NL, N) ISW=. TRUE. C DO CZT 10 CONTINUE N2=N*2 N2P=LOG2 (N2) NL2=NL*2 C Z=Z*EXP(- I*2*PI*N**2/NL2) CALL CMPY (IX1, IY1, IX, IY1, ICX, ICY, NL) NL1=NL+1 N2M=N2-NL 1+1 CALL CZERO(IX1(NL1), IY1(NL1), N2M) C FAST CONVOLUTION OF IX1 WITH IFZ C WHERE TRANSFORM OF IFZ WAS PRECOMPUTED ISW2=. TRUE. CALL FXCV(IX1, IY1, IFX, IFY,IFC, IEZ, N2P, ICO, ISW2) C Z =*EXP(- I*2*PI*K**2/NL2) CALL CMPY (IX1, IY1, lX1, IY1, ICX, ICY, NL) ICHAR=ICO RETURN END SUBROUTINE FXCV(IXO, IYO, IX2, IY2, IC2, IEXP, NEXP, ICO, ISW2) C IZO= FAST CONVOLUTION OF IZO WITH IZ2 C IZO= (IXO, IYO) AT OUTPUT C IZ1=(IXO, IYO) AT INPUT C IZ2=(IX2, IY2) CAN BE CONTROLLED BY ISW2 C NEXP=FFT LENGTH C ASSUMES IZO AND IZ2 PRESTRUCTURED(ZERO EXTENDED) FOR FFT

157 C ISW2=. TRUE. => IZ2 ALREADY TRANSFORMED, OTHERWISE ISW2. FALSE. C ICO=ICO+IC1+ IC2 IS TOTAL # OF NODES SCALED BY C 1/2 IN THE 2 FFT'S AND THE IFFT DIMENSION IXO(1), IYO(1), IX2(1), IY2(1), IEXP(1) LOGICAL ISW2 NX = 2**NEXP C TRANSFORM IZ 1 CALL FXCTC(IXO, IYO, IEXP, NEXP, IC1) C UNLESS ISW2IS.TRUE., TRANSFORM IZ2 IF (ISW2) GO TO 1 CALL FXCTC(IX2, IY2, IEXP, NEXP, IC2) C IZO(F) = IX1(F) * IZ2(F) 1 CALL CMPY(IXO, IYO, IXO, IYO, IX2, 1Y2, NX) C IZO(K)= IFFT (IXO, IYO, IEXP, NEXP, ICO) CALL CONJZ(IYO, NX) CALL FXCTC(IO, IYO, IEXP, NEXP, ICO) CALL CONJC(IYO, NX) ICO= ICO+ IC1 + IC2 RETURN END SUBROUTINE CZTO (ICX, ICY, IFX, IFY, IFC, IEZ, NL, N) C GENERATE CZT COEFS DIMENSION ICX(1), ICY(1), IFX(1), IFY(1), IEZ(1) C ICZ = CZT COEF= EXP(-I*2*PI*N**2/2*NL) C IFZ = FFT ((ICZ + )+ (ICZ- 1)) N2 =N*2 N2P= LOG2(N2) NL2 =NL*2 PI= 3. 14159 ARGO = 2. *PI/ FLOAT (NL2) FN=N ARG = ARGO*FN*FN IX = COS(ARG)*32767. TY = -SIN(ARG)*32767. ICX(N + 1) = IX ICY(N+ 1) =IY IFX(N+ 1) =IX IFY(N+ 1)=IY ICX(1) = 32767. ICY (1)= 0. IFX(1) = 32767. IFY(1) = 0. DO 1 J = 2, N

158 FJ1= FLOAT(J-1) ARG = ARGO*FJ1*FJ1 IX= COS(ARG)*32767. IY = SIN(ARG)*32767. IY =-IY ICX(J)= IX ICY(J)= IY IFX(J) = IX IFY(J) = Y NP=N2-(J-1)+ 1 ICX (NP)= IX ICY (NP) = IY IFX(NP)= IX 1 IFY(NP)= IY CALL CONJZ(IFY, N2) CALL FXCTC(IFX, IFY, IEZ, N2P, IFC) RETURN END SUBROUTINE CMPY(IX1, IY1, 1X2, IY2, IX3, IY3, N) SCALED FRACTION IX1(1), IY1(1), IX2(1), IY2(1), IX3(1), Y3 (1) SCALED FRACTION IAX, LAY, IEX, IEY C IZ1(I) = IZ2(I)*IZ 3 (I), (= 1, N) DO 1 I=1, N IAX = X2 (I) IAY = IY2(I) IEX = IX3 (I) IEY = IY3 (I) IX 1 (I) = IEX*IAX- IEY *IAY IY 1 (I) = IEX*IAY+IEY*IAX RETURN END FUNCTION LOG2(N) DO 1 I=0, 15, 1 K= 2 **I KD= K-N IF(KD) 1, 3, 1 3 LOG2 = I RETURN 1 CONTINUE

159 WRITE (6. 100) 100 FORMAT (30H ERROR PAUSE IN LOG2') PAUSE END SUBROUTINE CONJZ (IY, N) DIMENSION IY(1) DO 1 I=1, N 1 IY I) (I)- () RETURN END SUBROUTINE CZERO(IX, IY, N) DIMENSION IX(1), IY(1) DO 1 I= 1, N Ix(I) = 1 Y(I)= RETURN END

REFERENCES 1. Heitmeyer, R. M., Underwater Sound Propagation in the Straits of Florida: The Preliminary Analysis of the MIMI Experiment of 1970, C. E. L. Technical Report No. 213, Cooley Electronics Laboratory, The University of Michigan, Ann Arbor, February 1972. 2. Veenkant, R. L., Preliminary Report on CANDOR: Complete Analysis with Decision Oriented Recording, C. E. L. Technical Report No. 221, Cooley Electronics Laboratory, The University of Michigan. (To Be Published) 3. Kailath, T., "Measurements on Time-Variant Communication Channels," IRE Trans. Information Theory IT-8, S229-S236 (Sept. 1962). 4. Tucker, D. G., and B. K. Gazy, Applied Underwater Acoustics, Permagon Press, Oxford, 1966. 5. Steinberg, J. C. and T. G. Birdsall, "Underwater Sound Propagation in the Straits of Florida," Journal of the Acoustical Society of America, Vol. 39, No. 2, February 1966. 6. Birdsall, T. G., Acoustic Signal Processing, (Final Report) Cooley Electronics Laboratory, The University of Michigan, Ann Arbor, June 1972. 7. Steinberg, J. C., et al., "Fixed-System Studies of Underwater Acoustic Propagation," JASA, Vol. 52, No. 5 (Part 2), 1972, pp. 1521-1536. 8. Birdsall, T. G., R. M. Heitmeyer, K. Metzger, Modulation by Linear Maximal Shift Register Sequences: Amplitude, Biphase, and Complement-Phase Modulation, C.E. L. Technical Report No. 216, Cooley Electronics Laboratory, The University of Michigan, Ann Arbor, December 1971. 9. Clark, J. G., "Multipath Signal Interference in Time-Dependent Propagation Channels," JASA, Vol. 52, No. 1 (Part 2), 1972, pp. 452-454. 160

161 REFERENCES (Cont.) 10. Clark, J. G., et al., "Refracted, Bottom-Reflected Ray Propagation in a Channel with Time-Dependent Linear Stratification, JASA, Vol. 53, No. 3, 1973, pp. 802-818. 11. Deferrari, H. A., "Time-Varying Multipath Interference of Broadband Signals Over a 7 NM Range in the Florida Straits," JASA, Vol. 53, No. 1, 1973, pp. 162-180. 12. Hatter, Norman, Triband: T ThThree Band Filter for the Continuing MIMI Experiment, C. E. L. Technical Report No. 201, Cooley Electronics Laboratory, The University of Michigan, Ann Arbor, February 1970. 13. Kennedy, R. M., "Phase and Amplitude Fluctuations in Propagating Through a Layered Ocean, " JASA, Vol. 46, No. 3 (Part 2), 1969, pp. 737-745. 14. Metzger, K., Private Communication on MIMI Signal Design, Cooley Electronics Laboratory, The University of Michigan, Ann Arbor. 15. Unger, R., and R. Veenkant, Underwater Sound Propagation in the Straits of Florida: The MIMI Experiment of 3 and 4 February 1965, C. E. L. Technical Report No. 183, Cooley Electronics Laboratory, The University of Michigan, Ann Arbor, May 1967. 16. Unger, R., and R. Veenkant, Underwater Sound Propagation in the Straits of Florida: The MIMI Continuous and Sampled Receptions of 11, 12, and 13 August 1966, C. E. L. Technical Report No. 186, Cooley Electronics Laboratory, The University of Michigan, Ann Arbor, June 1967. 17. Veenkant, R., and E. Tury, Underwater Sound Propagation in the Straits of Florida: The MIMI Lunar-Cycle Receptions, C. E. L. Technical Report No. 219, Cooley Electronics Laboratory, The University of Michigan, Ann Arbor, January 1972. 18. Bar-David, I., "Estimation of Linear Weighting Functions in Gaussian Noise, " IEEE Trans. on Information Theory, Vol. IT-14, No. 3, May 1968, pp. 395-407.

162 REFERENCES (Cont.) 19. Bello, P. A., "Some Techniques for the Instantaneous RealTime Measurement of Multipath and Doppler Spread, " IEEE Trans. on Comm. Tech., Vol. 13, No. 3, September 1965, pp. 285-292. 20. Bello, P. A., "Measurement of Random Time-Variant Linear Channels, " IEEE Trans on Information Theory, Vol. IT-15, No. 4, July 1969, pp. 496-475. 21. Bello, P. A., "On the Measurement of a Channel Correlation Function," IEEE Trans on Information Theory, Vol. IT-10, No. 4, October 1964, pp. 381-383. 22. Bello, P. A., "Time-Frequency Duality," IEEE Trans. on Information Theory, Vol. IT-10, No. 1, January 1964, pp. 18-33. 23. Gaarder, N. T., "Scattering Function Estimation, " IEEE Trans. on Information Theory, Vol. IT-14, No. 5, September 1968, pp. 684-693. 24. Root, W. L., "On the Measurement and Use of Time-Varying Communication Channels, " Information and Control 8, 1965, pp. 390-422. 25. VanTrees, H. L., Detection, Estimation, and Modulation Theory, Part III, Wiley, New York, 1971. 26. Bluestein, L. I., "A Linear Filtering Approach to the Computation of the Discrete Fourier Transform, " Nerem Rec., 1968, pp. 218-219. 27. Gentlemen, W. M., and G. Sande, "Fast Fourier Transforms - For Fun and Profit," in 1966 Fall Joint Computer Conference, AFIPS Conf. Proc., Washington, D. C.: Spartan, 1966, pp. 563-578. 28. Gold, B., and C. M. Rader, Digital Processing of Signals, McGraw-Hill, 1969. 29. Rabiner, L., R. Schafer, C. Rader, "The Chirp-Z Transform Algorithm," IEEE Trans. Audio and Electroacoustics, Vol. AU-17, June 1969.

163 REFERENCES (Cont.) 30. Singleton, R. C., "An Algorithm for Computing the Mixed Radix Fast Fourier Transform," IEEE Trans. Audio Electroacoustics, Vol. AU-17, June 1969, pp. 93-103. 31. Stockham, T. G., Jr., "High Speed Convolution and Correlation, 11 Spring Joint Computer Conference, AFIPS Proc., 28:220-233, 1966. 32. Bello, P. A., "Characteristics of Randomly Time-Variant Linear Channels," IRE Trans. Comm. Syst. CS-11, December 1963.

DISTRIBUTION LIST No. of Copies Office of Naval Research (Code 468) 1 (Code 102-OS) 1 (Code 480) 1 Navy Department Washington, D. C. 20360 Director, Naval Research Laboratory 6 Technical Information Division Washington, D.C. 20390 Director 1 Office of Naval Research Branch Office 1030 East Green Street Pasadena, California 91101 Dr. Christopher V. Kimball 1 Special Studies Group IAR/PGI Suite 4 9719 South Dixie Highway Miami, Florida 33156 Director Office of Naval Research Branch Office 495 Summer Street Boston, Massachusetts 02210 Office of Naval Research 1 New York Area Office 207 West 24th Street New York, New York 10011 Director Office of Naval Research Branch Office 536 S. Clark Street Chicago, Illinois 60605 164

165 DISTRIBUTION LIST (Cont.) No. of Copies Commander Naval Ordnance Laboratory Acoustics Division White Oak, Silver Spring, Maryland 20907 Attn: Dr. Zaka Slawsky Commanding Officer Naval Ship Research & Development Center Annapolis, Maryland 21401 Commander 2 Naval Undersea Research & Development Center San Diego, California 92132 Attn: Dr. Dan Andrews Mr. Henry Aurand Director 8 Naval Research Laboratory Attn: Library, Code 2029 (ONRL) Washington, D. C. 20390 Chief Scientist Navy Underwater Sound Reference Division P. 0. Box 8337 Orlando, Florida 32800 Commanding Officer and Director Navy Underwater Systems Center Fort Trumbull New London, Connecticut 06321 Commander Naval Air Development Center Johnsville, Warminster, Pennsylvania 18974 Commanding Officer and Director 1 Naval Ship Research and Development Center Washington, D. C. 20007 Superintendent 1 Naval Postgraduate School Monterey, California 93940

166 DISTRIBUTION LIST (Cont.) No. of Copies Commanding Officer & Director Naval Ship Research & Development Center* Panama City, Florida 32402 Naval Underwater Weapons Research & 1 Engineering Station Newport, Rhode Island 02840 Superintendent Naval Academy Annapolis, Maryland 21401 Scientific and Technical Information Center 2 4301 Suitland Road Washington, D. C. 20390 Attn: Dr. T. Williams Mr. E. Bissett Commander 1 Naval Ordnance Systems Command Code ORD-03C Navy Department Washington, D.C. 20360 Commander 1 Naval Ship Systems Command Code SHIPS 037 Navy Department Washington, D. C. 20360 Commander 2 Naval Ship Systems Command Code SHIPS OOV1 Washington, D. C. 20360 Attn: CDR Bruce Gilchrist Mr. Carey D. Smith Commanding Officer Fleet Numerical Weather Facility Monterey, California 93940 Formerly Mine Defense Laboratory.

167 DISTRIBUTION LIST (Cont.) No. of Copies Commander 1 Naval Undersea Research & Development Center 3202 E. Foothill Boulevard Pasadena, California 91107 Defense Documentation Center 2 Cameron Station Alexandria, Virginia 22314 Dr. James Probus 1 Office of the Assistant Secretary of the Navy (R&D) Room 4E741, The Pentagon Washington, D.C. 20350 Mr. Allan D. Simon 1 Office of the Secretary of Defense DDR&E Room 3E1040, The Pentagon Washington, D.C. 20301 Capt. J. Kelly 1 Naval Electronics Systems Command Code EPO-3 Washington, D.C. 20360 Chief of Naval Operations 1 Room 5B718, The Pentagon Washington, D.C. 20350 Attn: Mr. Benjamin Rosenberg Chief of Naval Operations 1 801 No. Randolph St. Arlington, Virginia 22203 Dr. Melvin J. Jacobson 1 Rensselaer Polytechnic Institute Troy, New York 12181 Dr. Charles Stutt 1 General Electric Company P.O. Box 1088 Schenectady, New York 12301

168 DISTRIBUTION LIST (Cont.) No. of Copies Dr. Alan Winder 1 EDO Corporation College Point, New York 11356 Dr. T. G. Birdsall Cooley Electronics Laboratory The University of Michigan Ann Arbor, Michigan 48105 Mr. Morton Kronengold 1 Director, Institute for Acoustical Research 615 S.W. 2nd Avenue Miami, Florida 33130 Mr. Robert Cunningham 1 Bendix Corporation 11600 Sherman Way North Hollywood, California 91606 Dr. H. S. Hayre 1 University of Houston Cullen Boulevard Houston, Texas 77004 Dr. Ray Veenkant 1 Texas Instruments, Inc. North Central Expressway Dallas, Texas 75222 Mail Station 208 Dr. Stephen Wolff John Hopkins University Baltimore, Maryland 21218 Dr. Bruce P. Bogert Bell Telephone Laboratories Whippany Road Whippany, New Jersey 07981 Dr. Albert Nuttall 1 Navy Underwater Systems Center Fort Trumbull New London, Connecticut 06320

169 DISTRIBUTION LIST (Cont.) No. of Copies Dr. Philip Stocklin Raytheon Company P. 0. Box 360 Newport, Rhode Island 02841 Dr. H. W. Marsh 1 Navy Underwater Systems Center Fort Trumbull New London, Connecticut 06320 Dr. David Middleton 35 Concord Avenue, Apt. #1 Cambridge, Massachusetts 02138 Mr. Richard Vesper Perkin-Elmer Corporation Electro-Optical Division Norwalk, Connecticut 06852 Dr. Donald W. Tufts University of Rhode Island Kingston, Rhode Island 02881 Dr. Loren W. Nolte Dept. of Electrical Engineering Duke University Durham, North Carolina 27706 Dr. Thomas W. Ellis 1 Texas Instruments, Inc. 13500 North Central Expressway Dallas, Texas 75231 Mr. Robert Swarts Honeywell, Inc. Marine Systems Center 5303 Shilshole Ave., N.W. Seattle, Washington 98107 Mr. Charles Loda 1 Institute for Defense Analyses 400 Army-Navy Drive Arlington, Virginia 22202

170 DISTRIBUTION LIST (Cont.) No. of Copies Mr. Beaumont Buck 1 General Motors Corporation Defense Research Division 6767 Holister Avenue Goleta, California 93017 Professor Richard A. Roberts 1 Department of Electrical Engineering University of Colorado Boulder, Colorado 80302 Capt. Jurgen 0. Gobien AFIT - ENE Air Force Institute of Technology Wright-Patterson AFB, Ohio 45433 Dr. John Steinberg Institute for Acoustical Research 615 South West 2nd Avenue Miami, Florida 33130 Dr. M. Weinstein Underwater Systems, Inc. 8121 Georgia Avenue Silver Spring, Maryland 20910 Dr. Harold Saxton 1 1601 Research Blvd. TRACOR, Inc. Rockville, Maryland 20850 Dr. Thomas G. Kincaid 1 General Electric Company P. 0. Box 1088 Schenectady, New York 12305 Applied Research Laboratories 2 The University of Texas at Austin Austin, Texas 78712 Attn: Dr. Lloyd Hampton Dr. Charles Wood

171 DISTRIBUTION LIST (Cont.) No. of Copies Dr. Paul McElroy 1 Woods Hole Oceanographic Institution Woods Hole, Massachusetts 02543 Dr. John Bouyoucos 1 Hydroacoustics, Inc. P. O. Box 3818 Rochester, New York 14610 Dr. Joseph Lapointe 1 Systems Control, Inc. 260 Sheridan Avenue Palo Alto, California 94306 Cooley Electronics Laboratory 22 University of Michigan Ann Arbor, Michigan 48105

SECURITY CLASSIFICATION OF THIS PAGE (fWhn Dte Enfterd) D~onot re""llz~essnu Dars: tREAD INSTRUCTIONS REPORT DOCUMENTATION PAGE BEFAD STRUCCOMPLETING FORM BEFORE COMPLETfNG FORM I. REPORT NUMBER 2. GOVT ACCESSION NO. 3. RCCIPIENT'S CATALOG kUMERC TR 226._ _,'_ 4. t.tLt.e (.. Subi.) S. TYPE OF REPORT & PERIOD COVERED INVESTIGATION OF THE PROPAGATIONTechnical Re rt STABILITY OF A TIME SPREAD UNDERWATEFI ecnc ACOUSTIC CHANNEL *. PERFORMINO ORG. REPORT NUMBER,, - ___~~__004860-4-T 7. AUTHOR() -' — ---—. CONTRACT OR GRANT NUMBERC)" Raymond L. Veenkant N00014-67-A-0181-0035 9. PERFORMING ORGANIZATION NAME AND ADDREIC 10. PROGRAM ELEMENT. PROJECT. TASK Cooley Electronics Laboratory ARCA & WORK UNIT NUMBERS The University of Michigan Ann Arbor, Michigan 48105 II. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE Office of Naval Research Ma 1974 Department of the Navy,. NUMBER OF PAGES Arlington, Virginia 22217 186 14. MONITORING AGENCY NAME A ADDRESS(iI iffTemt ffte CoenIItr.oll Oflefe) IS. SECURITY CLASS (io the rofitl) Unclassified 1-5. DECLASSIFICATION/DOWN GRAOING SCHEDULE 1*. DISTRIBUTION STATEMENT (of thin Repett) Approved for public release; distribution unlimited. 1?. DISTRIBUTION STATEMENT (*e thebtrc l atentted tn Week 20, it d'ifeHmttl tw Repo tl.) 1i. SUPPLEMECNTARY NOTES 15. KEY WORDS (Contlnuo on reverew oId. *.it n,c, ny I dentify by btec* nu.bor) Underwater Acoustic propagation Channel Digit Response Acoustic Signal processing Coherent Display Research Display Time Spread Channel I 20. AlSTRACT (Celntiue n rewver *ade 1 neeeaewry tad Idntly bly o, ek mmbr,) L An experimental investigation of analysis and display techniques for extracting stability information from underwater acoustic propagation data has shown the feasibility and usefulness of a specific display format, called the Channel Digit Response. All of the complex nature of the channel reception is retained in the display, but the format compresses the data and enhances the extraction of qualitative stability information. The investigation I DD, I ^: s 1473 EDITION Or I NOV.S IS OBSOLETE S/ 0 10o2-014- 601 1 SECURITY CLASSIFICATION OF THIS PAOE (IhWn 0De fnfRweI)

SCcuSTV CLASSIlCATlON OP THIS PAGE r, (Who ^ DeE. E,~nr ) I Block 20: and conclusions are limited to propagation tests using periodic transniissions, as periodic transmissions are the usual type used for studying varying multipath propagation. The investigation data base spanned 133 hours, from a 43 n. mile range across the Straits of Florida. The effective time resolution of the data was.02 seconds. Crosscorrelation, autocorrelation, and power spectrum analysis, and several threshold techniques based on time-lag crosscorrelation were investigated, and their effectiveness compared to the Channel Digit Response. I -- L_. ___ _ _ _ _____ SECURITY CLASSIFICATION OP THIS PAGOs1Wn Deat )ate4r O