Acoustic model-based matched filter processing for fading time-dispersive ocean channels: theory and experiment

IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 18, NO. 4, OCTOBER 1993 447

Acoustic Model-Based Matched Filter Processing for Fading Time-Dispersive

Ocean Channels: Theory and Experiment Jean-Pierre Hermand and William I. Roderick

(Invited Puper)

Absfruct- Propagation effects degrade the performance of active sonar systems operating in either deep or shallow water. The ocean medium distorts the transmitted signals by time dispersion and as a result, the performance (signal-to-noise ratio) of correlation receivers is reduced if the receiver does not account for energy spreading. Results from this study demonstrate that the performance of a conventional matched filter can be improved if the reference (replica) channel compensates for the distortion. A model-based matched filter is generated by correlating the received signal with a reference channel that consists of the transmitted signal convolved with the impulse response of the medium. The channel impulse responses are predicted with a broadband propagation model using in situ sound speed measured data and archival bottom loss data. The relative performance of conventional and model-based matched filter processing is compared for large time-bandwidth product linear frequency modulated signals propagating in a dispersive waveguide. From ducted propagation measurements conducted in an area west of Sardinia, the model-based matched filter localizes the depths of both the source and receiving array and the range between them. The peak signal-to-noise ratio for the model-based matched filter is always larger than the conventional.

Index Terms- Model-based matched filter, channel adaptive processing, time dispersion.

I. INTRODUCTION

CTIVE sonar systems that are required to detect, classify, A and localize targets in either a noise or reverberation background often have conflicting requirements on the sonar design parameters. One important design parameter of the system is the transmitted waveform. In the ideal case of a white-noise background and a distortionless medium, the detection is "best achieved" with a matched filter where the output signal-to-noise ratio (SNR) is proportional to the ratio of the received signal energy to the background noise spectral density [l]. In this case, the higher the transmit power and the longer the time duration of the signal, the better is the performance of the matched filter. However, if the background is reverbation, the interference levels due to

Manuscript received June 10, 1993; revised July 10, 1993. J.-P. Hennand was with the University of Brussels, Faculty of Applied

Sciences, Brussels, Belgium. He is now at SACLANT Undersea Research Centre, vide San Bartolomeo, 400, 1-19138 La Spezia, Italy.

W. I. Roderick is with the Naval Undersea Warfare Center Division Newport, RI 02841.

IEEE Log Number 9212718.

scattering from the ocean volume or boundaries also increase with signal energy and it is then necessary to design the waveform to minimize the background interference effects [2]. In the case of reverbation interference, the bandwidth of the signal becomes an important parameter to reduce the interference; and likewise, the bandwidth is important in reducing propagation fading, classifying the target by highlight structure, and localizing the target in range.

Sonar waveform design and matched filter processing must not only take into account the type of background interference encountered in the medium, but should also consider the propagation characteristics (multipath and time dispersion) of the medium and the features (speed, range, depth, structure highlights) of the target to be encountered in a particular environment. Time dispersion causes energy spreading and this results in a loss of matched filter processing gain. The purpose of this investigation is two-fold: Examine the possibility of recapturing the energy spreading losses caused by time dispersion of the transmitted waveforms with large time- bandwidth (TW) products and determine the possibility of localizing the target in both range and depth. In a previous study, the effects of multipath and Doppler on the conventional correlation processor were investigated for large TW-product linear frequency modulated (LFM) waveforms [3]. It was observed that for active sonar systems that transmitted large TW-product LFM signals, the correlation loss caused by Doppler distortion could be recovered by correlating against a bank of reference channels that had Doppler compensation (time compressed reference signals) to account for different anticipated target velocities. However, in a multipath environment, the correlator peak output did not generally occur at the correct Dopper reference channel. This was due to the constructive/destructive interference of the summation of complex delay-Doppler autocorrelation functions associated with each multipath arrival.

In this present study, the time dispersion due to refraction in the medium and reflection from the boundaries is incorporated into the reference channels of the matched filter as a function of anticipated target depth and range. Although the active sonar problem is concerned with two-way propagation, i.e., from source-to-target-to-receiver, this phase of the investigation examines theoretically and experimentally the relative matched filter performance over a one-way propagation that includes

0364-9059/93$03.00 0 1993 IEEE

448 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 18, NO. 4, OCTOBER 1993

time dispersion. The performance of the matched filter receiver is compared for two types of reference channels: The first type is the conventional matched filter (MF) processor that correlates the incoming signal with a reference channel that is the transmitted signal. The second is a model-based matched filter (MBMF) that correlates the signal with a reference channel that is the transmitted signal convolved with the range and depth-dependent broadband impulse response of the medium. The impulse response is generated by modifying an existing generalized ray-theory propagation model known as the Generic Sonar Model [4], [5]. This multipath expansion model accounts for diffraction effects in the propagation channel and the modification results from a Fourier synthesis of continuous wave (CW) solutions over the frequency band of the transmitted signal to develop the broadband transfer function of the medium. Both the MF and MBMF receiver outputs are compared with measured data obtained during a ducted propagation experiment that took place under winter conditions in the Mediterranean Sea in an area west of Sardinia.

In addition to active sonar signal processing, the MBMF techniques developed here can be applied to undersea com- munications, acoustic imaging and tomography. In the latter case of tomography, which as originally conceived, relies on determining the travel times of identifiable multipaths. The MBMF technique, which relies on the amplitude and phase of the signal, could also be used to infer environmental parameters such as sound speed profiles and geoacoustic parameters of the sea bottom.

The propagation of wideband signals in the ocean and the detrimental effects of dispersion on the correlation process has been studied previously. Gindler, Kravtsov, and Petnikov investigated the deterioration in the S N R of wideband signals that undergo propagation through a dispersive medium and found that intermodal and intramodal dispersion caused the loss in SNR from optimum values [6]. The intermodal dispersion causeD a difference between the group velocities of the individual modes and the intramodal dispersion was more of a detriment at the longer ranges. For the case of propagation in an acoustic waveguide, the theoretical study determined

model was qualitatively compared to the correlator output. It was observed that there was considerable dispersion in the shallow water waveguide even for narrowband hyperbolic frequency modulated signals with large time-bandwidth products. The acoustic model described satisfactorily the depth dependence of the acoustic field.

In a related study, Vavilin et al. examined the effects of intermodal and intramodal dispersion on the distortion of the envelope of the cross-correlation function as a function of source and receiver range separation [9]. Experiments were conducted in an ocean waveguide where HFM signals were transmitted from a sound source to a fixed hydrophone. The received signals were correlated with a reference signal. The reference signal consisted of the signal received at a range close to the source. Data were compared to theory by convolving the transmitted signal with the Green’s function of the waveguide. The qualitative correspondence between the measured and predicted results showed that the time dispersion and general shape of the correlator output were similar.

Research on a related study of localizing a source in range and depth is the well-known matched field processing of narrowband signals with vertical arrays [lo]. The work in this paper is analogous to the matched field techniques in the sense that the MBMF receiving array is at a single depth; but, the broad bandwidth of the signal is utilized to localize the source [11]-[13]. MBMF is a coherent process in the time domain over a full band of frequencies versus for the matched field technique which is a coherent process in the spatial domain at a single frequency.

11. THEORY

In this section, the matched filter theory is extended to include the effects of multipaths and time dispersion upon a wideband acoustic signal propagating through an ocean medium. A zero-Doppler one-way transmission between a source and receiver is considered (Fig. 1).

Let s ( t ) be the signal transmitted at time t = 0 in the form of a known modulated carrier,

that an optimum multimode receiver would ensure coherent s ( t ) = a ( t ) COS [wot + ~ ( t ) ] , 0 5 t 5 At; (1) summation of the signals of each mode. Also, for large time- bandwidth signals, the maximum SNR based on the envelope squared at the output of a correlator was proportional to the integral of the magnitude squared of the Green’s function in

where a( t ) ‘s the amp1itude modulation, the duration.

modulation, P( t ) is the de frequency, and At is

physical systems Only transmit is the carrier

the propagation medium. This result will be with the model-based matched filter discussed above.

later real-valued time functions, it is convenient to use a complex representation of such signals. The physical signal s ( t ) can be

been under investigation via different modeling approaches including Fourier synthesis of CW results [7]. The synthesis approach was applied to long range (30 km) propagation in shallow water (150 m depth) using a normal mode model. The results were qualitatively compared to a received linear FM signal with a 60-Hz bandwidth centered on 410 Hz. The dispersive character of the model results was also observed in the envelope of the measured data.

Dispersion distortion at the output of a correlator for propagation in a shallow water waveguide was also investigated by Bunkin, Gindler et al. [8]. A simplified theoretical waveguide

s ( t ) = Re [;(t) exp ( j w o t ) ]

where Re means “real part of’ and s”(t) is the complex envelope of s(t) . For narrowband signals, a good approximation of the analytic signal can be obtained by taking the complex envelope as

(3)

However, for wideband signals the complex envelope generally assumes a much more complicated form. For our purposes, the approximation (3) can be retained even if it is a poor

HERMAND AND RODERICK: ACOUSTIC MODEL-BASED MATCHED FILTER PROCESSING 449

approximation to the analytic signal. In the experimental work described later, a linear frequency modulated (LFM) signal was transmitted such that the angle modulation was quadratic and amplitude modulation was a constant. The complex envelope of a rectangular-weighted LFM waveform is approximately given by

p at some time t. For simplicity the power spectrum of the noise is assumed to be white,

(1 1) N ( w ) = No/2.

The Schw&’s inequality yields the upper bound on p,

2ET - Prnax(r) (12) NO (4) p( t , r ) I - .>I2 = i ( t ) = rect ( t / A t ) exp (jAwt2/2At) TNO SW 0

where the rectangular function is defined by

rect (x) = { i: where E, is the received energy. The value of pmax depends only on the ratio of the signal energy to the noise power density at the receiver input. The received energy spectrum is given by

(13)

where s(w) is the transmitted energy spectrum and G(w, r ) is the transfer function of the channel (or the Fourier transform of the Green’s function). me general expression for pmax is

forlzl 5 +; elsewhere. ( 5 )

Assume that the transmitted signal s ( t ) propagates from the source to the receiver through a deterministic stationary Ocean medium characterized by a Green’s function G(t, r), where r is the difference in radius vectors of the point source and receiver (or of their phase centers).

Let ~ ( t ) be the signal received at time t = T. The received

R ( w , r ) = G(w, r )S(w)

prnax(r) = - IG(w, r)S(w)I2 dw. (14)

The transfer function of the channel can be expressed in polar

SW signal is the convolution of the transmitted signal and the

r(t> = d t ) 63 s ( t )

K N o 0

time-invariant impu1se response Of the dt) so that

(6) form as

G(w, .) = IG(w, .)I exp bWw, .)I (15) where @ denotes convolution. We assume that the received signal is perturbed by an additive, zero-mean, stationary Gaussian where I G ( ~ , ,-)I is the amplitude response and r ) is the

can be decomposed arbitrarily into a linear function and a nonlinear function of frequency,

(16)

noise process n(t>. The input Of the receiver z ( t ) is given by phase response of the channel. In the general case the phase

(7) z ( t ) = T ( t ) + n(t).

A. Optimum Reception in Time Dispersive Media @(U, r ) = A(w, r ) + @ ( U , r ) Consider the receiver as a time-invariant linear filter with

impulse response denoted by h(t). The output of the receiver y ( t ) is given by

(8) y ( t ) = h(t) 8 x( t ) .

The SNR at the receiver output is chosen as the energy criterion of optimality to derive the filter response. The average output SNR with respect to power, evaluated at any time t > T, is defined by

(9)

where the linear phase response corresponds to a mean time delay of the channel (and a phase shift at zero frequency). The value of this delay is arbitrary and does not affect the value of the maximum SNR at the receiver output. Let denote by G’(w, r ) the function that does not include the phase-linear factor exp bA(w)].

The optimum receiver is now determined for the cases of a nondispersive channel, a time-dispersive channel, and a multipath time-dispersive channel.

Nondispersive Channel: An infinite “free space” environment is characterized by the Green’s function

where u(t) = h(t) 63 ~ ( t ) is the signal component and w ( t ) = G(t , r ) = 6 ( t - ~r~/c)/47r~r~ (17)

h(t) 8 n(t) is the noise component at the receiver Output y ( t ) = u(t)+w(t); the angle brackets denote the mathematical expectation. In the frequency domain the SNR is given by

where c is the phase speed of propagation in the medium. The Delta function is defined by

(18) for x = 0;

6(x) = {:I elsewhere.

For such an ideal medium the channel transfer function

1 I Jr ~ ( w , r ) H ( w ) exp ( j w t ) dwI2 P ( t , f -1 = - (10)

7r so00 IH(w)I2N(w)

where R ( w , r ) is the Fourier transform of the received signal (assumed here to be deterministic), N ( w ) is the power spectral density of the noise and H ( w ) is the Fourier transform of the

and henceforth over the interval [-CO, +CO].

In order to find the optimum receiver for a given received energy spectrum R ( w , r), it is necessary to determine the filter

G(w, r ) obeys the two following conditions. The amplitude response IG(w, r)I is constant for all frequencies, as shown by

filter impulse response. The spectral quantities are defined here IG(w, r)l = GO (19)

where Go = JG(r)( . The phase @ ( U , r ) is linear with frequency, as shown by

frequency response H ( w ) that maximizes the expression for @ ( U , r ) = -UT (20)


where T = IrI/c. The received signal is an attenuated and delayed, but undistorted version of the transmitted signal as shown by

where D = D(w0) and d = d(w0). The complex envelope of the transmitted signal is delayed by the constant group delay D and the carrier is delayed by the phase delay d. The phase delay and group delay assume a common constant value T only when the phase response is linear with frequency and T ( t ) = Go Re - T , exp [ j w o ( t - (21) Q(0) = 0. The information content of the signal is not altered by the channel but is delayed by D. The value of d does not distort the transmission. The signal transit time T is defined

A more general condition for distortionless transmission is that the phase response is

Q(w, r ) = -wT - 6'0 (22) unambiguously by D. As an example, for the LFM signal, the instantaneous frequency w ( t ) (which represents the signal - - \ ,

where 60 is the phase at zero frequency. This arbitrary initial phase does not affect the maximum value of the SNR at the receiver output.

information) is delayed by D, but is not d&rted,

(29) w ( t ) = WO + ( A w / A t ) ( t - D). The expression for pmax reduces to

where G'(r) is real-valued constant (independent on frequency) and

(24)

is the transmitted energy. The filter frequency response which results in the maximum SNR at a certain time t = T has the form

1 " E, = ;l IS(w)I2dw

Hopt(w, r ) = HoS*(w) exp ( - j w ~ ) (25)

where HO is an arbitrary complex-valued constant and T is a time delay such that T 2 T + At. The frequency response of the optimum filter is proportional to the complex conjugate of the transmitted energy spectrum with a linear phase shift introduced for physical realizability. The modulus and phase of HO do not affect the value of pmZ. The causal impulse response is proportional to the transmitted signal reversed and delayed in time.

Time-Dispersive Channel: The ocean is not the ideal medium described above. However, for narrowband signals, the conditions for distortionless transmission can be approximately satisfied by the channel. Assume that the channel amplitude response approximates a constant over the transmitted frequency band 11. For a modulated carrier of frequency WO and bandwidth Aw, the channel transfer response over the frequency band II 5 [WO - A w / 2 , WO + A w / 2 ] can represented in the form

G(w, r ) = Go exp [ j Q ( w , r ) ] (26)

Under such conditions the filter frequency response for optimal reception is basically unchanged with respect to the nondispersive case (25).

The important requirement for distortionless transmission in a time-dispersive medium is that the group delay response of the channel is nearly constant over the signal frequency band. A precise statement on how narrow the band has to be is strongly dependent upon the channel under consideration. In actual fact, the signal bandwidth A w is usually much smaller than the transmission band of the ocean medium R, which is defined as the frequency band over which its magnitude response IG(w, r ) I differs appreciably from zero. Wideband signals are always distorted due to multipath and time dispersion properties of the ocean medium. Even in a purely deterministic channel the wave packet is distorted due to the space-dependent sound speed and to interactions with the ocean boundaries. Examples are refracted multipaths in a sound duct and frequency-dependent bottom reflections. The amplitude and phase responses of such channels depend on frequency over a wide transmission band: The narrowband components of the transmitted signal are attenuated and delayed differently in passing through the channel. As a result of amplitude and phase distortion, the received signal has a different waveform from the transmitted signal. A short pulse of equivalent bandwidth is spread in time due to multipaths and each path signal is further spread when the group velocity along the path is dependent on frequency. Even for a single time-dispersive path the signal transit time is ambiguous and the group delay at the carrier frequency is meaningless. Returning to the example of a transmitted LFM signal, the received instantaneous frequency is not linear since the group delay D in (29) is not anymore a constant.

The energy spectrum for signals that satisfy the condition ~ 4 1

A ~ ( A U ) ~ / ~ ~ >> 2~ (30) where GO = IG(w0, r)l. The phase response can be expanded into a Taylor series about the frequency w = wo,

can be regarded as uniform in the frequency interval ll E Q ( w ) = - W O ~ ( ~ O ) - (U - ~ O ) D ( W O ) + . . (27) [WO - A w / 2 , WO + A w / 2 ] ,

(31) { So /2 , for w E -II, II; lS(w)I2 = 0, elsewhere.

For transmitted signals with such large time-bandwidth (TW) products the expression for pmax reduces to

where the function d(w) = - Q ( w ) / w defines the phase delay response of the channel, and D ( w ) = -aQ(w)/aw, the group delay. The ellipsis represent the higher order derivatives of the phase. If the group delay function D ( w ) is nearly constant over . ~~~~ ~

/ IG'(w, r)I2 dw E *p(r) (32) 2E, 1 the signal frequency band 11, the received signal approximates

(28) NO pmax(r) = --

r ( t ) = Re {s"(t - 0) exp [ jwo( t - d ) ] } No A w n

HERMAND AND RODERICK: ACOUSTIC MODEL-BASED MATCHED FILTER PROCESSING

~

45 1

where E, = S o A w / 2 ~ is the transmitted energy and E,P(r) E, is the received energy. Hence, the coefficient P(r) represents the transmission loss averaged over the frequency band II. It can be shown that the filter frequency response of the form

H,,t(w, r ) = HoG’*(w, r ) S * ( w ) exp ( - j w ~ ) ( 3 3 )

maximizes the SNR at time t = T with 7 > T + At. Consequently, it is the frequency response of the optimum receiver for a time-dispersive channel. The causality time delay accounts for the time spread of the received signal. The filter frequency response is proportional to the product of the complex-conjugated channel transfer function and transmitted energy spectrum. That is, the receiver is matched not only to the transmitted signal but also to the channel. The effective bandwidth of the received signal Aw,ff(r), as defined in [15], is smaller than the bandwidth of the transmitted signal Aw,

Accordingly, the input-output SNR gain of an optimum receiver is reduced by 10 log,, (Awe~/Aw) from the theoretical gain of 1010g,~ (AwAt) (which is achieved only in the case of an ideal medium).

Multipath Time-Dispersive Channel: In the case where propagation takes place through multiple time-dispersive propagation paths the channel transfer function can be decomposed into a sum of partial responses

m = l , M (35)

where Am(w) = -wTm(r) - d,(r), and M is the number of paths. Nondispersive propagation through a single or multiple paths ( a m ( w ) = 0), and dispersive propagation through a single path (M = 1) that has been discussed above can be regarded as particular cases of this model. Furthermore, if the propagation delays T, for these M paths are quite distinct so that the differences between all delays exceed the time- dispersion spread for each path plus twice the correlation width of the transmitted signal, then the multipath and time- dispersion effects can be considered separately. Specifically, the signal component of the MF output, which is equivalent to the cross-correlation of the transmitted and received signals, decomposes into a sum of M nonoverlapping terms,

u(t) = m = l , M

where g m ( t ) is the impulse response of the mth-path and R,,(t) is the autocorrelation function of the transmitted signal. In the latter case a SNR value p m can be assigned to each identifiable path of propagation and the preceding development is applicable. Hence an optimum receiver that matches an individual path, or any combination of paths, can be determined.

Fig.

I .c

OCEAN MEDIUM signal

Broadband propagation

Convolution

1. Principle of the conventional Matched Filter and Model-Based Matched Filter processing techniques,

Nonwhite Noise: The case of additive input noise with arbitrary power spectrum N ( w ) can be readily handled by using a prewhitening filter that converts N ( w ) to the constant power spectral density N0/2. For the dispersive case, the overall filter frequency response of the optimum receiver is given by

Unlike to the white noise case, the response depends on the input noise spectrum.

B. Model-Based Matched Filter

In practical situations, the receiver that is optimum for a given dispersive channel cannot be realized since the medium Green’s function is never known exactly. However, a modeled Green’s function which approximates the actual Green’s function can be used. The principle of model-based matched filter (MBMF) processing is depicted in Fig. 1. For reference, conventional matched filter (MF) processing is also shown. Measured environmental data are fed into a broadband propagation model to predict the channel impulse response, which convolved with the transmitted signal, produces the reference signal of the MBMF receiver.

By analogy with the optimal receiver the frequency response of the MBMF receiver takes the form

H m b ( W , r ) = H&’*(w, r ) S * ( w ) exp ( - j w ~ ) (38)

where the new symbol 8’ denotes a predicted transfer function with the (arbitrary) mean time delay removed from the phase factor. Replacing the postulated Hmb into the general expression for p ( t , r ) given by (lo), yields

(39) r ) = Prnax(r)IRG’E’(t - 7, . ) I 2 where pmax is given by (32) and

It is the complex-valued correlation coefficient of the deterministic functions G’ and G’ exp (jut) with

lRGfGr(t1 .)I 5 1. (41)


The maximum value of the output SNR,

Pmb(r) E m a t [P(t7 r)] (42)

is attained at the time t for which IRG’G’(t - 7, r)I is maximum. The maximum value characterizes the degree of knowledge about the medium. Two extreme cases need to be considered. If the Green’s function were known exactly, i.e., G’(w, r ) = G‘(w, r), Vw E II, then

Pmb(r) = Pmax(r) (43)

so that the MBMF is the optimum receiver. The signal transit time T is unambiguously determined by the value of the time delay which corresponds to the (autocorrelation) peak at the receiver output. If the Green’s function were totally unknown, i.e., G’(w, r) = 1, Vw E II, then

l2 G‘(w, r) exp ( j w t ) dw

The arbitrary constants in (38) and (45) must satisfy the relation

Nonstationary Channel: The preceding development can be generalized to deal with the nonstationary case. In a randomly inhomogeneous medium, each spectral component of the transmitted signal experiences somewhat different phase perturbations because the phase velocity depends on frequency, and hence each spectral component of the received signal exhibits different amplitude and phase scintillations (frequency-selective fading). The propagation channel is characterized by a random and slowly time-varying transfer function. The integrands in the expressions (44) for a, and (32) for ,8, must then be averaged over an ensemble of realizations of the channel transfer function. It follows that,

where the overbar denotes ensemble averaging and

The corresponding filter frequency response is & ( W i , w2; r) = (G’(wl7 r)G’*(wp, r ) ) (50)

is the complex-valued two-frequency correlation function [ 161. It measures the correlation between the fading at different frequencies. The expression for a(r) is maximum when w = w1 = w2 and equals

Hmf(w, r) = HoS*(w)exp(- jw). (45)

The above expressions correspond to the MF receiver that simply uses a replica of the transmitted signal as a reference. The MF receiver is regarded here as a particular case of the

The degradation of the peak SNR at the MF output due to

- MBMF receiver. p(r) = & L R G I ( W , r) dw (51)

time dispersion is given by the ratio where

-- pmf(r) - a(.) m a t I Jn G’(w, ~ X P ( j u t ) dw12 RG/(w, r) = (G’(w, r)G’*(w, r)) (52) Pmax(r) P ( r ) - A w s, IG’(w, .>I2 dw is a real-valued positive even function of w.

y(r) 5 1. (46) Determinacy of the Acoustic Field: The effect of modeling

The MF receiver is based upon the assumption of a distortionless transmission channel. Since the MBMF receiver uses a reference signal which accounts for the distortion of the transmitted signal, it is expected to yield better performance than the MF receiver provided that the channel transfer function is properly modeled. The relative performance of the MBMF and MF processing is quantified by the ratio

The MBMF processing gain relative to the MF is equal to the degree of time dispersion in the actual channel ( l /y 2 l), weighted by the degree of similarity (0 5 [RI2 5 1) between the actual and modeled channel responses, both evaluated over the frequency band of transmission. The product of these two quantities is not necessarily greater than one. In the event that the medium Green’s function is poorly modeled, the MF receiver can outperform the MBMF receiver.

To determine the effectiveness of the MBMF receiver it is convenient to normalize the MF and MBMF frequency responses to the same energy so that the output noise mean levels are equal, and the signal peak levels can be compared.

and environmental uncertainties on the MBMF performance can be quantified through a combined correlation coefficient function [17]. The correlation is between the measured acoustic field and the modeled field. The measured field can be corrupted by noise and the modeled field can be corrupted by model inaccuracies and by environmental inputs that have limited specificity in space and time. The normalized correlation coefficient of the functions G and G is

where G G ( w + R , r + R , t+T) . The function unifies averaging of the channel transfer functions over a certain space-time domain Q and averaging over an ensemble of realizations. The intervals along the coordinate axes !&et9 h e t and Ydet that characterize a high degree of determinacy (predictability) of a specific acoustic channel are determined from the condition that the above quantity decays to 1/2. These quantities can be greater than the corresponding correlation radii of the acoustic field itself. The frequency band Rdet can be much larger than the coherence band Rcoh

G ( w , r, t ) and 0

HERMAND AND RODERICK. ACOUSTIC MODEL-BASED MATCHED F1LTF.K PROCESSING 453

of the field. Also the time Ydet can be much larger than the fluctuation time of the environmental parameters that affect the acoustic transmission. Consequently, the MBMF processing technique can be less sensitive to uncertainty in knowledge about the source and receiver configuration, and about the environmental conditions than expected when the above quantities are considered separately. Therefore, compensation of distortion in the received signal can remain effective even in a randomly inhomogeneous dispersive channel for which Andet > Aw > Anco,,. Moreover, a MBMF receiver implemented as a bank of filters matched to a number of anticipated channels is expected to be robust, to some extent, to the uncertainty upon the environment.

The MF is the optimum receiver for a non frequency- selective channel, or for a flat Rayleigh fading channel for which the coherence bandwidth Anrob, greatly exceeds the bandwidth Aw of the transmitted signal. The coherence bandwidth OCoh centered at frequency wg is determined from the condition that [ 181

&(wg - AR/2. wg + Af2/2: r )

R ~ l ( w g . r )

1 ~ 2 2 ' (54)

The loss of channel coherence over the signal bandwidth severely degrades the performance of the MF receiver. The ideal MBMF, that perfectly accounts for the mediumhignal interaction, is the optimum receiver for a channel which is frequency-selective over the signal frequency band II. For a fading dispersive channel, improvement over flat-fading performance can be obtained with the MBMF receiver because of the frequency diversity inherent in a frequency-selective propagation environment. The fact that different spectral components of the signal tend to fade independently makes it unlikely that all of the spectral energies will simultaneously experience a deep fade [ 191. The ideal MBMF receiver makes full use of the total received energy by recombining all the spectral components coherently.

C. Eigenruy Model ,for the Channel Response

Without loss of generality in the present context, the ocean environment can be assumed to be horizontally stratified: The sound speed c = c ( z ) is function of depth only, and the ocean surface and bottom are horizontal reflecting boundaries. Eigenray models assume that the complex acoustic pressure due to an harmonic point source of frequency w satisfies the reduced wave equation with appropriate boundary conditions. The relative pressure is approximated by phased addition of the complex weights associated with each eigenray,

where A,, A,, and are respectively the amplitude, travel time, and phase shift of the mth eigenray at frequency w, and M is the number of eigenrays; A , and 4, are dependent on frequency. The phase shift is due to boundary interactions and caustics. Energy diffracted into shadow zones are represented by imaginary eigenrays which occur in pairs having identical travel times and inclination angles; the angles at the source and receiver are independent of range in a shadow zone IS] .

Latitude N 38' ....~ 00 Longitude E 06" 30

Fig. 2. Setup of the West Sardinia'89 MBMF experiment.

The channel transfer function, limited to the band n, is synthesized by adding coherently the computed eigenrays in the discrete time and frequency domains,

m =1, A1 11 = 1 .iV

. exp [-jw,,A,,(r) - ,j4l,L(wn, r ) ] , wn E n; (56)

where N is the number of discrete frequencies. For a medium which is dispersive only in time the travel time X associated with each eigenray does not depend on frequency. The frequency spacing between the individual CW solutions is determined in such a way that, for every eigenray, the variation in amplitude A and phase shift q!~ can be neglected over the frequency interval [w,, - Sw, w, + 6w]. Also, according to the Nyquist sampling theorem the discretization step is constrained by the inequality

sw 5 27rlAA (57)

where AA is the difference in time delay between the slowest and fastest selected eigenrays. The accuracy of the calculations can be checked by increasing the number of discrete frequencies which is N = Aw/6w + 1.

Eigenruy Filtering: As observed before, mismatch between the actual and predicted Green's functions is detrimental to the performance of the MBMF receiver. The sum of complex eigenrays in (56) is similar to the channel model in (35). When frequency-independent eigenrays largely separated in time can be attributed to physical propagation paths without dispersion, the two expressions are equivalent. Otherwise, subsets of frequency-dependent eigenrays closely-spaced in time can be attributed to propagation paths with dispersion. Hence, based on physical consideration, only the eigenrays that are expected to model properly the actual propagation paths can be retained. Also, only the eigenrays that contribute significantly to the propagated energy need to be selected for the calculation of the channel response.

111. AT SEA EXPERIMENT

The sea test, depicted in Fig. 2, took place under winter conditions (January 1989) at a deep water site in the Mediter- ranean Sea west of Sardinia. A source ship moved parallel

454 IEEE JOURNAL OF OCEANIC ENGINEERING. VOL. 18, NO. 4, OCTOBER 1993

to a receiving ship at an approximate range = 30 km and at speeds of 1.5-2.1 m/s ( 3 4 knots). Both ships covered a distance of 11 km (6 nautical miles) in 1; hour.

Acoustic Data: Low-frequency, wideband, linear frequency modulated (LFM) signals were transmitted from a broadband projector to a broadside beam of a 64 equidistant element horizontal receiving array. Source and receiver were towed near the channel axis at depths z , = 100 m, and z , = 150 m to 200 m. The array depth was dependent on actual tow speed. Data sets were collected at the nearly constant range separation of 30 km. The bandwidth of the transmitted signals Af was varied over one decade (50. 100, 150, 200, 2.50, 300, and 500 Hz) around a center frequency f o = 590 Hz (except for the case when Af = 500 Hz then .fo = 490 Hz). Signal peak power and time duration (At = 8 s) were constant for each member of the transmitted data set. The largest fractional bandwidth was Af/fo = 1 and the largest TW-product was AtAf = 4000. A total of 74 signals was transmitted at intervals of 1 minute and was received, with no Doppler shift, in the array beam steered in the direction of the source.

Environmental Data: The sound speed in the water column was calculated from expendable bathythermograph (XBT) data (down to 450-m depth) measured at the receiver site during the acoustic transmissions, from archival temperature (extension to deeper depths), and salinity winter mean data [20], [21]. The sea surface was smooth and therefore highly reflective. The water depth was 2825 m and the bathymetry was range- independent. Bottom reflection coefficients were taken from field data collected in the same area and frequency band [22].

Fig. 3 shows the upper 500 m of the calculated sound speed profile. The profile had two maxima at depths of 45 m and 170 m. This created a triple sound duct: a surface duct, and two refractive ducts with axes at depths of 95 m and 200 m. Fig. 4 is a ray representation of the refracted paths originating from a 100-m depth source every 0.1". Only the downgoing rays emitted from the source are shown. The steepest angle depicted is 13.6". The negative sound speed gradient of the main thermocline and the positive gradient of the isothermal layer continually refract the sound rays back toward the main axis of the channel. For the experimental conditions of a source located in the upper duct and a receiver located in the upper or lower ducts, the propagation took place along three sets of sound paths. The arrivals consisted of refractive-surface-reflected, entirely refracted and surface- reflected-bottom-reflected paths. In Fig. 5 , a set of selected eigenrays is depicted for both source and receiver placed in the upper duct ( z , = 100 m and z , = 150 m) at a distance of 7' = 30 km. The eigenrays are numbered according to the order of arrival. As an example, the number 5 refers to the family of ducted eigenrays.

IV. CHANNEL MODELING RESULTS

Sound speed (rn/s)

1 5 1 : : :: 0

F4

100

f 200

400

500

Sound speed (rn/s) 1506 1508 1510 1512 1514 0 1 : : : : : :

100

f 200

Q s 300

400

500

Fig. 3. Sound speed profile to a depth of 500 m calculated from at-sea data.

Range (krn) 0 10 20 30 40 50 60 70

50C

2500

3000 1

Fig. 4. Diagram of the refracted rays for a source of 100 m depth.

Range (krn) 0 10 20 30

Fig, 5. Diagram of representative eigenrays for a source and a receiver in the upper duct ( zs = 100 m, zr = 150 m).

theory propagation model, the multipath expansion eigenray model (MULTIP) of the Generic Sonar Model (GSM) was chosen to predict the range- and depth-dependent sound field [ 5 ] . This multipath expansion model accounts for the frequency- dependent diffraction effects in the transmission channel and incorporates the measured sound speed profile and archival boundary parameters.

Broadband predictions of channel frequency responses were In modeling the deep water experimental acoustic data,

the environmental characteristics were assumed to be both time- and space-invariant, Experimental results described later confirmed the validity of this assumption. A generalized ray-

obtained by Fourier synthesis of a number of CW solutions. At each frequency, the resulting real and imaginary (diffracted) complex eigenrays were added in phase according to (56). Multiple bottom-bounce eigenrays were excluded from the


Fig. 6. Predicted impulse response of the deep water propagation channel ( r = 30 km, c, = 100 m, 3, = 1.50 m, n = [ l S i . 7321 Hz) . Dotted line is the instantaneous impulse response and solid line is the envelope.

calculations since these paths did not contribute significantly to the total received energy. For all the propagation cases considered here, the time difference between the slowest and fastest selected eigenrays never exceeded AT' = 250 ms. With this consideration, the channel frequency responses were calculated at a frequency spacing of hf = 4 Hz in order to avoid aliasing in the time domain. Also, the channel responses were calculated over two octaves in frequency. The frequency band IT = [184: 7921 Hz was based on the power spectrum of the 500-Hz bandwidth LFM transmitted signal and a guard band of approximately 50 Hz on lower and upper sides of the half power points of the LFM spectrum.

Fig. 6 shows the predicted channel impulse response for the source and receiver configuration described above (7. = 30 km, z , = 100 m, 2,. = 150 m). Both the instantaneous response and its envelope, calculated via Hilbert transform, are shown. The origin of the time axis corresponds to the fastest deep refracted path. The amplitude scale is the ratio of the received pressure to the pressure at 1 m. The multipath arrivals, from the onset of the first refracted-surface-reflected arrival to the last bottom-reflected arrival, were distributed over a time interval of AT = 180 ms. The peaks are labeled according to the transmission paths represented in Fig. 5. The experimental conditions were such that both time resolvable and unresolvable multipaths (with no Doppler spread) were observed at the receiver.

Nonducted Propagation: The propagation delays of the upward-refracted and surface-reflected paths ( IA), and the surface-reflected and bottom-reflected paths (6-9), were sufficiently distinct to be resolved in time with a bandwidth of 100 Hz. These paths can be essentially modeled as nonfluctuating point channels. Each of these separate arrivals has a sinc envelope. The surface-interacted paths can be recognized by their 180" phase reversal. The bottom reflected paths were modeled by the Hastrup and Aka1 bottom loss versus grazing angle data with an assumed zero phase shift due to the boundary interaction [22]. It will be seen later that this arrival structure is in agreement with the measured data.

Ducted Propagation: The arrival structure associated with the dominant ducted multipath propagation (paths 5 ) was not resolved in time even with the wider transmission bandwidths used in the experiment. Hence, it appeared as a continum of arrivals distributed over some time and consequently, can be regarded as a singly spread (time-dispersive only) channel. The constituent eigenrays in this duct corresponded to real and

U J

200 300 400 500 600 700 800 Frequency (Hz)

(c)

Fig. 7. Predicted dispersion distortion associated with the transmission in the duct ( 1 . = 30 km, 3 , = 100 m, 3 , = 1.50 m): magnitude in dB referred to 1 m (a), nonlinear term of the phase in degrees (b) and group delay referenced to the time of first arrival (c).

diffracted arrivals. The eigenrays had phase factors different from zero in addition to the linear phase shift associated with the travel time along the corresponding path. In general, the phase factor was a nonlinear function of frequency and hence most of these paths were dispersive and moreover interfered with each other. Apart from a few eigenrays that were first reflected at the surface and then trapped into the duct, the eigenrays encountered no losses by reflection from the sea surface or the sea floor.

Fig. 7 illustrates distortion due to dispersion associated with the frequency-dependent refractive properties of the duct. The source and receiver configuration are as described previously ($1. = 30 km, z , = 100 m, z , = 150 m). Only the eigenrays trapped in the duct were retained for the calculation of the medium frequency response. The magnitude and phase of the spectrum are shown, respectively, in Figs. 7(a) and (b). The dashed line in Fig. 7(a) represents the frequency-averaged transmission loss. It can be seen that there are deviations greater than 10 dB across the band. Fig. 7(b) shows the phase nonlinearities which remain after removal of the linear trend in the unwrapped phase. There is considerable phase distortion for frequencies below 500 Hz. For the first octave in frequency there is a deviation of over 200". Fig. 7(c) represents the group delay referenced to the travel time of the fastest eigenray. The dashed line represents the frequency- averaged group delay. The nonconstant group delay over the frequency band of interest, weighted by the nonconstant magnitude, results in the distortion of the complex envelope of the transmitted signal and the stretching of the corresponding autocorrelation function at the MF output. This can also be inferred from the smearing of the impulse response observed in the corresponding arrival structure labeled 5 in Fig. 6.

456 IEEE JOIJRNAL OF OCEANIC ENGINEERING. VOL. 18, NO. 4, OCTOBER 1993

in time from the other arrivals. The model-based processing presented in this paper deals mainly with this restricted set of paths.

Fig. 8 shows the amplitude responses for two cases: propagation in the ducted channel and propagation across the duct. In this example, the responses were depicted for a source depth of 100 m and at two receiver depths of 150 m and 185 m. The amplitude variations are shown after the geometrical spreading loss has been removed. The band- limited responses, at each range, were normalized to the same total energy. The pseudocolor scale is from -20 dB (blue) to 0 dB (red). Also, in this example, only eigenrays associated with ducted propagation are included-see Fig. 5 , and the arrivals designated by number 5. In the two frames, the discontinuity in the frequency-selectivity pattern at 14-km range is an artifact due to the eigenray filtering process. In the bottom frame, the other discontinuities are due to the cross-coupling between the two ducts. For a receiver in the upper duct (top frame)

20 40 60 ao 100 the frequency-selectivity pattern was highly range-dependent for ranges less than 40 km. Consequently, at the 30-km range of the experiment, the purely ducted energy was expected to be strongly dependent on the transmitted frequency band. For

RANGE (km)

(a)

20 40 60 80 100 RANGE (km)

(b)

Fig. 8. Frequency-selectivity characteristics of in-duct (a) (top) and cross-duct (b) (bottom) transmission as a function of range. Source depth is 100 m and receiver depths are 150 m (a) (top) and 185 m (b) (bottom). Pseudocolor scale: -20 dB and below (blue) to 0 dB (red).

It follows that broadband modeling was required to describe accurately the frequency dependent amplitude and phase characteristics of the complicated dispersive propagation in the sound duct. However, it was observed that modeling at a single frequency would be sufficient for the deep-refracted propagation. The propagation is essentially nondispersive, and would only require accurate determination of the time delays within a small fraction of the reciprocal bandwidth. The ducted multipath arrivals conveyed most of the spread acoustic energy and, at the 30-km range of the experiment, were separated

ranges greater than 40 km there was an optimum frequency of propagation at 360 Hz, as evidenced by the elongated axis of lower-loss values. For a receiver in the lower duct (bottom frame) the frequency selectivity pattern changed much less with range in the region of interest. Most of the propagated energy was contained in the wide frequency band [400, 6001 Hz. Consequently, the resolution in both depth and range was expected to be higher when the source and the receiver were both positioned in the upper duct. As will be seen later, this was confirmed by the experimental results.

The channel impulse responses that correspond to the top frame of Fig. 8 are displayed in Fig. 9 as range-stacked time series at intervals of I km. For each trace the origin of the time axis corresponds to the arrival time of the first refracted path that was trapped in the duct. As range increases, intramodal and intermodal dispersion spreads the pulse and decomposes it into a series of multiple arrivals. The time difference between the first and last ducted eigenrays is 110 ms at 100-km range. The temporal spread of the most energetic arrivals increases linearly with range; it is approximately I O ms at the 30-km range of the experiment.

M F and MBMF Per$ormance Prediction: The effect of time dispersion upon the transmission of a widely spread spectrum signal can be interpreted from the two-frequency correlation function of the channel response. The shape of its magnitude and phase is related to the shape of the received pulse. Fig. 10 shows a deterministic version of the two-frequency correlation function of the duct response at selected ranges and for the same source and receiver depths as seen previously. Each surface represents the normalized magnitude on a linear pseudocolor scale. The functions are symmetric about the line f l = ,f2. The peaks along the diagonal reveal the frequency coherence bands of the channel. A vertical cut along the diagonal represents the magnitude of the channel frequency response as in Fig. 7(a). Vertical cuts perpendicular to the diagonal reveal the coherence bandwidths

HERMAND AND RODERICK ACOUSTIC MODEL BASED MATCHkD F1LTt.R PROCtSSlNG 451

h

E s W s d

40

30 1 h

E ?5

20 4

..

01 'i 0 50

W CY z 6 a

c -- I

90 t

80

70 1 t I

E;n I V"

50 100

TIME (ms) TIME (rns)

Fig. 9. lmpulsc responws of thc uppcr duct propagation channel for ranges between 1 km and 100 krn at I-km intervals. Source and receiver depth\ are respectively 100 m and IS0 m.

associated to the corresponding carrier frequencies. At short ranges the function is nearly flat over the entire frequency domain under consideration. As range increases the function is spread into a multitude of peaks and the pattern becomes highly dependent on range. As range further increases the function is progressively reduced to a single narrow peak that indicates an optimum frequency of propagation at 360 Hz. The result in the time domain is distortion of the MF output waveform and smearing of the received signal energy over a number of resolution cells, which depends upon the coherence bandwidth.

Fig. 11 show the coefficients r i , [j, and y as a function of range for given source and receiver depths (z , = 100 m and z , = 150 m). The coefficients are expressed in dB referred to a range of 1 m. The results were obtained from the range-dependent frequency response of the sound duct only. The responses were calculated every 1 km, and were numerically integrated over the band II = [184. 7921 Hz according to (44) and (32). In Fig. I 1 (a), the d curve represents the mean transmission loss in this frequency band. It is also the output peak SNR of a MBMF receiver perfectly matched to the transmission channel. This is for the condition when the transmitted signal energy-to-noise spectral density ratio is unity. The a curve represents the output peak SNR of a MF receiver, which is matched to the transmitted signal only. In Fig. 11 (b), the coefficient y characterizes the degradation of the SNR at the MF output due to the time dispersion properties of the duct. It corresponds to the gain of an ideal MBMF receiver with respect to the MF receiver. Processing with narrower bandwidths showed that as the bandwidth was progressively reduced, the (Y curve tended to the [I curve. Notice that the two curves would be coincident for a CW

transmission. Furthermore, the 17: curve exhibited deeper nulls for smaller bandwidths due to the range-dependent frequency selectivity properties of the duct. This was true particularly for ranges less than 40 km. Identical results to the cy and /j curves were obtained for MF and MBMF receiver outputs, respectively, when the transmitted large TW-product LFM waveforms had equivalent frequency bands. In Fig. 1 l(c) the effective bandwidth Au,ff of the received signal, defined by (34), decays rapidly from the full bandwidth of 608 Hz at short ranges to approximately 250 Hz at 50 km; and thereafter it remains nearly constant with range at the longer ranges. Considering the ideal MBMF receiver the reduced effective bandwidth corresponds to a decrease of input-output SNR gain of 10 log,,, (Au,ff/Aw) from the theoretical as indicated by the dotted line in Fig. 1 I(b).

Fig. 12 shows the coefficient y as a function of range and bandwidth, for the given source and receiver depths ( 2 , = 100 m, 2,. = 150 m). The frequency band was centered about the optimum frequency for long range propagation in the upper duct (fO = 360 Hz). The pseudocolor scale is from -7.7 dB (blue) to 0 dB (red). The - 3 dB bandwidth corresponds to the limit of the red color region. It can be seen that the bandwidth of the received signal is highly range dependent and decreases to approximately 100 Hz at a range of 100 km. For the case of long range ducted propagation, it is a waste of transmitted energy to distribute the energy over a bandwidth wider than that depicted here.

Fig. 13 shows the coefficient y versus the lower and upper cutoff frequencies of a rectangular transmitted spectrum, for given range (T = 30 km), source depth (z, = 100 m) and two receiver depths. The upper and lower triangular maps are for a receiver depths of respectively 150 m and 185 m.

458 IEEE JOURNAL OF OCEANIC ENGINEERING. VOL. 18. NO. 4, OCTOBER 1993

-601\ A

100

(a) 80

40 (h)

20 4":: 200 20 40 RANGE (krn) 60 80 100

(c)

Fig. 10. Magnitude of the two-frequency correlation functio duct channel response at different ranges. Source and receii respectively 100 m and 150 m. Pseudocolor scale: 0 (blue) to

The pseudocolor scale is from -6.3 dB (blue) to The diagonal (dotted line) corresponds to CW tr;

10

Fig. 1 I . Performance prediction of thc MF and MBMF receivers based on the measured environmental conditions: coefficients o and 3 (a), coefficient -, (hi and effective bandwidth Ab,<,= (ci. The investigated frequency band is Il = [164. 7921 Hz.

5

n of the upper #er depths are

1 (red).

0 dB (red). ansmissions

for which y = 0 dB. Any perpendicular line to the diagonal corresponds to a constant carrier frequency and the distance from the diagonal corresponds to bandwidth. This diagram shows that, for the investigated environmental conditions, the degradation of the MF performance (output SNR) is strongly dependent on the frequency band (and not only bandwidth) of the acoustic transmissions. For reference the end frequencies of the large TW-product LFM signals, which were used in the experiment, are indicated by the crosses. For a receiver depth of 150 m, the wider frequency band for which the SNR degradation at the MF output does not exceed 1 dB (limit of the red color region) is [320, 6201 Hz. This corresponds to an optimum carrier frequency of f o = 470 Hz. For a receiver depth of 185 m, the output SNR deteriorates very rapidly as the bandwidth is increased about some peculiar carrier frequencies like f o = 327 Hz and f o = 619 Hz.

20 40 60 80 100 RANGE (h)

Fig. 12. Degradation of the SNR at the MF output (-;) versus range and signal bandwidth. Source receiver depths are respectively 100 m and 150 m. The bandwidth is centered at fo = 360 H7. Pseudocolor scale: -7.7 dB (blue) to 0 dB (red).

V. MBMF PROCESSING RESULTS

Model-based matched-filter (MBMF) processing and matched filter (MF) processing were applied to the complete set of acoustic data (74 signals). As discussed previously, the MBMF receiver reference signals were derived from the predicted distortion due to multipath and time dispersive transmission in the refractive medium. These reference signals were obtained by convolving the transmitted signal with the predicted channel impulse responses, and were generated for


-2

0 0 01 0 02 0 03 TIME (sj

Fig. 14. receiver experimental configuration: I' = 30.3 km, m and II = [lS-l. 7921 Hz.

Predicted channel impulse response for an in-duct source and = 10s m, 2, - = 1.3s

200 300 400 500 600 700 FREQUENCY (Hz)

Fig. 13. Degradation of the SNR at the MF output (-, ) versus the cutoff frequencies of a transmitted rectangular spectrum, for an in-duct (upper triangle) and a cross-duct (lower triangle) source/receiver configuration. Pseudocolor scale: -6 .3 dB (blue) to 0 dB (red).

a large number of hypothesized ranges, source depths, and receiver depths.

A. MBMF versus M F Peflormance

Results are shown for the source and the receiver in the upper duct (T = 30.3 km, z , = 108 m, 2,. = 158 m) and for one large TW-product LFM signal ( f o = 5'30 Hz, Af = 200 Hz, At = 8 s).

Fig. 14 shows the predicted broadband impulse response for the in-duct transmission under investigation. The amplitude scale is the relative pressure referenced to 1 m. The time scale extends over the relative arrival times of all the ducted multipaths; the origin corresponds to the first arrival. The corresponding set of eigenrays consisted of 39 real eigenrays and 2 pairs of imaginary eigenrays that represented respectively the purely refracted and diffracted energies in the duct at each frequency. The full frequency response calculation over the band [184, 7921 Hz was based on a total of 6579 complex- weights. The source and receiver geometry and sound speed profile confined the downward and upward directed eigenrays to angles between 2.6" and 3.3" at the source and between 0" and 2.1" at the receiver. Their arrival times were distributed over a duration of 37.8 ms with most of the energy being contained in a time range of 15 ms.

Fig. 15 shows the MF and MBMF outputs obtained with the at-sea acoustic data. The reference signals of each filter were normalized to the same energy in order to compare the output amplitudes. For display purposes, the largest MF peak value was set to unity and the origin of the time scale was placed at the MBMF peak.

In Fig. 15(a), the MF output essentially depicts the band- limited impulse response of the overall deep water propaga-

1 . 5 7

-0.1 -0.05 0 0 05 0.1 TIME (s)

(b)

data (A.f = 200 Hzj.

-1.5'

Fig. 15. MF (a) and MBMF (b) outputs for at-$ea acoustic and environmental

tion. More precisely, it is the convolution of the transmitted autocorrelation function, a 5-ms wide sinc function, with the medium impulse response. When compared with the predicted full channel response in Fig. 6, the nonducted arrivals are recognized. Their amplitude and relative arrival times are somewhat different because of the increased range, source depth and receiver depth. In particular paths 6 and 7 arrived earlier and overlapped the low-energy ducted arrivals. Notice that none of the eight peaks is stretched in time which confirmed that the nonducted arrivals were essentially nondis-


1

0 3

0.5

5 0 a I Q -0.5

1

0 0.01 0.02 0.03 -0.01 TIME (s)

-0.1 -0.05 0 0.05 0.1 -1.5

TIME (s)

I -0.1 -0.05 0 0.05 0.1

-1.51 '

TIME (s)

(b)

Fig. 16. MF (a) and MBMF (b) outputs for simulated acoustic data based on at-sea environmental data (to compare with Fig. 15).

persive. The ducted energy was spread over three resolution cells (15 ms), which agreed with the modeled response of the duct (Fig. 14). The different peaks that appear in the latter were not fully resolved by the MF because of the limited transmitted bandwidth (Af = 200 Hz). The vertical lines delineate the portion of the channel response which was modeled for the MBMF processing, except for the two lateral peaks which do not belong to the ducted propagation (paths 6 and 7).

The MBMF receiver output is shown in Fig. 15(b). The MBMF receiver processed the same received signal as the MF receiver shown above in Fig. 15(a). However, now the reference signal simulated both the amplitude and phase distortion of the received signal which propagated from the source, through the duct, to the receiver. The MBMF reference compensated for the time spreading associated with the ducted arrivals only; and the deep refracted and boundary reflected paths were neglected in these calculations. In effect, if the simulated reference signal perfectly matched the received signal, the signal component of the MBMF output would be the autocorrelation of the received signal. But the resolution of the received autocorrelation function would be less than the resolution of the transmitted signal autocorrelation due to the effective bandwidth of the received signal being smaller than the transmit. That is, the attenuation of certain spectral components of the transmitted signal due to destructive interference caused the peak to be wider than the transmitted autocorrelation function. Although the MBMF reference signal does not perfectly match

Fig. 17. MF output and MBMF outputs for different matchings of the channel frequency response; MF (solid), amplitude only (dash), phase only (dashdot) and both (dot).

the received waveform, the process effectively recombines the spectral components of the received signal in phase and recom- presses the received signal. Comparison of the MF and MBMF outputs shows that model-based processing increased the peak SNR by 2.8 dB with respect to the conventional. The time difference of 25 ms between the MF and MBMF largest peaks corresponded to the time duration between the low energy arrival coming first and the high energy arrivals that contributed to the MF main peak. The nonducted single-path arrivals were not properly resolved in time at MBMF output since only the ducted arrivals were modeled for this calculation.

To illustrate the detail to which the interference structure of the ducted arrivals could be modeled; the transmitted signal was convolved with the channel impulse response predicted from the measured environmental data (Fig. 14). The resulting simulated acoustic data were processed exactly in the same manner as the at-sea data. The MF and MBMF outputs obtained with the simulated acoustic data are displayed in Fig. 16. In both plots, the peaks that represent the nonducted arrivals do not appear since the corresponding eigenrays were not included into the calculation of the channel impulse response. Comparison of the modeled responses in Fig. 16 with their measured counterparts in Fig. 15 shows considerable agreement. The measured and simulated ducted arrivals were remarkably similar in both relative time and amplitude. The MBMF output is the autocorrelation function of the simulated acoustic data. The peak squared-amplitude represents the energy trapped in the duct. The ratio of MBMF and MF peak amplitudes closely approximates the highest achievable gain that can be obtained under the stated acoustic and environmental conditions. Comparison with the peak amplitude obtained from the at-sea acoustic data indicated that most of the energy spread in the ducted sound channel was recombined coherently by the MBMF processing. Other results for the cross-duct transmission of a 300-Hz bandwidth signal were discussed in [12].

B. Amplitude and Phase Matching

In the frequency domain, matched filtering can be decomposed into two matching conditions: amplitude and phase [23]. Fig. 17 compares the MF output (solid line) with the MBMF outputs for three matching conditions of the duct frequency response: amplitude only (dash), phase only (dashdot),

T

HERMAND AND RODERICK: ACOUSTIC MODEL-BASED MATCHED FILTER PROCESSING

I 500Hz

t- A - - 300Hz

250Hz A -

150Hz

0 0.05 0.1 0.15 0.2 0

TIME (s)

46 1

!5

Fig. 18. MBMF (blue) and M F (gray) squared-envelope outputs for the 200-Hz bandwidth data set

and both-amplitude and phase (dot). Squared-envelopes are shown. The two forms of distortion, that is amplitude and phase, contributed to the SNR degradation at the MF output. Referring to the MBMF output, phase matching produced a single output peak and amplitude matching gave this peak its optimum value. Most of the energy spread in the duct was recombined coherently into a single peak with about twice the energy at the correct time delay. When only phase distortion was assumed, a narrower main lobe was obtained, but at the expense of a lower SNR. This demonstrated that the model- based matching considered both the amplitude and phase structure of the received signal spectrum. It also indicated that the environment maintained phase coherence over the processing time (> At = 8 s). Consideration of the phase distortion was particularly important for the angle-modulated waveforms with widely spread spectra which were used in this experiment-see the example of phase distortion in Fig. 7(b). Other results showed that the amplitude distortion, as well as the phase distortion, affected the precise value of the peak time.

C. Successive Receptions

Fig. 18 shows the processing results for repeated transmissions of the 200-Hz bandwidth signal. The superimposed blue and gray traces are respectively the MBMF and MF squared- envelope outputs. The time scale was arbitrarily set to cover all the arrivals. The origin corresponds to a fixed time delay after each transmission which occurred every minute. The structural change in the MF traces from one signal to the next indicates that the constructive/destructive interference pattern of the ducted multipaths varied slowly with time. This was mostly due to small variations in range and sourceheceiver depths and, most likely, to slow spatial and temporal fluctuations in duct sound speed. Each MBMF trace corresponded to the range

and depth parameters for which the largest gain was obtained. Since the MBMF accounted for the dispersion distortion associated with every anticipated condition (see multichannel MBMF processing described later) it consistently gathered the multipath-spread signal energy back into a single output peak. The delay between the MBMF and the MF responses corresponds to the time difference between the low-energy ducted signals arriving first, accounted for in the MBMF reference signal, and the high-energy ducted arrivals, which contributed to the main peak at the MF output.

D. Efect of Transmission Bundwidth

The traces in Fig. 19 provide examples of the MF and MBMF squared-envelope outputs for each of the seven signal bandwidths transmitted in the experiment. For display purposes, pairs of MBMF and MF outputs were normalized separately for each trace. Gains with respect to the MF were obtained with all the bandwidths. Even for the 50-Hz bandwidth there was a gain of 1.7 dB, which indicated that the phase distortion in the duct was correctly compensated for in the MBMF processing. The misalignment in time between the traces is due to range differences associated with these nonconsecutively transmitted signals. The MBMF gain was dependent on the amount of multipath delay spread. The time resolution at the MBMF output was dependent on the frequency-selective fading characteristics of the point-to-point transmission channel.

E. Ducted und Nonducted Energy Recombination Deep signal fades occurred occasionally in the ducted

propagation for the smaller signal bandwidths (Af = 50 Hz and 100 Hz). For these particular events all the propagation paths were included in the generation of the MBMF reference signals. Fig. 20 shows the MF (solid line) and MBMF (dashed


0 0.05 0.1 0.15 0.2 0.25

TIME (s) Fig. 19. Examples of the MBMF (blue) and MF (gray) squared-envelope outputs for each transmission bandwidth used in the experiment.

I -0.1 -0.05 0 0.05 0.1 0.15

TIME (s)

Fig. 20. Outputs of the MF (solid line) and of the MBMF (dashed line) that incorporated broadband modeling of the overall deep water propagation for the case of a strongly faded 50-Hz bandwidth signal.

line) squared-envelope outputs for a severely faded signal of 50-Hz bandwidth. The first and second major MF peaks correspond, respectively, to the deep-refracted and ducted arrivals. All the spectral components of this narrowband signal were identically attenuated by the duct (flat fading). Hence, the MBMFMF relative gain of 3.6 dB was achieved mostly by phased recombination of all the multipath arrivals. It can seen that the energy in the MBMF peak is greater than the sum of the energies in the resolved MF peaks.

F. Comparison with Energy Spreading Loss

Fig. 21 compares the MBMF gain (with respect to the MF receiver) to the energy spreading loss (ESL) for each of the received transmissions. Where ESL is defined as the ratio of the energy in the largest resolved peak to the total spread energy measured at the MF output. This metric was calculated according to [24]. Most importantly, for every transmission,

4.0

3.5

3.0

2.5

B 2.0 1.5

1 .o

0.5

0.0 - ~ ~ o I . ~ Y ) ~ o I . m c n 0 1 c - - N N N O O G P P m m G % % ?

Data Number

Fig. 21. MBMFMF relative output SNR gain and ESL for the complete acoustic data set. Data numbers follow the order of transmission. Correspond- ing signal bandwidths are 1-16: Af = 300 Hz; 18-26: Af = 200 Hz;

Af = 50 Hz; 64-75: Af = 500 Hz. 2 7 4 2 : A f = 100 Hz; 43-50: A f = 250 Hz; 51-57: A f = 150 Hz; 58-63:

the MBMF achieved a gain with respect to the MF. The gain was proportional to the energy time spreading measured at the MF output, which is related to the transmission bandwidth and the actual source and receiver positions. These calculations included only the ducted arrivals in the MBMF processing.

G. Range and Depth Determination

MBMF processing was extended to provide estimates of the range, and depths of the source and receiver. Ambiguity functions were determined for each received signal to represent the largest MBMF output peaks obtained with a family of reference signals. The reference signals were generated for closely spaced range, source depth, and receiver depth increments. The range and depth parameters of the MBMF reference that resulted in a maximum peak SNR gain, with respect to the MF, provided the range and depth

HERMAND AND RODERICK. ACOUSTIC MODEL-BASED MATCHED FILTER PROCESSING 463

dB

3 3

R 0.5

0.0

Fig. 22. Rangeheceiver-depth MBMF ambiguity surface for source and receiver located respectively in the upper and lower ducts (A.f = JOO Hz). A source depth of 100 m was assumed for the calculation. Thc MBMF gain in dB is referenced to the peak SNR at the MF output.

estimates. The parameter space was for range, 7’ E [ 2 5 . 351 km, for source depth, z , E [SO. 1501 m, and for receiver depth z , E [loo. ‘LOO] m; range and depth increments were respectively h,r = 100 m and hz = 1 m.

As a first example, results are presented for a signal of 300- Hz bandwidth transmitted in the upper duct (z,, z 100 m) and received in the lower duct (2,. 185 m). Fig. 22 displays a three-dimensional plot of the rangeheceiver depth ambiguity surface calculated for the approximate source depth ( z , ~ = 100 m). The surface is based on the correlation peaks obtained with 10201 range/depth reference signals. The reference level of 0 dB corresponds to the correlation peak obtained when the reference signal is a replica of the transmitted signal. The dark-blue region represents a loss in peak SNR with respect to conventional processing. The other regions represent a gain with respect to conventional processing. The global maximum has a level of 3 dB and is located at (30.7 km, 186 m) range/depth coordinate. Other local maxima are due to the imperfect matching between the measured and predicted sound fields. In particular the nonducted arrivals were ignored in the prediction. Simulation results based on the at-sea environmental data showed that the ideal ambiguity surface had a single maximum (not shown). It is emphasized that the range, as well as the receiver depth, were determined from the time dispersion characteristics of the received complex envelope rather than from the time delay associated to the main peak as in conventional MF processing.

Fig. 23 shows the three projections of the ambiguity volume that corresponded to the approximately correct range, source and receiver depths. Note that there is an ambiguity in source depth. Maxima occur at two other depths (78 m and 124 m) located symmetrically about the correct source depth (101 m). There is no ambiguity in receiver depth. The simulated ambiguity volume behaved similarly (not shown).

Fig, 23. Projections of the range/source-depth/receiver-depth MBMF ambiguity volume that corresponds to I’ = 30 km, z , = 100 m and zr = 185 m. Reference level of 0 dB corresponds to the peak SNR at the MF output.

Fig. 24. Same as Fig. 23 but for both source and receiver located in the upper duct (1.f = .>OO Hz) . The projections correymnd to the global maximum of 1.4 dB a1 I ’ = 3 0 . 7 km, z , = 101 m, and z , = 150 m.

The depth resolution is higher for the source than for the receiver-the half-power widths of the ambiguity contour are respectively 13 m and 36 m. The sharp transition in gain at 28-km range and 170-m depth that is apparent in the three projections is due to the barrier sound speed at a water depth of 170 m (Fig. 2). At that particular range and depth the multipath interference pattern changed abruptly due to the particular characteristics of the acoustic coupling between the two adjacent ducts [25]. Notice that the channeling effect occurs at a number of discrete ranges (see the magnitude of the cross-duct frequency response in Fig. 8(b)).

Fig. 24 shows a second example of range/depth determination in the case where both source and receiver were located in the upper duct ( zs M 100 m, z,. x 150 m). The three projected


ambiguity surfaces correspond to the range and depths at which the global maximum of 1.4 dB was found (T = 30.7 km, z, = 101 m, z, = 150 m). There is no ambiguity in both range and depth and the resolution is higher than in the previous cross-duct example because of the greater complexity of the acoustic field associated with the in-duct configuration and of the larger transmitted bandwidth.

For most of the acoustic data that was analyzed, the ambiguity volume had a global maximum located at the correct range/depth coordinate. Most importantly the level of the global maximum always corresponded to an increase of the correlation peak value with respect to the conventional MF receiver (Fig. 21). This gave confidence in the location estimates and demonstrated the robustness of the multichannel MBMF receiver. Other localization results are discussed in [13].

VI. CONCLUSION The results of this paper have demonstrated that the perfor-

mance of a conventional matched filter can be improved if the reference channel compensates for the amplitude and phase distortion occurred in a time dispersive medium. In addition to achieving a higher SNR on every transmission with the model-based matched filter processor, it was also possible to isolate in depth and range the source that emitted the acoustic signal and the depth of the receiving array. Range and depth estimates were obtained from ambiguity functions by varying the reference signals in closely spaced range, source depth, and receiver depth increments.

The effects of distortion on the correlation process was investigated and it was found that the MBMF output had the highest SNR when both amplitude and phase was accounted for in the reference signal. Considering bandwidth as a vari- able, the MBMF processing showed a gain for each of the seven transmitted bandwidths including a gain of 3.6 dB for the 50-Hz bandwidth transmissions.

The results obtained for the MBMF processor were possible even from a sparse set of environmental data that consisted of a measured near-surface temperature profile, a deeper depth archival temperature data, and a depth dependent salinity profile. Only one sound speed profile was used in the range independent modeling.

The next phase of this research will include relative motion between the source and receiver such that there is a Doppler shift (or time compressiodexpansion) in the received signal [26], [27]. Also, natural extensions to this work include an investigation into the performance gains that are achievable when the background interference is reverberation instead of noise. It is expected that the gain over reverberation will be dependent on the differences in the spectral characteristics of the reference signal with respect to the spectrum of the reverberation. Lastly, it is important to investigate the dispersion associated with two-way propagation. This problem is more pertinent to the active sonar problem. The signal reflected from the target is the convolution of the transmitted signal with the impulse response of the medium between the source and target which is convolved with the target impulse response. The received signal is then the target reflected signal convolved

with the impulse response of the medium between the target and the receiver. It is expected, that in addition to the gain of the MBMF over the MF, target parameters (velocity, range, and depth) can be estimated and classification clues (highlight structure) can be obtained through deconvolution techniques.

ACKNOWLEDGMENT

The authors would like to thank Mr. Bernie Cole and Mr. Roy Deavenport of the Naval Undersea Warfare Center for their helpful comments and suggestions. Also, the technical support of Mr. Renzo Belle, Mr. Silvio Bongi and Mr. Ettore Capriulo of the SACLANT Undersea Research Centre in the experimental phase of this work is appreciated.

REFERENCES

A. D. Whalen, Detection of Signals in Noise. New York Academic Press, 1971. H. L. Van Trees, Detection, Estimation and Modulation Theory, Pan III. New York: Wiley, 1971. J-P. Hermand and W. I. Roderick, “Delay-Doppler resolution performance of large time-bandwidth-product linear FM signals in a multipath ocean environment,” Journal of the Acoustical Society of America, vol. 84, no. 5, pp. 1709-1727, 1988. H. Weinberg and R. Burridge, “Horizontal ray theory for ocean acoustics,” Journal of the Acoustical Society ofAmerica, vol. 55, no. 1, pp. 63-79, 1974. H. Weinberg, “Generic Sonar Model,” Naval Underwater Systems Center, New London, CT, 1985, NUSC Tech. Document 5971D. I. V. Gindler, Yu. A. Kravtsov, and V. G. Petnikov, “Signal-to-noise ratio in the reception of wideband pulses in dispersive media,” Soviet Physics Acoustics, vol. 33, no. 3, pp. 26G261, 1987. F. B. Jensen, “Wave theory modeling: A convenient approach to CW and pulse propagation modeling in low-frequency acoustics,” IEEE Journal of Oceanic Engineering, vol. 13, no. 4, pp. 186197, 1988. F. V. Bunkin, I. V. Gindler, A. R. Kozel’skii, Yu. A. Kravtsov, and V. G. Petnikov, “Dispersion distortions of complex acoustic signals in shallow ocean waveguides,” Soviet Physics Acoustics, vol. 35, no. 5 , pp. 461464, 1990. A. V. Vavilin, A. R. Kozel’skii, V. G. Petnikov, V. M. Reznikov, and E. A. Rivelis, “Characteristics of the dispersion distortions of pulse signals in acoustic waveguides,” Soviet Physics Acoustics, vol. 33, no. 5, pp. 481483, 1987. A. B. Baggeroer and W. A. Kuperman, “Matched field processing in ocean acoustics,” in Proceedings of the NATO Advanced Study Institute on Acoustic Signal Processing for Ocean Exploration, J. M. F. Moura and I. M. G. Lourtie, Eds. Dordrecht: Kluwer Academic Publishers, 1992, pp. 79-1 14. J-P. Hermand and W. I. Roderick, “Channel-adaptive matched filter processing of large time-bandwidth-product signals: Preliminary results,” Journal of the Acoustical Society ofAmerica, vol. 89, no. 4, Pt. 2, 1991. J-P. Hermand and W. I. Roderick, “Model-based processing of large time-bandwidth product signals in a time dispersive ducted sound channel,” in Proceedings of the NATO Advanced Study Institute on Acoustic Signal Processing on Ocean Exploration, J. M. F. Moura and 1. M. G. Lourtie, Eds. J-P. Hermand and W. I. Roderick, “Channel-adaptive reception of wideband underwater acoustic signals,” in Proceedings of the Euro- pean Conference on Underwater Acoustics, M. Weydert, Ed. London: Elsevier, 1992, pp. 71-74. R. L. Mitchell and A. W. Rihaczek, “Matched filter responses of the linear FM waveform,” IEEE Trans. Aerosp. Electron. Syst., vol. 4, no. 3, pp. 417432, 1968. D. E. Vakman, Sophisticated Signals and the Uncertainty Principle in Radar. New York: Springer-Verlag, 1968. R. S. Kennedy, Fading Dispersive Communication Channels. New York: Wiley, 1969. Yu. A. Kravtsov and V. G. Petnikov, “Partial determinacy of wave- fields,” Soviet Physics Doklady, vol. 30, no. 12, pp. 1039-1040, 1986. 1. V. Gindler and Yu. A. Kravtsov, “Degree of determinacy of a wave field and coherent processing of wideband signals,” Soviet Physics Acoustics, vol. 34, no. 2, pp. 142-144, 1988.

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! ,

Jean-Pierre Hermand reccived the Ingenieur Civil degree in electronic and electrical engineering from the University of Brussels (ULB) in 1981.

He then conducted research in the Department of Acoustics and Optics on sound intensimetry, and ultrasonic tissue characterization for medical diag- nosis. He joined the SACLANT Undersea Research Centre, La Spezia, Italy, in 198.5 as a scientist where he has been engaged in research and development work involving underwater acoustics and magnetics. From 1991 to 1993 he was a consultant to the Naval

Undersea Warfare Center (NUWC) on model-based signal processing for active sonar application. Since 1991 he has been a lecturer of a course in image processing at the International School of Optical Technologies (AILUN), Nuoro, Italy. He is currently with the Applied Acoustics Group of the SACLANTCEN conducting research activities related to ocean acoustic tomography.

William Roderick received the B.S degree in electncal engineenng from the University of Rhode Island and the M S. and Ph.D. degrees in electronic and electncal engineenng from the University of Birmingham, Birnungham, England.

He currently serves the Naval Undersea Warfare Center (NUWC) Newport Division as the Director for Science and Technology. Pnor to this position he served as program manager for the division’s sub- mannelsurface ship ASW surveillance exploratory development program, He has received the organi-

zation’s award for Excellence in Science for his research and development work involving underwater acoustics and signal processing Dr. Roderick joined the Naval Underwater Sound Laboratory, a forerunner to NUWC, in 1966

Acoustic model-based matched filter processing for fading time-dispersive ocean channels: theory and experiment

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