Signal-to-Reverberation Ratio Comparison of Linear

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Signal-to-Reverberation Ratio Comparison of Linear Frequency Modulated Continuous Active Sonar and Pulsed Active Sonar

Jeffrey R. Bates Stefan M. Murphy Brian H. Maranda DRDC – Atlantic Research Centre Douglas A. Abraham CausaSci LLC Journal of Oceanic Engineering Institute of Electrical and Electronics Engineers (IEEE) Xplore Pages: 11 DOI: 10.1109/JOE.2020.2994605 Date of Publication from Ext Publisher: June 2020

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IEEE JOURNAL OF OCEANIC ENGINEERING 1

Signal-to-Reverberation Ratio Comparison of LinearFrequency Modulated Continuous Active Sonar and

Pulsed Active SonarJeffrey R. Bates , Stefan M. Murphy, Brian H. Maranda, Member, IEEE,

and Douglas A. Abraham , Senior Member, IEEE

Abstract—Continuous active sonar (CAS)waveforms provide anadvantage over conventional pulsed active sonar (PAS) waveforms,which is, they can be processed to provide a higher target updaterate through subpulse processing. Performance in reverberationlimited conditions is particularly important in shallow water. Thisarticle compares the signal-to-reverberation ratio (SRR), echolevel, and reverberation level of simultaneously transmitted lin-early frequency modulated (LFM) PAS with an equal bandwidthLFMCASwaveforms processedwith differentCAS subpulse dura-tions in a littoral environment. Data from an experimental sea trialshowed that the LFM PAS waveform outperformed the full-bandLFM CAS waveform in terms of SRR by 3.0 ± 2.1 dB. The SRRof the CAS waveform degraded by less than the expected 3 dB perhalving of the subpulse bandwidth and duration. Energy spreadingloss, which increases with bandwidth, was shown to be the domi-nant cause of the deviation from expected degradation rate. Thedetection performance of the full-band LFM CAS waveform wasapproximately equal to that of theLFMPASwaveformasmeasuredby a receiver operating characteristic analysis.

Index Terms—Acoustic signal processing, reverberation, sonardetection.

I. INTRODUCTION

R ECENT improvements in sonar systems allow for anincrease in the transmit duty cycle of active sonar wave-

forms, from a pulsed active sonar (PAS) mode to a continuousoperation mode. This continuous operation mode is called highduty cycle or continuous active sonar (CAS) and has applicationsin antisubmarine warfare [1], [2]. CAS offers the advantageof increasing the target update rate though subpulse process-ing [3]. This higher update rate can reduce a tracker’s uncertaintygrowth [4] and improve tracking performance [5], [6].

Manuscript received January 9, 2020; revised April 20, 2020; accepted May7, 2020. This work was supported by the LCAS MN-JRP, including the NATOCentre for Maritime Research and Experimentation, the Defence Science andTechnology Group (AUS), Defence Research and Development Canada (CAN),the Defence Science and Technology Laboratory (GBR), Centro di Supporto eSperimentazione Navale-Italian Navy (ITA), the Norwegian Defence ResearchEstablishment (NOR), the Defence Technology Agency (NZL), and the Officeof Naval Research (USA), as participants. (Corresponding author: Jeffrey R.Bates.)

Associate Editor: L. Culver.Jeffrey R. Bates, Stefan M. Murphy, and Brian H. Maranda are with

the Defence Research and Development Canada Atlantic Research Centre,Dartmouth, NS B3A 3C5, Canada (e-mail: [email protected];[email protected]; [email protected]).

Douglas A. Abraham is with CausaSci LLC, Ellicott City, MD 21041 USA(e-mail: [email protected]).

Digital Object Identifier 10.1109/JOE.2020.2994605

Subpulse processing reduces the processed energy (and band-width for frequency swept waveforms), which can negativelyimpact the detection performance for targets with low signal-to-noise ratio in noise-limited conditions or signal-to-reverberationratio (SRR) in reverberation-limited conditions. Performancein reverberation-limited conditions is particularly important inshallow water, and SRR will be the focus of this article. Se-lecting the optimal subpulse bandwidth and duration dependson the target range, range rates [3], [7], [8], required Dopplersensitivity [9], [10], maneuverability [11], and the acousticalenvironment [3], [12]–[14]. Target detection and, therefore, SRRare of critical importance.In this article, Sections II and III describe the experimental

setup and the data processing, respectively. Section IV describesthe theoretical echo level (EL), reverberation level (RL), andSRR scaling for CAS subpulses as a function of coherent pro-cessing duration in ideal and time-spread channels. Section Vcompares the theoretical results with an experiment where PASand CAS waveforms were transmitted simultaneously. The re-sults show the tradeoff between subpulse bandwidth and SRRfor a linear frequency modulation (LFM) CAS waveform ina different reverberation-limited environment than previouslyinvestigated [14]. In addition, this article shows that energyspreading loss (ESL) [15], [16] causes a lower than expected gainin SRR against reverberation for both PAS and CASwaveforms.This article also compares the detection performance of PAS andCASwaveforms using a receiver operating characteristic (ROC)analysis. The findings are summarized in Section VI.

II. EXPERIMENT

The Littoral CASMulti-National Joint Research Project helda sea trial off the coast of Taranto, Italy, on October 2016 tocompare the performance of CAS and PAS waveforms. OnOctober 23, the NRV Alliance towed a sonar source at a depthof 70 m that transmitted two LFM waveforms simultaneouslyin separate frequency bands. The lower band was 1.8–2.6 kHzand the upper band was 2.7–3.5 kHz. Note that both upper andlower bands had equal bandwidth of 800 Hz. NRV Alliance alsodeployed a towed array receiver with 64 triplet hydrophones ata depth of approximately 75 m.The sonar system on NRV Alliance attempted to detect an

echo repeater (ER) towed by the CRV Leonardo at a depth

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2 IEEE JOURNAL OF OCEANIC ENGINEERING

Fig. 1. Run geometry. Source and receiver towed by NRV Alliance shown ingray and surrogateER target towedbyCRVLeonardo in black.Distance betweenship tracks is approximately 3.75 km. Background shows the bathymetry.

Fig. 2. (a) Spectrogram of two LFM PAS waveforms with a duration of 1 sand frequency bands of 1.8–2.6 kHz and 2.7–3.5 kHz, respectively. The pingrepetition interval is 20 s. (b) Spectrogram of an LFM PAS (duration of 1 s,2.7–3.5 kHz) and LFM CAS (duration of 20 s, 1.8–2.6 kHz) waveform with aping repetition interval of 20 s.

of approximately 70 m to act as a surrogate target. The CRVLeonardo sailed parallel to the NRV Alliance at a range ofapproximately 3.75 km, as shown in Fig. 1. Both vessels traveledat approximately 3.5 kn (≈1.8 m/s). Fig. 1 also shows thebathymetry, acquired using aKongsberg EM302, 30-kHzmulti-beam echosounder. The sound-speed profile was downwardrefracting with a 35-m mixed layer.Two runs are investigated herein. In the first run (referred to

as the PAS-PAS run), the NRV Alliance and the CRV Leonardotraveled southeast, and a 1-s LFM PAS waveform (Tukey win-dowed with a cosine fraction of 0.05) was transmitted in theupper and lower bands as shown by the spectrogram in Fig. 2(a).The two waveforms had equal source level to determine theimpact of differing center frequencies. The run had a durationof 57 min, spanning 171 ping cycles. In the second run (referredto as the CAS-PAS run), the two ships traveled northwest, anda 1-s LFM PAS (Tukey windowed with a cosine fraction of0.05) waveform was transmitted in the upper band and a 20-sLFM CAS waveform (Tukey windowed with a cosine fractionof 0.0025) was transmitted in the lower band with the same starttime as shown by the spectrogram in Fig. 2(b). The source level

TABLE IPARAMETERS OF CAS SUBPULSE REPLICAS WITH 50% OVERLAP

Subpulse replicas were processed independently and the resultingnumber of detection opportunities in each 20-s ping cycle correspondto the number of replicas.

of the CAS waveform was decreased by 10 log10(20 s/1 s) =13 dB relative to the PAS waveform, such that they had equaltotal energy per ping. The run had a duration of 65min, spanning194 ping cycles.

III. DATA PROCESSING

The towed-array data were cardioid beamformed [17] into128 cosine-spaced beams (63 port, 63 starboard, 1 forward, and1 aft), then matched filtered. For PAS processing, the replicaused in the matched filter was the entire LFM PAS waveform,also called a full-band replica. ForCASprocessing, the full-bandLFM CAS replica was similarly used, as well as a series of sub-pulse replicas that were extracted from it. The subpulse replicasare defined by their duration (and therefore bandwidth), and theoverlap between subpulses. In total, six processing bandwidthswere used for CAS, each had a 50% overlap. The duration,bandwidth, and number of replicas per ping are shown in Table I.For example, the largest subpulse had a bandwidth of 400 Hzand was formed by applying a 10-s Hann window to the 0–10-,5–15-, and 10–20-s regions of the full-band replica, yieldingthree subpulse replicas with 50% overlap. Each subpulse replicawas processed independently such that the ping rate was effec-tively multiplied by the number of subpulse replicas to form asequence of target detection opportunities within each 20-s pingcycle.The matched-filter output was basebanded and lowpass fil-

tered such that the sampling period was equal to half of theeffective subpulse matched-filter resolution, which is approx-imately equal to twice the reciprocal of the processing band-width for Hann-windowed LFM waveforms [18, Sec. 8.5.1].The matched-filter output was scaled such that echoes withequal total energy had equal matched-filter EL, however thematched-filter output was not calibrated in absolute terms. Thesampling period was set as such to minimize scalloping loss.It was from this time series that the target EL was measured.RL was measured by taking the median of samples in 0.17-swindows on both sides of the target echo sample; the medianwas corrected via [18, eq. 8.383] to obtain an unbiased estimate.The SRR was computed by taking the ratio of the EL and the



BATES et al.: SRR COMPARISON OF LINEAR FREQUENCY MODULATED CAS AND PAS 3

RL. The process was implemented as a median normalizingfilter, which resulted in a normalized matched-filter time seriesthat was used for performing detection by applying a constantthreshold. Threshold crossings within 0.1 s and three beamswere grouped (clustered) into contacts. The EL was measuredby picking the largest EL in the cluster.Echoes from the surrogate target were identified based on

the known location of the CRV Leonardo. The SRR, EL, andRL were recorded and linear means were calculated for PAS,full-band CAS, and subband CAS processing. The mean PASvalueswere calculated from the total number of full-band-replicadetections per run. For CAS, the mean was taken over thedetections across all of the subpulses with a given subpulseduration.Post-matched-filter integration (PMFI) [16],[18, Sec. 8.8.1]

was used as an optional processing step. A sliding 0.04-s boxcarwindowwas used to integrate the data before normalization. Theintegration time was selected to correspond to the resolution ofthe 25-Hz subpulse, which is the limiting case where the PMFIinterval corresponds to one sample and has no effect. At theother extreme, the PMFI interval for the 800-Hz subpulse was32 samples long.

IV. THEORETICAL EL, RL, AND SRR FOR SUBPULSEPROCESSING

A. Echo Levels (ELs)

1) Perfect Reflection Without Propagation Effects: Assum-ing a point reflector without propagation effects, the targetEL is expected to scale proportionally with the energy, andtherefore duration, of the processed subpulse.When the subpulsebandwidth depends linearly on the subpulse duration, as is thecase for LFMwaveforms, the target EL is also expected to scaleproportionally with subpulse bandwidth.2) Including Scattering and/or Propagation Effects: Real-

world targets and propagation result in target echoes that arespread in time and Doppler. In this analysis, we will focus onlyon time spreading. When the range resolution is sufficient toresolve multipath arrivals, there is a reduction in the measuredEL compared to the level that would be achieved with a lowerresolution, where the arrivals would be summed in the matchedfilter. This is referred to as ESL [15], [16], [18, Sec. 8.8.1]. ESLgenerally increases with increasing signal bandwidth, but also isdriven by and depends on the duration of the impulse responseof the target scattering and environmental propagation effectsrelative to the matched-filter resolution. The EL of a realistictarget in a realistic environment using subpulse LFMwaveformsis therefore expected to scale proportionally with the subpulseduration with a discrepancy that depends on the ESL, whichgenerally increases with subpulse bandwidth.When the range resolution is insufficient to resolve multipath

arrivals, the matched filter adds the multiple arrivals coherentlyand the sum depends on the relative phase of the arrivals. Theexpectation value (mean) of the level of unresolved paths isequal to an incoherent sum of levels from the unresolved paths,assuming a deterministic signal with a uniform random phase

offset between the paths [18, Sec. 8.8.1], which is described inmore detail in the following.3) Effect of PMFI: PMFI can be used to incoherently recover

ESL [16], [18, Sec. 8.8.1]. In practice, the integration durationis selected to optimize detection performance; however, hereinthe integration duration is selected to make a fair comparisonamong the CAS subpulses.We state a distributional result that will be used later in the

analysis. The statistic that is thresholded at the detector output,after PMFI ofM samples, will be of the form

Y �M∑

m=1

|μm + Vm|2 (1)

where both μm and Vm are complex random variables (r.v.’s).In our application, μm is a signal-related component and Vm

is a noise or reverberation component sample; the r.v.’s μm

and Vm are assumed to be statistically independent for eachm.We also assume that Vm have zero mean and identical varianceE{|Vm|2} = λ. Now

Y =M∑

m=1

(|Vm|2 + μ∗mVm + μmV ∗

m + |μm|2) (2)

so the mean of Y is given by

E{Y } = Mλ +

M∑m=1

E|μm|2. (3)

The cross-term expectations are zero because μm and Vm arestatistically independent and E{Vm} = 0.Equation (3) holds under conditions that are not very strin-

gent, even including the case when Vm and Vn are statisticallydependent for m �= n. In the specific case that Vm are complexGaussian r.v.’s that are independent and identically distributed(a typical assumption for noise samples) and μm are in factconstants, Y would be proportional to a noncentral chi-squaredrandom variable. Such distributional knowledge would be re-quired to compute the theoretical detection performance, forexample. However, the more general case with the weak as-sumptions presented earlier is adequate for our purposes.To predict the trend of the EL after PMFI in a realistic envi-

ronment consider a passband channel demodulated to baseband,yielding an equivalent lowpass channel response given by [19,Sec. 7.1]

h(t) =

Ntotal∑n=1

Ane−jω0τnδ(t− τn) (4)

where τn is a monotonically increasing time delay of individualmultipath arrivals, An is the arrival amplitude, and ω0 is thedemodulation frequency. We define θn � ω0τn mod 2π andwe assume that the changes in the value ofω0τn withn aremuchgreater than 2π, so that θn can be modeled as uniformly randombetween 0 and 2π [19, Sec. 7.1]. Ntotal is the total number ofsignificant paths in the channel, and δ is the delta function.




The complex envelope x received at time t is then equal to

x(t) = h(t) ∗ u(t) + V (t) =

Ntotal∑n=1

Ane−jθn u(t− τn) + V (t)

(5)where u(t) is the complex envelope of the transmitted waveformand V (t) is the reverberation noise, which is assumed to havezero mean and to be independent of the signal component.Assuming u(t) is an LFMwaveform and the above expression

for x(t) is matched filtered with a subpulse replica, the matched-filter output will be proportional to the energy in the processedsubpulse, which is proportional to subpulse duration Tp. Wewillnow make this explicit by defining s(t) = u(t)/

√Tp such that∫ Tp

0 |s(t)|2 = 1.Equation (5) now becomes

x(t) =√Tp

Ntotal∑n=1

Ane−jθn s(t− τn) + V (t). (6)

The resulting matched-filter output xMF(t) is given by

xMF(t) =√Tp

Ntotal∑n=1

Ane−jθnR(t− τn) + VMF(t) (7)

where R(τ) is the LFM autocorrelation function, having amaximum value of 1 at zero delay, i.e., τ = 0. We make thefollowing rough approximation: it will be assumed that in agiven range cell (at time tR, say), we have R(tR − τn) ∼= 1 forN arrivals and R(tR − τn) ∼= 0 for the others. Then

xMF(tR) =√

Tp

no+N−1∑n=no

Ane−jθn + VMF(tR) (8)

for some starting index no. The value of N is discussed in thefollowing.We now form the detection statistic Y = |xMF(tR)|2. From

(3) withM = 1, we have E{Y } = λ + E|μ1|2, and here

E|μ1|2 = Tp E

∣∣∣∣∣no+N−1∑n=no

Ane−jθn

∣∣∣∣∣2

= Tp

no+N−1∑n=no

|An|2. (9)

Due to the random phases, the terms proportional to AiAk withi �= k are zero. In summary, the mean of Y is

E{Y } = λ + Tp

no+N−1∑n=no

|An|2. (10)

The value ofN will depend on the range resolution, the delaystructure of the multipath channel, the time tR, etc. We considertwo extreme cases. In the first case, we look at a short-durationsubpulse (i.e., narrowbandwidth) of durationTs. Since the rangeresolution is poor, it is assumed that the maximum-amplituderange cell includes all Ntotal arrivals; that is, N = Ntotal and

E{Y } = λ + Ts

Ntotal∑n=1

|An|2. (11)

In the second case, we consider a long-duration subpulse ofduration T�. Owing to the wide bandwidth of this subpulse, it is

assumed that the Ntotal arrivals are individually resolved at thematched-filter output. That is, in any given range cell, there is atmost N = 1, so that a cell containing an arrival has E|μn|2 =T�|An|2 for some n. We now apply a PMFI that sumsM rangecells to produce YPMFI; assuming that all arrivals are capturedby the integrator, it follows from (3) that

E{YPMFI} = Mλ + T�

Ntotal∑n=1

|An|2. (12)

We examine more closely the issue of how to choose Mto capture all Ntotal arrivals. The idea is to set the integrationtime equal to the time resolution of the short subpulse: then,at the same time position (equivalently, range) where the shortsubpulse included all Ntotal arrivals, the integrator should alsocapture them. Now, since the time resolution is given by theinverse bandwidth, we set M = W�/Ws, where Ws and W�

denote the bandwidth of the short- and long-duration subpulses,respectively. For an LFMwith sweep rate β, we haveWs = βTs

and W� = βT�. Therefore, it also follows that M = T�/Ts.Using this last relation in (12), we find

E{YPMFI} = T�

(λ

Ts+

Ntotal∑n=1

|An|2). (13)

Writing (11) in the form

E{Y } = Ts

(λ

Ts+

Ntotal∑n=1

|An|2)

(14)

and comparing with (13) for a fixed Ts, we see that for anLFM waveform, the expected value of the signal plus noisescales proportionally with the subpulse duration, and thereforebandwidth for LFM waveforms, after the PMFI integrates anequal number of multipath arrivals. A more detailed analysiswould show that this conclusion holds for intermediate subpulselengths.

B. Reverberation Levels (RLs)

1) Matched-Filter RL: The RL at the output of the MF isexpected to be proportional to the transmitted energy and in-versely proportional to the bandwidth of the processed LFMwaveform. The result is an exact cancellation such that the RLis independent of the subpulse duration and bandwidth.2) Effect of PMFI on Reverberation: The PMFI RL is ex-

pected to increase proportionally with the number of integratedrange cells. By removing the signal (An terms) from (13) and(14), the expectation value of the RL (term∝ to λ) can be shownto scale proportionally with the subpulse duration, and thereforethe bandwidth for LFMwaveforms, after the PMFI as describedearlier.

C. Signal-to-Reverberation Ratio (SRR)

1) Matched-Filter SRR: As discussed in Section IV-A thesubpulse EL is expected to scale proportionally to the sub-pulse duration and, correspondingly, the bandwidth for LFMwaveforms, with a discrepancy that depends on the ESL. As




Fig. 3. Matched-filter output for a single ping of PAS, 800-Hz CAS, and32nd subpulse of 25-Hz CAS in red-brown, blue, and yellow, respectively. Eachwaveform is reverberation limited until approximately 10 s.

described in Section IV-B, the RL is expected to be independentof duration (and bandwidth) without PMFI. Consequently, theSRR is expected to scale proportionally to the subpulse duration(and bandwidth) with a degradation from this trend that dependson the amount of ESL.2) Effect of PMFI on SRR: With PMFI, the EL and RL scale

proportionally to the duration; therefore, the SRR is expected tobe independent of duration for LFM waveforms after the PMFIintegrates the samenumber ofmultipath arrivals.However, aswewill show in the following, this does not mean that the detectionperformance is independent of CAS processing duration asthe statistical distribution of clutter and reverberation is alsoimpacted by PMFI.

V. RESULTS

As a first step in the analysis, we will show that the targetechoes are reverberation limited. Fig. 3 shows the squaredenvelope of the matched-filter output, before normalization, ofa single ping along the target bearing for the PAS, full-bandCAS, and 25-Hz CAS subpulse (subpulse #32 of 63) duringthe CAS-PAS run. The direct arrival is always at approximately0 s as the run is a monostatic geometry. Note that in all cases,the interference background is decreasing as a function of time(range) until approximately 10 s, indicating that the region isreverberation limited. The target echoes in both runs arrive at ap-proximately 5 s after transmission and are reverberation limited.Note that the results shown herein are uncalibrated although thedifferent subpulses and waveforms have a consistent reference.

A. Echo Levels (ELs)

1) PAS inUpper andLowerBands: During the PAS–PAS runthe influence of the different center frequencies of the lower andupper transmission bands is investigated. Fig. 4(a) shows thepeak envelope matched-filter EL of the ER target from upper

and lower bands PAS. The EL in the upper band was higher thanthat in the lower band, with a mean difference (upper–lower)of 3.5 ± 1.2 dB, where the uncertainty is given by the 95%confidence interval (CI). Fig. 4(b) shows the matched-filter ELafter PMFI fromupper and lower bands PAS. PMFI has the effectof increasing the level, as discussed in Section IV-A. The meandifference (upper–lower) in level after PMFI is 2.9 ± 1.2 dB.The difference in EL between upper and lower bands may be

due to frequency dependence in source level, ER target strength,and/or propagation. Both the source and ER were equalizedbefore the experiment to avoid frequency dependence; however,a calibration error on the order of themeasured difference earlieris possible given the calibration uncertainties. The performancedifference in the two frequency bandsmust be taken into accountwhen comparing CAS, which was transmitted in the lower band,with PAS, and was then transmitted in the upper band.2) CAS Versus PAS: Next, we will consider the EL during

the CAS-PAS run. Fig. 5(a) shows a zoom-in picture of Fig. 3and an example of the matched-filter output from a single pingas measured by PAS, full-band CAS, and one of the 25-HzCAS subpulses during the CAS-PAS run. The effect of thematched-filter bandwidth on range resolution is readily apparent.Multiple arrivals are resolved by the PAS and 800-Hz CASwaveforms [the three strongest arrivals are indicated by blackarrows in Fig. 5(a)], whereas the multipath arrivals, indicatedby black arrows, are unresolved and combined in two rangeresolution cells by the waveform with a 25-Hz subpulse. Themultipath arrivals, indicated by gray arrows, are also unresolvedand combined into a different range resolution cell by the wave-form with a 25-Hz subpulse. Note that the 25-Hz CAS subpulseEL is lower due to the lower energy level in the subpulse, despiteincluding more multipaths.The effect of PMFI on the matched-filter output can be ob-

served in Fig. 5(b), where all subpulses are now included. The25-Hz subpulse is not affected because the PMFI duration wasselected to correspond to the 25-Hz subpulse resolution. Thepeak corresponding to the target echo has flattened due to theintegration duration being longer than the time extent of themultipath returns.Themean level over the runof the peakCASecho as a function

of subpulse bandwidth is shown by the blue points in Fig. 6(a).The red-brown diamond is the mean level of the PAS echo. Theerror bars are given by the 95% CI. Recall that the PAS–PAScomparison showed levels that were 3.5 ± 1.2 dB higher in theupper frequency band. When this frequency band correction isapplied to the upper frequency band PAS waveform here, theresult is the PAS EL shown by the yellow square. The CI isestimated as the sum of two independent distributions.The black line in Fig. 6(a) is the theoretical trend of the

CAS EL as a function of bandwidth, with the lowest bandwidthsubpulse used as an arbitrary reference point. The interceptionof the trend line and the red-brown PAS EL is coincidental. Theblue points in Fig. 6(a) have some discrepancy from the expectedtrend and indicate that the measured environment is not ideal(i.e., not a perfect reflection without propagation effects) andincludes multipath arrivals.




Fig. 4. (a) Target EL for upper and lower bands PAS in red-brown points and blue crosses, respectively. (b) Target EL for upper and lower bands PAS after PMFIin red-brown points and blue crosses, respectively.

Fig. 5. (a) Zoom-in image of Fig. 3 showing matched-filter output for a single ping of PAS, 800-Hz CAS, and 25-Hz CAS in red-brown, blue, and yellow,respectively. The black arrows indicate the location of the strongest three resolved arrivals. The gray arrows indicate two weaker arrivals. (b) Matched-filter outputafter PMFI up to the resolution of the 25-Hz CAS resolution.

Fig. 6(b) shows the mean EL after PMFI to compare the trendwith equal number of multipath arrivals per cell. The expectedtrend, which no longer requires an ideal environment and target,is 3 dB per doubling of the subpulse bandwidth and thereforethe duration. Fig. 6(b) shows that the EL after PMFI scales as2.6 ± 0.2 dB per doubling, as calculated by a least squaresfit in log–log space and indicated by the dashed blue fit line.This result shows that the majority of the trend in non-PMFI ELobserved in Fig. 6(a) is a result of ESL. Possible reasons for theremaining 0.4 ± 0.2 dB discrepancy in slope include channelcoherence loss (as higher bandwidth results in higher durationfor LFM waveforms), increased Doppler sensitivity of higherbandwidth subpulses, and/or the nonzero expectation value ofthe interaction between multipath of the unresolved arrivals (seeSection IV-A).

When the frequency-band correction is applied to the upperfrequency band PAS waveform, the result is the PMFI PAS ELshown by the yellow square in Fig. 6(b).

B. Reverberation Levels (RLs)

1) PAS in Upper and Lower Bands: The RL at the outputof the MF will now be considered similar to the EL analysispresented in Section V-A. Recall that the RL is estimated froma 0.17-s window on either side of the target echo using a medianfilter that was corrected to obtain an unbiased estimate.Fig. 7(a) shows the RL at the target as measured by up-

per and lower band PAS waveforms. The mean difference(upper−lower) in RL is −2.1 ± 0.2 dB. Fig. 7(b) shows theRL at the target after PMFI as measured by upper and lower




Fig. 6. (a) Mean received level for CAS and PAS echoes in blue points and red-brown diamonds, respectively. The yellow square shows the PAS EL correctedby the difference in EL between frequency bands in the PAS-PAS run. The black line shows the expected trend for a perfect reflection without propagation effects.(b) Mean received level after PMFI for CAS and PAS echoes in blue points and red-brown diamond, respectively. The yellow square shows the PAS PMFI ELcorrected by the difference in PMFI EL between frequency bands in the PAS–PAS run. The black line shows the expected trend and the dashed blue line shows afit to the measured trend.

Fig. 7. (a) RL at target echo for upper and lower band PAS waveforms in red-brown points and blue crosses, respectively. (b) RL at target echo for upper andlower band PAS waveforms after PMFI in red-brown points and blue crosses, respectively.

band PAS waveforms. PMFI increases the RL, as described inSection IV-B. The mean difference in RL after PMFI is −2.4±0.2 dB. These differences in RL will be used to compare CASwith PAS, as was done for EL.2) CAS Versus PAS: Fig. 8(a) shows the mean RL of the PAS

and CAS echoes as a function of bandwidth in the red-browndiamond and blue points, respectively. The RL is approximatelyindependent of CAS subpulse bandwidth and agrees with theexpected trend shown by the black line. The higher RL at 25 Hzmay be due to the signal level having a larger impact on thereverberation estimate when fewer independent samples areused.

Recall that the PAS–PAS comparison showed that the meanRL was 2.1 ± 0.2 dB lower in the upper frequency band. Whenthis correction is applied to the upper frequency band PASwave-form here, the result is the PAS RL shown by the yellow square.Fig. 8(b) shows themeanRL of the PAS andCAS echoes after

PMFI as a function of bandwidth in the red-brown diamond andblue points, respectively. The error bars are given by the 95%CI.The RL after PMFI trend as a function of subpulse bandwidthagrees with the expected 3 dB per doubling (see Section IV-B)as shown by the black line. When the frequency band correctionis applied to the upper frequency band PASwaveform, the resultis shown by the yellow square.




Fig. 8. (a) Mean RL for CAS and PAS at target echo in blue points and red-brown diamonds, respectively. The yellow square shows the PAS RL corrected by thedifference in RL between frequency bands in the PAS–PAS run. The black line shows the expected trend. (b) Mean RL after PMFI for CAS and PAS at target echoin blue points and red-brown diamonds, respectively. The yellow square shows the PAS RL after PMFI corrected by the difference in PMFI RL between frequencybands in the PAS–PAS run. The black line shows the expected trend which agrees with the measured data.

Fig. 9. (a) Mean SRR for CAS and PAS in blue points and red-brown diamonds, respectively. The yellow square shows the PAS SRR corrected by the differencein SRR between frequency bands in the PAS–PAS run. (b) Mean SRR after PMFI for CAS and PAS in blue points and red-brown diamonds, respectively. Theyellow square shows the PAS SRR after PMFI corrected by the difference in PMFI SRR between frequency bands in the PAS–PAS run. The black line shows theexpected trend that agrees with the measured data.

C. Signal-to-Reverberation Ratio (SRR)

Sections V-A and V-B discussed the measured EL and RL.The ratio of EL to RL, SRR, is of particular importance fortarget detection and will be investigated in the following.1) PAS in Upper and Lower Bands: The mean difference in

SRR between upper and lower bands was calculated to be 5.6±1.2 dB by subtracting the mean difference in RL from the meandifference in EL. Similarly, the mean difference in SRR afterPMFI is 5.4 ± 1.2 dB.2) CAS Versus PAS: The blue points in Fig. 9(a) show the

mean SRR for the CAS echoes as a function of subpulse band-width. The red-brown diamond is the mean SRR of the PAS

echoes. The error bars are given by the 95% CI. Recall that thePAS–PAS comparison showedSRR thatwas 5.6± 1.2 dBhigherin the upper frequency band. When this correction is applied tothe upper frequency band PAS waveform here, the result is thePAS SRR shown by the yellow square. The corrected PAS SRRis 3.0 ± 2.1 dB greater than the full-band CAS SRR, wherethe CI is estimated as the difference between two independentdistributions.A black reference line in Fig. 9(a) shows the expected trend

of the SRR as a function of bandwidth. The expected trend wascalculated by subtracting the expected RL from the expected ELdescribed earlier. The measured trend in SRR is similar to theEL trend because RL is approximately constant. The measured




Fig. 10. ROC curve of upper frequency band PAS and lower frequency bandPAS in red-brown and blue curves, respectively. The solid region represents the95% CI and the dashed lines represent the ROC curves after PMFI.

SRR in Fig. 9(a) does not agree with the expected trend forthe same reason as the EL trend. The results in Fig. 9(a) showqualitative agreement with previous work in another shallowenvironment [14].The blue points and red-brown diamond in Fig. 9(b) show the

mean SRR after PMFI as a function of subpulse bandwidth forthe CAS and PAS echoes, respectively. The yellow square showsthe estimated mean SRR after PMFI of the PASwaveform in thelower frequency band, which agrees, within error, to the meanSRR after PMFI measured using the full-band CAS waveform.Similar to the EL trend, discussed earlier, the results in Fig. 9(b)show that the imperfect trend in measured SRR in Fig. 9(a) is aresult of ESL.Note that the SRR has decreased after PMFI. Although this

suggests a decrease in performance, the PMFI is also smooth-ing the reverberation, which changes the detection statistics.Therefore, ROC analysis is required to compare detection per-formance.

D. Receiver Operating Characteristic (ROC)

Detection performance is better characterized by comparingthe probability of detection with the false alarm rate using anROC curve. An ROC curve is calculated by running a detectorwith a series of detector decision thresholds and calculating theprobability of detection and mean false alarm rate per update foreach decision threshold. Probability of detection is calculatedas the ratio of number of contacts on target to the number ofopportunities for each decision threshold. The false-alarms-per-updatemetric was selected because PAS and subpulse CAS havedifferent update rates and it is expected that the data will bepassed through a tracker. For example, there is one update per20-s ping cycle for PAS while the number of updates in the 20-sping cycle varies for the various CAS subpulses.1) PAS in Upper and Lower Bands: The solid lines in Fig. 10

showROCcurves for the twoPASwaveforms transmitted during

Fig. 11. ROC curve of PAS in the upper frequency band and CAS in the lowerfrequency band with varying subpulse bandwidth. The solid region representsthe 95% CI and the dashed lines represent the ROC curves after PMFI.

the PAS–PAS run. The solid region shows the 95%CI calculatedassuming that the probability of detection is a Gaussian distri-bution [18, Sec. 5.3.5]. The greater SRR in the upper frequencyband, as observed in Section V-C, results in clear separability indetection performance at low false alarm rates. At higher falsealarm rates, this conclusion has less support as the upper andlower bands agree within the 95% CI.The dashed lines in Fig. 10 show that PMFI degrades the

detection performance in this case. The CI is not shown. It isimportant to note that the PMFI duration was selected such thata comparison could be made with the shortest bandwidth CASsubpulse. It was not selected to optimize detection performance.The optimal PMFI durationwould bematched to the time spreadand structure of the signal. When the PMFI duration is shorterthan the signal duration, the signal energy is only partiallyintegrated. When the PMFI duration is longer than the signalduration, the signal effectively becomes averaged out due tooversmoothing. The effect of a mismatched PMFI duration is adegradation in detection performance.2) CAS Versus PAS: Fig. 11 shows ROC curves for PAS and

CAS with varying subpulse bandwidths. Despite the greaterSRR for PAS than full-band CAS, the detection performanceof the two waveforms is similar, and they deviate only at lowfalse alarm rates. In fact, full-band CAS is likely outperformingPAS given that the lower band in which CAS operated hadworse performance in the PAS–PAS ROC analysis. However,clutter may also be affected by the degradation in SRR, whichcould explain the improved ROC performance of full-band CASdespite the lower target SRR. The PMFI ROC curves are slightlylower than the non-PMFI curves, which is also observed in thePAS–PAS run, again this is because the PMFI duration was notoptimized for detection performance.Fig. 11 also shows that the single-update detection perfor-

mance reduces as subpulse bandwidth decreases. This is dueto the lower SRR in the subpulses. Despite the lower detection




performance at the contact level, the higher update rate of theshorter subpulses is expected to improve detection performanceat the output of a tracker.

VI. SUMMARY

An experiment was conducted to compare LFM PAS withLFM CAS waveforms. EL is expected to be proportional tosubpulse duration (energy). The measured trend had a lowerslope, and it was shown using PMFI that the lower slope wascaused by ESL. RL is expected to be constant across subpulsesand themeasured values closelymatched the expected trend. Theratio (SRR) therefore had the same trend as the EL. SRR is animportant measure because it is a general indicator for detectionperformance, although the actual performance depends on theping-to-ping fluctuations of the signal as well as the statisticalproperties of the reverberation. The SRR of full-band CAS was3.0 ± 2.1 dB lower than the SRR for PAS, indicating that PASshould outperform CAS for the full band. The difference ispossibly due to coherence loss associated with the longer CASwaveform and/or increased Doppler sensitivity due to the largertime–bandwidth product. However, the ROC analysis showedthat despite the difference in SRR, the two waveforms hadsimilar detection performance. In this article, PMFI was mainlyused to examine ESL, and the PMFI duration chosen for thispurpose slightly degraded performance at the ROC level, whichis expected to occur when the PMFI duration is not matched tothe time spread of the signal. Analysis on the effect of varyingthe PMFI duration was not performed. Further information onthe incoherent integration effects of PMFI can be found in [18,Sec. 8.8.1 and 8.8.2].It was shown that increasing the update rate comes at the

cost of decreasing the SRR, although the cost is less thanexpected because the smaller bandwidths effectively integratemore multipath signal and recover ESL. The lower SRR withthe increased update rates translated to reduced single-updatedetection performance as shown by the ROC analysis. Despitethe lower SRR and detection performance, the increased updaterate may increase tracker performance as long as the SRR doesnot become too low. The LCAS16 experiment was a straighttrack designed to make many measurements of SRR for similarechoes, so tracking analysis was not considered in this article.A topic for future investigation is the comparison of CAS withPAS against a manoeuvering target at the output of a tracker.

ACKNOWLEDGMENT

The authors would like to thank Dr. G. Ferri, the Scientist inCharge of the LCAS16 sea trial.

REFERENCES

[1] P. C. Hines, “Experimental comparison of continuous active and pulsedactive sonars in littoral waters,” in Proc. Int. Conf. Exhib. UnderwaterAcoust., May 2013, pp. 51–58.

[2] A. Munafò, G. Canepa, and K. D. LePage, “Continuous active sonarsfor littoral undersea surveillance,” IEEE J. Ocean. Eng., vol. 44, no. 4,pp. 1198–1212, Oct. 2019.

[3] R. Plate and D. Grimmett, “High duty cycle (HDC) sonar processing inter-val and bandwidth effects for the TREX’13 dataset,” in Proc. IEEE/MTSOCEANS Conf., 2015, pp. 1–10.

[4] D. J. Grimmett, “Target AOU growth containment using LFM highduty cycle sonar,” in Proc. Int. Conf. Exhib. Underwater Acoust., 2014,pp. 839–846.

[5] D. J. Grimmett, J. J. Itschner, D. A. Abraham, and L. Mazutti, “High dutycycle sonar tracking performance as a function of coherent processinginterval for LCAS’15 data,” inProc. Int. Conf. Exhib. Underwater Acoust.,2019, pp. 569–576.

[6] J. R. Bates, G. Canepa, and A. Tesei, “Improved tracking of a surrogatetarget using continuous active sonar,” inProc. Int.Conf. Exhib.UnderwaterAcoust., 2019, pp. 585–592.

[7] J. R. Bates, P. C. Hines, G. Canepa, A. Tesei, G. Ferri, and K. D.LePage, “Doppler estimates for large time-bandwidth products using linearFM active sonar pulses,” in Proc. Int. Conf. Exhib. Underwater Acoust.,2017, pp. 169–176.

[8] P. C. Hines, S. M. Murphy, J. R. Bates, and M. Coffin, “Ambiguityfunctions, wide band and narrowband approximations, and high duty cyclesonars,” inProc. Int. Conf. Exhib. Underwater Acoust., 2017, pp. 161–168.

[9] S. A. Kramer, “Doppler and acceleration tolerances of high-gain,wideband linear FM correlation sonars,” Proc. IEEE, vol. 55, no. 5,pp. 627–636, May 1967.

[10] Z. Lin, “Wideband ambiguity function of broadband signals,” J. Acoust.Soc. Amer., vol. 83, no. 6, pp. 2108–2116, 1988.

[11] D. A. Abraham, D. J. Grimmett, and J. J. Itschner, “Optimizing a slidingm-of-n track initializer in clutter,” in Proc. Int. Conf. Exhib. UnderwaterAcoust., 2019, pp. 577–584.

[12] D. A. Abraham, S. M. Murphy, P. C. Hines, and A. P. Lyons, “Matched-filter loss from time-varying rough-surface reflectionwith a small effectiveensonified area,” IEEE J. Ocean. Eng., vol. 43, no. 2, pp. 506–522,Apr. 2018.

[13] P. C. Hines, S. M. Murphy, D. A. Abraham, and G. B. Deane, “Thedependence of signal coherence on sea-surface roughness for high andlow duty cycle sonars in a shallow-water channel,” IEEE J. Ocean. Eng.,vol. 42, no. 2, pp. 298–318, Apr. 2017.

[14] S. M. Murphy and P. C. Hines, “Sub-band processing of continuous activesonar signals in shallowwater,” in Proc. IEEE/MTSOCEANSConf., 2015,pp. 1–4.

[15] D. E. Weston, “Correlation loss in echo ranging,” J. Acoust. Soc. Amer.,vol. 37, no. 1, pp. 119–124, 1965.

[16] S. M. Garber, “High resolution sonar signals in a multipath environment,”IEEE Trans. Aerosp. Electron. Syst., vol. AES-2, no. 6, pp. 431–440,Nov. 1966.

[17] D. T. Hughes, “Aspects of cardioid processing,” SACLANTUndersea Res.Centre, Spezia, Italy, Tech. Rep. SR-329, 2000.

[18] D. A. Abraham, Underwater Acoustic Signal Processing. New York, NY,USA: Springer, 2019.

[19] J. G. Proakis, Digital Communications. New York, NY, USA: McGraw-Hill, 1983.

Jeffrey R. Bates received the B.A.Sc. degree in engi-neering physics from Queen’s University, Kingston,ON, Canada, in 2006 and the Ph.D. degree in physicsfrom McGill University, Montreal, QC, Canada, in2013.

He is currently a Scientist with the Anti-SubmarineWarfare Group, Defence Research and DevelopmentCanada, Dartmouth, NS, Canada, working in the fieldof active sonar signal processing. Previously, he helda position at the NATOCentre for Maritime ResearchandExperimentation, LaSpezia, Italy, and at theUltra

Electronics Maritime Systems, Dartmouth, NS, Canada.

Stefan M. Murphy received the B.Sc. (honors) degree in physics from AcadiaUniversity,Wolfville,NS,Canada, in 2006 and theM.A.Sc. degree inmechanicalengineering from Dalhousie University, Halifax, NS, Canada, in 2008.He is currently a Scientist with the Sonar andAnti-SubmarineWarfare Group,

Defence Research and Development Canada, Dartmouth, NS, Canada, workingin the field of active sonar signal processing and focusing on experimentation atsea.




Brian H. Maranda (Member, IEEE) received theB.Sc. degree in mathematics and physics and theM.A.Sc. degree in electrical engineering from theUniversity of British Columbia, Vancouver, BC,Canada, in 1979 and 1983, respectively.

In his 35+ year career as a Research Scientist work-ing with Defence Research and Development Canadaand its predecessors, he has concentrated on signalprocessing algorithms in active and passive sonarsystems and on the evaluation of their performance.His main interests lie in the fields of detection andestimation.

Douglas A. Abraham (Senior Member, IEEE) re-ceived the B.S., M.S., and Ph.D. degrees in electricalengineering and the M.S. degree in statistics from theUniversity of Connecticut, Storrs, CT, USA, in 1988,1990, 1993, and 1994, respectively.

He is currently the President of CausaSci LLC,Ellicott City, MD, USA. Previously, he held posi-tions at the Naval Undersea Warfare Center, NewLondon, CT, USA, the NATO SACLANT UnderseaResearch Centre, La Spezia, Italy, the University ofConnecticut, and the Applied Research Laboratory,

Pennsylvania State University, State College, PA, USA, including an intergov-ernmental personnel assignment to the U.S. Office of Naval Research. His workis primarily in the area of statistical signal processing applied to underwateracoustics applications. His current research interests include characterizing andaccounting for clutter in active sonar signal processing algorithms for detection,classification, and localization.


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Signal-to-Reverberation Ratio Comparison of Linear Frequency Modulated Continuous Active Sonar and Pulsed Active Sonar

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Bates, J. R.; Murphy, S. M.; Maranda, B. H.; Abraham, D. A.

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Acoustic Signal Processing, Reverberation, Sonar Detection

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Continuous active sonar (CAS) waveforms provide an advantage over conventional pulsed active sonar (PAS) waveforms, which is, they can be processed to provide a higher target update rate through subpulse processing. Performance in reverberation limited conditions is particularly important in shallow water. This article compares the signal-to-reverberation ratio (SRR), echo level, and reverberation level of simultaneously transmitted linearly frequency modulated (LFM) PAS with an equal bandwidth LFM CAS waveforms processed with different CAS subpulse durations in a littoral environment. Data from an experimental sea trial showed that the LFM PAS waveform outperformed the full-band LFM CAS waveform in terms of SRR by 3.0 ± 2.1 dB. The SRR of the CAS waveform degraded by less than the expected 3 dB per halving of the subpulse bandwidth and duration. Energy spreading loss, which increases with bandwidth, was shown to be the dominant cause of the deviation from expected degradation rate. The detection performance of the full-band LFM CAS waveform was approximately equal to that of the LFM PAS waveform as measured by a receiver operating characteristic analysis.

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