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Broadband, Ultra-sparse Array Processing

for Low Complexity Multibeam Sonar

Imaging

Jeffrey A. Neasham, Raghav Menon and Oliver R. Hinton

Abstract Despite the rapidly reducing cost of DSPtechnology and other digital electronics, the cost of multibeamsonar systems remains very high. This is largely due to largereceiving arrays (typically 100-200 channels) each withtransducer, amplifier/filters and ADC. The powerconsumption of such complex systems is also a problem forbattery operated systems such as AUVs. This paper describesnovel work to investigate if such imaging can be achievedwith an "ultra-sparse array" of no more than 4 elements,exploiting the broad bandwidth provided by modern piezo-composite transducers which can far exceed range resolutionrequirements.

Index Terms- sonar, beamforming, phased array, broadband.

I. INTRODUCTION

M/[ultibeam sonar is widely used in applications where thescanning rate of a mechanically scanned system is

unacceptably slow. Examples of this are profiling/bathymetryand obstacle avoidance systems, particularly when deployedon a rapidly moving platform [1]. Such multibeam systemscan achieve high resolution imaging at several frames persecond, by insonifying a broad swath and then using electronicbeamforming to resolve the angular distribution ofbackscatter. However this comes at the cost of considerablehardware complexity [2]. A modem multibeam system maycomprise an array of 100-200 channels each requiring ahydrophone, amplifier, filter and analog-to-digital converter(ADC). Furthermore the digital beamforming calculation for

Manuscript received March 30, 2007. This work was supported in part byTritech International Ltd who supplied composite transducers for theexperimental system.

Jeffrey A. Neasham is a Senior Research Associate at the University ofNewcastle upon Tyne, School of Electrical, Electronic and ComputerEngineering, Merz Court, Newcastle upon Tyne, NE17RU, UK (phone: +44191 2228850; email: j.a.neasham0ncl.ac.uk).

Raghav Menon is a PhD student at the University ofNewcastle upon Tyne,School of Electrical, Electronic and Computer Engineering, Merz Court,Newcastle upon Tyne, NE17RU, UK (email: raghav.menon 0ncl.ac.uk).

Oliver Hinton is Professor of Signal Processing at the University ofNewcastle upon Tyne, School of Electrical, Electronic and ComputerEngineering, Merz Court, Newcastle upon Tyne, NE17RU, UK (email:oliver.hinton oncl.ac.uk).

such an array results in a large computational load which mustbe met by powerful, often parallel, DSP structures. Althoughthe cost per MIP of digital processors is rapidly falling, theconstruction of the many analog channels remains very costlyand hence the capabilities of multibeam systems are out ofreach for many applications such as fisheries, archeology andlow cost surveying platforms [4].Another significant issue with current multibeam technologyis the high power consumption of such complex electronicsystems, often exceeding 1OOW. This can be a problem fordeployment on AUV systems with limited battery energy.Interferometry techniques have been widely used in sonar forbathymetry and profiling applications, where the imaging issubject to strict geometric constraints. The purpose of thispaper is to investigate the possibility of using novel broadbandinterferometric techniques, as a means of achieving multibeamimaging with a low cost, ultra-sparse sonar array.

II. THEORY

A. Interferometry PrinciplesIn an interferometric sonar system, the backscattered signalsare divided into corresponding range cells and the direction ofarrival of the signal is estimated for each range cell. This isachieved by measuring phase shift, in the case of narrow bandsignals, or time delay, in the case of broader band signals,between two or more receiving transducers, often spaced bymultiple wavelengths. This approach is straightforward forbathymetry applications where we assume that only onereflection arrives in each range cell. However for moregeneral imaging, difficulty occurs when multiple signals arrivefrom different angles in the same range cell and very limitedwork has been published on the solution to this problem. Themain theory behind this work is that if one transmits a signal,with bandwidth many times greater than the reciprocal of therequired time (range) resolution, then most practical targetswill produce a "complex" echo, whose autocorrelation has adistinguishable peak and whose cross-correlation with othertargets is reduced. This being the case, it is possible to deducethe existence of multiple, angularly separated targets from thecross-correlation of portions of the signal received on twochannels.

1-4244-0635-8/07/$20.00 ©2007 IEEE

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B. Transmitter/Receiver Array GeometryThe array geometry of the sonar system is illustrated by the 2element linear array which is shown in Figure 1, which is usedfor the determination of the angle of arrival of backscatteredsignal(s). Both transmitting and receiving elements areassumed to have a broad "fan beam" directivity pattern so asto cover a broad swath in one plane, and a narrow angularrange in the orthogonal plane.

signal in order to establish the similarity between the signals[4] [5]. It involves successive shifting of two signals and thenfinding the comparison of the signals for each shift. Considertwo signals x1(t) and x2(t) being correlated. The correlation isgiven as:

limR(r) =

T -< oo "

T

0X (OX2 (t0

(5)

Tx/Rxl4 > Rx2

Target

Figure 1: Array Geometry

In the above figure Tx (transmitter) and Rxl are coincidentand Rx2 is the second receiver. Also:d the distance of separation between the two receivers.6x the extra distance traveled by the backscattered signal tothe receiver Rx2.O = the angle of arrival which has to be calculated.

From figure 1:

6x c.6t (1)c. n. T (2)

Where c is the speed of sound in water which is taken to be1500m/s, n is the difference in samples between the signalsreceived by Rxl and Rx2 and T is the sampling rate.In the right angled triangle above:

sin(O)= 6x/d= c.n.T/d (3)

Hence

0= sin-'(c.n.T/d) (4)

by determining the angle of arrival and the range at which theobject is located it is possible to obtain an image of the target.The method used in order to obtain the angle of arrival and therange is briefly described in the following paragraphs.

C. Correlation Methodfor Determining Time DelayCorrelation can be in general be defined as a mathematicalprocess of comparison of one signal with another or more

which can be given as:

00

R(l) = Ex (n)X2 (n -1) (6)_00

In the above equation the value of 'I' gives the amount of lagor lead in the signal. Graphically when the absolute value ofthe correlation of the two signals is plotted, the correlationcoefficient peaks whenever the two signals are similar and thepeak occurs at the center when there is no delay. In case of alead or a lag the peak moves accordingly. This is shown in thefigure 3 as follows:

to=Figure 2: Correlation of signals

This property of the shifting of the peaks can be used todetermine the relative lag of the signal arriving at tworeceivers.

D. Formation ofImageIn the previous section the mathematical meaning ofcorrelation and how it can be applied in order to determine thelead or lag of two signals was explained. In this section, theformation of image using the information from the correlationof two signals is discussed. A chirp signal, sweeping between200-400kHz over a period of 5ms was used as the transmittedsignal for the purpose of simulation. This bandwidth waschosen as the maximum achievable using modempiezocomposite transducers. The first stage of processing inthe receiver is to matched filter for this chirp waveform, thusachieving high signal-to-noise ratio. The received signal afterundergoing various losses is received at the receiver elements.The received signal is divided into range cells of y (in m). The

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number of samples of the received signal that represent theabove range cell can be given by

n=y*Flc 7

algorithm. A simulation result is shown below, with figure4(a) showing the simulated target geometry and the figure 5brepresenting the image resulting from the methods describedabove.

Where

n - is the number of samples representing the range cell of xm.F- is the sampling frequency in Hz.c - is the speed of sound (1500 m/s).

-20

-40

-60

In order to form he image the signals received are correlated.Now ifthe distance between the receiver elements is d then weknow that the maximum lag a signal can have with respect tothe other signal would be proportional to the array spacing.From the knowledge of the beam angle it is possible to findthe maximum number of samples that represent a lag or leadcorresponding to that beam angle. This can be explainedbriefly with the help of figure 3.

Rxl

0

d Rx2250 300 350 400 450 500 550

Figure 4(a): Position of Target plotted from Original data

0

Figure 3: Beam angle and Receivers

It is possible to say that the signals received by the receiversarrive at an angle which is less than or equal to the beam angle'0'. Since the distance between the receiver elements is small,compared to the range (far field) the error in the angle ofarrival is very small. The angle of arrival of the signal can becalculated by the process explained in section B, knowing thenumber of samples and hence the distance 'ax'.

After finding the angle of arrival then it is required todetermine the rectangular coordinates (i.e. the x-y coordinates)from the usual trigonometric formulas. Since the entire signalis divided into range cells the range at which the target islocated can also be determined.

Simulation results were generated using a distance betweenreceiver elements of 0.3 m. The range cell used was 0.75m.Realistic targets were simulated by using a randomdistribution (cluster) of ideal point targets ofrandomly varyingsize. The first scenario considered was that of only a singletarget to verify correct operation of the correlation processing

Figure 4(b): Image produced by correlation algorithm

The above figure verifies that a single target occurring in a

range cell is clearly resolved by broadband correlationmethods. This principle has been demonstrated in the past forswath bathymetry applications, where a single direction ofarrival has been estimated for each range cell, as in [6].However the situation becomes much more complicated whenwe simulate multiple, angularly separated targets occurring inthe same range cell.

-80

-100

-120

-140

-160

-180

-200200-m l-

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The above procedure was repeated, this time distributing thetargets in order to form a sinusoidal bottom profile at a meanrange of 150m and the image obtained by a simple 2 element,correlation processing is shown in figure 5 below.

Step 3. Afterfinding the threshold choose the values which areabove the threshold and determine the RMS value of theresulting values.

Step 5. In case of 'n' receiver elements it is possible to get' n-1' images. Hence repeat the Step 3for each ofthese images.

Step 4. Add the average ofthe values obtained in Step 5 to thethreshold in order to get the new valuefor the threshold

Step 6. Now using the condition that if each of the values inthe 'n- ' images is greater than or equal to the new thresholdvalue, the value is chosen otherwise it is taken as '0'.

Step 7. Using the image formation algorithm determine theimage.

The above processing algorithm was applied to the sinusoidalprofile that is shown in the figure 5 and the result afterapplying the algorithm is shown in figure 6 below

Figure 5: Image of a Sinusoidal bottom profile generatedby simple correlation processing of 2 element Rx Array

The above case now leads to multiple target returns withinindividual range cells. Since the cross-correlation betweenthese targets is unlikely to be negligible (this is only possiblefor mathematically formulated orthogonal waveforms), a largenumber of "correlation artifacts" or clutter appear on theimage leading to very poor discrimination of the true targetscene. More advanced processing is required to reduce thisclutter to an acceptable level, as described in the followingsection.

E. Multi-look Processing AlgorithmIn order to reduce the level of clutter caused by unwantedcross-correlation between targets, a "multi-look" approachwas adopted using 4 array elements with the same spacing asbefore. From these 4 elements, we can actually create 3 sub-arrays of two elements and combine the correlation results ofeach. Since the elements are spaced by several wavelengthsand a very broad bandwidth is used, we find that there is verygood diversity between the sub-arrays and in fact thecorrelation artifacts are poorly correlated in each. Rather thansimply use a linear combination of the sub-array outputs,maximum gain in image quality is achieved by using a non-linear approach as described below:

Step]. Before the image formation the correlation results(after dividing the signals received into range cells and thencorrelating) into are taken in an array.

Figure 6: "Multi-look" correlation processing on a 4element Rx array

Thus we find that the unwanted clutter has been vastlyreduced and the simulated target scene is clearly visible. Thesimulation was repeated for the targets distributed along astraight line bottom profile at 140m range, using the samesignal parameters. Figures 7 and 8 show the result of a simple2-element, correlation process and the 4 element, multi-lookprocessing algorithm respectively. In figure 7 we can see thatwhere the target surface is parallel to the array, a large numberof targets occur in the same range cell leading to clutterspreading over the entire angular range. Whereas in figure 8we see how the multi-look processing is able to clearlydiscriminate the desired targets.

Step2. For each range cell find the threshold by determiningthe average.

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beamforming on the 4 element array. As expected, due to thelarge spacing of the array (many wavelengths) the level ofgrating lobes (spatial aliasing) results in very little angulardiscrimination, almost completely obscuring the image. Aswith the above simulation results, the correlation processingon a 2 element array was also found to produce anunacceptable level of correlation artifacts.

However the 4 element array produces a vastly improvedimage with the target returns in broad agreement with theexpected picture, as shown in figure 9(d). Especially pleasingis the ability to clearly discriminate the stem of the twomoored boats in the distance, from the adjacent dock wall.This result was found to be repeatable over many successivepings. The array was also rotated to vary the angle ofincidence of the various targets with consistent results.

Figure 7: Image of a Straight line profile generated bysimple correlation processing of 2 element Rx Array

Figure 9(a): Target scene for forward looking sonar

Figure 8: "Multi-look" correlation processing for aStraight line profile on a 4 element Rx array

III. EXPERIMENTAL RESULTS

Following encouraging simulation results, an experimentalsonar system was constructed for validation of these ideas inthe field. Due to limited budget, some available piezo-composite transducers, which did not have the idealcharacteristics, were assembled into a 4 element receivingarray and a 5th element was used as an illuminator. Theseelements had a useable band of 325-425 kHz and a beam-width of 30 in one plane and 200 in the other. The sonar wasconfigured as a forward looking system for experiments in theshallow water of a local estuary. The transmitted signal was a325-425kHz chirp over a period of 5ms with an approximateSPL of 190dB re luPa g Im. Received signals were capturedat 1MHz sampling rate for offline processing on a PC. Figure9(b) shows the approximate target geometry with a 200 swathilluminated. Figure 9(c) shows the result of conventional

Figure 9(b): Target geometry showingIlluminated area

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REFERENCES

[1] Rodney F.W Coates, Underwater Acoustic Systems,Macmillan.

[2] Roger F. Dwyer, 'Advances in sonar signal processing inthe 90's', OCEANS '96. MTS/IEEE. 'Prospects for the 21stCentury'. Conference Proceedings, Vol. 1, 23-26 Sept.1996, pp.364 - 372

[3] Gary D. Melvin, Norman A. Cochrane, and Yanchao Li,'Extraction and comparison of acoustic backscatter from acalibrated multi- and single-beam sonar', ICES Journal ofMarine Science Volume 60, Issue 3 , June 2003, pp. 669-677.

Figure 9(c): Image obtained from conventional [4] Sanjit K Mitra, Digital Signal Processing A Computerbeamforming on 4 element array Based Approach, Second Edition, Tata Macgraw Hill.

[5] Davies H and McNeill D J, Digital Signal Processing InAcoustics Part 2, Phvs. Educ, 21, 1986.

[6] Lawlor, M.A.; Adams, A.E.; Hinton, O.R.; Riyait, V.S.;Sharif, B.S, Further results from the SAMI syntheticaperture sonar, Proceedings of Oceans '96, MTS/IEEE,Volume 2, 23-26 Sept. 1996 Page(s):545 - 550 vol.2

Figure 9(d): Image from 4 element array

IV. CONCLUSION

Both simulation results and experimental results support theview that, with a different approach to signal processing, aneffective multibeam sonar can be constructed from as few as 4elements spaced by many wavelengths. This is only possiblewith a very high bandwidth system, ideally as much as oneoctave, so modern piezo-composite devices are required. Astheory would suggest, traditional beamforming approaches onsuch a sparse array are virtually useless due to spatial aliasingbut non-linear and statistical techniques applied to this arraycan be very effective. The computational load of suchalgorithms is substantial, but compared to a full multibeamarray, this approach may offer very significant savings inoverall system cost and power consumption. Further workplanned by the authors, will investigate other statisticalprocessing algorithms, wider experimental testing with idealtransducers, scalability for other frequency bands and a realtime implementation on FPGA/DSP hardware

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