Left-Right R

Jojish Jo

1,2,3Naval 1jojish@gmail.co

Abstract—Towed linedistinguish between tato solve this uses a vointroduces a method wconstrained beam forsolutions and gives bereal time implementati

Index Terms— Lineartime implementation

1. Introduction

Passive linear array systems used equi-spaced line arraysthat are towed behind the shipreceivers. Advantages of linsimplified construction and ehandling. Linear array beamomni-directional sensors asymmetric and cannot disttargets on the left or right (figthe operational use of line aseveral methods have been sthis problem including twinmaneuvers and vector sensopaper we analyze the lefmethods and compare themethod using constrainapproach for solving left-ripresented and the real timresults of this approach are pr

PROCEEDINGS OF S

Resolution Methods in Towed Aroseph V1, SarathGopi2, and D SubhadraBhai3

Physical and Oceanographic Laboratory, Kochi. om,2gopisarath@gmail.com,3subhadrabhaid@gmail.c

ear arrays suffer from the inherent problem of being uargets on the left or right side of the array. Normal appolumetric array or by own platform manoeuvres. Thwhich maximizes the left-right rejection ratio by memer approach. It is compared with different conteetter results in terms of rejection ratios and is well sion.

r arrays, left-right resolution, constrained beamform

have traditionally s of hydrophones p as their acoustic ne arrays include ase of mechanical m formers using are cylindrically tinguish between

gure 1). This limits array sensors and suggested to solve n arrays, platform ors [1,2]. In this ft-right resolution eir efficiency. A ed beamformer ight ambiguity is e implementation

resented.

Figure 1 : Symmetric bea

Appropriate volumetric arhydrophones are able to uniazimuth and elevation angle anleft-right ambiguity. The prototarray under consideration(figurN triplet sets of hydrophoneidentically oriented equilateralsides of length ‘d’ and separate‘L’.

SYMPOL-2013

rays

om

unable to proaches his paper eans of a emporary uited for

ming, real

am pattern

rrangements of iquely measure nd thus resolve type volumetric

re 2) consists of es arranged as l triangles with ed by a distance

Jojish et al.: Left-Right resolution methods in towed arrays

Figure 2 : Triplet Array Configuration (a) Geometry (b) Individual triplet (c)

Planar view

The effectiveness of any left-right resolution scheme is to be measured by the rejection ratio, which is the ratio of beam-former gain for the two complementary directions. Since the performance of the linear array deteriorates as we move towards end-fire directions, the left-right rejection ratio over the entire look angles need to be measured.

In this paper three separate ways of resolving the left-right ambiguity are presented. The first method is a straight forward method of considering the triplet array as a planar array and a two dimensional beam forming being performed. The second method is an optimum cardioid formation using the triplets by assuming a correlation pattern among the triplet elements followed by beam-forming [3]. The third approach is to constrain the response along one direction to a zero while keeping the response in the complementary direction to a fixed value. This is a constrained beam forming approach where a cardioid pattern is generated from the triplet elements by applying a constrained beam former. The resultant cardioid pattern gives good left–right resolution as it forces a null in the complementary direction.

All the three methods are compared for the left-right rejection ratio performance across different bearings and at different signal-to-noise ratio levels. It is shown that the proposed

constrained beam-former gives better rejection ratios over all the bearings at various SNRs.

2. Planar BeamformerApproach

In the planar beam former approach the entire triplet array is considered as a planar array with no difference being ascribed to the elevation angle. The planar structure of the array gives rise to different steering vectors for targets in the left side and right side thus overcoming the ambiguity encountered in uniform linear arrays. A two dimensional beam-forming is done on the planar array and separate beams are formed on the left and right side of the array. Assuming a plane wave model for the source we can compute the steering vector s for a planar array as given by the two-dimensional matrix

curij

ijijes /.= [1]

where r is the position vector of the elements given by the x and y coordinates on the rectangular grid and u is the unit vector along the direction of arrival of the source. Vector s is the two dimensional planar steering vector and the beam output is computed as

xsy H .= [2]

where both s and x are 2 –d vectors.

The left-right rejection ratio is calculated as the ratio of the power output obtained at the beam former output in the correct direction to its complementary direction. This ratio gives an indication of how capable is the processing scheme in rejecting the components from the opposite direction.

Planar array using triplets has the drawback that since the elements are located very close to each other there is significant noise-correlation among the triplet elements there by limiting the discrimination that can be obtained by beam-forming. The conventional beam forming approach is unable to give desired array gain in

PROCEEDINGS OF SYMPOL-2013

the presence of correlated noise and this affects the resolution capability of the planar beam – former method.

The performance of the planar beam former was simulated and the left – right rejection ratio was computed over the various bearings at different SNR levels. The result is given in figure 3.

We have considered a volumetric array of 28 triplets separated by a distance of 0.5λ (λ=wavelength corresponding to the highest frequency of the received signal) to avoid spatial aliasing. The signal frequency is assumed to be 2 KHz and the inter-triplet distance now becomes 0.375m.The distance between the elements in a triplet, d is chosen as 0.04m.The Left-Right Rejection Ratio (LRRR) versus bearing angle is plotted at three different levels of signal-to-noise ratios in figure 3.The figure shows that in positive signal to noise ratio conditions from angles 40 degree to 140 degree the rejection ratio is about 6db average with peak rejection obtained at the broadside and being equal to 8db. The performance of the planar beam former method resolver degrades with signal to noise ratio and at a low signal to noise ratio of -10db the rejection ratio at broadside came down to 4db.

3. Optimum Triplet Beamformer

The optimum–triplet beam former [3] is made use of to improve the signal to noise ratio under higher noise correlation. Optimum just denotes that the triplet gain is maximized. For a given direction and frequency the optimum triplet beam former depends only on the inverse of the triplet noise correlation matrix.

The Capon minimum variance beam former gives the optimum weight to be used in presence of correlated noise sources as

sRssRw H 1

1

−

−

= [3]

where R is the noise correlation matrix. A model for the noise correlation matrix is formulated in [4]. This model includes both uncorrelated noise arising out of flow noise and correlated noise due to platform noise, sea noise etc. The noise correlation matrix R is decomposed as

ccunn RIR 222 σσσ += [4]

where σ2u is the uncorrelated σ2

c is the correlated and σ2

n is the total noise variance.

σ2 = σ2u /σ2

c is their ratio.

The complex matrix Rn has the form

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

11

1

ρρρρρρ

nR [5]

For sea noise, the correlation coefficient ρ is modeled as

21)3(sin

σρ

+=

krc [6]

where )3(sin krc , is the spatial noise correlation for omni-directional noise received

Figure 3: LRRR vs Angle for planar beamformer

0 20 40 60 80 100 120 140 160 1800

1

2

3

4

5

6

7

8

9

Angle in degrees

L R R R

SNR=10dBSNR=0dBSNR=-10dB

Jojish et al.: Left-Right resolution methods in towed arrays

on the hydrophones which are placed at a distance of 3r [5][6] . This model for noise correlation has been verified on real sea noise data in [7]. The model depends on only one parameter namely σ which is the ratio of flow noise and sea noise. This depends on the tow speed and sea-state. For simulation purposes this ratio is taken as 0.1 which is reasonable under normal sea-conditions and low tow speeds.

The weight vectors for forming the resolved beams from the triplet elements are computed from the noise correlation model. The triplet gain maximization is done for different directions on the beams formed using the individual arrays. So the processing takes place in two steps. In step one the three line arrays which make the triplet array are subject to conventional frequency domain beam-forming.

This results in three beams for each look direction which are still having the left – right ambiguity. The triplet formation and individual beams to the left and right are obtained by combing these beams with the weights obtained from the assumed noise correlation model.

The same array configurations were used to simulate the performance of the optimum triplet beam former. The Left-Right Rejection Ratio was estimated for different look directions and at different signal to noise ratios. The Left-Right Rejection Ratio (LRRR) versus bearing angle is plotted at three different values of SNR’s. The LRRR is having a peak value of 22dB at broadside (SNR=10dB), and drops sharply as we move towards end fire directions. The optimum triplet method gives much better results than the planar beam former by virtue of its property of being able to de-correlate the noise and getting the desired beam former gain. At positive signal to noise ratio conditions the optimum triplet beam former gives a rejection ratio of over 12db in the range of angles from 40degree to140degrees but the performance falls to zero level as we move to end fire directions. Even at lower signal to noise ratios

the rejection ratio is maintained at 6db which is higher than what we obtained from planar beam former based implementation.

4. Constrained Beamformer

Both the planar beam former method and the optimum beam former method aims to maximise the triplet gain to the desired direction. But if Left-Right Rejection Ratio is the desired criterion maximising LRRR would be best achieved by forming a null in the complementary direction. While this might reduce the gain from the desired direction as compared to the other methods, it has the advantage of nulling any signal from the undesired direction and thus achieving maximum rejection ratio. The constrained beam-former is an approach to maximise the rejection ratio by placing a null in the complementary direction.

Constrained beam formers ensure signal preservation at the location of interest while minimizing the variance effects of signals originating from other locations. Here we introduce a simple constrained approach to resolve the left – right ambiguity.

Suppose the signal of interest comes from

0 20 40 60 80 100 120 140 160 1800

5

10

15

20

25

Angle in degrees

L-R

Rej

ectio

n R

atio

in d

B

LRRR versus Bearing Angle

SNR= 10dB

SNR= 0dB

SNR= -15dB

Figure 4: LRRR vs Angle for Optimum triplet beam former

PROCEEDINGS OF SYMPOL-2013

any angle ‘θ’ then constrained beamformer can be formulated as follows:

1=ws Hθ [7]

0360 =− ws Hθ [8]

In matrix form this can be written as

Aw=b [9]

where A is a M×2 matrix given by

⎥⎦

⎤⎢⎣

⎡=

−H

H

ss

Aθ

θ

360

,

w is the 1×M weight matrix given by

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

Mw

ww

w..

2

1

b is the 12 × matrix given by ⎥⎦

⎤⎢⎣

⎡=

01

b

and M is the number of sensors in the array.

By Linear Least Squares Method, equation (9) can be solved as [8]

bAAAw HH 1)( −= [10]

We have done the performance analysis of the constrained beam former with the same parameters as was tried out for the previous two approaches. The LRRR versus bearing angle is plotted for different values of SNR.

Figure 3 : LRRR for constrained

beamformer

From the figure we see that for the constrained beam former method the left-right rejection ratio is steady for a wider cross section of look directions. The highest value of the rejection ratio is obtained at about 21db for broad side direction and the ratio is above 10db in the range of angles from 20 degree to 160 degree. Even at low signal to noise ratios the rejection ratio is held consistently over a much wider range of angles by the constrained beam former method.

5. Real time implementation

The constrained beam former was implemented on an ADSPTS-201 based signal processing board. The ADSP-TS201 [8] is a 128-bit, high performance digital signal processor.

The data coming from the sensor array has to be accumulated and stored in a ping pong buffer. The constrained weight vectors were stored in the internal memory of the processor. In applications were the size of the array and number of beams are very large these weight vectors can be stored in memory module which is located outside the processor and can be accessed over the processor bus. The incoming

0 20 40 60 80 100 120 140 160 180-5

0

5

10

15

20

25

Angle in degreesL-

R R

ejec

tion

Rat

io in

dB

LRRR versus Bearing Angle

SNR=0dBSNR= -15dBSNR=10dB

Jojish et al.: Left-Right resolution methods in towed arrays

triplet sensor data is first transformed into the frequency domain and ordered as the input vectors. The weight vectors are applied on these weight vectors to generate the output vectors. The magnitude of the output vectors are computed and exponentially integrated before being sent to the display processor. The integration also adds to the signal to noise ratio of the processor. The block diagram of the real time implementation scheme is shown below. The constrained beam former was implemented on the TigerSHARCDSP platform (TS-201) from Analog Devices. The code development was done on the Visual DSP++ environment and the system was simulated and verified using recorded data sets in the development environment.

A snapshot of the beam power output for a static target case when the target is at sixty degrees is shown in figure 5. In this case we have formed one hundred and twenty eight beams spanning 360˚ and the target is clearly marked at only one angle thus resolving the left-right ambiguity problem.

Figure 5 : Beam output of the DSP output in

a real time implementation

6. Conclusion

The problem of resolving the left right ambiguity while using a linear array is being addressed in this paper. The normal approach is to use a triplet based array and use signal processing method to maximize gain in the desired direction. The two well known methods of planar beam former approach and a later optimum triplet beam former approach are simulated and their performance with respect to the left – right rejection ratio at different target angles and different signal-to-noise ratios are obtained. A new scheme of left-right resolution which steers nulls to the mirror direction by means of constrained beam forming is proposed and its performance evaluation is done. It is seen to offer better left-right rejection ratios over a wider range of target angles than the planar beam former approach and the optimum triplet approach. This method was also implemented in real time using ADSP-TS201 signal processor based DSP board and worked well in experiments with recorded data from triplet arrays.

ACKNOWLEDGMENTS Authors are immensely grateful to Shri.

S. Ananthanaranyanan, Sc ‘H’, Director, NPOL Dr. A. Unnikrishnan, Sc ‘H’ and Shri. S. K. Shenoi, Sc ‘G’ for their support and encouragement.

Figure 4 : Block Diagram of

real time implementation

Channel wise FFT

Input vector creation

Constrained Beam former

Weight vector generation

Beam Power Output

Sensor Data

DSP

TS-

PROCEEDINGS OF SYMPOL-2013

References

[1] J.P. Feuillet, W.S. Allensworth, and B.K. Newhall, “ Nonambiguous beamforming for a high resolution twin line array,” J. Acoust. Soc. America, vol 97, no.5, p. 3292, may 1995

[2] T. Warhonowicz, H. Schmidt-Schierhorn, and H. Höstermann, “Port/Starboard discrimination performance by a twin line arrayfor a LFAS sonar system,” in Proc. Underwater Defense Technology(UDT), Europe, 1999, p. 398.

[3] Groen. J, Beerens.S.P, Doisy,Y, “Adaptive port_starboard beamforming of triplet sonar arrays”, IEEE Journal Of Oceanic Engineering,vol.30, no.2, April 2005. [4] G. W. M. van Mierlo, S. P. Beerens, R. Been, Y. Doisy, and E. Trouvé, Port-

Starboard discrimination on hydrophone triplets in active and passive towed arrays,” in Proc. Underwater Defence Technology(UDT), Hamburg, Germany, 1997, pp 176-181. [5] S.P.Beerens, S.P. van IJsselmuide, C. Volwerk, E.Trouve, and Y.Doisy, “Flow noise analysis of towed arrays,” Proc. Underwater Defense Technology(UDT), Europe, 1999, pp.392-396. [6] J. N. Maksym and M. S. Sandys-Wunsch, “ Adaptive beamforming against reverberation for a three sensor array,” Journal of Acoustic Society of America, vol. 102, no.6, pp.3433-3438, Dec.1997 [7] Harry L Vantrees, Optimum Array Processing. Wiley [8] ADSP-TS201- Product Manual, http://www.analog.com/en/processors-dsp/tigersharc/adsp-ts201s/products/product.html