Subarray adaptive beamforming for reducing the impact of flow noise on sonar performance

Transcription

1 Subarray adaptve beamformng for reducng the mpact of flow nose on sonar performance C. Bao 1, J. Leader and J. Pan 1 Defence Scence & Technology Organzaton, Rockngham, WA 6958, Australa School of Mechancal Engneerng, the Unversty of Western Australa, Crawley, WA 6009, Australa Abstract-The performance of a hull-mounted sonar array s adversely affected by the presence of own-shp self noses such as propeller nose, machnery nose and flow nose. Among those self noses, the effect of flow nose can be very dffcult to combat due to ts near-feld and non-statonary nature. In ths paper, we nvestgate the effectveness of usng two stage subarray adaptve beamformng for reducng the mpact of flow nose. Two subarray adaptve beamformng schemes are consdered. These are adaptve-conventonal and adaptve-adaptve beamformng. The performances of these two schemes are evaluated aganst the performance of a full array adaptve beamformer whch provdes a benchmark n terms of the array gan. In the study, we model the flow nose as a stream of movng quadrupoles. The nvestgaton shows that subarray beamformng s able to acheve hgher array gans than a full array adaptve beamformer. The reasons for ths are analysed. It s found that the tme requred for full array adaptve beamformng to converge s too long n a fast tme-varyng envronment. I. INTRODUCTION The performance of a hull-mounted sonar array s adversely affected by the presence of own-shp self nose such as propeller nose, machnery nose and flow nose. Recent advances n shp slencng technology have greatly reduced propeller and machnery nose. As a consequence, the effect of flow nose on a sonar system has become more promnent. In general, advanced array processng technques such as adaptve beamformng are able to reduce the effect of ownshp self nose to some extent. However, the effect of flow nose on the sonar array wth a large number of elements s very dffcult to reduce by tradtonal adaptve beamformng technques. Ths s because adaptve processng needs a certan length of tme to estmate the characterstcs of sgnals and nose. For adaptve processng usng rapd convergence technques such as the sample-matrx-nverson (SMI) approach, ths tme depends on the number of elements of the array. The more elements, the more tme samples are needed to reach a stable estmate of the sample-matrx. On the other hand, the fast tme-varyng or non-statonary nature of flow nose means that wthn the length of tme requred for a stable sample-matrx the characterstcs of the nose has changed. Thus, the estmate s naccurate and the adaptve array processng becomes less effectve. One way to rectfy ths problem s to use the subarray beamformng technque. Subarray beamformng was ntally developed for reducng the computatonal complexty assocated wth adaptve processng [1, ]. Lately, t has been used for dealng wth non-statonary sgnals or noses n sonar applcatons. Lee and others have presented subarray beamspace adaptve beamformng for a dynamc long towed array [3]. Ther obectve s to recover the sgnal loss caused by tradtonal adaptve processng when the array undergoes sgnfcant manoeuvrng. The algorthm s however not ntended for reducng the effect of flow nose. Cox and La have employed sub-aperture beam-based adaptve beamformng for large dynamc arrays [4]. In ther approach, non-adaptve conventonal beams were formed n the frst stage, and then based on these conventonal beams adaptve beams were formed n the second stage. Ths s a conventonal-adaptve beamformer. They dd not explore other schemes such as adaptve-adaptve or adaptveconventonal beamformng. Musha and Kkuch have used subarray adaptve beamformng for reducng flow nose [5]. They proposed an adaptve-conventonal beamformer and compared ther result only to that of a full array non-adaptve conventonal beamformer. In our earler study [6], we have nvestgated the effectveness of usng subarray adaptve beamformng for suppressng near-feld nose from movng monopoles. All three possble schemes,.e., conventonal-adaptve, adaptveconventonal and adaptve-adaptve beamformng, have been explored. Ther performances have not only been compared aganst that of a full array non-adaptve conventonal beamformer but also a full array adaptve beamformer. The nvestgaton has shown that the adaptve-conventonal and adaptve-adaptve schemes are able to acheve consderably hgher array gans than a full array adaptve beamformer. The use of conventonal-adaptve beamformng, on the other hand, s not benefcal when varous veloctes of movng monopoles are consdered. Ths work s an extenson of our earler study. We examne the suppresson of nose from movng quadrupoles, whch s a more realstc model of flow nose. Only the adaptveconventonal and adaptve-adaptve schemes are consdered, as the conventonal-adaptve scheme has been proven to be neffectve [6]. II. FLOW NOISE MODEL The modern theory of aerodynamcally nduced nose s founded on Lghthll s 195 and 1954 papers [7] whch ntroduced an acoustc analogy whereby the shearng of flud n turbulence can be represented by a stream of acoustc pont

2 sources n each average eddy volume, thus lnkng the energy to the propagaton of longtudnal dsplacements (sound waves). These eddes are well correlated blobs of flud n moton wth a random phase compared to other eddes - persstent vortces caused for example by separaton of the flud passng over a bluff body. In fact, the analogy that Lghthll gves for sound generated by pure shearng of an solated flud s exact. Conservaton of mass and momentum wthn the flud yeld the followng two equatons, ρ + ρu t x = 0 (1) ρ u + ( ρuu + p ) = 0 () t x vortces passng over the array as shown n Fgure 1, s employed n ths study. III. CONFIGURATION OF SUBARRAY BEAMFORMING A. Subarray beamformng Full array 1 st stage Sub Sub Sub Element space Beam space where ρ s densty, t tme, x space, u velocty, and p pressure. Combnng these two equatons yelds Lghthll s nhomogeneous wave equaton, where t T T a ρ = (3) x x = ρu u + p a ρδ 0 s defned as the Lghthll stress tensor. There are three components: the nstantaneous Reynolds stress, ρu u, the stress tensor, p, contanng normal and shear components, and fnally a small correctonal term that allows the equaton to be related to the classcal form of lnear acoustcs. Fgure 1: Flow nose model of movng quadrupoles. To use ths equaton to solve for densty at a gven pont n space tme we requre knowledge of the external stress feld T. Ths s no trval task, as fndng the tensor s a complex problem of flud dynamcs requrng the compressble Naver Stokes equatons and a model of the probablstc nature of turbulence. More useful s the dmensonal relatonshp that ths analogy has produced. Two space dervatves on the rght hand sde mples a quadrupole dstrbuton, and Lghthll places one quadrupole n each average eddy volume. Thus a movng quadrupole model, whch can be vsualzed as dscrete (4) nd stage Beamformng () Fgure : Schematc representaton of subarray beamformng. Subarray beamformng nvolves two-stage processng, as shown n Fgure. A full array s dvded nto a number of equal-szed subarrays. The frst stage beamformng s performed on each subarray. The output beams from ths frst stage form a beam space where the second stage beamformng s performed. Dependng on the type of beamformng at each stage, there are three possble subarray adaptve beamformng schemes:.e., frst stage conventonal and second stage adaptve (conventonal-adaptve), frst stage adaptve and second stage conventonal (adaptve-conventonal), and both stage adaptve (adaptve-adaptve). As the conventonaladaptve scheme s proven to be neffectve aganst flow nose [6], only the adaptve-conventonal and adaptve-adaptve schemes are explored n ths study. It should be noted that the subarrays at the frst stage can have dfferent overlappng confguratons, from nonoverlappng to the maxmum overlappng of one element spacng between the consecutve subarray centers. In order to avod spatal alasng at the hgh frequency end of the system, the maxmum overlappng s adopted n ths study. All beamformng n ths study s carred out n the frequency doman. The frequency doman verson of delayand-sum (DAS) beamformng s used n the conventonal part of the processng, and the mnmum varance dstortonless response (MVDR) beamformer s used n the adaptve part. B. General confguraton The sonar array used n ths study s a unform lnear array of 64 elements wth 0.75 metre spacng between consecutve

3 elements. The samplng frequency of the sonar system s 8000 Hz. The sound speed n the water s assumed to be 1500 m/s. The sgnal to be detected s a broadband plane wave of 0 db n power wth flat spectrum from 100 to 1000 Hz. The nose at the sonar array conssts of two components: ndependent and dentcally-dstrbuted (IID) nose of 0 db n power and a seres of movng quadrupoles of 0 db n power. The quadrupoles move parallel to the array. The dstance between the quadrupoles and the array s 0.1 meters. Two man crtera to evaluate the performance of dfferent beamformng confguratons n ths study are the array gan and the half power beam wdth (wdth of the man beam at - 3dB). The array gan s an mportant parameter of the sonar equaton and measures the SNR mprovement by beamformng. It s defned as: SNRarray = 10 log (5) SNRelement AG 10 where SNR array s the SNR of the beamformer output and SNR element s the SNR of the array element. IV. PERFORMANCE EVALUATION AND ANALYSIS Fgure 4 shows the array gans acheved by the adaptveconventonal and adaptve-adaptve beamformers, respectvely, n a scenaro where the sgnal s o to the broadsde of the array and the flow velocty s 0 knots. Also plotted n the fgure are the array gans of a full array adaptve beamformer and a full array conventonal beamformer as references. The followng observatons can be made. C. Subarray sze Array gan (db) Fgure 4: Array gans of adaptve-conventonal (), adaptveadaptve (), full array adaptve (A) and full array conventonal (C) beamformers. The array gan of the full array adaptve beamformer s hgher than that of the full array conventonal beamformer even n a non-statonary nose envronment. The performances of the adaptve-conventonal and adaptve-adaptve beamformers are smlar, and better than that of the full array adaptve beamformer Subarray sze 35 Fgure 3: Array gan aganst subarray sze n subarray beamformng. One mportant ssue n subarray beamformng s to choose an approprate subarray sze. In ths study, the subarray sze s chosen to maxmze the array gan. Fgure 3 plots the broadband array gans n the frequency band of 100 to 1000 Hz aganst the subarray sze n a scenaro where the sgnal s o to the broadsde of the array and the velocty of the movng quadrupoles s 0 knots. It shows that for both schemes the array gan ntally ncreases wth the subarray sze untl t reaches ts peak (at subarray sze 8 n ths case), and then t drops to ts mnmum at around subarray sze 40. After that, t ncreases agan towards the value of the array gan of a full array adaptve beamformer (about 7 db). The results wth other sgnal bearngs exhbt a smlar trend. Obvously, subarray sze 8 s a rght choce for ths confguraton. A rray gan (db ) 5 0 A C Velocty (knots) Fgure 5: Array gans of adaptve-conventonal (), adaptveadaptve (), full array adaptve (A) and full array conventonal (C) beamformers at 500 Hz as functon of the flow velocty. It should be noted that the above observatons were made for a scenaro wth flow velocty of 0 knots. Ths rases the queston of whether the observatons stll hold for dfferent flow veloctes. Fgure 5 shows the array gans acheved by

4 the two subarray and the two full array beamformers, respectvely, at 500 Hz wth the flow velocty varyng from 8 to 0 knots. It can be seen that the above observatons are stll vald for all veloctes from 8 to 0 knots, although the mprovement of subarray beamformng over full array adaptve beamformng reduces wth smaller flow veloctes. adaptve beamformer s not able to adapt quckly enough to acheve a smlar performance to the subarray adaptve beamformers A rray gan (db ) Bearng resoluton (deg) Freq. (Hz) Fgure 7: Bearng resolutons of the adaptve-conventonal () and adaptve-adaptve () beamformers Number of snapshots Fgure 6: Array gans of adaptve-conventonal () and adaptveadaptve () beamformers at 500 Hz as functon of the number of snapshots. The reason for the better performance of the subarray adaptve beamformers to the full array adaptve beamformer can be explaned as follows. As mentoned n Secton 1, the key to achevng a better performance n a non-statonary envronment s to shorten the tme requred for correlaton matrx estmaton. Ths s clearly demonstrated n Fgure 6 where the array gan s plotted aganst the number of snapshots (one snapshot equals one FFT perod) for the two subarray adaptve beamformers at 500 Hz. It shows that the array gan decreases as the number of snapshots ncreases. The array gans of the adaptve-conventonal and adaptve-adaptve beamformers drop about 16 and 14 db respectvely from ther maxmums when the number of snapshots exceeds 40. Indeed, to have a satsfactory performance the number of snapshots should not be greater than 16 n ths case. Once the relatonshp between the array gan and the number of snapshots n subarray adaptve beamformng s revealed, the reason for the poor performance of the full array adaptve beamformer becomes apparent. It s because the number of snapshots requred for the full array beamformer s greater than that of the subarray beamformers. Mathematcally, the mnmum number of snapshots for the type of adaptve beamformng that we used equals the number of array elements n beamformng. Note that the number of snapshots for the optmal beamformng s often larger than those mnmum numbers as demonstrated n Fgure 6 (the mnmum number of snapshots n ths case s 8 but optmal number of snapshots s 1). For the full array (of 64 elements) adaptve beamformer, the mnmum number of snapshots requred s 64, whch s already consderably larger than 16, the number not to exceed for a good performance. As a result, the full array Fgure 8: Bearng-tme-hstory plots of the adaptve-conventonal () and adaptve-adaptve () beamformers, wth two targets at 0 and 15 degrees respectvely. As the array gans acheved by the adaptve-conventonal and adaptve-adaptve beamformers are almost dentcal, n order to compare these two subarray beamformers the other performance metrcs such as the bearng resoluton and the computatonal complexty need to be taken nto account. Fgure 7 plots the bearng resolutons (measured by the man lobe beamwdth) of the two beamformers. It can be seen that the adaptve-adaptve beamformer acheves a hgher bearng resoluton (about 0% hgher) than the adaptve-conventonal beamformer. Ths hgher resoluton can make a dfference when separatng close targets, as shown n the bearng-tmehstory plots of Fgure 8. The two targets are clearly shown n the plot of the adaptve-adaptve beamformer whereas only one target can be seen n the plot of the adaptve-conventonal beamformer. In terms of complexty, the rato of computatonal tme of the adaptve-adaptve beamformer to the adaptve-conventonal beamformer n ths case s 1.05, whch means that the computatonal complexty of the former s only slghtly (5%) hgher than the latter. On balance, the

5 performance of the adaptve-adaptve beamformer s superor to that of the adaptve-conventonal beamformer. V. CONCLUSION The performance of subarray adaptve beamformng for reducng the mpact of flow nose on a sonar array wth a large number of elements has been nvestgated. Two schemes of subarray adaptve beamformng were consdered,.e., adaptve-conventonal and adaptve-adaptve beamformng. Ther performances were evaluated aganst that of a full array adaptve beamformer whch provdes a benchmark n terms of array gan. A stream of movng quadrupoles was used to model flow nose. The nvestgaton has shown that the adaptve-conventonal and adaptve-adaptve schemes are able to acheve hgher array gans than a full array adaptve beamformer. The adaptve-conventonal and adaptve-adaptve beamformers have smlar performances n terms of array gan, but the adaptve-adaptve beamformer acheves hgher bearng resoluton. Ths can make a dfference when separatng close targets. Further nvestgaton usng expermental data s underway. REFERENCES [1] N. Owsley and D. Abraham, Preprocessng for hgh resoluton beamformng, Proceedngs of 3 rd Aslomar Conference, Nov [] J. Nuttall and P. Wllett, Adaptve-adaptve subarray narrowband beamformng, Proceedngs of IEEE ICASSP 1993, Vol. 1, pp [3] Y. P. Lee, H. Freese and W. W. Lee, Subarray beam-space adaptve beamformng for a dynamc long towed- array, Proceedngs of IEEE ASAP 004, Mar. 004 [4] H. Cox and H. La, Sub-aperture beam-based adaptve beamformng for large dynamc arrays, Proceedngs of 38 th ACSSC, IEEE Press. 004, Vol., pp [5] T. Musha and T. Kkuch, Adaptve sgnal processng for reducng nearby generated flow nose, Appled Acoustcs, Vol. 66 (005), pp [6] C. Bao, D. S and J. Pan, On the effectveness of subarray adaptve beamformng for suppressng near-feld movng nose, Proceedngs of ISMA010, Sept [7] Lghthll M.J, On Sound Generated Aerodynamcally. I. General Theory, Proceedngs of the Royal Socety of London. Seres A, Mathematcal and Physcal Scences, Vol. 11, No. 1107, Mar. 195, pp On Sound Generated Aerodynamcally. II. Turbulence as a Source of Sound, Proceedngs of the Royal Socety of London. Seres A, Mathematcal and Physcal Scences, Vol., No. 1148, Feb. 1954, pp. 1-3.