DIFFERENTIAL MICROPHONE ARRAYS FOR THE UNDERWATER ACOUSTIC CHANNEL. Rotem Mulayoff, Yaakov Buchris, and Israel Cohen

Transcription

1 DIFFERENTIAL MICROPHONE ARRAYS FOR THE UNDERWATER ACOUSTIC CHANNEL Rotem Mulayoff, Yaakov Buhris, and Israel Cohen Tehnion, Israel Institute of Tehnology, Tehnion City, Haifa 32000, Israel ABSTRACT Design of underwater aousti sensing and ommuniation systems is a very hallenging task due to several hannel effets like multipath propagation and Doppler spread. In order to ope with these effets, beamforming tehniques have been applied to the design of suh systems. The broadband nature of aousti systems motivates the use of beamformers with frequeny-invariant beampattern. Moreover, in some ases, these systems are limited by their physial dimensions. Differential mirophone arrays (DMAs) beamformers, whih have been used extensively in reent years for broadband audio signals, may omply with these requirements. DMAs are smallsize arrays whih an provide almost frequeny-invariant beampatterns and high diretivity. In this paper, we present a pool experiment whih shows the ompatibility of DMAs for the underwater aousti hannel. Additionally, we show how to ompensate for the array mismath errors leading to muh better performane level and robust beamformers. Index Terms Underwater aousti hannel, differential mirophones, broadband beamforming, array mismath errors. 1. INTRODUCTION In the last several deades, underwater aousti ommuniation and aousti sensing beame essential for several real-world appliations, both ommerial and military [1]. To name a few, oil drilling, laying able and gas pipeline on the seabed, are some of the important ommerial appliations. In military appliations, we an indiate the underwater warfare via submarines, ommando operations, and many more. Numerous devies were developed throughout the years to fill the needs of these appliations like Sound Navigation and Ranging (SONAR), Remotely Operated Vehile (ROV), Underwater ommuniation systems, and others. Design of underwater aousti devies for the underwater environment is very hallenging due to the underwater aousti hannel whih is haraterized as a time-varing spatially unorrelated fading hannel. It introdues several effets like frequeny-dependent aousti attenuation, Doppler effet, ambient noise, and diretional noise like mahinery and propeller avitation noise of nearby vessels. Typially, the underwater aousti signals are broadband in nature [2] as a result of attenuation that inreases with the frequeny. Therefore, when designing beamformers for underwater aousti systems, it is desirable to design them with frequenyinvariant beampatterns. Additionally, sine in some of the systems the beamformers are integrated into small payloads, the apertures of the arrays should be ompat. This researh was supported by the Israel Siene Foundation (grant no. 576/16), Qualomm Researh Fund and MAFAAT-Israel Ministry of Defense. One of a well-known family of frequeny-invariant beamformers is the differential mirophone arrays (DMAs), originally applied to speeh signals [3 9]. DMAs refer to arrays that ombine losely spaed sensors to respond to the spatial derivatives of the aousti pressure field. These small-size arrays yield nearly frequenyinvariant beampatterns, and inlude the superdiretive beamformer [10] as a partiular ase. In this paper, we apply the DMAs onept to the underwater aousti hannel. We present a pool experiment whih proves the feasibility of DMAs for the underwater aousti environment. The array was onstruted from omni-diretional hydrophones and therefore was unalibrated. As a onsequene, essential part of the deoding proess deals with estimation and ompensation of array mismath errors like gain and phase errors. The results show that DMAs an be utilized for the underwater aousti environment and may provide small-size frequeny-invariant robust beamformers. 2. SIGNAL MODEL We onsider an underwater aousti soure signal, X(ω), that propagates in an anehoi underwater aousti hannel at the speed of sound, i.e., 1500m/s, and impinges on a uniform linear array of M sensors, where the distane between two suessive sensors is equal to δ. The diretion of X(ω) to the array is denoted by the azimuth angle θ. Assuming a far-field propagation, the time delay between the mth mirophone and the first mirophone is (m 1) δ os θ. Therefore, the mth mirophone signal is [7] Y m(ω) = e j(m 1)ω δ os θ X(ω) + V m(ω), (1) where j = 1, ω = 2πf is the angular frequeny, f > 0 is the temporal frequeny and V m(ω) is the additive noise at the mth mirophone. In a vetor form, (1) beomes y(ω) = [Y 1(ω) Y M (ω)] T = d(ω, θ)x(ω) + v(ω), (2) where T denotes the transpose operator, and d(ω, θ) = [1 e jω δ os θ e j(m 1)ω δ os θ] T is the steering vetor. The vetor v(ω) is defined similarly to y(ω). Aording to the DMA model, it is assumed that the desired signal arrives from the diretion θ = 0, and the aousti wavelength λ = /f is muh larger than the element spaing, δ, i.e., λ δ, to approximate the differential of the pressure signal. In order to design the beamformer, the signal of eah mirophone is multiplied by a omplex gain H m(ω), m = 1, 2,..., M, and the beamformer output signal is Z(ω) = (3) M Hm(ω)Y m(ω) = h H (ω)y(ω), (4) m=1

2 where the supersript denotes the omplex onjugate operator, H denotes the Hermitian operator, and h(ω) is defined as h(ω) = [H 1(ω) H 2(ω) H M (ω)] T. (5) The beampattern of a given beamformer h(ω) is defined as B [h(ω), θ] = h H (ω)d(ω, θ). (6) The theoretial frequeny-invariant beampattern of an Nth-order DMA is given as [3] B N (θ) = N a N,n os n (θ), (7) n=0 where {a N,n} N n=0 are real oeffiients. An Nth-order DMA an be designed using at least M = N + 1 sensors, satisfying N attenuation onstraints and one distortionless onstraint. Taking M > N + 1 may lead to a more robust beamformer [8], but in this work we will onentrate on the ase of M = N + 1. Figure. 1 presents examples of (7) for the ase of N = 1, 2, 3. Following the approah suggested at [7] for design of DMAs, we an design a DMA beamformer with a desired beampattern by solving the linear system: D(ω, θ)h(ω) = β, (8) (a) (b) where θ = [0 θ 1 θ M 1] T (9) β = [1 β 1 β M 1] T, (10) {θ m} M 1 m=1 are set of angles aording to the desired theoretial beampattern, {β m} M 1 m=1 are the values of BN (θ) at the diretions speified by θ, and the matrix D(ω, θ) is a M M matrix given by D(ω, θ) = d H (ω, 0) d H (ω, θ 1). d H (ω, θ M 1) From (8) we an derive the beamformer vetor. (11) h(ω) = D 1 (ω, θ)β. (12) It an be shown that the beampattern ahieved by this method is approximately frequeny-invariant. This fat may be exploited for the underwater senario. 3. EXPERIMENTAL SETUP & COURSE In this setion, we present a detailed desription of an experiment aimed to test the potential of DMAs for the underwater senario. The experiment took plae in a measurement pool at RAFAEL Ltd, Haifa. The measurements pool is 10 meters high, 20 meters long, and 10 meters wide. We used one omni-diretional hydroaousti projetor as the transmitting soure. The transmitter model was D11BB manufatured by NEPTUNE Ltd with roughly flat Transmit Voltage Response (TVR) of 150dB re 1µPa/V@1m at the relevant frequenies. The transmitter was deployed at 5 meters depth. Using this transmitter we broadasted broadband signals with 2kHz bandwidth around 10kHz entral frequeny. () Figure 1: Theoretial beampatterns produed by (7): (a) First-order dipole with a single null at 90 0, (b) seond-order ardioid with nulls at 90 0 and 180 0, () third-order hyperardioid with nulls at 55 0, and 145 0, (d) third-order pattern with nulls at 90 0, 120 0, and To onstrut the mirophone array, we used M = 4 similar hydrophones model TC4034 manufatured by Teledyne RESON Ltd, with flat Open-Ciruit Voltage (OCV) sensitivity in the relevant frequenies of approximately 216dB re1v/µpa@1m. Additionally, we self-manufatured a mounting base for the linear array by drilling in a wood board four holes equally spaed and roughly aligned with element spaing of δ 2 m. After that, we plaed the hydrophones inside the holes to form a linear mirophone array. The ables were ground shielded to prevent signal leakage between the sensors. The final produt an be seen in Fig. 2. We onneted the array to a rod and deployed it 5 meters deep into the water, and approximately 6 meters away from the soure. This distane ensures that we are in the far-field of the soure, and the inoming waves are approximately plane waves. The dry part of the rod was plaed in a protrator to reord the array angle with respet to the soure. During the experiment we sanned the array by rotating it from the endfire diretion (i.e., θ = 0 ) in steps of 2 degrees, up to θ = 180, and reorded the reeived signals. The other side (i.e., from θ = 180 to θ = 360 ) is symmetri and thus was not reorded. Figure. 3 illustrates this struture. In this setup, refletions from the water surfae and the side walls of the pool an also be reeived by the array. These ehoes impating the beamformer in many diretions, espeially not in the angle that we are aiming for, and thus they an distort the measured beampattern. Therefore, we loated this setup in the enter of the pool, and transmitted broadband pulses with short durations that (d)

3 2017 IEEE Workshop on Appliations of Signal Proessing to Audio and Aoustis Otober 15-18, 2017, New Paltz, NY depends also on the diretion θ. Signals arriving from the endfire are more unevenly gained between the sensors than signals arriving from the broadside. This effet was aused by the geometry of our setup, due to the large size of the reeiving hydrophones with respet to the wavelength. Thus, an extended model of (1) whih onsiders all these mismath origins an be written as Ym (ω, θ) = am (ω, θ)e jω(τm + Figure 2: The onstruted mirophone array of M = 4 sensors. Figure 3: The setup of the experiment. enabled time separation between the diret path and its refletions. Throughout the experiment we sampled the reeived signals using 2 MHz NI USB-6366 sampler. The sampling was performed simultaneously in all hannels and not serially, to anel additional delays. Furthermore, analog equipment was used to filter and amplify the analog signals. The underwater sound veloity is known to be strongly influened by the water temperature, salinity, depth and more [11]. We measured the underwater sound veloity by using probe model SVP 70, manufatured by RESON Ltd. The reorded sound veloity was = m/se, and we used this value for the proessing proedure. 4. DATA ANALYSIS In this setion, we present the deoding proess of the reorded data. An essential part of it was to estimate and ompensate for array mismath errors whih are the main reason for performane degradation. In the following, we desribe and address the model mismath errors. The model of the inoming signal speified by (1) assumes a unity gain for eah sensor, relative delays due to different propagation distanes between different sensors, known and onstant element spaing, and a known value of the sound veloity in water. Pratially, the signals that have been reeived by the array s mirophone passed through analog equipment suh as piezoeletri sensors, analog filters and amplifiers. Eah part of this analog hain has a transfer funtion whih an be both sensor and frequeny dependent. Moreover, we observed that the gain of the inoming signal δm os θ) X(ω) + Vm (ω), (13) where is the measured veloity, am (ω, θ) is the gain of the mth sensor whih depends both on frequeny and θ, τm is the analog delay introdued by the mth sensor, and δm is the distane between the first sensor and the mth sensor. We assumed for simpliity that the analog hain auses a linear delay between the signals. Additionally, we negleted the dependeny of the gain on the frequeny and assumed that am (ω, θ) am (θ). In the following results we show that suh an approximation leads to satisfying results, yet, the onsideration of the dependeny of the gain on frequeny is indeed a topi for future researh. Assuming high SNR level, estimation of am (θ) an be done by taking the root-meansquare (RMS) of the orresponding temporal signal ym (t, θ) for eah diretion and sensor. Sine we are interested in the gain differene between the sensors, and not in the amplitude of the reeived signal, we normalized the RMS value of eah sensor by the RMS of the referene signal, i.e., m = 1. This an be written mathematially as RMS{ym (t, θ)} a m (θ) =, (14) RMS{y1 (t, θ)} where for a general signal v(t), the RMS{v(t)} is given by: s Z 1 T 2 v (t)dt. (15) RMS{v(t)} = T 0 The phase mismath is estimated from the sampled signals by a two-step algorithm. In the first step we estimate the total time delay between the mth sensor and sensor 1, denoted by Tm (θ), for eah angle θ in the time domain. Then, in the seond step we estimate the values of τm and δm based on information from the first step. In the first step we used standard orrelation method, that is: Z T m (θ) = arg max y1 (α + t, θ)ym (α, θ)dα. (16) t In the seond step we look at the following relation: Tm (θ) = τm + δm os θ, (17) whih is a linear relation between Tm (θ) and os θ. Let {θl }L l=1 be the set of measured angels in our experiment. Thus, we have L 2 measurements of Tm (θ) for eah sensor. Using the Least Squares (LS) method we an estimate τm and δm. The LS estimation is given by: [τ m, δ m ] = arg min τ,δ L X δ ktm (θl ) τ os θl k2. (18) l=1 Finally, in order to ompensate the mismath errors desribed above, we rewrite (3) as below δ 1 d (ω, θ) = a 1 (θ) a 2 (θ)e jω(τ 1 + os θ) a M (θ)e δ jω(τ M + M os θ) (19) T,

4 and thus the beamformer oeffiients formula follows: ĥ(ω) = ˆD 1 (ω, θ)β (20) where ˆD(ω, θ) is onstruted similarly to D(ω, θ) from ˆd(ω, θ). 5. RESULTS After the alibration proess desribed in the previous setion, we used ĥ(ω) to alulate the beamformer output. Then for eah angle we omputed the beamformer output signal in the frequeny domain as presented in Setion 2. Next we alulated the power of the beamformer output signal for eah angle. The power levels were normalized so that the maximal power was 0dB. Figure 4 presents the normalized power vs. θ of the four examples presented in Fig. 1. The blak dashed line is for the ase of using ĥ(ω), while the blue irles line is obtained by ignoring the mismath and using h(ω) (12). One an see the resemblane of the blak dashed line to the original patterns presented in Fig. 1, and also the improvement ahieved by taking into aount the mismath errors. Figure 5 presents the white noise gain (WNG) of the beamformer whih is given by W [h(ω)] = hh (ω)d(ω,θ s) 2 h H (ω)h(ω). (21) Figure 6 presents the diretivity fator (DF) whih is given by D [h(ω)] = hh (ω)d(ω,θ s) 2, (22) h H (ω)γ dn (ω)h(ω) [ ω where [Γ dn (ω)] ij = sin (ˆδ j ˆδ ] i). In both figures, the red solid line represents the theoretial value where no mismath errors exist, while the blue dashed line is obtained by using ĥ(ω). It an be seen that the proposed beamformer provides near optimal results. We also note that the relatively onstant value of the DF implies that the beamformer is approximately frequeny invariant as we expeted. The above results of the WNG and DF are for the ase of a first-order dipole, yet, similar results were obtained also for the other patterns in Fig. 1. These results show the ompatibility of DMA beamforming for the underwater aousti hannel. The results are quite satisfying and even expeted to improve by onsidering more aurate models for errors mismath like frequeny dependent gains. Moreover, errors originating from the fat that sensors are not aligned and errors due to the physial size of the sensors were not addressed at all. (a) () Figure 4: Normalized measured power of the four shapes presented in Fig. 1: (a) First-order dipole with a single null at 90 0, (b) seondorder ardioid with nulls at 90 0 and 180 0, () third-order hyperardioid with nulls at 55 0, and 145 0, (d) third-order pattern with nulls at 90 0, 120 0, and The blak dashed line is the beampattern ahieved by using ĥ(ω) and the blue irles line is the beampattern ahieved by using h(ω). Figure 5: WNG vs. frequeny for the first-order dipole. The red solid line is the theoretial value, while the blue dashed line is the proposed beamformer. (b) (d) 6. CONCLUSION We have applied the onept of DMA beamforming for the underwater aousti hannel. To prove its feasibility, we onduted a pool experiment and transmitted broadband signals via the underwater medium whih were reeived by a DMA of four sensors. This array was built with off-the-shelf hydrophones and therefore several mismathed errors were introdued. We presented a pratial algorithm whih deals with these errors and provided better results. The results prove the ompatibility of DMAs for underwater devies involving broadband signals. 7. ACKNOWLEDGMENT The authors would like to thank the engineers at the signal proessing and algorithm department in RAFAEL Ltd. Espeially Jilbert Abitbol and Gilad Avrashi who made this experiment possible. Figure 6: DF vs. frequeny for the first-order dipole. The red solid line is the theoretial value, while the blue dashed line is the proposed beamformer. 8. REFERENCES [1] I. F. Akyildiz, D. Pompili, and T. Melodia, Underwater aousti sensor networks: researh hallenges, Ad Ho Net-

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