Acoustic beamforming: microphone phased array synthesis and development

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1 Acoustic beamforming: microphone phased array synthesis and development Mario Amoruso a) Università Federico II, Dept. of Biomedical, Electronics and Telecommunications, Via Claudio, Napoli, Italy Pietro Vinetti b) Michele D Urso c) SELEX Sistemi Integrati S.p.A., Innovation Team, Via Circumvallazione Esterna di Napoli, 814 Giugliano in Campania (NA), Italy Vincenzo Quaranta d) CIRA, Italian Aerospace Research Centre, Vibration & Acoustics Laboratory, Via Maiorise, 8143 Capua (CE), Italy The analogies between electromagnetic and acoustic fields allow for the application of classical concepts of antenna electromagnetic synthesis to the design of passive acoustic systems based on phased array of microphones and beam-forming techniques for sound source detection and localization. In this work, standard techniques for synthesis of linear aperture antennas, such as Chebyshev, are investigated to be applied in the acoustic field, along with innovative techniques, such as density taper iterative algorithms, based on convex programming. To this end two different arrays, both made of ten microphones, were designed and manufactured, the first characterized by a regular layout and the second by an aperiodic one. These two configurations were tested in the semi-anechoic chamber of CIRA. The comparison between the results obtained from experimental data processing and numerical simulation provided a very good correlation. In this context, the present work represents a good starting point to develop advanced techniques for the synthesis of arrays of microphones taking advantages of the knowledge developed in other application fields such as electromagnetic. Furthermore, the increasing interest in passive acoustic systems for sound source detection and localization, both in military and civil areas, require to further investigate on advanced techniques of electromagnetic antenna synthesis. In this context an important step forward would be the design of advanced geometry of microphones phased array to reduce the size and the number of transducers a mario.amoruso85@libero.it b pvinetti@selex-si.com c mdurso@selex-si.com d v.quaranta@cira.it

2 keeping unchanged antenna performances, thus lowering both production and maintenance costs. 1 INTRODUCTION Electromagnetic (EM) and Acoustic (AC) waves are two distinct physical phenomena which have some common interesting features, especially in terms of the mechanisms of propagation 1. Those analogies lead to consider the use of systems, exploiting acoustic principles, as a support or even a replacement for those based on the electromagnetic ones. Indeed, according to the considered operating scenario, the use of acoustic waves can provide some advantages, and in particular the possibility to pass through metallic surface (electromagnetic barriers) and the possibility to detect objects with low electromagnetic (radar) signature (stealth aircraft or hidden objects flying at low altitude). Furthermore, acoustic system require typically low cost hardware components for high quality devices (microphones) and also do not contribute to electromagnetic radiation (EM pollution) into the surrounding environment, avoiding EM interference with other operating systems and to be subjected to legislative regulation. The above mentioned analogies between EM and AC waves are particularly evident when array of elements, i.e. alignment of sensors/sources (antennas in the EM case) are concerned. Indeed, the mathematical modelling of the array turns out to formally equivalent despite of underling physical phenomena. Accordingly, it is possible to apply EM antenna techniques to the design of microphone arrays. In this paper we report the effective design, the manufacturing and the successful experimentally characterization of three array configurations, by exploiting standard and advanced synthesis approaches, introduced in the antenna field. The paper is organized as follows: Section 2 presents a brief overview about the possible applications and introduces some reference projects where acoustic waves find application; then, Section 3 introduces the mathematical statement of the synthesis problem and the adopted formulations to tackle it. Finally, Section 4 discusses the experimental results of the three types of manufactured arrays. 2 APPLICATIONS AND PROJECTS Acoustic antennas were used initially (188) to determine the presence and location of ships in fog. Following devices more complex, but based on the same principle, were used by half of the WWI to the early years of WWII for the passive detection of bombers from the recognition of the engine noise. Such systems became obsolete during the WWII, following the introduction of RADAR. With the development of phased array of microphones and advanced beam-forming algorithm, acoustic antenna are now of great interest for several applications in different field and, consequently, under improvement in more than a few research projects. Current applications of acoustic localization devices, for which there are systems already on the market, concern mainly the identification of noise sources of a machine or equipment, in order to identify those most noisy and take action to lower the levels of sound power emitted. Some recent research for the application of this device regards early detection of fire in forest; airplane localization and identification aimed at improving the management and control of air traffic in ATZ (Aerodrome Traffic Zone); surveillance of critical targets (skyscrapers, factories, nuclear plant, etc.) from terrorist attacks; gunfire and explosion real-time detection, location and classification on wide urban area.

3 The European project EU-FIRE 2 was aimed at developing a network of acoustic antenna to monitor large areas such as woods and forests in order to make early detection and location of outbreaks of fire from the noise emitted by burning vegetation. The GUARDIAN project 3, funded by MIUR (Italian Ministry of University and Research), was aimed at designing and developing a novel acoustic system for the improvement of cooperative management of ATZ control. The GUARDIAN sensor system was a multi-modal, inair passive acoustic device working in arrayed/sparse configuration, by means of an innovative ensemble of digital processing stages, based on Delay and sum Beamforming 4,5 and triangulation techniques. 3 STATEMENT OF THE SYNTHESIS PROBLEM In general, the synthesis of an alignment of sensor/sources elements (array) consists of determining the proper conditioning (amplification and delay) of the signals acquired/sent from the elements in order to satisfy pre-assigned design specifications on the behaviour of the alignment (array factor as far as antenna are dealt) in terms of its far-field angular sensitivity (directivity pattern specifications) 4, 6, 7 to receiving/radiating waves 4, 6. Constraints, naturally, can be imposed also on elements spacing, system bandwidth, near-field radiation, in order to control the physical dimensions of the alignment, the mutual coupling between elements, the operating requirements and costs. As far as pencil beam (PB) are concerned, the goal of the synthesis procedure is (at least ideally) to design the geometry of the alignment and the controlling signals of the elements in order to achieve an array factor (AF), such that the array is sensitive to only one or to an interval of pre-assigned angular directions as much as possible, and insensitive to all the others directions. From the practical point of view, as discontinuities (sharp angular variations) in the AF are physically unfeasible, PB design turns out always into the design of an AF providing as much sensitivity as possible into an angular region (main beam) with non-zero measure, while in other angular regions (side lobes) as low sensitivity as possible. Arrays providing PB directivity pattern are suitable for all those applications where a high sensitivity to a limited angular interval is required, such as point-point connections or source localization. It s worth noting that alignment of elements are typically deployed on regular uniform lattice, made of uniformly-spaced positions and, hence, referred as periodic arrays 4, 6, 7, 12, but in general the elements can be also arranged on an irregular lattice The latter case is referred as a-periodic or unequally spaced or sparse arrays. In this paper we present the synthesis of both periodic and a-periodic array configurations providing PBs. More specifically, the synthesis of three arrays configurations are presented in the followings by means of different and methods, which are: 1. Periodic array: synthesized by means of analytical techniques; 2. A-periodic isophoric array: a non-equispaced array of elements where conditioning signals of the elements have all constant amplitudes (isophoric) and differ only in time delay (phase shift); 3. Aperiodic array, where full control (amplitudes and phase shift) of the conditioning signals of its elements is exploited. Figure1 shows schematically a linear distribution of elements of an array

4 Where x i represents the position of the i-th element of the array and N is the overall number of the array elements. The schematic accounts for both a-periodic and periodic: indeed the particular case of x i =-a+(i-1) d, where d is the inter-element spacing, lead to the uniform lattice. Considering the reference system of Fig. 2, under the assumption that each element of the alignment has exactly the same behaviour (neglecting mutual coupling effects) it is possible to define the AF as follows: N = 1 AF( u) cne n= u = β cos( ψ ) u = β cos( ψ ) j[ xn ( u u )] (1) being c n the excitation coefficients (i.e. the conditioning of signals coming from or sent to the array elements), Ψ the angle between the direction of observation, the acoustic wave-number defined as β = 2π λ, λ the wavelength 6, Ψ the beam pointing direction. For periodic alignment Eqn. (1) is particularized to: N = 1 j AF( u) cne n= u = β d cos( ψ ) [ n ( u u )] (2) 3.1 Periodic Array: Chebyshev sysnthesis procedure An analytical approach to the synthesis of a periodic array has been developed by Chebyshev 7, 12. The approach exploits a proper representation of the AF by means of polynomials, which enables to determine the optimal set of c n with n=,1,,n-1 and the interelement spacing, able to satisfy the design specifications in terms of: Side Lobe Level (SLL) ratio, i.e. the ratio between the maximum value of the AF in the main lobe region and in the side lobe region; Beam Width (BW), defined as the dimension of the region where the main beam is confined. By means of Chebyshev synthesis procedure it is possible to determine the SLL level given the BW or, conversely, the BW given the desired SLL level. It s worth noting that the Chebyshev solution is the optimal solution for a PB based on a periodic arrays. Indeed, it provides the periodic array configuration with the smallest BW assigned a SLL level or, vice versa, the lowest SLL level assigned the BW. By implementing design formulas into Matlab routines, imposing a SLL ratio equal to 19dB for a N=1 element array we obtain the directivity pattern shown in Fig. 3. The corresponding spacing between elements is.9 λ, for a total size of 8.1λ, while the BW (null-to-null) is equal to 14.5.

5 3.2 Aperiodic Isoporic Array: Density Taper Unfortunately, analytical approaches able to determine the design solution for aperiodic arrays, such as that one introduced by Chebyshev for the periodic case, is not available. Many techniques have been developed and exploited to design sparse (antenna) arrays 8-1. In this paper we refer to an effective approach 11, based on the concept of density tapering, which has demonstrated to be particularly effective and suitable to the design of isophoric sparse arrays, i.e. arrays whose elements are excited by a constant amplitude ( c n =const). The basic idea is to refer to a periodic equivalent array and distribute the elements of the sparse array according to the amplitudes of excitation coefficients of an equivalent distribution, satisfying the design specifications. Practically speaking, the design is tackled by referring to the case of a continuous function, say h(x), whose Fourier transform, say H(u), satisfies the assigned pattern mask, than the elements of a-periodic array are placed closer where the excitations of the periodic one are higher while the elements are spaced larger where the excitations are lower. We hereafter sketch the mathematical formulation of density taper, but we remand to 11 for a more detailed description of the method. In order to calculate the positions of the sparse array, it is necessary to refer to an ideal function h( x ), that we assume to be a proper Taylor distribution 11, then we introduce the continuous function: Then dividing the interval [ a, x ] n After this subdivision is obtained a set of N points { xˆ ˆ },..., xn x IC ( x) = h( ξ ) dξ a (3) into N-1 subintervals each having the same area ( ) 1 N. xˆ ˆ, with N = x = a, so that: I ( xˆ ) I ( xˆ ) = 1 N C n C n 1 xˆ xˆ = d n n 1 n (4) (5) The generic n-th element is positioned in the center of gravity of the range [ xˆ, ˆ ] n xn 1 according to the formula: ( ) xˆ n n = xˆ n 1 (6) x N xh x dx The result of the density taper applied to the considered case, for a array of N=1 elements, is the set equal of positions: d = [-2.3,-1.45,-.96,-.55,-.18,.18,.55,.96,1.45, 2.3] (7) Density taper provides only the positions of the array elements. As the amplitudes of the excitation coefficients are all set and equal to a constant value (which has been chosen equal to 1), only phase coefficients can be exploited as further degree of freedom in order to satisfy the pattern. By means of a proper optimization procedure, implemented with a Matlab routine, and

6 assuming the same target SLL level of 19dB achieved in the periodic case, it has been possible to determine the optimal set of phase coefficients. The obtained the pattern is showed in Fig. 4. The total size of the array is 6 λ, while the BW (null-to-null) is equal to Even if the number of the degrees of freedom for the array is the same of the previous case (N phase control and N positions), the larger BW is due to the fact that the elements positions control cannot replace exactly the amplitude control of the periodic array, unless allow very small spacing between elements which lead to unfeasible solutions 1, Aperiodic Array: convex optimization The geometrical aperiodic layout of the alignment, which has been determined by density taper as discussed in the previous section, has been also considered for the design of a nonisophoric array. Indeed, by relaxing constraints on the (constant) amplitudes of excitation coefficients, it is possible to recover further degrees of freedom to be optimized in order to improve the directivity pattern of the array. The synthesis problem, hence, turns out to be the determination of the optimal complex (amplitude and phase) excitations set of the array elements, given a non-uniformly spaced grid of positions, in order to satisfy a pre-assigned pattern mask. In particular, we require that the directivity pattern of the designed array presents the highest amplitude value in a pre-assigned angular direction, say u, while it is smaller of a pre-assigned mask function, say M(u), in a given interval of angular directions. From the mathematical point of view, the synthesis problem is then to find the set: c = N ( c, c1, c2,..., c 1) (8) such that: [ u ] N 1 i xn u ) c e, u 1, n n = max F( u u c = 2 (9) and subject to: 2 [ β d, u ] [ u, βd ] F( u) M ( u), u I = 1 2 (1) where u 1 and u 2 are given angular directions. Such a problem is formulated as a convex optimization problem 15 and accordingly can be easily tackled by means of convex programming techniques. In this paper we refer to an effective approach which has been presented in 11. In order to compare the result achieved by the considered approach to the previous design of a uniform Chebyshev array, u1 and u2 has been chosen in such a way that the main lobe region has a BW equal to The synthesized pattern is shoved in Fig. 5. As expected the value of SLL is higher if compared to the uniform Chebyshev array, indeed the achieved SLL in this case is -9 db. On the other side, the BW of the array is again 14.5 such in the periodic case.

7 4 PHASED ARRAYS MANIFACTURING A classical BSWA type MPA466 condenser microphone has been used for arrays manufacturing. It is a ¼ inch diameter pre-polarized microphone, consisting of a capsule electrets condenser and an IEPE preamplifier, well suited for free field measurements. Despite being a ¼ diameter microphone it is characterized by a high sensitivity of 5 mv/pa. The frequency response is linear in the range: 2 2 Hz and the phase tolerance is less than 3 deg, appropriate for phased array measurements. As mentioned earlier, numerical synthesis methods have been used to design two microphone arrays, both made of 1 microphones: the first based on the Chebyshev synthesis and the second based on the aperiodic positioning method. A wooden support has been used for the practical realization of each array. The transducers have been inserted into purposely drilled holes. The positions of these holes have been established using the results of the synthesis method. By imposing a working frequency of 4 khz, a constant transducers distance was evaluated for the periodic array, equal to.77 m, thus obtaining a linear array of.69 m length. In the aperiodic case the positioning vector for the transducers was the following, in which the coordinates are expressed in meters: [-.17,-.12,-.8,-.4,-.1,.1,.4,.8,.12,.17 ] (11) In this case the total size of the array was.34 m. To drastically reduce wave reflections, sound absorber material has been glued on the surface of the wooden support. The two arrays are shown in Fig. 5, the dimensions can be inferred by comparison with a 2 euros coins. A tripod with a swivel head fixed at the geometric centre of the array has been used as a support for both antennas. The rotation device is shown in Fig. 6. It is ideal for fine 5 degree tuning the angular orientation of any component after rotating it to an approximate angle. In Figure 7 the final setup for the periodic array is reported. 5 TESTING AND RESULTS The experimental test has been performed to validate the numerical results in terms of antennas directivity pattern. 5.1 Test setup Measurements were carried out in the semi-anechoic chamber of the vibration and acoustics laboratory of C.I.R.A., the Italian Aerospace Research Centre. This environment is able to simulate free hemi-space conditions above the cut-off frequency of 9 Hz. A paramount view of the test setup in the chamber can be observed in Fig Test equipment The Bruel & Kjaer OmniSource type 4295 has been used as an omni-directional sound source. It uses a single high-power loudspeaker, radiating through a conical coupler to a circular orifice. The size of the orifice and the shape of the OmniSource have been designed to radiate

8 sound evenly in all directions. Furthermore, it is capable of emitting a sound power of 15 db re 1 pw. A signal generator Agilent type 3322A has been used in conjunction with an amplifier Bruel & Kjaer type 2716 to drive the sound source. The data acquisition system was the LMS SCADAS III with LMS Test Lab software. 5.4 Test procedure The response of both arrays to a pure tone of 4 khz, used as reference sound source, were acquired and analyzed through a Matlab code purposely developed. The antennas directivity pattern have been evaluated keeping the sound source fixed and varying the relative angle by rotating the array. The number of relative angles examined in the range [-9, 9 deg] was set to 35 for the periodic array and 19 for the aperiodic one. Before the test the array microphones were individually calibrated by means of a pistonphone. 5.5 Test results In Figure 9 the responses obtained for the periodic array in case of a 9 degree relative angle, are reported in frequency domain. As expected, for a pure tone excitation in an acoustically dead room, the signal to noise ratio is very high (about 8 db). The experimental data have been compared to the numerical predictions. In Figures 1-12 the comparisons are reported for Convex programming, Density Taper and Chebyshev predictions respectively, in which a very good correlation can be observed. 6 CONCLUSIONS Taking advantage of analogies between acoustics and electromagnetism, a standard technique, such as Chebyshev synthesis, and also innovative techniques, such as density and taper iterative algorithms based on convex programming, were verified for the design of acoustic antennas. To this end two linear microphone arrays were developed and tested: the first with a regular layout and the second with an aperiodic scheme. The two configurations, both made of 1 microphones, were tested in the semi-anechoic chamber of CIRA to derive the antennas array pattern. The comparison between experimental and numeric predictions provided a very positive outcome. This work can be seen as a good starting point to develop advanced techniques for the synthesis of innovative acoustic antenna by referring to techniques developed in other application area, such as electromagnetic field. The target to design advanced microphone arrays, characterized by higher gain, longer range and better angular resolution, without increasing the number of transducers and the antenna size, could be accomplished by using the proposed techniques. 7 REFERENCES 1 Carcione J.M.; Cavallini F., On the acoustic-electromagnetic analogy, Wave Motion, Volume 21, Number 2, March 1995, pp (14). Publisher: Elsevier

9 2 Blaabjerg C.,Haddad K., Song W., Dimino I., Quaranta V., Gemelli A., Corsi N., Viegas D. X., Pita L. P., Detecting and Localizing Forest Fires from Emitted Noise, VI International Conference on Forest Fire Research, november 21, Coimbra Portugal. 3 Quaranta V.,Ameduri S., Donisi D., Bonamente M., An in-air passive acoustic surveillance system for air traffic control - GUARDIAN project, ESAV 211, September 12-14, Island Of Capri, Italy. 4 Balanis C. A., Antenna Theory Analysis and Design, Third Edition, a John Wiley & Sons, Inc., Publication, Brandstein M., Ward D., Microphone Arrays, Springer, Berlin 21, pp Stratton, J.A., Electromagnetic Theory, IEEE Press Series on Electromagnetic Wave Theory), Hoboken, Wiley & Sons Inc., Mailloux, R. J.; Phased Array Antenna Handbook, Boston, Artech House, Ishimaru, A.; Theory of unequally spaced arrays, IRE Transaction on Antennas and Propagation, issue 6, vol. 1, pp , Tokan, F.; The multi-objective optimization of non-uniform linear phased arrays using the genetic algorithm, Progress in Electromagnetics Research B, vol. 17, pp , Ling Cen; Zhu Liang Yu; Ser, W.; Antenna array synthesis in presence of mutual coupling effect for low cost implementation, Integrated Circuits, ISIC '9. Proceedings of the 29 12th International Symposium on, pp , Bucci, O.M.; D'Urso, M.; Isernia, T.; Angeletti, P.; Toso, G., Deterministic Synthesis of Uniform Amplitude Sparse Arrays via New Density Taper Techniques, Antennas and Propagation, IEEE Transactions on, vol. 58, issue 6,pp , C. L. Dolph, A current distribution for broadside arrays which optimizes the relationship between beam width and side-lobe level, Proc. IRE, vol. 34, pp , June Elliott, R.; O'Loughlin, W., The design of slot arrays including internal mutual coupling Antennas and Propagation, IEEE Transactions on, vol. 34, Issue 9, pp , 1986.

10 Figure 1 Reference system Figure 2 Reference system 1 Pattern di Chebychev ψ [deg] Figure 3 Amplitude of the AF (directivity pattern) of a Chebyshev array of 1 elements and SLL equal to 19 db (black line), pattern mask (red line) Array aperiodico 1-1 SLL [db] φ [deg] Figure 4 amplitude in decibel of AF of the isophoric sparse array, obtained by density taper (black line); pattern mask (red line)

11 Figura 5 Periodic and aperiodic array Figura 6 Newport 481-A-S Rotation Stage Figura 7 The Periodic array setup Figura 8 Test setup paramount view Figure 9 Frequency domain response

12 [db] Numerical Experimental ψ [deg] Figure 1 Convex programming pattern -1 Numerical Experimental [db] φ [deg] Figure 11 Density Taper pattern -1-2 Numerical Experimental [db] ψ [deg] Figure 12 Chebyshev pattern

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