of the coupling matrix is realized as a passive analog phase shifter and attenuator in a similar fashion as that of conventional analog beamforming, in the ...
A PASSIVE COUPLING MATRIX DESIGN FOR IMPROVED RESOLUTION SMALL APERTURE DIRECTION FINDING Guohua Wang†, Joni Polili Lie†, Chong-Meng Samson See†‡ †Temasek Laboratories@NTU, 50 Nanyang Drive, Singapore 637553 ‡DSO National Laboratories, 20 Science Park Drive, Singapore 118230 ABSTRACT In this paper, we present an approach to design passive coupling matrix to overcome the performance limitation of direction finding using small aperture array. This approach is inspired by the sound localization acuity of a parasitic fly called Ormia ochracea. Motivated by the requirement from practical implementation that each element of the coupling matrix is realized as a passive analog phase shifter and attenuator in a similar fashion as that of conventional analog beamforming, in the proposed approach we confine the magnitude of each element to being no larger than 1. By taking the advantage of the coupling mechanism, this approach can design compact aperture antenna array yet with much improved direction finding performance. Furthermore, the proposed design is applicable to arbitrary array geometry. Numerical examples illustrate the effectiveness of the proposed approach and show a performance gain of 30 over the uncoupled array of the same aperture of 10 cm diameter at 40 MHz. Index Terms— Array signal processing, compact arrays, direction finding, mutual coupling. 1. INTRODUCTION Sensor array processing has important applications to many fields ranging from communications, radar, and sonar to radio astronomy and even medical imaging. In the past few decades, the problem of estimating the direction of arrival (DOA) using sensor arrays has attracted significant attention, as reflected by the rich literature [1] and references therein. One solution to this is the spectral analysis based approaches. In these approaches, beamforming based spatial filtering (and even high resolution subspace based methods) has a limitation determined by the array aperture size, and prefers larger aperture size to meet higher performance requirements. However, large aperture arrays are not frequently used in tactical applications in spite of their performance advantage. Although the implementation cost and array size can be reduced with array geometry optimization methods, such as [4] [5], and more recently [16], the typical nature of the operating environment can still pose significant challenges in the deployment of large aperture arrays. In consequence, small aperture arrays are frequently used in many tactical applications, especially at VHF and HF band, in spite of their poorer performance [2] [3]. Recently, inspired by the biological studies on the Ormia ochracea’s mechanically coupled hyperacute directional hearing ears [6, 7], bio-inspired small aperture array has attracted much interest from antenna and signal processing researchers [8–13]. From a receiver processing perspective, the high resolution property of the mechanically coupled compact array is studied in [9], and the realistic realization problem of the actual coupling mechanism is discussed in [11]. Also, from a transmission perspective, coupled
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beampattern design for small aperture array is studied in [13]. In this paper, we draw inspiration from these studies and propose an approach to design coupling matrix to overcome the performance limitation of small aperture antenna array on direction finding. We start by reviewing the coupling model proposed in [7] and examining the coupling mechanism from a receiving array processing perspective, which provides us the essential concept of coupled antenna array for small aperture direction finding. Then, motivated by the finding that the resolution improvement is mainly due to the phase enhancement achieved by the coupling mechanism, we propose a method to determine the coupling matrix coefficients for multi-element antenna array to achieve enhanced DOA estimation under small aperture constraint. Some problems related to the real implementation issues such as the passive constraint on the coupling matrix element are also addressed in the proposed method. We also show in our design example that the performance enhancement of the proposed approach is valid for the complete range of angle of arrivals and can deal with scenarios considering multiple impinging signals. Although the proposed approach is derived in a 1D scenario, the extension to 2D is straightforward. This paper is organized as follows. In section 2 we first review the principle of the Ormia’s hearing mechanism from an array processing perspective, laying out the foundation for the proposed coupling matrix design. Then in section 3 we propose a method to design coupling matrix for multiple element compact arrays, with both the design method and numerical demonstration presented. And finally, Section 4 concludes this paper. 2. BACKGROUND Biological studies in [6] and [7] find that female parasitoid Ormia can locate its parasitic host, a male cricket, in spite of its very limited eardrum separation, with very high direction sensitivity by operating its eardrums as a mechanically coupled system. Based on these studies, the response of Ormia’s eardrums to signal impinging from angle θ is given by [9] ac (ω, θ) = Ψ(jω)a(ω, θ)
(1)
where Ψ(jω) is the coupling matrix determined by Ψ(jω) = (K + (jω)C + (jω)2 M)−1
(2)
and a(ω, θ) is the vector response of the conventional uncoupled eardrums at frequency of interest ω. The matrix terms and parameters used to determine the coupling matrix are as follows: K = [k1 + k3 , k3 ; k3 , k2 + k3 ], M = [μ, 0; 0, μ], C = [c1 + c3 , c3 ; c3 , c2 + c3 ], the constant μ is the mass of the eardrums, k1 , k2 , and k3 are the spring constant and c1 , c2 , and c3 are the damping coefficients.These parameters were empirically measured and can be found in [7].
ICASSP 2011
Studies in [7] and [12] showed increased interaural time delay and level difference between the responses of the coupled eardrums over a range of frequencies. Here, we illustrate the coupling effect from an array processing perspective. In particular, we examine the phase difference between two eardrum responses to one frequency over different DOA angles. For this purpose, we let aperture size d = 0.53 mm and the center frequency of cricket’s song 5 KHz according to [7]. We compare the phase difference of the coupled and uncoupled apertures. To indicate the enhancement effect, we also show the phase difference of an aperture with aperture size 20d. From Fig. 1, we can observe that the enhancement of phase difference after coupling is about 20, independent of angles, leading to resolution improvement by a factor around 20. Meanwhile, based on our simulation study, the level difference is found to be dependent on angles, and shows no apparent contribution to resolution when processed by current array processing methods. For brevity, the results are not shown here.
several assumptions to design the receiver array equivalent of the Ormia’s coupled ears. We assume that the internal noise of the hearing organ is not coupled by the coupling matrix and that the external noise sources are negligible compared to the dominant internal noise (mainly due to the down-conversion, digitization, and quantization, etc.). This consideration is similar to that reported in [16]. Thus, the receiving signal model for the coupled array is x(k) = Ψ(jω)a(ω, θ)s(k) + n(k)
where x(k) is the snapshot at index k, s(k) is the signal component, and n(k) stands for the dominant internal noise. Based on this signal model, the mechanical model proposed in [7] can be expressed as a receiving array equivalent form in radio frequency domain as shown in Fig. 2, where the desired coupling matrix is specified by the coefficients {hij }. Antenna 1
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Antenna 2
Antenna N
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