EFFECTS OF ARRAY SCALING ON THE ANGULAR RESOLUTION OF MICROPHONE ARRAY SYSTEMS
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Array detection systems have been in use for nearly a century and have proven useful in a variety of applications. The most ubiquitous form of array is the active radar array, but in the past four decades microphone arrays have become increasingly common. Microphone arrays have traditionally been very large devices. This is because of the limited angular resolution of the traditional Delay-and-Sum (DAS) beamforming algorithm. Improved frequency-domain beamforming (FDBF) methods were developed in the 1980’s using the Fast Fourier Transform. More advanced methods have been developed in the past decade, including deconvolution methods (DAMAS, DAMAS2), methods based on the spatial coherence of point sources and sidelobes in the frequency domain (CLEAN-SC), and spatial coherence methods in the time domain (TIDY). In this investigation two sets of experiments were carried out to better understand the angular resolution characteristics of scaled microphone arrays and associated beamforming algorithms. In the first experiment five scaled microphone arrays with diameters from 0.73m to 10.98m were constructed and tested, and the data was analyzed with a variety of beamforming algorithms. In the second experiment three scaled microphone arrays and one alternative array geometry were tested with both free-field and reflective boundary conditions. The results show that the Rayleigh criterion can be exceeded under certain conditions. However, several other parameters are also important. For example, Signal-to-Noise Ratio (SNR), z-axis correction, and reflective boundaries all impact aspects of the array’s performance. In addition to increasing the array diameter and the signal frequency, results show that effective strategies to improve the angular resolution performance of an array include careful selection of beamforming algorithm, the use of appropriate beamforming integration times, and minimizing boundary reflections. The DAS algorithm is shown to offer the lowest angular resolution performance because it does not separate the acoustic source map from the point spread function of the array. The DAMAS algorithm offers the greatest angular resolution because it numerically deconvolutes the acoustic source map from the point spread function. However, deconvolution-based algorithms are the most negatively affected by the boundary reflection effects commonly seen with larger arrays. This is because the pressure field becomes contaminated with reflections and image sources, and the deconvolution approach does not make use of significant simplifying assumptions as several of the other algorithms do. The logarithmic spiral array is shown to offer versatile performance across a wide range of frequencies, while an alternative quasiperiodic array yields results that are highly frequency-dependent. It is demonstrated that this is because of gaps in the source-to-element differences coverage, and the gaps in coverage correspond to half-wavelengths of frequency bands with significantly lower angular resolution performance.