In this paper, we explore the use of synthetic aperture processing for optimizing the spatial covariance estimation capabilities of a moving linear co-prime sensor array. The linear co-prime sensor array geometry is a thinned linear array that is constructed by nesting uniform linear arrays with interrelated element spacing factors. The application of synthetic aperture processing in this setting is designed to create virtual sensors at missing half-wavelength intervals up to the degree required to produce a hole-free difference co-array across the full aperture of the synthetic array. Once a full set of spatial covariances are estimated covariance matrix based array processing methods can be applied as if the synthetic array were a uniform linear array. In this sense, the synthetic array is designed to approximate a uniform linear array while it retains a thinned linear array structure. We show simulation results examining the quality of the uniform linear array approximation afforded by this application synthetic aperture processing.
Co-prime array geometries have received a great deal of attention due to their ability to discriminate O(MN) sources with only O(M + N) sensors. This has been demonstrated both theoretically and in simulation. However, there are many practical limitations that make it difficult to realize the enhanced degrees of freedom when applying co-prime geometries to real acoustic data taken on a horizontal line array. For instance, co-prime sampling leads to grating lobes that can obscure lower signal-to-noise-ratio acoustic signals making them difficult to detect. In this work, a synthetic aperture (SA) method is presented for filling in holes and increasing redundancy in the difference co-array by exploiting array motion. The SA method is applied to acoustic data collected off the Southeastern shore of Florida on a fixed large aperture horizontal array. Array motion is simulated by taking a co-prime sampled subarray and virtually moving it along the horizontal aperture of the fixed array. It is demonstrated that SA processing on real acoustic data results in reduced side-lobe and grating lobe levels compared to that of the physical co-prime aperture.
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