Abstract
A coprime sensor array (CSA) is a non-uniform linear array obtained by interleaving two uniform linear arrays (ULAs) that are undersampled by coprime factors. A CSA provides the resolution of a fully populated ULA of the same aperture using fewer sensors. However, the peak side lobe level in a CSA is higher than the peak side lobe of the equivalent full ULA with the same resolution. Adding more sensors to a CSA can reduce its peak side lobe level. This paper derives analytical expressions for the number of extra sensors to be added to a CSA to guarantee that the CSA peak side lobe height is less than that of the full ULA with the same aperture. The analytical expressions are derived and compared for the uniform, Hann, Hamming, and Dolph-Chebyshev shadings.
Highlights
A sensor array spatially samples a propagating space-time signal
This paper focuses on coprime linear arrays for different shadings
This paper derives the number of additional sensors required in the subarrays for a coprime sensor array (CSA) to match the peak side lobe of a uniform linear arrays (ULAs) with the equivalent resolution for different standard tapers
Summary
A sensor array spatially samples a propagating space-time signal. A beamformer combines the samples measured by an array to estimate properties of the space-time signal, such as the direction of arrival for signals of interest [1]. This paper derives the number of additional sensors required in the subarrays for a CSA to match the peak side lobe of a ULA with the equivalent resolution for different standard tapers (uniform, Hann, and Hamming). Adding more sensors to each subarray while keeping the intersensor spacing fixed reduces the main lobe and grating lobe widths of the subarrays This reduction of the main lobe and grating lobe widths decreases the peak side lobe of the CSA beam pattern formed by the product of the two overlapping grating lobes in the subarray beam patterns, such as near u = 1/M+1/N = 0.45 in the top panel of Figure 3. The total power output (black solid line) still has a larger contribution from the second term than the first In this example, the power spectral estimate at us is overwhelmed by the interference coming through the side lobe at ui, motivating the need for reducing the side lobes of the CSA beamformer
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