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.

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Co-prime sensor arrays (CSAs) interleave two uniform linear subarrays that are undersampled by co-prime factors. The resulting nonuniform array requires far fewer sensors to match the spatial resolution of a fully populated ULA of the same aperture. Choosing the co-prime undersampling factors as close to equal as possible minimizes the number of sensors in the CSA. However, the peak side lobe of the CSA is higher than the peak side lobe of the equivalent full uniform linear array (ULA). Increasing the number of sensors in the CSA subarrays by half while maintaining the interelement spacing gurarantees that the CSA peak side lobe is less than that of the full aperture ULA when both arrays use rectangular windows.

Coprime sensor arrays (CSAs) achieve the resolution of a fully populated uniform linear array (ULA) with the same aperture using fewer sensors. The conventional CSA prod uct beamformer suffers from a smaller array gain due to the reduced number of sensors. This paper derives that the condi tional PDFs for detecting Gaussian signals in spatially white Gaussian noise with the CSA product processor are products of Bessel functions. The resulting ROCs are compared with those of the ULA energy detector for a conventional beam former. The Bessel function CSA detection PDFs asymptot ically converge to exponential distributions like the ULA de tection PDFs, revealing that the detection gain of the nonlin ear CSA processor is still proportional to the number of sen sors. Monte Carlo simulations confirm the validity of the an alytic results and the asymptotic approximations to the PDFs.

A semi-coprime array (SCA) interleaves two undersampled uniform linear arrays (ULAs) and a Q-element standard ULA. The undersampling factors of the first two arrays are QM and QN, respectively, where M and N are coprime. The resulting non-ULA is highly sparse. Taking the minimum of the absolute values of the conventional beampatterns of the three arrays results in a beampattern that is free of grating lobes. A SCA requires fewer sensors than other popular sparse arrays such as coprime arrays, nested arrays, and minimum redundant arrays for a given aperture. Also, a SCA exhibits better side lobe patterns than other sparse arrays. This means that a SCA is better able to mask signals away from the look direction and detect weak sources in the presence of strong interferers. In this paper, the author explores the direction of arrival estimation with the SCA. The results illustrate the SCA's ability to reduce the number of sensors and decrease system cost and complexity in various signal processing applications.