Testing spatial co-prime sampling theory

Abstract

An array of sensors can be used to estimate the direction of arrival of a narrowband signal in the far field with the use of conventional beamforming. In order to avoid spatial aliasing, the distance between the sensors have to be d ≤ λ/2 apart. This is analogous to the Nyquist theorem for sampling in time with fs= 2fo. Co-Prime arrays are non-uniform arrays that can predict what a uniform array with an aperture of L = M×N total sensors can using fewer sensors; they have a total number of sensors L = M + N—1 while maintaining an aperture of M×N sensors in a full uniform line array with λ/2 spacing between elements. Each subarray is uniform linear, equally spaced by Nλ/2 or M λ/2 and then combined to create a non-uniform linear array. The result with the different inter-element spacing between the subarrays is grating lobes in different locations with the exception of the true DOA. Conventional beamforming is done with both subarrays and the outputs are then multiplied together to yield a single beam pattern. The theory to this will be tested using a uniform array of 30 sensors and selecting the data from certain sensors to achieve co-prime sampling.