Effects of lag redundancy on array beam patterns and redundancy patterns for extended co-prime arrays

Abstract

Lag redundancy describes the number of times a given spatial lag is measured by an array. For sparse arrays, the reduction of lag redundancies is generally desirable for lowering cost and processing overhead. However, as lag redundancies determine the natural weighting function of an array’s spectral estimates, the pattern of redundancies dictates the natural beam pattern of a given array. We consider the impact of array sparsity on sidelobe level and array gain in both weighted and unweighted conventional beamforming. This analysis is then applied to co-prime arrays, for which redundancy patterns can be determined based solely on the choice of array length and co-prime factors. It is also shown that the spatial positions of lag redundancies are semi-regular, a desirable feature for sampling some complex environments.