LAUSR

Sparse arrays reduce the number of redundant measurements for lags on an array in comparison to fully populated arrays. For ideal measurements, where spatial stationarity is maintained and measurement error is minimal, the performance of such arrays can be shown to be similar to that of a uniform array of the same length with appropriate processing techniques. However, for complex environments with limited spatial coherence or noisy measurements, array sparsity can impact performance. We construct a simple model that relates the relative positions of redundant measurements and channel coherence length to the variance of covariance function estimates, determine a set of lag measurement weightings that minimize said variance for a given set of redundant lag positions, determine a set of conditions on which a uniform weighting is optimal, and demonstrate that regularly spaced lag repetitions optimally sample a spatially varying covariance function.