Non-Integer Arrays for Array Signal Processing

Abstract

Linear arrays with sensors at integer locations are widely used in array signal processing. This paper considers arrays where sensor locations can be rational numbers. It is demonstrated that such rational arrays have some important advantages over integer arrays. For example, they offer more flexibility and reduced DOA estimation error when a limited number of sensors are to be distributed in a fixed aperture. Sparse and coprime rational arrays are introduced to achieve this. Extensive Monte-Carlo simulations demonstrate that rational arrays can perform close to CRB even at low SNR and a small number of snapshots compared to the integer arrays. Furthermore, they can resolve the closely spaced sources and provide smaller MSE for almost all two-DOA configurations. Next, if the signals are impinging from a restricted spatial scope, rational arrays can better utilize this information and place sensors over a larger aperture while still maintaining unique identifiability property. Results on steering vector invertibility of general rational arrays and unique identifiability with rational coprime arrays are provided. In order to do this, some rational extensions of integer number theoretic concepts such as greatest common divisor and coprimality are required, which are introduced as well. The theoretical results are further extended to arbitrary arrays where sensor locations may even be irrational.

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