Performance analysis of coarray-based MUSIC and the Cramér-Rao bound

Abstract

Sparse linear arrays, such as co-prime and nested arrays, can identify up to O(M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) sources with only O(M) sensors by using co-array based MUSIC. We conduct analytical performance analysis of two coarray based MUSIC algorithms, namely the direct augmentation based MUSIC, and the spatial smoothing based MUSIC. In addition, we analyze the Cramér-Rao bound for sparse linear arrays, and show that for co-prime and nested arrays, it can decrease at a rate of O(M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> ) as the number of sensors M goes to infinity, in contrast to O(M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> ) in the ULA case. We use numerical examples to demonstrate our analytical results.