Direct-MUSIC on sparse arrays

Nested and coprime arrays are sparse arrays which can identify O(m²) sources using only m sensors. Systematic algorithms have recently been developed for such identification. These algorithms are traditionally implemented by performing MUSIC or a similar algorithm in the difference-coarray domain. This paper considers the use of nested and coprime arrays for the case where the number of sources is less than m. It will be demonstrated that there are some important advantages even in this case. With the number of sources limited like this, it is possible to use MUSIC directly on the nested or coprime array rather than in the coarray domain. But owing to array sparsity, the unambiguous identifiability property has to be revisited. This paper first mentions two results for such identifiability. Second, the improvement in the Cramer-Rao bound (over uniform linear arrays or ULAs) is analyzed. One conclusion is that the CRB improvements of nested and coprime arrays are comparable to those of other known sparse arrays such as MRAs. It is also observed that nested and coprime arrays have higher resolvability than the ULA, for a fixed number of sensors.