Support recovery for source localization based on overcomplete signal representation

We analyze the performance of a direction-of-arrival (DOA) estimation scheme based on overcomplete signal representation in this paper. We formulate the problem as a support recovery problem with joint sparsity constraints and analyze it in a hypothesis testing framework. We derive both upper and lower bounds on the probability of error by using Chernoff bound and Fano´s inequality, respectively. The lower bound implies that the minimal number of samples necessary for accurate DOA estimation is proportional to the logarithm of the discretization level for arbitrary isotropic sensor arrays. We apply the upper bound to study the effect of noise. For uniform linear array (ULA) with only one source, the upper bound exponent indicates that the optimal overcomplete representation is achieved by uniform partition of the wave number space instead of the DOA space.