A lower bound for the maximum likelihood ratio: Sparse antenna array applications

The authors recently introduced a novel approach for detection-estimation of more uncorrelated Gaussian sources than sensors in sparse linear antenna arrays that is critically dependent on accurate likelihood-ratio (LR) maximisation over the set of candidate model covariance matrices. Here we introduce a non-asymptotic lower bound for the maximised LR. Any solution could now be tested against this bound with a high probability of correctly identifying a non-optimal solution. We demonstrate that existing techniques, based not on the exact LR criteria, but on related criteria, fail to give solutions that approach this lower bound for typical sparse array applications. A novel LR optimisation technique is introduced; for such sensitive sparse array problems, this technique is shown to generate a class of solutions that statistically exceed the lower bound. Some properties of solutions belonging to this class are discussed.