Designing good estimators for low sample sizes: Random matrix theory in array processing applications

Traditional signal processing architectures are usually designed to perform well in large sample size situations, i.e. when the number of observations increases to infinity while their dimension remains fixed. In practice, though, these algorithms must work with a relatively low number of samples, and this degrades their performance significantly. This paper proposes the use of general statistical analysis (a branch of random matrix theory) as a systematic approach to derive signal processing architectures that have an excellent performance even when the number of samples and their dimension have the same order of magnitude. The basic rationale is to provide estimators that are consistent when both the number of samples and their dimension increase without bound at the same rate. We demonstrate the usefulness of the approach deriving an estimator of the (asymptotically) optimum loading factor in a minimum variance beamformer for combating the finite sample size effect.