Strong consistency of FSD detection schemes

Recently, a fast signal subspace decomposition technique (FSD) suitable for parallel processing which achieves a significant reduction in computational complexity for large arrays with few sources was developed. Two new detection schemes used in conjunction with the FSD algorithm are presented. One is based on a series of statistical hypothesis tests; the other uses an information theoretic criterion. Unlike conventional information criterion and minimum description length detection schemes, the new FSD detection schemes do not require knowledge of all the eigenvalues, and therefore can be carried out at each intermediate step of the FSD algorithm. Using numerical analysis and multivariate statistics, FSD-based detection schemes are shown to be strongly consistent, i.e., estimation of the signal subspace dimension will be correct with probability one as the number of data samples tends to infinity