Improved adaptive detection performance via subspace processing

The performance of subspace adaptive detection is examined for the generalized likelihood ratio detector of E.J. Kelly (1986) and Kelly and K.M. Forsythe (1989). The probability of false alarm (PFA) is independent of the subspace transformation, and depends only upon subspace dimension. The probability of detection depends upon the subspace transformation through a non-adaptive signal-to-noise ratio (SNR) parameter. Subspace processing results in an SNR loss that tends to decrease performance and a gain in statistical stability that tends to increase performance. It is shown that the statistical stability effect dominates the SNR loss for short data records and subspace detectors. A method for designing the subspace transformation to minimize the SNR loss is proposed and illustrated via simulations