Detection Loss of the Sample Matrix Inversion Technique

The sample matrix inversion (SMI) technique is used for Doppler and/or array processing. Previous analysis of the technique has been in terms of signal-to-interference plus noise ratio (SINR). For Gaussian statistics, this performance measure gives the same loss values as does a probability of detection analysis for linear-time invariant systems. It is often somewhat less valid for nonlinear or time variant systems. As SMI is a nonlinear technique, a probability of detection analysis has been performed. It is shown that the detection loss is larger than that computed by the SINR measure. It is also shown that though the loss predicted by the SINR measure only depends upon the number of measurements used to estimate the covariance matrix, the detection loss depends upon the false alarm probability and the number of adaptable elements in addition to the number of measurements.