Extension of the Reed-Mallett-Brennan loss for application to stap with collected data

The post-processed signal-to-interference-plus-noise ratio (SINR) has emerged as a critical performance metric in the assessment of space-time adaptive processing (STAP) as applied to radar data collected from multidimensional arrays. In their seminal analysis, Reed, Mallett and Brennan analytically characterized the loss in SINR (ldquoRMB lossrdquo) realized due to the use of an estimate of the interference environment with a finite set of samples relative to the exact result under certain conditions. While providing several well-known ldquorules-of-thumbrdquo that allows the RMB loss to be incorporated into system level analysis, this original formulation can not generally be directly applied to collected radar data since it assumes knowledge of the exact interference covariance which typically is not available. In this paper, the RMB loss is extended to the practical situation where the exact covariance is not available, as with collected radar data. As a consequence, both the adaptive weight and residual interference-plus-noise power must be estimated in computing SINR. Three new approaches for accomplishing this are analyzed and compared in terms of their theoretically derived probability distribution functions, means and variances relative to each other as well as the original RMB loss result. The developed theory is extensively verified with simulation results. A key result is the need for two independent sets of training data to accurately compute the SINR when sample support is limited. New rules-of-thumb are suggested for the amount of training data needed from these two sets of data (i.e. two groups of local range data) to achieve an accurate assessment of SINR loss. This work provides new analytical tools that can be used to better understand the true SINR loss performance of STAP with collected radar data.