Band-Inverse TVAR Covariance Matrix Estimation for Adaptive Detection

We characterize a sequence of M interference observations by a time-varying autoregressive model of order m (TVAR(m)). We recently demonstrated that the maximum-likelihood (ML) TVAR(m) covariance matrix estimate (CME) of Gaussian data is the Dym-Gohberg transformation of the sample (direct data) covariance matrix averaged over the T independent training samples (snapshots), provided that T > m. Here we investigate the efficiency of adaptive filters and adaptive detectors based on this CME which (for m << M) permits a significant reduction in training sample support compared with the traditional sample matrix inversion (SMI) method that requires T >= M samples. We analyze truly TVAR(m) or AR(m) (autoregressive) interferences, focusing on the signal-to-noise-ratio (SNR) loss factors in these adaptive filters and adaptive detectors that are due to the finite-sample support T, and the accuracy of false-alarm threshold calculation. We compare the performance of diagonally loaded adaptive matched filter (LAMF) and TVAR(m) adaptive detectors, and find that, even for TVAR(m) interferences, the question of which detector is better strongly depends on the eigenspectrum of the interference covariance matrix. When properly applied, both detectors are significantly better than the adaptive matched filter (AMF) detector (that uses the conventional sample CME with more than M training samples).