Persymmetric generalised adaptive matched filter for range-spread targets in homogeneous environment

This study deals with the problem of adaptively detecting range-spread targets in Gaussian environment, by assuming a persymmetric structure of covariance matrix. A persymmetric detector based on the two-step generalised likelihood ratio test design scheme is devised to reduce secondary data requirement, which ensures the constant false alarm rate property. Moreover, the general closed-form expressions of the probabilities of the false alarm and detection for the proposed detector are derived, in both cases of deterministic and fluctuating scatter models. Furthermore, the compact versions of forenamed expressions are presented in a special case when the joint space-time dimension of the received signal is odd. Finally, the numerical results of these derived statistical expressions are confirmed with those of Monte Carlo trials.