Fast FOCUSS method based on bi-conjugate gradient and its application to space-time clutter spectrum estimation

The focal underdetermined system solver（FOCUSS） is a powerful tool for sparse representation in complex underdetermined systems. This paper presents the fast FOCUSS method based on the bi-conjugate gradient（BICG）, termed BICG-FOCUSS, to speed up the convergence rate of the original FOCUSS. BICGFOCUSS was specifically designed to reduce the computational complexity of FOCUSS by solving a complex linear equation using the BICG method according to the rank of the weight matrix in FOCUSS. Experimental results show that BICG-FOCUSS is more efficient in terms of computational time than FOCUSS without losing accuracy. Since FOCUSS is an efficient tool for estimating the space-time clutter spectrum in sparse recoverybased space-time adaptive processing（SR-STAP）, we propose BICG-FOCUSS to achieve a fast estimation of the space-time clutter spectrum in mono-static array radar and in the mountaintop system. The high performance of the proposed BICG-FOCUSS in the application is demonstrated with both simulated and real data.