Mismatched filter optimization via quadratic convex programming for radar applications

In this article, we consider the problem of computing the optimal mismatched filter with respect to the Peak-to-SideLobe Ratio (PSLR). We propose to solve this problem via a convex quadratically constrained quadratic program that permits to obtain an optimal solution of the problem. The solution is obtain numerically by interior point methods. We show that this convex program can be modified to take into account additional constraints, for instance on the loss in processing gain, the mainlobe or sidelobe shapes and the Integrated Sidelobe Level. This strategy is applied to solve the PSLR problem for phase codes in radar applications, and for antenna arrays with a non negligible number of defective antennas. The results obtained show an interesting improvement of the PSLR for a predefined acceptable loss in processing gain, for both applications.