Approximated optimal mismatched filter for off-grid-delayed sampled continuous-phase modulations

In this article, we consider the problem of sidelobes created by off-grid targets in a mismatched filter framework. We show that the optimal mismatched filter computed from the sampled signal is not robust to off-grid delays and may thus produce relatively high sidelobes for such delays. We thus propose to compute an optimal filter that mitigates the sidelobe level for any off-grid delay contained in the delay resolution cell. The proposed solution is an approximation obtained by adding constraints on several sub-delay samples in the general optimization problem. The new problem remains convex and can thus be solved efficiently. Results on sampled chirp signals enable to show the robustness of the proposed solution, and the gain with respect to a Hamming window while ensuring the same loss and mainlobe width.