A Sidelobe Level Minimization Mismatched Filter using Continuous Phase Frequency-Shift Keying Codes for the Off-Grid Delay Problem

Sidelobe suppression is an essential criterion for radar performance, especially for off-grid points of sampled signals. In this paper, a mismatched filter that minimizes the average sidelobe energy over a continuous time interval is proposed. The main contribution of this paper is the optimization of this problem for continuous phase modulated signals, which present relevant properties for a dual radar-communications system. It is shown that the optimization problem is convex, thus it provides an optimal solution. The performance of the proposed filter in terms of mean Integrated Sidelobe Level is then compared to the classical matched filter, as well as to the usual on-grid mismatched filter, through simulations. The obtained results show that the proposed filter presents greater performance over the continuous sampling cell than the others.