Mismatched filter optimization for radar applications using quadratically constrained quadratic programs

This paper deals with the problem of optimal filter computation for specific radar applications.We consider here a method for finding the mismatched filter that minimizes the peak-to-sidelobe ratio. This method is based on a reformulation of the optimization problem as a convex quadratically constrained quadratic program (QCQP) and ensures that any found solution is a global solution of the problem. This formulation also enables the insertion of additional constraints, e.g., a constraint on the loss in processing gain of the optimal filter. We study in this context the robustness of the proposed filter to phase errors. Then, we propose to adapt this QCQP to deal with Doppler shifts and provide results for specific applications. Next, we investigate the possibility to use mismatched filters to reduce the high sidelobe level observed along the range axis of multiple-input multiple-output (MIMO) ambiguity functions produced by phase codes. We propose two MIMO receiver architectures that enable the integration of mismatched filters. The first architecture tries to minimize all autocorrelations and cross-correlations of the transmitted phase codes, while the second architecture computes mismatched filters adapted to the signals transmitted in different angular direction. The latter approach enables us to obtain a MIMO ambiguity function close to the perfect thumbtack shape.