Optimal Mismatched Filter Design by Combining Convex Optimization With Circular Algorithm

Mismatched filters (MMF) have been intensively explored for linear-frequency modulation (LFM) waveform sidelobe reduction. Unlike other design strategies, the use of convex optimization (CO) techniques is able to find the optimal design. However, existing studies for CO-based MMF design have focused on minimizing peak sidelobe level (PSL), which might not take the mainlobe widening sacrifice into account. To address this issue, this paper proposes a weighted CO model targeting a flexible tradeoff between sidelobe suppression and mainlobe widening. Moreover, to better control the optimization problem via the presented CO model, the cyclic algorithm (CA) is employed to determine upper limits on mainlobe width. Consequently, the proposed tradeoff MMF design by combining CA with CO would be feasible to meet the requirements of different target detection scenarios. Comprehensive simulations have been carried out to demonstrate the effectiveness of our presented MMF design.