Optimal Mismatched Filter Design for Radar Using Bounded Real Lemma

Mismatched filters can be used in remote sensing, particularly in radars, for sidelobe and interference attenuation. By correlating the received signal with not a copy of the transmitted waveform but a slightly modified signal, it is possible to adjust the sidelobes and interference level at the cost of reduced SNR. We show that the Bounded Real Lemma can be used to find the filter coefficients directly as a solution to a convex problem without need for any approximation or relaxation. Thus, contrary to the previous methods, the globally optimal mismatched filter can be found efficiently even when the Doppler shift of the received signal is significant, such as in the case of slow-time coded radar pulses.