Mismatched filter design for radar waveforms by semidefinite relaxation

Radar systems commonly require use of waveforms with low sidelobes and also low cross-correlation if multiple waveforms are being used. It is possible to decrease the apparent peak sidelobe and cross-correlation levels at the receiver by employing a mismatched filter. In this paper, we propose mismatched filter design method that minimizes the peak sidelobe and cross-correlation levels for all Doppler frequencies. The proposed design method is formulated as an optimization problem employing sum of squares representation of nonnegative polynomials and solved using semidefinite relaxation.