An optimal mismatched filter design method

based on the second order cone programming (SOCP)

is proposed for the suppression of sidelobes of the quasi-step frequency waveform.On the basis of derivation of the SNR loss expression

practical application consideration is given to the optimal mismatched processing criteria.A conditioned Min-Max criterion is developed

i.e.

to minimize the maximum sidelobe level with an upper limitation of SNR loss.The optimal mismatched filter design problem is then converted to the dual problem in SOCP.The filter coefficients are obtained by using efficient primal-dual interior-point method for solving SOCP.Thus

sidelobes suppression with constant loss in process gain is implemented.