A Mismatched Filter for Integrated Sidelobe Level Minimization over a Continuous Doppler Shift Interval

A mismatched filter that minimizes the phase code sidelobe level in the presence of Doppler shifts is presented. Taking into account the Doppler shift is essential, as for non-robust to Doppler shift phase codes, the sidelobe level may increase dramatically. The proposed filter is obtained as the solution of an optimization problem that is based on the use of the mean Integrated Sidelobe level over a given Doppler interval. Its cost function can be simply expressed as the product between the zero-Doppler cost function and the generating matrix of the Discrete Prolate Spheroidal Sequences. Comparison with known filters from the literature, for different filter lengths and Doppler interval ranges, shows that the proposed solution provides improved results in terms of mean Integrated Sidelobe Ratio over the considered Doppler interval.