Design of mismatched filters for long binary codes

Several approaches for sidelobe suppression of pulse compression radar using mismatched filters were proposed for more than 30 years. Barker code of length 13 was invariably used for the performance comparison of these methods. Present day pulse compression radars with large time-bandwidth products use binary code lengths much greater than 13. Very few results of mismatched filter performance were shown for binary codes of length greater than 100. One of the reasons why the results were limited to shorter code lengths was the computational complexity involved in mismatched filter optimization. For example, to apply one of the earlier methods to reduce peak sidelobes, repeated inversion of 1000-by-1000 matrix would be needed for 1000-tap mismatched filter. In this paper, a simple iterative processing algorithm coupled with minimax optimization to reduce peak sidelobe level is proposed that demonstrates mismatched filter performance for code lengths far greater than 1000. The performance of the proposed mismatched filters approaches that of Wiener filtering techniques but with much less complexity and therefore could be applied for designing longer mismatched filters. Furthermore, with this approach mismatched filter iteration could be stopped to stay within the mismatch loss budget.