Pulse compression codes are designed such that the transmitted energy is uniformly spread in time while the autocorrelation function (ACF) has most of its energy in the mainlobe. Upon matched filtering of such codes, the output is their ACF. The peak sidelobe level (PSL) in the ACF of any good code is required to be as low as possible. Barker codes have the least PSL (of unity magnitude) among all biphase codes. In most applications, it is desirable to reduce the sidelobes further. This is achieved via mismatched filters.
Mismatched filters for sidelobe suppression can be based on both Infinite Impulse Response (IIR) and Finite Impulse Response (FIR) filters. FIR mismatched filters can either be designed directly or as sidelobe suppression (SLS) filters in cascade with a matched filter. Length-optimal filters for sidelobe suppression produce the best possible sidelobe suppression for a given filter length. Since all their coefficients are optimized, length optimal filters are not hardware efficient.
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