Mismatched Filtering of Doppler Tolerant Codes for Multi-code Sonar Systems

Sets of transmitted signals used for sonar sensing applications must have good correlation properties, conformance of the magnitude to a target profile, and Doppler tolerance. Achieving an optimal solution with all three constraints along with the receiver, transmitter and channel effects is a complex and non-convex problem. Whereas optimising signals for the first two constraints is relatively easy, a Doppler shift degrades the sidelobe levels considerably so that achieving low and flat sidelobe levels is not guaranteed with the use of a matched filter. An alternative is to design a mismatched filter for reducing the sidelobe levels beyond the limits achievable with a matched filter. Designing a mismatched filter which is longer in length than a matched filter offers greater flexibility in terms of the filter coefficients that can be tuned. Designing a signal may be a non-convex problem, but with the signal fixed, design of a mismatched filter is convex. We compare two different methods for designing mismatched filters for Doppler tolerant codes. Results from both our designs show flat sidelobes at least 2 dB lower than those of a matched filter.