On ambiguity function shaping for broadband constant-modulus signals

Abstract

Constant-modulus signals such as m-sequences are known to have good autocorrelation properties, as well as good peak-to-average power ratio that allows for full utilization of the transmitter’s power. However, the broadband ambiguity surface for such signals exhibit high sidelobe levels that are undesirable in applications where the signal is subject to broadband Doppler. We formulate an optimization problem to minimize the maximum sidelobe levels of such signals over a set of delay-Doppler values. This problem is non-convex and difficult to solve. We explore a convex regularization of the problem that can readily be solved using semi-definite programming, and show that optimal or near-optimal signals can be designed using this method. We further explore some heuristic methods to reduce computational and memory complexity of the solution, to enable us to design longer signals. We demonstrate the advantage of our signal design over conventional unimodular signals for target detection in strong clutter in a continuous active sonar application.