On ambiguity function shaping for broadband constant-modulus signals

• Published in: Signal processing 2020-01, Vol.166, p.107224, Article 107224
• Main Authors: Chitre, Mandar, Tian, Jing, Vishnu, Hari
• Format: Article
• Language: English
• Subjects: Broadband ambiguity function; Continuous active sonar; Doppler; Semi-definite programming; Unimodular signal design; Wideband ambiguity function
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2019.07.017

•Broadband signal design formulation to minimize maximum sidelobe level with Doppler.•Biconvex optimization based solution to solve the signal design problem.•Computationally efficient version of the method to speed up method by 100x.•Study of tuning of free parameters tuning for good performance.•Demonstration of the method for a continuous active sonar application. 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.