Unimodular Waveform Design that Minimizes PSL of Ambiguity Function over A Continuous Doppler Frequency Shift Region of Interest

In active sensing systems, waveforms with ambiguity functions (AFs) of low peak sidelobe levels (PSLs) across a time delay and Doppler frequency shift plane (delay-Doppler plane) of interest are desirable for reducing false alarms. Additionally, unimodular waveforms are preferred due to hardware limitations. In this paper, a new method is proposed to design unimodular waveforms with PSL suppression over a continuous Doppler frequency shift region, based on the discrete-time ambiguity function (DTAF). Compared with existing methods that suppress PSL over grid points in the delay-Doppler plane by using the discrete ambiguity function (DAF), we regard the DTAF optimization problem as of more practical interest because the Doppler frequency shifts observed in echo signals reflected from targets are inherently continuous rather than discrete. The problem of interest is formulated as an optimization problem with infinite constraints along with unimodular constraints. To the best of the authors' knowledge, such a problem has not been studied yet. We propose to reformulate a non-convex semi-infinite programming (SIP) to a semidefinite programming (SDP) with a finite number of constraints and a rank-one constraint, which is then solved by the sequential rank-one constraint relaxation (SROCR) algorithm. Simulation results demonstrate that the proposed method outperforms existing methods in achieving a lower PSL of AF over a continuous Doppler frequency shift region of interest. Moreover, the designed waveform can effectively prevent false alarms when detecting a target with an arbitrary velocity.