

Kumar Vijay Mishra (US ARL)
Time: 9:30 am on Friday, October 7th, 2022
Phase retrieval for radar waveform design
The ability of a radar to discriminate in both range and Doppler velocity is completely characterized by the ambiguity function (AF) of its transmit waveform. Mathematically, it is obtained by correlating the waveform with its Dopplershifted and delayed replicas. We consider the inverse problem of designing a radar transmit waveform that satisfies the specified AF magnitude. This process may be viewed as a signal reconstruction with some variation of phase retrieval methods. We provide a trustregion algorithm that minimizes a smoothed nonconvex leastsquares objective function to iteratively recover the underlying signalofinterest for either time or bandlimited support. The method first approximates the signal using an iterative spectral algorithm and then refines the attained initialization based upon a sequence of gradient iterations. Next, we consider recovering the radar waveform from the magnitude of the fractional Fourier transform (FrFT) formulation of its AF. The advantage of this formulation is that the recovery of the waveform now becomes a convex optimization problem. Our theoretical analyses for both AF and FrFTbased AF problems show that unique waveform reconstruction is possible using signal samples no more than thrice the number of signal frequencies or time samples. We demonstrate the recovery via numerical experiments.


