Phase Retrieval for Radar Waveform Design

Abstract

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 Doppler-shifted and delayed replicas. We consider the inverse problem of designing a radar transmit waveform that satisfies the specified AF magnitude. This process can be viewed as a signal reconstruction with some variation of phase retrieval methods. We provide a trust-region algorithm that minimizes a smoothed non-convex least-squares objective function to iteratively recover the underlying signal-of-interest for either time-or band-limited 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. Our theoretical analysis shows that unique signal reconstruction is possible using signal samples no more than thrice the number of signal frequencies or time samples. Numerical experiments demonstrate that our method recovers both time-and band-limited signals from even sparsely and randomly sampled AFs with mean-square-error of 1×10 −6 and 9 × 10 −2 for the full noiseless samples and sparse noisy samples, respectively.

Near-Field Low-WISL Unimodular Waveform Design for Terahertz Automotive Radar

“…The key idea here is to obtain a complex-valued waveform in the spectral domain such that y u matches the magnitude of the desired beampattern as in (11). Related techniques also include phase-retrieval-based waveform design [45,46]. We address the near-field version of this problem without resorting to phase retrieval methods.…”

Variable electro-optic shearing interferometry for ultrafast single-photon-level pulse characterization

“…are limited to the global phase, reflection and spectral or temporal shift. [15]. The latter two stem from the inability of the method to infer the sign of the cubic part and linear spectral phase, respectively.…”

“…The latter two stem from the inability of the method to infer the sign of the cubic part and linear spectral phase, respectively. Retrieving E (𝑡) is interestingly an inverse problem known to the radar remote sensing technique with a range of available algorithm, well-understood ambiguities and a subject of ongoing vivid research [15].…”