Dr. Kumar Vijay Mishra of University of Maryland, College Park

The ability of a radar to discriminate in both range andDoppler 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 may 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. 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 FrFT-based 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 experiment

Biography:

Dr. Mishra obtained a Ph.D. in electrical engineering and M.S. in mathematics from
The University of Iowa in 2015, and M.S. in electrical engineering from Colorado State University
in 2012, while working on NASA’s Global Precipitation Mission Ground Validation (GPM-GV)
weather radars. He received his B. Tech. summa cum laude (Gold Medal, Honors) in electronics
and communication engineering from the National Institute of Technology, Hamirpur (NITH),
India in 2003. is the Distinguished Lecturer of the IEEE Communications Society (2023-2024),
IEEE Aerospace and Electronic Systems Society (AESS) (2023-2024), IEEE Vehicular Technology
Society (2023-2024), IEEE Geoscience and Remote Sensing Society (2024-2025), and IEEE Future
Networks Initiative (2022).

Address:University of Maryland, College Park, , MD 20742, USA · 301.405.1000, United States, MD 20742