TY - JOUR
T1 - Quartic Gradient Descent for Tractable Radar Slow-Time Ambiguity Function Shaping
AU - Alhujaili, Khaled
AU - Monga, Vishal
AU - Rangaswamy, Muralidhar
N1 - Funding Information:
Dr. Monga is an elected member of the IEEE Image Video and Multidimensional Signal Processing Technical Committee and is currently on the Editorial Boards of the IEEE TRANSACTIONS ON IMAGE PROCESSING, IEEE SIGNAL PROCESSING LETTERS, and IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY. He is a recipient of the US National Science Foundation CAREER award and a 2016 Joel and Ruth Spira Teaching Excellence award.
Funding Information:
The work of M. Rangaswamy was supported by the Air Force Office of Scientific Research under the Dynamic Data and Information Processing program through project 17RYCOR481.
Publisher Copyright:
© 1965-2011 IEEE.
PY - 2020/4
Y1 - 2020/4
N2 - We consider the problem of minimizing the disturbance power at the output of the matched filter in a single antenna cognitive radar set-up. The aforementioned disturbance power can be shown to be an expectation of the slow-time ambiguity function (STAF) of the transmitted waveform over range-Doppler bins of interest. The design problem is known to yield a nonconvex quartic function of the transmit radar waveform. This STAF shaping problem becomes even more challenging in the presence of practical constraints on the transmit waveform such as the constant modulus constraint (CMC). Most existing approaches address the aforementioned challenges by suitably modifying or relaxing the design cost function and/or the CMC. In a departure from such methods, we develop a solution that involves direct optimization over the nonconvex complex circle manifold, i.e., the CMC set. We derive a new update strategy [quartic-gradient-descent (QGD)] that computes an exact gradient of the quartic cost and invokes principles of optimization over manifolds toward an iterative procedure with guarantees of monotonic cost function decrease and convergence. Experimentally, QGD can outperform state-of-the-art approaches for shaping the ambiguity function under the CMC while being computationally less expensive.
AB - We consider the problem of minimizing the disturbance power at the output of the matched filter in a single antenna cognitive radar set-up. The aforementioned disturbance power can be shown to be an expectation of the slow-time ambiguity function (STAF) of the transmitted waveform over range-Doppler bins of interest. The design problem is known to yield a nonconvex quartic function of the transmit radar waveform. This STAF shaping problem becomes even more challenging in the presence of practical constraints on the transmit waveform such as the constant modulus constraint (CMC). Most existing approaches address the aforementioned challenges by suitably modifying or relaxing the design cost function and/or the CMC. In a departure from such methods, we develop a solution that involves direct optimization over the nonconvex complex circle manifold, i.e., the CMC set. We derive a new update strategy [quartic-gradient-descent (QGD)] that computes an exact gradient of the quartic cost and invokes principles of optimization over manifolds toward an iterative procedure with guarantees of monotonic cost function decrease and convergence. Experimentally, QGD can outperform state-of-the-art approaches for shaping the ambiguity function under the CMC while being computationally less expensive.
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U2 - 10.1109/TAES.2019.2934336
DO - 10.1109/TAES.2019.2934336
M3 - Article
AN - SCOPUS:85083424711
SN - 0018-9251
VL - 56
SP - 1474
EP - 1489
JO - IEEE Transactions on Aerospace and Electronic Systems
JF - IEEE Transactions on Aerospace and Electronic Systems
IS - 2
M1 - 8793214
ER -