Prof. Vishal Monga
Department of Electrical Engineering
The Pennsylvania State University
Dr. Muralidhar Rangaswamy
Senior Advisor for Radar Research
Air Force Research Laboratory
The main theme of the tutorial is to motivate, describe and illustrate the application of convex optimization principles for radar signal processing. The scope of the tutorial is to introduce a variety of optimization problems for adaptive radar processing, including disturbance covariance matrix estimation and waveform design, encountered by real-world systems under challenging practical constraints. Incorporating the aforementioned constraints often results in ill-posed problems where no unique solutions are available and no globally optimal solutions are guaranteed. The central thrust of the tutorial is to introduce novel optimization approaches to solve estimation, detection and waveform design problems core to modern radar signal processing that are complicated by a plethora of real world effects arising from systems and environmental considerations. A key example of a resource constraint in this context is limited number of homogenous training samples for estimating statistics such as disturbance and clutter covariance. Phenomenology based constraints involve understanding and exploiting clutter rank in covariance estimation. On the other hand, hardware limitations force the inclusion of constant modulus constraint in waveform design. With advances in cognitive and multiple-input-multiple-output (MIMO) radar, newer constraints such as orthogonality of waveform codes across multiple transmit antennas, and spectral co-existence with communication systems have emerged. Many of these constraints such as constant modulus and orthogonality are non-convex and tractable methods are needed for their joint incorporation. The tutorial will extensively employ the theory of non-linear optimization, convex analysis, and approximation to expand on recent exciting progress in convex optimization for radar systems.