Optimization Theory in Radar Signal Processing
The objective of this lecture is to provide a systematic overview of innovative radar signal processing algorithms based on modern optimization theory according to a rigorous and academic style. Specifically, the theoretical basis to address constrained design problems is given, illustrating in the radar context some key/relevant results of modern optimization theory about convex and non-convex problems.
1. Introduction to convex optimization theory:
• Historical notes on the use of optimization theory in Radar;
• Preliminaries on the Constrained Optimization Problems;
• Convex Optimization;
• Convex sets and Radar Examples;
• Convex Functions and Radar Examples,
• Taxonomy of Convex Programming Problems.
2. Convex optimization problems in radar and their solution via CVX:
• Linear Programming (mismatched filter for real observations);
• Quadratic Problems (Capon filter, Knowledge-Based beamformer);
• Second Order Cone Programming, SOCP (Lp-norm minimization filter, robust beamformer);
• SemiDefinite Programming, SDP (MIMO Matrix Beamformer, MIMO Waveform Design in Tracking Applications);
• Max-Det (constrained precision matrix maximum likelihood estimate).
3. Non-convex design problems in radar and the implementation of effective algorithms for their solution:
• Hidden Convex Quadratic Problems based on Rank-One Decomposition (robust detection, waveform design with similarity constraint);
• NP-hard Quadratic Problems based on Relaxation & Randomization (waveform design with phase/PAR constraint);
• Fractional Quadratic Programming (robust detection, robust constrained Doppler filters).