Paper Info
Title
Robust Adaptive Beamforming for General-Rank Signal Model With Positive Semi-Definite Constraint via POTDC
Abstract
The robust adaptive beamforming (RAB) problem for general-rank signal model with an additional positive semi-definite constraint is considered. Using the principle of the worst-case performance optimization, such RAB problem leads to a difference-of-convex functions (DC) optimization problem. The existing approaches for solving the resulted non-convex DC problem are based on approximations and find only suboptimal solutions. Here, we aim at finding the globally optimal solution for the non-convex DC problem and clarify the conditions under which the solution is guaranteed to be globally optimal. Particularly, we rewrite the problem as the minimization of a one-dimensional optimal value function (OVF). Then, the OVF is replaced with another equivalent one, for which the corresponding optimization problem is convex. The new one-dimensional OVF is minimized iteratively via polynomial time DC (POTDC) algorithm. We show that the POTDC converges to a point that satisfies Karush-Kuhn-Tucker (KKT) optimality conditions, and such point is the global optimum under certain conditions. Towards this conclusion, we prove that the proposed algorithm finds the globally optimal solution if the presumed norm of the mismatch matrix that corresponds to the desired signal covariance matrix is sufficiently small. The new RAB method shows superior performance compared to the other state-of-the-art general-rank RAB methods.
Year
DOI
Venue
2012
10.1109/TSP.2013.2281301
IEEE Transactions on Signal Processing
Keywords
DocType
Volume
array signal processing,concave programming,convex programming,covariance matrices,polynomial matrices,DC optimization problem,KKT optimality condition,Karush-Kuhn-Tucker optimality condition,POTDC algorithm,RAB problem,difference of convex function optimization problem,general rank signal model,nonconvex DC problem,one dimensional OVF,one dimensional optimal value function,polynomial time DC algorithm,positive semi-definite constraint,robust adaptive beamforming,signal covariance matrix,worst case performance optimization,Difference-of-convex functions (DC) programming,general-rank signal model,non-convex programming,polynomial time DC (POTDC),robust adaptive beamforming,semi-definite programming relaxation
Journal
61
Issue
ISSN
Citations 
23
1053-587X
15
PageRank 
References 
Authors
0.71
20
2
Name
Order
Citations
PageRank
Arash Khabbazibasmenj118611.70
sergiy a vorobyov21563113.46