TF: Dimension Reduction Approach to Convex Optimization: Theory, Algorithms, and Applications

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ABSTRACT0515358Irving S. ReedU of Southern CaliforniaIn this research we will study a methodology for solving a class of convex optimization problems (COPs) in analytically feasible and computationally efficient ways. These problems are frequently encountered in many information processing applications, especially in wireless communication systems equipped with multiple transmit (Tx) and receive (Rx) antennas for beamforming, equalization, joint optimal design of Tx-Rx and power control. Two types of convex optimization will be investigated in this research: (1) un-constrainedor constrained with equalities, and (2) constrained with mixed equalities and inequalities. Most ofconventional beamformings (diversity combining) at Rx fall into the first type, whereas, when joint Tx-Rx optimizations with power control are involved, the problems tend to be complicated with mixed constraints, and become the second type. The closed-form solutions to related COPs of the first type are known in many cases, but difficult to compute in real time, whereas some COPs of the second type may not be analytically solvable.