MIMO/OFDM convex optimization applications

Convex optimization techniques are widely used in the design and analysis of variety of problems especially in communications and signal processing. Many communication problems can either be defined as or be converted into convex optimization problems. Convex optimization makes the analysis and numerical solutions much easier. In this paper, a convex optimization survey is presented. It introduces the recent progress in convex optimization algorithms which are used in digital communications and signal processing applications. The goal of this paper is to give an overview of basic concepts of convex sets, functions and convex optimization problems. Hence, engineering problems using modern convex optimization can be recognized and formulated. Multi-Input-Multi-Output (MIMO) and Orthogonal Frequency Division Multiplexing (OFDM) problems are discussed in more details. As a proposed work, a special problem is discussed. Formulation of this problem as a convex problem and its solution is proposed.