Matching pursuit algorithms with applications in wireless communication systems

Abstract

Signal decomposition finds its applications in a wide range of areas. The problem of basis selection for signal decomposition consists of determining a small, possibly smallest, subset of vectors chosen from a large redundant set of vectors to match the given data. However, it is shown that finding the sparsest solution to linear systems is a nondeterministic polynomial time (NP) hard problem and requires combinatorial search. For a simpler solution, greedy heuristic algorithms, namely matching pursuit (MP) algorithms are proposed. These algorithms require sequential selection of basis vectors from a set of vectors, termed as dictionary. This dictionary can be undercomplete, overcomplete or complete, depending on the number of basis vectors it contains. The contributions of this dissertation are composed of two complementary parts. In the first part, the limitations of the MP based algorithms are considered. Combination of orthogonal matching pursuit (OMP) algorithm with tree-based combinatorial search techniques is proposed in order to overcome the limitations of the greedy heuristic algorithms. A novel flexible tree-search based OMP (FTB-OMP) algorithm is introduced for sparse signal representations. The algorithm provides some design parameters, giving flexibility to establish a tradeoff between performance and complexity. The efficiency is achieved by using a correlation based pruning in the search tree, and reducing the number of leaves as the depth of nodes increases. It must be noted that this algorithm can be applied to any kind of detection problem that can be modeled as a set of linear equations. In the second part of the dissertation, parameter estimation problems related to wireless communications are considered. These problems are channel estimation, direction of arrival (DOA) estimation and multi-user detection (MUD). These problems are modeled with different types of dictionaries due to their physical characteristics. The channel estimation problem is modeled with undercomplete dictionary. DOA estimation and MUD have overcomplete and complete dictionary models, respectively. It is shown that the family of MP algorithms, especially FTB-OMP, provides a low complexity solution for parameter detection problems with different types of dictionaries. These algorithms provide a practical solution for detection and estimation problems that are widely encountered in wireless communications.