Applications of Basis Selection Algorithms in Communication Problems

In this paper, we study the application of sequential basis selection (SBS) algorithms in two different communication problems. These problems represent different cases in terms of the structure of their set of equations. The two considered cases are; undercomplete set of equations (sparse channel estimation problem) and overcomplete set of equations. These cases are carefully selected in order to demonstrate that SBS algorithms can be applied to both types of equations. The basic matching pursuit (BMP) and the orthogonal matching pursuit (OMP) algorithms are selected as the SBS algorithms. In sparse channel estimation problem, the BMP and the OMP algorithms are compared with the least square channel estimates and the minimum variance unbiased estimates (MVUE). It is shown that the OMP algorithm gives estimates that are almost converging to MVUE. In angle of arrival (AOA) detection problem, the detection performances of the BMP and OMP algorithms are compared with the well known MUSIC algorithm and the Cramer Rao bounds. It is shown that their performances exceed that of MUSIC for correlated signals.