Stopping Criteria Analysis of the OMP Algorithm for Sparse Channels Estimation

Wireless propagation environment utilised by broadband transmission systems usually has a sparse nature, i.e. only several isolated propagation paths are essential for information transfer. Receiver can recover the parameters of the particular paths using greedy, iterative algorithms that belong to the family of compressed sensing techniques. How to stop the iterative procedure, if no precise knowledge about the order of the channel sparsity is available in the receiver a priori, is a key question regarding a practical implementation of the method. The paper provides stopping criteria analysis of the Orthogonal Matching Pursuit (OMP) algorithm that is used as the core of the channel impulse response estimation method for Time-Domain Synchronous OFDM transmission system. There are investigated the residual error and the difference of successive residual errors of the OMP algorithm, as the possible metrics applied to stop the iteration procedure. Finally, a new heuristic stopping rule based on these two errors is proposed and numerically examined.