Stage-Determined Matching Pursuit for Sparse Channel Estimation in OFDM Systems

As a sampling paradigm to recover the sparse or compressible signals from very few incoherent linear measurements, compressed sensing (CS) has spurred much interest in recent years. Since tractable recovery algorithm is a crucial and major issue of CS, the greedy pursuit (GP) algorithms are generally preferred to enable accurate reconstruction of sparse or compressible signals from very few noisy incoherent measurements. While selecting multiple “correct” indices per iteration to improve the running time of orthogonal matching pursuit algorithm, the chosen indices are usually not the optimal one due to the iterative short-sighted decisions. In this paper, since the demand for fast reconstruction algorithms-possibly operating in linear time-is of significant interest, an algorithm namely, stage-determined matching pursuit (SdMP) is proposed. The SdMP algorithm exploits the selection of few indices (below the target signal sparsity level) per iteration, and then combines a backtracking or pruning step in some later iterations-albeit after satisfying a sparsity level conditions to refine the selected set. Using the restricted isometry property, the theoretical analysis of the SdMP algorithm and the sufficient conditions (guarantees) for realizing an improved reconstruction performance are presented. Through numerical simulations, it is shown that SdMP outperforms many GP algorithms that select multiple indices per iteration in terms of reconstruction accuracy and the running speed.