Sparse channel estimation of MIMO-OFDM systems with unconstrained smoothed l 0 -norm-regularized least squares compresse
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Sparse channel estimation of MIMO-OFDM systems with unconstrained smoothed l0-norm-regularized least squares compressed sensing Xinrong Ye1,2*, Wei-Ping Zhu1,3, Aiqing Zhang1,2 and Jun Yan1
Abstract This paper investigates the sparse channel estimation issue of multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. Beginning with the formulation of least squares (LS) solution to sparse MIMO-OFDM channel estimation, a compressed channel sensing (CCS) framework based on the new smoothed l0-norm-regularized least squares (l2-Sl0) algorithm is proposed. Three methods, namely quasi-Newton, conjugate gradient, and optimization in the null and complement spaces of the measurement matrix, are then proposed to solve the l2-Sl0 unconstrained optimization problem. Moreover, the two former are also applied to solve the l2-Sl0 channel estimation. A number of computer simulation-based experiments are conducted showing a better reconstruction accuracy of the l2-Sl0 algorithm as compared with the smoothed l0-norm (Sl0) algorithm in the presence of noise. The proposed CCS approach can save nearly 25% pilot signals to maintain the same mean square error (MSE) and bit error rate (BER) performances as given by the conventional LS method. Keywords: Sparse channel estimation; Smoothed l0-norm; l2-norm; MIMO-OFDM
1. Introduction Coherent detection and equalization in multiple input multiple output orthogonal frequency division multiplexing (MIMO-OFDM [1]) systems require channel state information (CSI) at the receiver. In real wireless environments, however, the CSI is not known. Therefore, channel estimation is of crucial importance to MIMO-OFDM systems. In various wireless propagation environments, the channel may consist of only a few dominant propagation (nonzero) paths, even though it has a large propagation delay. Thus, the channel impulse response has a sparse nature [2-4]. However, conventional methods, such as least squares (LS), ignore this prior information about the unknown channel leading to lower spectral efficiency. Recently, sparse channel estimation with an objective of decreasing the training sequence to improve spectral efficiency is becoming a hot research topic.
* Correspondence: [email protected] 1 Institute of Signal Processing and Transmission, Nanjing University of Posts and Telecommunications, Nanjing 210003, China 2 College of Physics and Electronic Information, Anhui Normal University, Wuhu 241000, China Full list of author information is available at the end of the article
Previously reported approaches for sparse channel estimation can broadly be categorized into two types, namely the most significant tap (MST) detection and compressed channel sensing (CCS). The MST detection methods [4-6] used a measure to determine if a channel tap was nonzero (‘active’). The disadvantage of this type of methods is that a large number of pilots are needed to render an accurate MST detection and effective channel estimation. The CCS methods are based on the co
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