Compressed sensing has been employed to reduce the pilot overhead for channel estimation in wireless communication systems. Particularly, structured turbo compressed sensing (STCS) provides a generic framework for structured sparse signal recovery with reduced computational complexity and storage requirement. In this paper, we consider the problem of massive multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) channel estimation in a frequency division duplexing (FDD) downlink system. By exploiting the structured sparsity in the angle-frequency domain (AFD) and angle-delay domain (ADD) of the massive MIMO-OFDM channel, we represent the channel by using AFD and ADD probability models and design message-passing-based channel estimators under the STCS framework. Several STCS-based algorithms are proposed for massive MIMO-OFDM channel estimation by exploiting the structured sparsity. We show that, compared with other existing algorithms, the proposed algorithms have a much faster convergence speed and achieve competitive error performance under a wide range of simulation settings.
Compared with the recent work @cite_29 , the novelty of our work consists of the following aspects. First, we employ a Markov model to efficiently exploit the clustered sparsity of the massive MIMO channel in the angle-frequency domain and angle-delay domain, while @cite_29 uses the nearest neighbor sparsity pattern learning (NNSPL) algorithm first proposed in @cite_12 to exploit the sparsity structure. Note that @cite_19 uses the NNSPL algorithm to exploit the angle domain sparsity of the channel, while @cite_8 uses the NNSPL algorithm to exploit the delay domain sparsity. @cite_29 presents a comprehensive version of the NNSPL algorithm to jointly handle the angle-delay domain sparsity. Second, STCS-FS achieves a considerably lower mean square error (MSE) performance than the NNSPL algorithm with frequency support, while STCS-DS performs slightly better than the NNSPL algorithm with delay support. Third, the computational complexity of STCS is much lower than that of NNSPL. In this regard, we show that the per-iteration complexity of STCS is lower than that of NNSPL; we further show that STCS converges much faster than NNSPL.
@cite_19 @cite_29 @cite_12 @cite_8
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In this letter, we reveal that in the massive multiple-input multiple-output system with large bandwidth, sub-channels of orthogonal frequency division multiplexing share approximately sparse common support due to the frequency difference of subcarriers. We use the approximate message passing with nearest neighbor sparsity pattern learning (AMP-NNSPL) algorithm to adaptively learn the underlying structure for improving the accuracy of channel estimation, where the learning strategy is newly derived by solving an optimization problem. In addition, the performance of the AMP-NNSPL is well predicted by the state evolution. Simulation results demonstrate the superiority of the algorithm in systems with large bandwidth. In millimeter wave (mm-wave) massive multiple-input multiple-output (MIMO) systems, acquiring accurate channel state information is essential for efficient beamforming (BF) and multiuser interference cancellation, which is a challenging task since a low signal-to-noise ratio is encountered before BF in large antenna arrays. The mm-wave channel exhibits a 3-D clustered structure in the virtual angle of arrival (AOA), angle of departure (AOD), and delay domain that is imposed by the effect of power leakage, angular spread, and cluster duration. We extend the approximate message passing (AMP) with a nearest neighbor pattern learning algorithm for improving the attainable channel estimation performance, which adaptively learns and exploits the clustered structure in the 3-D virtual AOA-AOD-delay domain. The proposed method is capable of approaching the performance bound described by the state evolution based on vector AMP framework, and our simulation results verify its superiority in mm-wave systems associated with a broad bandwidth. We consider the problem of recovering clustered sparse signals with no prior knowledge of the sparsity pattern. Beyond simple sparsity, signals of interest often exhibits an underlying sparsity pattern which, if leveraged, can improve the reconstruction performance. However, the sparsity pattern is usually unknown a priori. Inspired by the idea of k-nearest neighbor (k-NN) algorithm, we propose an efficient algorithm termed approximate message passing with nearest neighbor sparsity pattern learning (AMP-NNSPL), which learns the sparsity pattern adaptively. AMP-NNSPL specifies a flexible spike and slab prior on the unknown signal and, after each AMP iteration, sets the sparse ratios as the average of the nearest neighbor estimates via expectation maximization (EM). Experimental results on both synthetic and real data demonstrate the superiority of our proposed algorithm both in terms of reconstruction performance and computational complexity. To address the challenging problem of downlink channel estimation with low pilot overhead in massive multiple-input multiple-output (MIMO) systems, an empirical Bayesian block expectation propagation (EP) algorithm is proposed. Specifically, a block Bernoulli–Gaussian prior channel model is proposed to fit the underlying block sparsity, and a block EP algorithm is derived to estimate the channels more accurately by clustering all the channel taps that pertain to the same delay, while the model parameters are learned by minimizing the Bethe free energy. Simulation results show that the proposed algorithm achieves considerable reduction of pilot overhead in a massive MIMO system with tens of antennas, while maintaining superior channel estimation performance.