Massive Massive Multiple-input Multiple-output Channel Research Articles

Semi-blind sparse channel estimation using regularized expectation maximization

In Massive multiple-input multiple-output (MIMO) systems, channel estimation is crucial. The large size of the antennas causes a significant pilot and feedback overhead, making it challenging to estimate channels in massive MIMO systems. Besides, the studies have shown that mmWave channels are sparse due to the limited number of dominant propagation paths. Therefore, the motivation of this paper is to exploit the inherent sparsity of the massive mmWave MIMO channels to develop a semi-blind channel estimation with reduced number of pilots. To this goal, an expectation maximization (EM) based technique has been developed which leverages the sparsity of the underlying channel for its better estimation. An iterative approach is proposed to solve the modeled problem which simultaneously updates the channel coefficients and data symbols using available data and system structure at each iteration. The proposed method imposes sparsity with the aid of Smoothed L0 norm (SL0) in the M-step. The simulation results demonstrate the proposed method have quick convergence and lower channel estimation error compared to the existing methods. As a quantitative evaluation, the proposed method attains the normalized mean square error of 9×10−2 and 7×10−3 at SNR=5dB and SNR=15dB, respectively.

An Optimized Sequence for Sparse Channel Estimation in a 5G MIMO System

ABSTRACT Recently, the massive Multiple-Input Multiple-Output (MIMO) system has been integrated with machine learning approaches to realise automatic channel state information detection. These methods need high computational complexity due to the lack of optimal training sequences and the failure to control the sparsity assembly based on massive MIMO. Moreover, it does not consider optimised training sequences based on a compressive sensing approach in the presence of contamination. Thus, this paper proposed an enhanced deep learning model with an optimised pilot training sequence for sparse channel estimation in a 5 G massive MIMO system. Initially, the system and sparse block channel impulse response model will be constructed by considering the time-domain synchronous Generalized Frequency Division Multiplexing (GFDM) system and additive white Gaussian noise (AWGN). In the proposed work, a seagull optimisation algorithm is developed to design the training pilot sequence depending on the coherence properties of the sensing matrix, which is used to recover the channel impulse response. Then, the sparse massive MIMO channel is evaluated by proposing a new deep channel estimator with an enhanced stacked auto encoder (D-ESAE). The proposed channel MSE is 10−6, the bit error rate is 0.04, and NMSE is 10−9 at 40 dB SNR through Matlab simulation.

Low-Complexity Variational Bayesian Inference Based Groupwise Detection for Massive MIMO Uplinks

This paper proposes a low-complexity groupwise detection scheme for massive multiple-input multiple-output (MIMO) systems based on two key features of massive MIMO channels. First, most inter-user correlations tend to be negligible as the number of antennas <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> at the base station (BS) increases, while some users might have a high correlation that is indistinguishable for linear projection-based detectors. We hence develop a variational Bayesian inference-based groupwise (VBI-G) detector based on a factorization approximation of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> probability of transmitted symbols, which sequentially performs nonlinear detection for small groups of highly correlated users without computations of large-scale matrices. Second, the variation of normalized inter-user correlation is insignificant over a wide range of frequency, thereby user grouping based on correlation coefficients can be performed on a wideband basis. Accordingly, we propose a low-complexity incremental greedy grouping algorithm for minimizing the Kullback-Leibler divergence of the unconditioned posterior probabilities with the constraint of a maximum group size. Theoretical analysis proves that for a BS equipped with a uniform linear array, the maximum group size grows logarithmically with the number of users <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> with high probability in the regime <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M,K</i> → ∞ with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K/M</i> < 1/2 under the worst line-of-sight propagation condition. Simulation results verify that the proposed VBI-G detector achieves superior performance with an extremely low computational overhead for massive MIMO systems.

A Novel THz Massive MIMO Beam Domain Channel Model for 6G Wireless Communication Systems

In this paper, a three dimensional (3D) geometry based stochastic model (GBSM) considering planar antenna array is firstly proposed for the sixth generation (6 G) terahertz (THz) massive multiple-input multiple-output (MIMO) wireless communication systems. Then, a novel beam domain channel model (BDCM) is derived from the proposed GBSM based on the Fourier transform matrix from the spatial domain to the angle domain in horizontal and vertical directions simultaneously. The THz propagation characteristics, including non-negligible diffuse scattering and limited order of reflection, are considered in these two channel models. In addition, the proposed GBSM and BDCM can capture the spherical wavefront and spatial non-stationarity characteristics in massive MIMO channels by deriving steering vectors of near-field clusters and partly visible clusters, respectively. The angle-domain sparsity property of the BDCM can be observed, which helps reduce the complexity of the GBSM and improve the mathematical tractability. Typical statistical properties of the proposed GBSM and BDCM are derived and compared. The effects of the spherical wavefront on space-time-frequency correlation functions (STF-CFs) and channel capacity are also studied for the proposed GBSM and BDCM. The power leakage of the BDCM caused by the spherical wavefront and visible region (VR) is thoroughly analyzed. It is found that the statistical properties of the GBSM and BDCM fit well and are considerably influenced by the spherical wavefront and VRs.

A Fully Bayesian Approach for Massive MIMO Unsourced Random Access

In this paper, we propose a novel fully Bayesian approach for the massive multiple-input multiple-output (MIMO) massive unsourced random access (URA). The payload of each user device is coded by the sparse regression codes (SPARCs) without redundant parity bits. A Bayesian model is established to capture the probabilistic characteristics of the overall system. Particularly, we adopt the core idea of the model-based learning approach to establish a flexible Bayesian channel model to adapt the complex environments. Different from the traditional divide-and-conquer or pilot-based massive MIMO URA strategies, we propose a three-layer message passing (TLMP) algorithm to jointly decode all the information blocks, as well as acquire the massive MIMO channel, which adopts the core idea of the variational message passing and approximate message passing. We verify that our proposed TLMP significantly enhances the spectral efficiency compared with the state-of-the-arts baselines, and is more robust to the possible codeword collisions.

A Novel 3D Beam Domain Channel Model for UAV Massive MIMO Communications

Due to the agile maneuverability, unmanned aerial vehicles (UAVs) have shown great promise for on-demand communications in the next-generation wireless networks. Considering the massive multiple-input multiple-output (MIMO) configuration, this paper proposes a novel three-dimensional (3D) beam domain channel model (BDCM) for UAV communications. Through dividing the large antenna array into several sub-arrays and classifying multipath components as near-field and far-field components, the proposed BDCM takes the spherical wave front (SWF) and array non-stationarity into account. Channel statistical properties including spatial-temporal-frequency correlation function (STF-CF), root-mean-squared (RMS) Doppler spread, beam spread, channel matrix collinearity (CMC), and stationary time interval are derived and simulated for the proposed BDCM. Influences of SFW and non-stationary properties on the statistical properties and system performance are analyzed. Simulation results show that, compared with the equivalent geometry-based stochastic model (GBSM), the proposed BDCM has better temporal correlation, while BDCM and GBSM are equivalent in the system performance evaluation. Furthermore, the performance of the proposed BDCM is evaluated in terms of accuracy, complexity, and pervasiveness. The results show that the proposed BDCM can represent massive MIMO channel properties accurately with low complexity and good compatibility.

Two-Stage Channel Estimation Using Convolutional Neural Networks for IRS-Assisted mmWave Systems

Intelligent reflecting surface (IRS) is expected to be an essential component of next-generation wireless communication networks due to its potential to provide similar or higher array gain with lower hardware cost and energy consumption compared with massive multiple-input--multiple-output (MIMO) technology. However, channel estimation in IRS-assisted communication systems is more challenging than that in conventional systems. In this article, we propose a two-stage channel estimation approach using deep learning in millimeter-wave (mmWave) communication systems with a hybrid passive/active IRS structure. In the first stage, the sparsity of the mmWave massive MIMO channel in the angular domain is exploited to estimate the amplitude of the sparse channel through a convolutional neural network. In this way, the indices of the nonzero entries of the sparse channel can be simultaneously obtained. In the second stage, the channel is reconstructed by solving a least squares problem with the acquired indices. The simulation results show that the proposed channel estimation scheme could achieve better performance with manageable complexity over the existing solutions.

Sparse angular reciprocity learning for massive MIMO channel estimation

Sparse angular reciprocity refers to the fact that downlink and uplink channels share common sparsity in angular domain. This sophisticated sparsity can be exploited to improve the channel estimation performance for massive multiple-input multiple-output (MIMO) systems. All the existing sparse angular reciprocity methods solve the uplink channel estimation problem independently with an LS estimator in the first stage, and then assist the downlink channel estimation with the sparse angular reciprocity in the second stage. Such a two-stage scheme, as well as the prior LS estimator, will inevitably result in performance loss. To overcome the drawback, we consider the downlink and uplink channel estimation problems as a whole one, and present a new sparse angular reciprocity learning framework to leverage the sparse angular reciprocity. Since the framework provides a joint solution for the downlink and uplink channel estimation in the sense of Bayesian optimality, it is expected to yield higher channel estimation accuracy. Moreover, we devise an efficient variational Bayesian inference (VBI)-based algorithm to automatically decouple the uplink channel. The proposed method can further enhance the channel estimation performance as the prior LS estimator is avoided. Another advantage is that it can be applied to the underdetermined uplink channel estimation problem, where the number of uplink pilot symbols is less than the number of MUs. Simulation results verify the superiority of the proposed method.

A Novel 3-D Beam Domain Channel Model for Maritime Massive MIMO Communication Systems Using Uniform Circular Arrays

In this paper, we first propose a 3-dimensional (3-D) non-stationary geometry-based stochastic model (GBSM) for maritime massive multiple-input multiple-output (MIMO) communication systems with the uniform circular array (UCA) configuration. To reduce the model complexity and improve the mathematical tractability, a novel beam domain channel model (BDCM) is then proposed based on the transformation of the corresponding GBSM from the array domain to the beam domain for maritime communications. In the proposed BDCM, the beamforming matrices suitable for UCA structures are constructed and their invertibility is demonstrated to ensure the practicability of the BDCM. Two methods are used to characterize the array non-stationarity in maritime massive MIMO channels. First, the evolution of clusters over the large UCA is modeled by the visibility regions (VRs) attached to individual multipath components (MPCs). Second, the sphere wavefront (SWF) effect is captured by dividing the UCAs into several sub-arrays. Based on the proposed GBSM and BDCM, some important channel statistical properties are studied and compared, including channel power, power leakage, space-time-frequency correlation function (STF-CF), and root-mean-square (RMS) Doppler/beam spreads. Also, the importance of considering the array non-stationarity in maritime communication channels is revealed.

Deep learning-based massive MIMO channel estimation with reduced feedback

The downlink channel state information (CSI) must be available on the base station (BS) side to take advantage of all the features of massive multiple-input multiple-output (MIMO) systems. The channel estimation in massive MIMO systems is a challenging task because of the huge pilot and feedback overhead due to the large size of antennas. In this paper, we have proposed a multi task deep network for the channel estimation with the aim of decreasing the pilot and feedback overhead. An encoder network is designed to compress the received signal and reduce the feedback overhead. Furthermore, a decoder network is developed to reconstruct the compressed feedback. The estimator network is suggested to provide the channel estimation from the reconstructed feedback. The performance of the presented scheme has been evaluated in various simulation scenarios. The results confirm that the proposed method is capable of estimating the channel more accurately than the contemporary works. Moreover, this method has reduced the feedback and pilot overhead to a great extent.

A Novel 3D Beam Domain Channel Model for Massive MIMO Communication Systems

Massive multiple-input multiple-output (MIMO) channels are distinctly characterized by their array non-stationarity, which has not been considered in the existing beam domain channel models (BDCMs). In this paper, the array non-stationarity of massive MIMO channels is modeled by the spatially consistent visibility regions (VRs) over a large uniform planar array (UPA) in terms of individual multipath components (MPCs). Based on this, a novel three-dimensional (3D) BDCM incorporating the effects of array non-stationarity is proposed. Statistical properties of the proposed BDCM including channel power, power leakage, space-time-frequency correlation function (STF-CF), and beam spread are derived. The ergodic and outage capacities are evaluated. The impacts of array non-stationarity on those statistics and channel capacity are analyzed. Results suggest that the beamwidths or spatial resolutions of the BDCM for different directions are not equal due to the array non-stationarity. This in turn increases the power leakage and correlation between channel elements and reduces the beam domain channel capacity.

Covert Communication for Spatially Sparse mmWave Massive MIMO Channels

Covert communication, also known as communication with low probability of detection, aims to provide reliable communication for legal users and prevent any other user from detecting the occurrence of legal communication. Motivated by the strong need of security links of the next generation communication systems, we study covert communication with millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) hybrid beamforming. Consistent with existing studies on covert communication, we use the Kullback-Leibler (KL) divergence and the total variation (TV) distance as the covertness measure. Under both covertness measures, for block fading channels, we derive the covert transmission rate with and without artificial noise. These results are obtained by optimizing the transmit power and the jamming power to satisfy the covertness constraints and to maximize the transmission rate. Specifically, when artificial noise is allowed, we show that there exists an optimal jamming power to achieve the covert transmission rate given the transmit signal power. Furthermore, we propose a metric to measure the inherent sparsity of the mmWave massive MIMO channel in the spatial domain, and study its effect on the covertness measures and the corresponding covert transmission rates. Our results provide insights and benchmarks for the design of practical covert communication systems with mmWave massive MIMO.

A Novel 3D Non-Stationary Massive MIMO Channel Model for Shortwave Communication Systems

In this paper, a novel three-dimensional (3D) non-stationary massive multiple-input multiple-output (MIMO) channel model for shortwave communication systems is proposed. Three transmission modes, i.e., groundwave, near vertical incident skywave (NVIS), and long-distance skywave are considered to eliminate the blind area and realize the full-coverage for shortwave communication. The ionospheric absorption loss and surface reflection loss during multi-hop transmissions are explored in the proposed channel model. In addition, new massive MIMO channel characteristics including the near-field spherical wavefront effect and spatial non-stationarity are considered. Temporal and frequency non-stationarities are also modeled due to the receiver (Rx) mobility and large relative bandwidth, respectively. The analytical and simulated space cross-correlation function (SCCF), time autocorrelation function (TACF), and frequency correlation function (FCF) of the proposed model are compared. The simulated path loss and singular value spread (SVS) are compared with those of the corresponding channel measurements, illustrating good fittings. In addition, the delay power spectral density (PSD) and Doppler PSD, and channel capacity are also simulated and analyzed. The proposed model can be used as a basis for the design and construction of shortwave communication systems.

Noncoherent space-time coding for correlated massive MIMO channel with Riemannian distance

This paper considers a massive multiple-input multiple-output (MIMO) uplink system in correlated Rayleigh fading channels. A transmitter with two antennas needs to send data timely to a base station with a large number of antennas. We assume the channel coefficients keep constant during two consecutive time slots and change independently in the following two successive time slots. We construct a Riemannian-distance (RD) based noncoherent detector for such a system. Also, we propose a novel noncoherent parametric space-time coding method. We first attain the closed-form solutions of the optimal sub-constellation structures for fixed modulation orders with the max-min rule. Then, we determine the optimal modulation order for each sub-constellation. The analytical results show that our proposed scheme can attain a larger RD distance than the existing massive uniquely factorable constellation coding (MUFC) scheme. Further, we illustrate that our proposed coding scheme enables a low-complexity RD decoding algorithm. Simulation results show that our proposed scheme performs better than the current phase shift keying modulation scheme and MUFC scheme.

Classification and Comparison of Massive MIMO Propagation Channel Models

Considering great benefits brought by massive multiple-input–multiple-output (MIMO) technologies in the Internet of Things (IoT), it is of vital importance to analyze new massive MIMO channel characteristics and develop corresponding channel models. In the literature, various massive MIMO channel models have been proposed and classified with different but confusing methods, i.e., physical versus analytical method and deterministic versus stochastic method. To have a better understanding and usage of massive MIMO channel models, this work summarizes different classification methods and presents an up-to-date unified classification framework, i.e., artificial intelligence (AI)-based predictive channel models and classical nonpredictive channel models, which further clarify and combine the deterministic versus stochastic and physical versus analytical methods. Furthermore, massive MIMO channel measurement campaigns are reviewed to summarize new massive MIMO channel characteristics. Recent advances in massive MIMO channel modeling are surveyed. In addition, typical nonpredictive massive MIMO channel models are elaborated and compared, i.e., deterministic models and stochastic models, which include the correlation-based stochastic model (CBSM), geometry-based stochastic model (GBSM), and beam-domain channel model (BDCM). Finally, future challenges in massive MIMO channel modeling are given.

Clustered Sparse Bayesian Learning Based Channel Estimation for Millimeter-Wave Massive MIMO Systems

In this article, we present two clustered sparse Bayesian learning (Cluster-SBL) channel estimation algorithms for millimeter-wave (mmWave) massive multiple-input-multiple-output (MIMO) systems. Different from prior literature, channel path correlations at both the transmitter and the receiver are considered and exploited for estimation performance enhancement. Specifically, we first propose a Kronecker product-based multivariate Gaussian (KP-Gaussian) prior model for mmWave massive MIMO channels, which captures not only sparsity but also the widely existing clustering channel property in mmWave communications. Then, a channel approximation method is derived and leveraged to overcome the challenge caused by channel priors' uncertainty due to the varying propagation environments and improve the robustness of the channel estimation algorithm against channel sparsity. After that, the Cluster-SBL channel estimation algorithm, which is developed based on the expectation maximization (EM) framework and has superior estimation accuracy and high robustness, is proposed. Moreover, to reduce the computation complexity in the channel estimation for practical applications, we also propose an efficient Cluster-SBL (eCluster-SBL) channel estimation algorithm. It is highly beneficial to mmWave massive MIMO systems, especially when the angular resolution is relatively high. Numerical results reveal that, compared with the existing compressed sensing-based and Bayesian criterion-based algorithms, the proposed two channel estimation algorithms exhibit the better performance from both the aspect of estimation accuracy and the aspect of robustness.

Enforcing Statistical Orthogonality in Massive MIMO Systems via Covariance Shaping

This paper tackles the problem of downlink data transmission in massive multiple-input multiple-output (MIMO) systems where user equipments (UEs) exhibit high spatial correlation and channel estimation is limited by strong pilot contamination. Signal subspace separation among UEs is, in fact, rarely realized in practice and is generally beyond the control of the network designer (as it is dictated by the physical scattering environment). In this context, we propose a novel statistical beamforming technique, referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MIMO covariance shaping</i> , that exploits multiple antennas at the UEs and leverages the realistic non-Kronecker structure of massive MIMO channels to target a suitable shaping of the channel statistics performed at the UE-side. To optimize the covariance shaping strategies, we propose a low-complexity block coordinate descent algorithm that is proved to converge to a limit point of the original nonconvex problem. For the two-UE case, this is shown to converge to a stationary point of the original problem. Numerical results illustrate the sum-rate performance gains of the proposed method with respect to spatial multiplexing in scenarios where the spatial selectivity of the base station is not sufficient to separate closely spaced UEs.

MpNet: Variable Depth Unfolded Neural Network for Massive MIMO Channel Estimation

Massive multiple-input multiple-output (MIMO) communication systems have a huge potential both in terms of data rate and energy efficiency, although channel estimation becomes challenging for a large number of antennas. Using a physical model allows to ease the problem by injecting a priori information based on the physics of propagation. However, such a model rests on simplifying assumptions and requires to know precisely the configuration of the system, which is unrealistic in practice. In this paper we present mpNet, an unfolded neural network specifically designed for massive MIMO channel estimation. It is trained online in an unsupervised way. Moreover, mpNet is computationally efficient and automatically adapts its depth to the signal-to-noise ratio (SNR). The method we propose adds flexibility to physical channel models by allowing a base station (BS) to automatically correct its channel estimation algorithm based on incoming data, without the need for a separate offline training phase. It is applied to realistic millimeter wave channels and shows great performance, achieving a channel estimation error almost as low as one would get with a perfectly calibrated system. It also allows incident detection and automatic correction, making the BS resilient and able to automatically adapt to changes in its environment.

A 3-D Non-Stationary Model for Beyond 5G and 6G Vehicle-to-Vehicle mmWave Massive MIMO Channels

This paper proposes a novel three-dimensional (3D) non-stationary irregular-shaped geometry-based stochastic model (IS-GBSM) for beyond fifth-generation (B5G) and sixth-generation (6G) vehicle-to-vehicle (V2V) millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) channels. By distinguishing dynamic clusters and static clusters, the proposed IS-GBSM for the first time explores the impact of vehicular traffic density (VTD) on channel statistics in B5G/6G V2V mmWave massive MIMO scenarios. Furthermore, a novel method is developed to model the channel space-time-frequency non-stationarity. In the developed method, dynamic/static correlated clusters are first generated by an improved <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -Means clustering algorithm. Then, by employing a birth-death process based on correlated clusters, the consistency in birth and death between dynamic/static correlated clusters during time-array evolution is modeled. Key channel statistical properties, e.g., space-time-frequency correlation function (STF-CF) and Doppler power spectral density (DPSD), are derived. Simulation results demonstrate that the space-time-frequency non-stationarity is captured and the influence of VTDs on channel statistics is explored. Finally, the close agreement is achieved between simulation results and measurements, verifying the utility of proposed IS-GBSM.

Hierarchical-Block Sparse Bayesian Learning for Spatial Non-Stationary Massive MIMO Channel Estimation

This letter provides a novel hierarchical-block channel estimation scheme for massive multiple-input multiple-output (MIMO) systems based on Bayesian learning frameworks. Specifically, considering the spatial non-stationarity of massive MIMO channels introduced by a large-scale antenna array, we first exploit a hierarchical-block prior to characterize the delay-domain sparse channel structure across the antenna array and then develop an iterative Bayesian learning scheme to infer the channel vector as well as its hyperparameters associated with the hierarchical-block prior. Meanwhile, the Cramer-Rao bound (CRB) is derived as a reference line. To evaluate our proposed scheme, we modify the standardized 3GPP channel model with birth-death process to capture the spatial non-stationarity of practical massive MIMO channels. Simulation results demonstrate that our proposed scheme can recover channels effectively and attain a significant performance improvement over comparison methods.