Massive Multiple-input Multiple-output Channel Research Articles

An adaptive compressive sensing method on hybrid-field channel estimation for a massive MIMO system

Massive MIMO (Multiple-input-multiple output), crucial for 5 G and Beyond 5 G (B5G) networks, faces challenges with terahertz frequencies in B5G as the communication shifts from far-field to near-field. This shift disrupts traditional Massive MIMO channel estimation, leading to increased pilot overhead and limited performance. The current study used the hybrid-field orthogonal matching pursuit (HF-OMP) algorithm from the compressive sensing (CS) framework to estimate the channel with scatters from both far-field and near-field. The method, however, needs more flexibility regarding scatter location in the field of interest. Also, the usage of HF-OMP under a single measurement vector (SMV) scheme limits the overall performance of the existing method. To address these, we have proposed an adaptive hybrid-field simultaneous-OMP algorithm under multiple measurement vector (MMV) of the CS framework which selects multiple atoms having common support within a single iteration. This innovative approach tackles channel estimation for both far-field and near-field scatters while adapting to their varying distributions. Compared to classical methods, simulations show the new algorithm achieves up to a 14 % improvement in normalized mean square error within a 0 dB to 10 dB signal-to-noise ratio range. This translates to significant reductions in pilot overhead and enhanced channel reliability, paving the way for more efficient and robust wireless networks in the future.

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.

Channel Parameter Estimation of mmWave MIMO System in Urban Traffic Scene: A Training Channel-Based Method

In frequency selective channel environment, channel estimation in hybrid precoding millimeter-wave (mmWave) massive multiple input multiple output (MIMO) system is a challenge issue. To solve this problem, we propose an effective channel estimation scheme for frequency selective channel, which is based on the training channel model in urban traffic environment. Considering that the practical mmWave MIMO channel is sparsity and the subcarrier multi-channels have the same sparse structure, we regard the channel estimation problem as the sparse channel recovery, and propose a multipath simultaneous matching tracking estimation method. It is assumed that the noise between the practical channels has a certain correlation, and the noise correlation has an impact on the selection of the optimal atomic support set in the process of channel recovery. Therefore, noise weighting is introduced in our proposed method. The simulation results prove the validity of this proposed method in frequency selective mmWave MIMO channel. Without increasing the complexity of the algorithm, the proposed method can achieve better local performance than the traditional classical methods.

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.

Machine learning based low-complexity channel state information estimation

In 5G communications, the acquisition of accurate channel state information (CSI) is of great importance to the hybrid beamforming of millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) system. In classical mmWave MIMO channel estimation methods, the exploitation of inherent sparse or low-rank structures has demonstrated to improve the performance. However, most high-accurate CSI estimators incur a high computational complexity and require the prior channel information, which hence present the major challenges in the practical deployment. In this work, we leverage machine learning to design the low-complexity and high-performance channel estimator. To be specific, we first formulate the CSI estimation, in the case of sparse structure, as one classical least absolute shrinkage and selection operator problem. In order to reduce the time complexity of existing compressed sensing (CS) methods, we then approximate the original optimization problem to another one, by imposing the other low-rank constraint that was barely considered by CS. We thus solve this new approximated problem and attain the near-optimal solution of the original problem. One new method excludes any prior channel information, and greatly improves the estimation performance, which only incurs a low time complexity. Simulation results demonstrate the superiority of our proposed method both in the estimation accuracy and time complexity.

Sub-Array-Based Millimeter Wave Massive MIMO Channel Estimation

Combination of millimeter wave (mmWave) and massive multiple input multiple output (MIMO) forms a promising technology for future sixth generation networks. As the number of antennas increases, propagation channel starts yielding spherical wavefronts, for which the traditional channel estimation algorithms are no longer applicable. To overcome this technical gap, a novel MIMO channel estimation scheme based on the assumption of spherical wavefront is proposed in this work. The large antenna array is first divided into several sub-arrays, and then the channel estimation is performed for each sub-array based on the orthogonal matching pursuit algorithm. In addition, the joint estimation of angle of arrivals and departures (AoAs and AoDs) of each uniform planar sub-array is transformed into separate estimation by dimensionality reduction. Next, an iterative estimation is performed using Taylor expansion to continuously approximate the real grid points to recover the AoAs/AoDs. Lastly, the superiority of the proposed algorithm is verified by numerical simulations, where the proposed algorithm exhibits the best NMSE performance, compared with the existing MIMO channel estimation methods.

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.

Secure Communication for Spatially Correlated RIS-Aided Multiuser Massive MIMO Systems: Analysis and Optimization

This letter investigates the secure communication in a reconfigurable intelligent surface (RIS)-aided multiuser massive multiple-input multiple-output (MIMO) system exploiting artificial noise (AN). We first derive a closed-form expression of the ergodic secrecy rate under spatially correlated MIMO channels. By using this derived result, we further optimize the power fraction of AN in closed form and the RIS phase shifts by developing a gradient-based algorithm, which requires only statistical channel state information (CSI). Our analysis shows that spatial correlation at the RIS provides an additional dimension for optimizing the RIS phase shifts. Numerical simulations validate the analytical results which show the insightful interplay among the system parameters and the degradation of secrecy performance due to high spatial correlation at the RIS.

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.

Double-Layer Precoder and Cluster-Based Power Allocation Design for LEO Satellite Communication With Massive MIMO

In this work, we propose a double-layer precoder and cluster-based power allocation design for low earth orbit (LEO) satellite communication with massive multiple input multiple output (MIMO). Specifically, spectral efficiency (SE) is chosen as the evaluation metric with hardware complexity, transmit power, instantaneous channel state information (iCSI) and statistical channel state information (sCSI) considered. We simplify the three-dimension (3D) air-to-ground MIMO channel under satellite environment with the angular spread model. Then, a double-layer precoder is proposed to reduce the hardware complexity and eliminate the inter-user interference (IUI) among each user cluster. With angle of departure (AoD) information, the user clustering criteria to maximize the SE and eliminate inter-cluster interference (ICI) is derived. After that, a cluster-based power allocation scheme is proposed by dividing the total transmit power into two parts, one to meet the user’s minimum service requirement and the other to get optimal SE performance by waterfilling algorithm. Simulation results show that the proposed scheme achieves better SE performance compared with other feasible approaches.

Hybrid CPU–GPU implementation of the transformed spatial domain channel estimation algorithm for mmWave MIMO systems

Hybrid platforms combining multicore central processing units (CPU) with many-core hardware accelerators such as graphic processing units (GPU) can be smartly exploited to provide efficient parallel implementations of wireless communication algorithms for Fifth Generation (5G) and beyond systems. Massive multiple-input multiple-output (MIMO) systems are a key element of the 5G standard, involving several tens or hundreds of antenna elements for communication. Such a high number of antennas has a direct impact on the computational complexity of some MIMO signal processing algorithms. In this work, we focus on the channel estimation stage. In particular, we develop a parallel implementation of a recently proposed MIMO channel estimation algorithm. Its performance in terms of execution time is evaluated both in a multicore CPU and in a GPU. The results show that some computation blocks of the algorithm are more suitable for multicore implementation, whereas other parts are more efficiently implemented in the GPU, indicating that a hybrid CPU–GPU implementation would achieve the best performance in practical applications based on the tested platform.

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.