Massive Multiple-input Multiple-output Channel Research Articles

Multiuser Correlation and Sum-Rate in Outdoor Measured Massive MIMO Channels

This letter analyzes the impact of interuser distance and angular separation on the channel correlation and achievable sum-rate for a massive multiple-input–multiple-output (MIMO) system in non-line-of-sight (NLOS) conditions. The investigation is based on outdoor measurements on a channel sounding system capturing the dynamic channel of two user arrays. The letter analyzes correlation and sum-rate with varying interuser distance and angular separation of dominant beams toward the users. A large span of correlation and sum-rate values are found across the range of distances and angular separation. The investigation shows a moderate link between interuser distance and correlation, but a strong impact on correlation is found only for low angular separation of the users. The results of this NLOS scenario suggest that a distance-based criteria alone is not sufficient to accurately model shared clusters and their correlation.

Sparse Bayesian Multi-Task Learning of Time-Varying Massive MIMO Channels With Dynamic Filtering

Sparsity of channel in the next generation of wireless communication for massive multiple-input-multiple-output (MIMO) systems can be exploited to reduce the overhead in the training. The multi-task (MT)-sparse Bayesian learning (SBL) is applied for learning time-varying sparse channels in the uplink for multi-user massive MIMO orthogonal frequency division multiplexing systems. In particular, the dynamic information of the sparse channel is used to initialize the hyperparameters in the MT-SBL procedure for the next time step. Then, the expectation maximization based updates are applied to estimate the underlying parameters for different subcarriers. Through the simulation studies, it is observed that using the dynamic information from the previous time step considerably reduces the complexity and the required time for the convergence of MT-SBL algorithm with negligible sacrifice of the estimation accuracy. Finally, the power leakage is reduced due to considering angular refinement in the proposed algorithm.

Secure Communication for Spatially Sparse Millimeter-Wave Massive MIMO Channels via Hybrid Precoding

In this paper, we investigate secure communication over sparse millimeter-wave (mm-Wave) massive multiple-input multiple-output (MIMO) channels by exploiting the spatial sparsity of legitimate user’s channel. We propose a secure communication scheme in which information data is precoded onto dominant angle components of the sparse channel through a limited number of radio-frequency (RF) chains, while artificial noise (AN) is broadcast over the remaining nondominant angles interfering only with the eavesdropper with a high probability. It is shown that the channel sparsity plays a fundamental role analogous to secret keys in achieving secure communication. Hence, by defining two statistical measures of the channel sparsity, we analytically characterize its impact on secrecy rate. In particular, a substantial improvement on secrecy rate can be obtained by the proposed scheme due to the uncertainty, i.e., “entropy”, introduced by the channel sparsity which is unknown to the eavesdropper. It is revealed that sparsity in the power domain can always contribute to the secrecy rate. In contrast, in the angle domain, there exists an optimal level of sparsity that maximizes the secrecy rate. The effectiveness of the proposed scheme and derived results are verified by numerical simulations.

Learning and Analysis of Damping Factor in Massive MIMO Detection Using BP Algorithm With Node Selection

In a massive multiple-input multiple-output (MIMO) system, belief propagation (BP) detection is known as a method to separate and detect received signals. In BP detection, a MIMO channel is represented by a factor graph and the transmitted symbols are estimated by message passing. However, the convergence property of BP deteriorates due to multiple loops included in the MIMO channel. As a method to improve the convergence property and the detection performance, the damped BP that averages two successive messages with a weighing factor (called damping factor) is known. To train the damping factors off-line for each antenna configuration, deep neural network-based damped BP (DNN-dBP) has been reported. The problem with DNN-dBP is that the detection performance deteriorates when there is a difference of the channel correlation between training and test. This is because the optimal damping factors vary with the channel correlation. In this paper, to solve this issue, we derive the damping factors of BP with the node selection (NS) method that selects nodes to be updated to lower spatial correlation using DNN-dBP. By applying the NS method, the channel correlation among the selected nodes in BP detection is lowered. Therefore, the proposed method can improve the detection performance deterioration due to the mismatches of the channel correlations between training and test in DNN-dBP. In addition, the convergence property of BP is improved by applying the NS method. Therefore, the proposed method has the same detection performance with low computational complexity as the conventional DNN-dBP. By computer simulation, it is shown that the proposed method significantly improves the bit error rate (BER) performance deterioration due to the mismatches of the channel correlations between training and test in DNN-dBP. The results also show that the proposed method can show the same BER performance with low computational complexity as the conventional DNN-dBP. We also investigate the distribution of the trained damping factors and evaluate the tendency of that.

Power Allocation and Beam Scheduling for Multi-User Massive MIMO Secret Key Generation

Secret key generation in multi-user massive multiple-input multiple-output (MIMO) communication suffers from high computation complexity, pilot overhead, and inter-user interference caused by the large dimension of the massive MIMO channel. To address these problems, this paper proposes a novel key generation approach that exploits the beam domain channel for channel feature extraction. The proposed approach can effectively reduce the channel feature dimension and mitigate the inter-user interference, via the well-designed power allocation and beam scheduling algorithms. Specifically, the multi-user key generation model is built and the design problem of channel feature extraction matrices is formulated as a sum key rate maximization problem. To tackle this problem, we derive an upper bound of the secret key rate and prove that the upper bound maximization is a convex optimization. After solving the upper bound maximization, the base station (BS) obtains the sum beams for all the users. To allocate the selected beams to each user, an efficient beam scheduling algorithm is proposed, which converges to a locally optimal solution with low computational complexity. Numerical results illustrate that in the proposed scheme, the bit disagreement ratio (BDR) of legitimate users achieves 10 -2 , while that of the eavesdropper tends to 0.5, confirming the feasibility and security of the proposed scheme.

Low-Complexity Compressed Sensing Downlink Channel Estimation for Multi-Antenna Terminals in FDD Massive MIMO Systems

In frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems, the overhead of downlink channel estimation is complex in terms of the pilot overhead, the calculation cost and the estimation process. In this paper, we propose a low-complexity downlink channel estimation scheme based on compressed sensing for mobile multi-antenna terminals. In the scheme, the mobile terminal estimates the downlink massive MIMO channel and utilises the characteristics of the spatial sparsity of the massive MIMO channel to reduce the feedback overhead by feeding back the nonzero value of the sparse channel. Specifically, we propose a low-complexity estimation algorithm based on compressive sensing for multi-antenna terminals to reduce the computational overhead of the terminal. Since different antennas of a terminal share the same support set, the algorithm estimates multiple indices per iteration, collecting the estimated indices of different antennas at the end of each iteration, thereby reducing the total number of iterations of the algorithm. Then, we derive a halting condition for a greedy algorithm that stops the iteration process according to the residual energy. The simulation results illustrate the efficiency of the halting condition for the greedy algorithm and the low complexity of the proposed algorithm. In contrast to different greedy algorithms and the Bayesian algorithm, the proposed algorithm has a complexity that decreases as the number of terminal antennas.

Channel Hardening in Massive MIMO: Model Parameters and Experimental Assessment

Reliability is becoming increasingly important for many applications envisioned for future wireless systems. A technology that could improve reliability in these systems is massive MIMO (Multiple-Input Multiple-Output). One reason for this is a phenomenon called channel hardening, which means that as the number of antennas in the system increases, the variations of channel gain decrease in both the time- and frequency domain. Our analysis of channel hardening is based on a joint comparison of theory, measurements and simulations. Data from measurement campaigns including both indoor and outdoor scenarios, as well as cylindrical and planar base station arrays, are analyzed. The simulation analysis includes a comparison with the COST 2100 channel model with its massive MIMO extension. The conclusion is that the COST 2100 model is well suited to represent real scenarios, and provides a reasonable match to actual measurements up to the uncertainty of antenna patterns and user interaction. Also, the channel hardening effect in practical massive MIMO channels is less pronounced than in complex independent and identically distributed (i.i.d.) Gaussian channels, which are often considered in theoretical work.

BER Performance of Spatial Modulation Systems Under a Non-Stationary Massive MIMO Channel Model

In this paper, the bit error rate (BER) performance of spatial modulation (SM) systems is investigated both theoretically and by simulation in a non-stationary Kronecker-based massive multiple-input-multiple-output (MIMO) channel model in multi-user (MU) scenarios. Massive MIMO SM systems are considered in this paper using both a time-division multiple access (TDMA) scheme and a block diagonalization (BD) based precoding scheme, for different system settings. Their performance is compared with a vertical Bell labs layered space-time (V-BLAST) architecture based system and a conventional channel inversion system. It is observed that a higher cluster evolution factor can result in better BER performance of SM systems due to the low correlation among sub-channels. Compared with the BD-SM system, the SM system using the TDMA scheme obtains a better BER performance but with a much lower total system data rate. The BD-MU-SM system achieves the best trade-off between the data rate and the BER performance among all of the systems considered. When compared with the V-BLAST system and the channel inversion system, SM approaches offer advantages in performance for MU massive MIMO systems.

Compressed sensing channel estimation in massive MIMO

Massive multiple-input-multiple-output (MIMO) emerges as a promising technology to meet the ever growing demand on a large volume of data transmission in an energy efficient manner in the upcoming fifth generation networks. This explores an integrated system model of improved wireless channel estimation (CE) and its consequent effect on image reconstruction, both done in compressed sensing (CS) framework. A massive MIMO channel exhibits sparse nature and has been modelled as a CS problem. Two CS-MIMO-CE algorithms, discrete cosine transform-based stagewise orthogonal matching pursuit and improved stagewise orthogonal matching pursuit (iStOMP), are suggested here. Low density parity check codes are also integrated to serve three-fold purposes, as a pilot signal, sensing matrix, and error control code, while Daubechies transform offers a sparse representation of the MIMO channel and transmitted image. The proposed iStOMP MIMO-CE algorithm offers ~ 6 dB gain in CE over the existing works and gain in 2 dB on image visual quality at 75% CS measurements.

Engineering the Eigenspace Structure of Massive MIMO Links Through Frequency-Selective Surfaces

We propose an efficient finite-difference time-domain (FDTD) computational paradigm to estimate the channel matrix of generic massive multiple-input–multiple-output (MIMO) systems. Working with a practical scenario with 196 base station (BS) elements and 6 equispaced user-equipment devices, we compute the dominant eigenspace for the uplink channel. The full-wave results are compared to conventional ray-tracing methods, with emphasis laid upon observing and understanding the electromagnetic (EM) impact of interelement mutual coupling and spherical wavefront illumination on the wireless MIMO channel properties. In particular, we investigate EM manipulation of massive MIMO channel structures by utilizing, especially, engineered wire-grid frequency-selective surfaces placed in the vicinity of the BS massive MIMO array. Using the in-house FDTD code, we demonstrate the capability of such passive structures to redistribute the illumination Poynting vector magnitude over the BS array aperture, as well as modifying the dominant eigenspace at certain design frequencies. This letter demonstrates the advantage of the synergy between rigorous EM analysis and stochastic communication theories and techniques, with expected applications in emerging wireless technologies (5G and beyond).

Channel Correlation-Based Approach for Feedback Overhead Reduction in Massive MIMO

For frequency-division duplex multiple-input–multiple-output (MIMO) systems, the channel state information at the transmitter is usually obtained by sending pilots or reference signals from all elements of the antenna array. The channel is then estimated by the receiver and communicated back to the transmitter. However, for massive MIMO, this periodical estimation of the full transfer matrix can lead to prohibitive overhead. To reduce the amount of data, we propose to estimate the updated channel matrix from the knowledge of the full correlation matrix at the transmitter made during some initialization time and the instantaneous measured channel matrix of smaller size, characterizing the link between the user and a limited number of reference array elements. The proposed algorithm is validated with measured massive MIMO channel transfer functions at 3.5 GHz between a $9 \times 9$ uniform rectangular array and different user positions. Since measurements were made in static conditions, the criteria chosen for evaluating the performance of the algorithm are based on a comparison of the predicted channel capacity calculated from either the measured or estimated channel matrix.

Real-Valued Sparse Bayesian Learning Approach for Massive MIMO Channel Estimation

This letter describes a real-valued sparse Bayesian learning (SBL) approach for massive multiple-input multipleoutput (MIMO) downlink channel estimation. The main idea of the approach is to introduce a certain unitary transformation into pilots, so as to convert complex-valued channel recovery problems into real ones. Due to exploiting the real-valued structure of the data matrices, the new approach brings a significant decrease in computational complexity, as well as a good noise suppression. Simulation results demonstrate that the new method can reduce the computation load and improve the channel estimation performance simultaneously.

Power Leakage Elimination for Wideband mmWave Massive MIMO-OFDM Systems: An Energy-Focusing Window Approach

When the large antenna array and the large bandwidth are deployed in a massive multiple-input multiple-output (MIMO) system, the spatial-wideband effect and the related beam squint effect make the energy of each multipath component distributed mainly within a square area in angle-delay domain rather than distributed like an impulse. With the finite numbers of antennas and subcarriers in practical massive MIMO-OFDM systems, the power leakage of each path outside the corresponding square area is non-negligible. In this paper, we first derive the millimeter-wave (mmWave) massive MIMO channel model for OFDM transceivers and then design an optimal energy-focusing window, which shapes the channel in spatial-frequency domain to maximally concentrate the energy of each multipath component inside the corresponding square area in angle-delay domain. With the help of this window, the power leakage can be significantly reduced. As a result, the sparsity of mmWave channels can be primely preserved and the inter-user interference can be significantly alleviated for angle- and delay-based channel estimation and precoding. Simulation results demonstrate the effectiveness of the proposed window design.

Learning the Structured Sparsity: 3-D Massive MIMO Channel Estimation and Adaptive Spatial Interpolation

This paper addresses the channel estimation problem for three-dimensional (3-D) massive multiple-input multiple-output (MIMO) systems, where the base station (BS) is equipped with a two-dimensional uniform planar array (UPA) to serve a number of user equipments (UEs). To implement with low hardware complexity, the number of available radio-frequency (RF) chains at BS is constrained to be much smaller than the number of antennas. The theoretical analysis of sparse property for 3-D massive MIMO channel reveals that there exists two kinds of sparse structures in beam-domain channel vector, namely the common sparsity structure among sub-arrays of UPA and block sparsity structure per sub-array. Based on this property, a novel structured sparse Bayesian learning framework is proposed to estimate the channel between BS and UE reliably. Moreover, an adaptive spatial interpolation scheme is proposed to further reduce the number of required RF chains at BS while maintaining the estimation performance. The simulation results show that the proposed scheme provides stable estimation performance for a variety of scenarios with different numbers of RF chains, transmit signal-to-noise ratios, Rician factors, and angular spreads, and outperforms the reference schemes significantly.

User Location Tracking in Massive MIMO Systems via Dynamic Variational Bayesian Inference

Accurate user location tracking is the key to enable location-based services and assist communications in 5 G networks. The massive multiple-input multiple-output (MIMO) technology employed in 5 G networks could potentially provide accurate user localization due to increased spectral efficiency and high directivity. In this paper, we propose an efficient user location tracking algorithm in massive MIMO systems. Firstly, we propose a temporal Markov group-sparse (TMGS) model based on a grid reference to capture the probabilistic temporal correlation and group sparsity of the massive MIMO channels jointly. Then we propose a dynamic variational Bayesian inference (D-VBI) algorithm to handle the TMGS priors under ill-conditioned measurement matrix in the location tracking problem. The proposed D-VBI can jointly recover the user's coarse location in the grid reference and refine the off-grid points to automatically learn the user's exact location to high accuracy. Moreover, the TMGS-based D-VBI algorithm can provide prior information about the user's next location and the possible arriving directions of the future channels to the consecutive time slot to improve the location tracking accuracy. Finally, we verify the superior performance of the proposed location tracking algorithm by extensive simulations.

D2D-Enabled User Cooperation in Massive MIMO

In this article, we investigate device-to-device (D2D) communication-enabled user cooperation in massive multiple-input multiple-output (MIMO) systems. In frequency-division duplexing massive MIMO systems, cascaded precoding has been adopted to reduce the overhead of channel estimation and limited feedback. The inner precoder in cascaded precoding depends on the spatial covariance matrix of the massive MIMO channel and can be the same for the users that are close to each other. When the users are close to each other, high-quality D2D links can be expected among the users and the users can form a virtual MIMO receiver via D2D links. Since the users may require different services, the required transmission rates of those users can also be different. To improve the overall user experience, utility functions are adopted in this article and two D2D-enabled user cooperation schemes, including the data-symbol-information exchanging and receive-signal-information exchanging, are proposed, which can allocate the overall transmission rate among the users adaptively in terms of the required transmission rates of different users. In this way, the overall utility function can be maximized.

Robust Bayesian learning approach for massive MIMO channel estimation

This paper addresses the problem of massive multiple-input multiple-output (MIMO) channel estimation in the presence of impulsive noise. In the literature, a sparse Bayesian learning (SBL) approach for outlier-resistant direction-of-arrival (DOA) estimation can be tailored to handle this problem. However, it suffers from two major shortcomings: first, it takes the impulsive noise as a part of the unknown signal-of-interest, which brings a high computational complexity due to the larger size of the problem; and second, the assumption that both the signal-of-interest and the impulsive noise have a common sparsity level is not always valid, which could cause a performance loss. To deal with these shortcomings, we resort to the variational Bayesian inference (VBI) methodology to separate effects from the signal-of-interest and the impulsive noise. Then, we introduce an improved two-stage hierarchical prior to enforce sparsity while guarantee a denser impulsive noise over the signal-of-interest simultaneously. Due to adopting the VBI separation and the new sparsity prior, our method can bring a considerable computational complexity reduction and achieve better channel estimation accuracy. Simulation results reveal substantial performance improvement over the existing methods.

A Study of Diffuse Scattering in Massive MIMO Channels at Terahertz Frequencies

The use of massive multiple-input multiple-output (MIMO) systems is becoming progressively feasible, as well as progressively important, as the carrier frequency increases. Terahertz (THz) frequencies lead to smaller-sized RF components including antennas, so that even antenna arrays with a large number of antennas have a reasonable form factor while providing large beamforming gain and multi-user MIMO (MU-MIMO) capability. However, the THz propagation mechanisms differ in various ways from previously explored channels. In fact, reflections by a rough surface and diffuse scattering mechanisms are the most critical features contributing to spatial and temporal dispersion at THz frequencies. For this article, first, we develop a hybrid modeling approach of 3-D ray-tracing simulations in a realistic office room at 300 and 350 GHz to obtain estimates of the impact of surface roughness on the channel capacity which depends on generic channel characteristics. Then, the indoor multipath propagation and its impact on massive MIMO channels considering smooth and rough surfaces are investigated by employing the Beckmann-Kirchhoff (B-K) model. Finally, channel capacities of indoor THz massive MIMO channels with different surface roughnesses for both line-of-sight (LoS) and non-LoS (NLoS) scenarios are calculated. Though based on modeling results, the scattering properties of materials can favorably be exploited to maximize spatial multiplexing gains, especially in LoS scenarios.

Fundamental Applicability of Spatial Modulation: High-SNR Limitation and Low-SNR Advantage

Spatial modulation (SM) is viewed as a promising multi-antenna technology for future communications. Numerous works on SM have been done on the specific optimized designs and performance analysis mainly based on high signal-to-noise ratio (SNR) union bound approximation. However, the existing information-theoretical investigation indicates that SM is more efficient in low SNR regimes. Therefore, the most prominent potential of SM with respect to the error performance is still not well understood. As a first step to filling this void, we consider the fundamental applicability of SM in multi-antenna channels. On the one hand, for high SNR regimes, by developing the optimal structure of multi-input single-output (MISO) and proposing efficient multiple-input multiple-output (MIMO) transmission schemes, we prove that the performance limits of SM-MISO and SM-MIMO with respect to the received minimum Euclidean distance (MED) can be outperformed even by single radio-frequency chain transmission. On the other hand, for the low-SNR regimes, we show the respective optimality of: 1) SM for single-user energy-based noncoherent massive MIMO (ED-MaMIMO) channels; and 2) dual SM of multi-user ED-MaMIMO which collaboratively modulates data onto both the indexes of transmitter antennas and those of the users. In addition, the dual SM for multiuser ED-MaMIMO has a practically important property that partial coordination via user index modulation can be as useful as full one. Our analytical findings and numerical results strongly suggest that more attention should be paid to the low-SNR behavior and designs of SM rather than the currently popular MED optimization in high-SNR regimes. This paper points out a direction, towards which SM should evolve, and also shows that combination of SM with the users' index modulation can be very useful for designing the optimal finite-alphabet nonorthogonal multiple-access.

Multi-frequency channel characterization for massive MIMO communications in lobby environment

In this paper, a massive multiple input multiple output (MIMO) channel measurement campaign with two setups is conducted in an indoor lobby environment. In the first setup, two types of 256-element virtual uniform rectangular arrays (URAs), i.e., the 4×64 virtual URA and the 64×4 virtual URA are used. The carrier frequency is 11 GHz; in the second setup, measurements are performed at 4, 6, 11, 13, 15, 18 GHz at two different user locations. The channel characterization is presented by investigating the typical channel parameters, including average power delay profile (APDP), K factor, root mean square (RMS) delay spread, and coherence bandwidth. Moreover, the channel characteristics in angular domain are investigated by applying the space-alternating generalized expectation-maximization (SAGE) algorithm. The extracted multipath components (MPCs) are preliminarily clustered by visual inspection, and related to the interacting objects (IOs) in physical environment. Multipath structures at multiple frequency bands are examined. Direction spread of departure is estimated to evaluate the directional dispersion at the base station (BS) side. The results in this paper can help to reveal the propagation mechanisms in massive MIMO channels, and provide a foundation for the design and application of the practical massive MIMO system.