Massive MIMO Channel Research Articles

3D Cluster-Based Ray Tracing Technique for Massive MIMO Channel Modeling

In this paper, a novel 3 dimensional (3D) approach is proposed for precise modeling of massive multiple input multiple output (M-MIMO) channels in millimeter wave (mmW) frequencies. This model is based on both deterministic and statistic computations to extract characteristics of the propagation channel. In order to increase algorithm execution speed, the physical channel is divided into two regions. The first region refers to those parts of the channel which can be mapped with simple planes such as walls, ramps and etc. The second region is usually complex which is defined by considering the channel with physical clusters. These physical clusters yield multipath components (MPCs) with similar angles of arrival (AoA) and time delay. The ray-tracing algorithm is utilized to find ray paths from transmitter (Tx) to receiver (Rx). Some characteristics of MPCs in each cluster are defined according to some appropriate statistical distribution. The non-stationary property of M-MIMO along the antenna array axis is considered in the algorithm. Due to the correspondence between the propagation environment and scatters, the accuracy of the model is highly increased. To evaluate the proposed channel model, simulation results are compared with some measurements reported in the literature.

Deep Neural Network for Compressive Sensing and Application to Massive MIMO Channel Estimation

In this paper, we consider the problem of sparse signal recovery using a learned dictionary in multiple measurement vectors (MMVs) case. Employing deep neural networks, we provide two new greedy algorithms to solve sparse MMV problems. In the first algorithm, we create a stacked vector of measurement matrix columns and a new measurement matrix, which can be assumed as the Kronecker product of the primary compressive sampling matrix and a unitary matrix. In order to reconstruct sparse vector corresponding to this new set of equations, a four-layer feed-forward neural network is applied. In the second algorithm, joint sparse structure of the sparse vectors is considered. Recurrent neural networks are employed to extract the joint sparsity structure. In addition, we utilize an over-complete dictionary obtained from an unsupervised learning procedure. Simulation results illustrate the benefit of using the proposed methods. Finally, the proposed algorithms are applied for pilot-based channel estimation in massive multiple-input multiple-output systems to improve the channel state information recovery performance.

Dominant Path Zero-Forcing Based on Low-Rank Matrix Approximation for Full-Dimensional Massive MIMO Systems

The conventional zero-forcing (ZF) precoding and the two dimensional (2D) ZF precoding are two popular schemes to cancel the interference in the downlink of the full-dimensional (FD) massive MIMO systems. However, the conventional ZF is of high complexity as a result of ignoring the structure of the FD massive MIMO channels while the 2D ZF has poor performance due to neglecting the elevation angular spread. In this correspondence, by exploiting the spatial correlation of the FD massive MIMO channels, we propose a dominant path zero-forcing precoding (DPZF) scheme based on the low-rank matrix approximation. The proposed DPZF scheme includes two stages. In the first stage, we obtain the elevation and the azimuth components of $r$ dominant paths for each user's channel by solving the rank- $r$ channel matrix approximation. In the subsequent stage, we reformulate the Gram matrix with the obtained components so as to zero force the most dominant path of each user's channel with low complexity. For the proposed DPZF, the upper bound of the performance gap to the conventional ZF is derived and the complexity is analyzed. The analysis and simulation results indicate that the proposed DPZF can yield a more elegant performance-complexity tradeoff than the existing precoding schemes.

Hardware Implementation and Performance Analysis of Improved Sphere Decoder in Spatially Correlated Massive MIMO Channels

Hardware Implementation and Performance Analysis of Improved Sphere Decoder in Spatially Correlated Massive MIMO Channels

Online Deep Neural Networks for MmWave Massive MIMO Channel Estimation With Arbitrary Array Geometry

In this paper, we propose an online training framework for mmWave Massive MIMO channel estimation (CE) with limited pilots, where the training is based on real-time received pilot samples from the base station without requiring knowledge of the true channel. To realize this, we propose four axioms for a legitimate online loss function, based on which we develop a model-free online training algorithm with convergence analysis. Simulation shows that the proposed online deep neural network (DNN) achieves comparable CE accuracy to model-based compressive sensing (CS) algorithms, while enjoying much faster computation. In addition, the proposed method is robust to various model mismatches and can adapt to the change of the underlying propagation environment.

Efficient Channel Estimation in Massive MIMO Partially Centralized Cloud-Radio Access Network Systems

This article investigates channel estimation problem in massive MIMO partially centralized cloud-RAN (MPC-RAN). The channel estimation was realized through compressed data method to minimize the huge pilot overhead, then combined with parallel Givens data projection method (PGDPM) to form a semi-blind estimator. Comparison and analysis of improved minimum mean square error (MMSE), fast data projection method (FDPM), compressed data, and PGDPM techniques was evaluated for achievable normalized mean square error (NMSE) in MPC-RAN. The PGDPM-based estimator had the lowest normalized mean square error. The FDPM and PGDPM based methods are comparable in performance with PGDPM based estimator having a slight edge over FDPM-based estimator. This vindicates PGDPM-based estimator as a method to be utilized in channel estimation since it compresses the massive MIMO channel information, hence mitigating the fronthaul finite capacity problem, and at the same time, it is geared towards efficient parallelization for optimal BBU resource utilization.

A Dynamic 3-D Wideband GBSM for Cooperative Massive MIMO Channels in Intelligent High-Speed Railway Communication Systems

Coordinated multipoint (CoMP) and massive multiple-input multiple-output (mMIMO) are two of promising technologies in future intelligent high-speed railway (HSR) communication systems, whose performance is fundamentally determined by the characteristics of cooperative mMIMO channels. This article proposes a dynamic three-dimensional (3-D) wideband geometry-based stochastic model (GBSM) for HSR cooperative mMIMO channels. The proposed GBSM employs a sphere model and two elliptic-cylinder models to describe common and uncommon clusters for different links, and integrates the dynamic cluster evolution in both time and array domains. Statistical properties of the cooperative mMIMO model are investigated, such as multi-link spatial cross-correlation function and sum rate capacity. A corresponding dynamic 3-D wideband simulation model for the HSR cooperative mMIMO channel is also proposed. Finally, numerical results of the statistical properties are analyzed, and the proposed model is validated by realistic HSR channel measurement data, in terms of dual-link spatial cross-correlation and channel capacity. This model is more practical and will be helpful for facilitating the design and performance evaluation of future intelligent HSR communication systems.

Solving Sparse Linear Inverse Problems in Communication Systems: A Deep Learning Approach With Adaptive Depth

Sparse signal recovery problems from noisy linear measurements appear in many areas of wireless communications. In recent years, deep learning (DL) based approaches have attracted interests of researchers to solve the sparse linear inverse problem by unfolding iterative algorithms as neural networks. Typically, research concerning DL assume a fixed number of network layers. However, it ignores a key character in traditional iterative algorithms, where the number of iterations required for convergence changes with varying sparsity levels. By investigating on the projected gradient descent, we unveil the drawbacks of the existing DL methods with fixed depth. Then we propose an end-to-end trainable DL architecture, which involves an extra halting score at each layer. Therefore, the proposed method learns how many layers to execute to emit an output, and the network depth is dynamically adjusted for each task in the inference phase. We conduct experiments using both synthetic data and applications including random access in massive MTC and massive MIMO channel estimation, and the results demonstrate the improved efficiency for the proposed approach.

Massive MIMO Channel Prediction Using Recurrent Neural Networks

Massive MIMO has been classified as one of the high potential wireless communication technologies due to its unique abilities such as high user capacity, increased spectral density, and diversity among others. Due to the exponential increase of connected devices, these properties are of great importance for the current 5G-IoT era and future telecommunication networks. However, outdated channel state information (CSI) caused by the variations in the channel response due to the presence of highly mobile and rich scattering is a major problem facing massive MIMO systems. Outdated CSI occurs when the information obtained about the channel at the transmitter changes before transmission. This leads to performance degradation of the network. In this work, we demonstrate a low complexity channel prediction method using neural networks. Specifically, we explore the power of recurrent neural network utilizing long-short memory cells in analyzing time series data. We review various neural network-based channel prediction methods available in the literature and compare complexity and performance metrics. Results indicate that the proposed methods outperform conventional systems by tremendously lowering the complexity associated with channel prediction.

Characterisation of Indoor Massive MIMO Channels Using Ray-Tracing: A Case Study in the 3.2–4.0 GHz 5G Band

In this paper, research results on the applicability of ray-tracing (RT) techniques to model massive MIMO (MaMi) channels are presented and discussed. The main goal is to show the possibilities that site-specific models based on rigorous RT techniques, along with measurement campaigns considered for verification or calibration purposes where appropriate, can contribute to the development and deployment of 5G systems and beyond using the MaMi technique. For this purpose, starting from the measurements and verification of the simulator in a symmetric, rectangular and accessible scenario used as the testbed, the analysis of a specific case involving channel characterisation in a large, difficult access and measurement scenario was carried out using the simulation tool. Both the measurement system and the simulations emulated the up-link in an indoor cell in the framework of a MaMi-TDD-OFDM system, considering that the base station was equipped with an array consisting of 10 × 10 antennas. The comparison of the simulations with the measurements in the testbed environment allowed us to affirm that the accuracy of the simulator was high, both for determining the parameters of temporal dispersion and frequency selectivity, and for assessing the expected capacity in a specific environment. The subsequent analysis of the target environment showed the high capacities that a MaMi system can achieve in indoor picocells with a relatively high number of simultaneously active users.

3‐D Massive MIMO Channel Model for High‐Speed Railway Wireless Communication

AbstractIn the fifth generation (5G) wireless communication, high‐speed railway (HSR) communication is one of the most challenging scenarios. By adopting massive multi‐input multioutput (mMIMO) technology in HSR communication, the design of the underlying communication system becomes more challenging. Some new channel characteristics must be studied, such as nonstationarity in space, time, and frequency domains. In this paper, two models are established for the two states of HSR. When the HSR stops, a three‐dimensional (3‐D) stationary channel model based on the single‐ring distribution of the scatterers is established. When the HSR moves, a 3‐D nonstationary geometric random channel model (GRCM) based on the cylinder distribution of the scatterers by introducing the birth and death process of the propagation path and time‐varying characteristics of the channel parameters is established. Moreover, a time evolution algorithm for time‐varying channel parameters is proposed, and a modularization study of key parameter update algorithms is conducted. Finally, based on the proposed 3‐D nonstationary geometric random channel model, important time‐varying channel statistical characteristics, such as time autocorrelation function (ACF), spatial cross‐correlation function (CCF), Doppler power spectral density (DPSD), and stationary interval are studied. Simulation results indicate that the properties of the proposed channel models, verified by simulation results, can match well with those of the theoretical model.

Massive MIMO Transmission for LEO Satellite Communications

Low earth orbit (LEO) satellite communications are expected to be incorporated in future wireless networks, in particular 5G and beyond networks, to provide global wireless access with enhanced data rates. Massive MIMO techniques, though widely used in terrestrial communication systems, have not been applied to LEO satellite communication systems. In this paper, we propose a massive MIMO transmission scheme with full frequency reuse (FFR) for LEO satellite communication systems and exploit statistical channel state information (sCSI) to address the difficulty of obtaining instantaneous CSI (iCSI) at the transmitter. We first establish the massive MIMO channel model for LEO satellite communications and simplify the transmission designs via performing Doppler and delay compensations at user terminals (UTs). Then, we develop the low-complexity sCSI based downlink (DL) precoder and uplink (UL) receiver in closed-form, aiming to maximize the average signal-to-leakage-plus-noise ratio (ASLNR) and the average signal-to-interference-plus-noise ratio (ASINR), respectively. It is shown that the DL ASLNRs and UL ASINRs of all UTs reach their upper bounds under some channel condition. Motivated by this, we propose a space angle based user grouping (SAUG) algorithm to schedule the served UTs into different groups, where each group of UTs use the same time and frequency resource. The proposed algorithm is asymptotically optimal in the sense that the lower and upper bounds of the achievable rate coincide when the number of satellite antennas or UT groups is sufficiently large. Numerical results demonstrate that the proposed massive MIMO transmission scheme with FFR significantly enhances the data rate of LEO satellite communication systems. Notably, the proposed sCSI based precoder and receiver achieve the similar performance with the iCSI based ones that are often infeasible in practice.

Non-Stationarities in Extra-Large-Scale Massive MIMO

Massive MIMO, a key technology for increasing area spectral efficiency in cellular systems, was developed assuming moderately sized apertures. In this article, we argue that massive MIMO systems behave differently in large-scale regimes due to spatial non-stationarity. In the large-scale regime, with arrays of around 50 wavelengths, the terminals see the whole array but non-stationarities occur because different regions of the array see different propagation paths. At even larger dimensions, which we call the extra-large scale regime, terminals see a portion of the array and inside the first type of non-stationarities might occur. We show that the non-stationarity properties of the massive MIMO channel change several important MIMO design aspects. In simulations, we demonstrate how non-stationarity is a curse when neglected but a blessing when embraced in terms of computational load and multi-user transceiver design.

Energy-Efficient Computation Offloading in Delay-Constrained Massive MIMO Enabled Edge Network Using Data Partitioning

We study a wireless edge-computing system which allows multiple users to simultaneously offload computation-intensive tasks to multiple massive-MIMO access points, each with a collocated multi-access edge computing (MEC) server. Massive-MIMO enables simultaneous uplink transmissions from all users, significantly shortening the data offloading time compared to sequential protocols, and makes the three phases of data offloading, computing, and downloading have comparable durations. Based on this three-phase structure, we formulate a novel problem to minimize a weighted sum of the energy consumption at both the users and the MEC server under a round-trip latency constraint, using a combination of data partitioning, transmit power control and CPU frequency scaling at both the user and server ends. We design a novel nested algorithm consisting of an inner primal-dual algorithm and an outer latency-aware descent algorithm to solve this problem efficiently. Optimized solutions show that for larger requests, more data is offloaded to the MECs to reduce local computation time in order to meet the latency constraint, despite higher energy cost of wireless transmissions. Massive-MIMO channel estimation errors under pilot contamination also causes more data to be offloaded to the MECs. Compared to binary offloading, partial offloading with data partitioning is superior and leads to significant reduction in the overall energy consumption.

Analysis of SVD-Based Hybrid Schemes for Massive MIMO With Phase Noise and Imperfect Channel Estimation

In hybrid analog-digital schemes, proposed to reduce the number of RF chains especially at millimeter waves, the precoding at the transmitter and the combining at the receiver are split into digital and analog parts. We analyze the sensitivity of hybrid schemes to phase noise and channel estimation errors and we compare them to a full-digital approach. The scheme adopted for the analog part employs fixed phase shifters, then the digital part is optimized by a singular-value decomposition. We derive analytical expressions for the interference and the SNR degradation arising from the imperfect decomposition due to phase noise and the channel estimation error, for typical millimter-wave massive MIMO channels. In particular we show that when the channel estimation is made in the beam-space, this hybrid scheme is more robust to the phase noise and to the channel estimation errors than a full-digital approach.

Massive MIMO Propagation Modeling With User-Induced Coupling Effects Using Ray-Tracing and FDTD

The article describes a numerical approach for Massive MIMO channel modeling that accounts for the effects of electromagnetic coupling between a user and the receiving device. The modeling is performed by a combination of the Finite-Difference Time-Domain and the Ray-Tracing methods, supplemented with a stochastic geometry model of the propagation environment. The influence of user-coupling on the channel properties was studied statistically using the singular value spread and matrix power ratio metrics of the channel correlation matrix. The time-averaged Poynting vector distribution in the near-field of the receiver was evaluated using a realistic human phantom model and the Maximum Ratio Transmission precoding scheme in the downlink. The average enhancement of the time-average Poynting vector magnitude at the receiver location, compared to the surrounding area, was found to be around 10 dB when using 36 antenna elements at the base station. The electromagnetic field exposure of the phantom was assessed in terms of the 10g-average peak-spatial Specific Absorption Rate and compared with the existing public guidelines. Comparison of the EMF and exposure results provides a new perspective on the future regulatory procedures.

Time-Varying Downlink Channel Tracking for Quantized Massive MIMO Networks

This paper proposes a Bayesian downlink channel estimation framework for time-varying massive MIMO networks. In particular, the quantization effects at the receiver are considered. In order to fully exploit the sparsity and time correlations of channels, we formulate the time-varying massive MIMO channel as the simultaneously sparse signal model. Then, we propose a sparse Bayesian learning (SBL) framework to estimate the model parameters of the sparse virtual channel. The expectation maximization (EM) algorithm is employed to reduce complexity. Specifically, the factor graph and the general approximate message passing (GAMP) algorithms are used to compute the desired posterior statistics in the expectation step, so that high-dimensional integrals over the marginal distributions can be avoided. The non-zero supporting vector of the virtual channel is then obtained from channel statistics by a k-means clustering algorithm. After that, the reduced dimensional GAMP-based scheme is designed to make the full use of the channel temporal correlation so as to enhance the virtual channel tracking accuracy. Finally, the efficacy of the proposed framework is demonstrated through simulations.

Massive MIMO channel estimation considering pilot contamination and spatially correlated channels

In this letter, we present a study on linear channel estimators and their respective mean square error (MSE) expressions acknowledging spatially correlated channels and pilot contamination. We also investigate the impact of imperfect channel covariance matrix knowledge.

Multi-user massive MIMO channel estimation using joint sparsity and non-ideal feedback modeling

In order to realize the advantages of the massive MIMO systems, the channel state information must be obtained at the base station (BS). However, it is a challenging task in the frequency division duplexing (FDD) systems due to the overwhelming overhead of downlink channel pilots and uplink channel feedback. In this paper, we consider the multi-user massive MIMO system and apply joint sparsity-based technique to reduce the overhead. Due to the shared scatterers in the physical propagation environment, the user channel matrices have a joint sparsity structure which has been utilized in the proposed algorithm. Furthermore, using the common sparsity pattern of the uplink and downlink channel, we have suggested a mixed weighted smoothed L0/L2 norm minimization technique to estimate the downlink channel with the aid of the uplink channel support. Moreover, in most of the works in the literature, the feedback channel has been considered as a simple additive white Gaussian noise (AWGN) channel which may result in poor performance in the real scenarios. To address this issue, we have presented a better modeling of the uplink feedback channel to increase the channel estimation accuracy and decrease the number of required pilot sequences. We have investigated the performance of the proposed method in different simulation scenarios. The results confirm that the suggested scheme is superior to the other state-of-the-art techniques in terms of the recovery accuracy and the pilot and feedback overhead.

Sparse Channel Estimation for Spatial Non-Stationary Massive MIMO Channels

In massive MIMO systems, the channel shows a spatial non-stationarity that has a significant impact on the design of sparse channel estimation scheme based on compressive sensing, due to the large size of antenna array. In this letter, the block matching pursuit (BMP)-based two-stage sparse channel estimation scheme is proposed for spatial non-stationary (SNS) channels. In this scheme, the BMP is introduced to search for the support blocks and the threshold-based denoising method is utilized to refine the supports of non-zero elements. In order to evaluate our scheme, we provide a simple SNS channel model modified from the 3GPP 3D channel model to capture the delay-domain special sparse characteristic. Simulation results demonstrate that the proposed scheme can recover channels effectively and achieve better performance than comparison methods.