Massive Multiple-input Multiple-output Channel Research Articles

Data Ridden Pilots Based Estimation of Sparse Multipath Massive MIMO Channels Using Orthogonal Matching Pursuit

Massive Multiple-Input Multiple-Output (MIMO) is envisioned to be a strong candidate technology for the upcoming 5th generation (5G) of wireless communication networks. This research work presents a novel Compressed Sensing (CS) and Superimposed Training (SiT) based technique for estimating the sparse uplink channels in massive MIMO systems. The proposed technique involves arithmetic addition of a periodic, but low powered training sequence with each user’s information sequence. Consequently, separately dedicated resources for the pilot symbols are not needed. Moreover, to attain the estimates of the Channel State Information (CSI) in the uplink, the sparsity exhibited by the MIMO channels is exploited by incorporating CS based Orthogonal Matching Pursuit (OMP) algorithm. For decoding the transmitted information symbols of each user, a Linear Minimum Mean Square Error (LMMSE) based equalizer is incorporated at the receiving Base Station (BS). Based on the obtained simulation results, the proposed SiT-OMP technique outperforms the existing Least Squares (SiT) channel estimation technique. The comparison is done using performance metrics of the Bit Error Rate (BER) and the Normalized Channel Mean Square Error (NCMSE).

A Cluster-Based Channel Model for Massive MIMO Communications in Indoor Hotspot Scenarios

Characterization and modeling of massive multiple-input multiple-output (MIMO) channel has been one of the research hotspots in the field of wireless communications. One important feature of the massive MIMO channel is the spatial non-stationarity. To statistically model the spatial non-stationary massive MIMO channels, a cluster-based channel model is proposed in this paper. The model incorporates both inter- and intra-cluster properties and the cluster evolution over the large-scale array. A hybrid data processing scheme is applied to extract the multipath components (MPCs) and clustering the MPCs over a large-scale antenna array. The global angular spread, cluster angular spread, and cluster delay spread are modeled with log-normal distributions. Observed cluster length and MPC length within clusters, which are introduced to describe the cluster existence over the array and MPCs existence within the cluster, respectively, are statistically modeled with the exponential distributions. Moreover, both the cluster and MPC arrival intervals, which are used, respectively, to describe the cluster occurrence position on the array and MPC occurrence position within the cluster, can be statistically modeled with the uniform distributions. Finally, the model implementation is validated by comparing with the different channel performance metrics between measurements and simulations.

Adaptive Grouping Sparse Bayesian Learning for Channel Estimation in Non-Stationary Uplink Massive MIMO Systems

This paper addresses wideband channel estimation in an uplink massive multiple-input multiple-output (MIMO) system, which consists of multiple single-antenna users and a base station (BS) equipped with a large number of antennas. Due to the spatially non-stationary characteristics in massive MIMO channels, the channel vectors corresponding to different BS antennas may take on different sparsity patterns in delay domain. Taking this into account, we propose an adaptive grouping sparse Bayesian learning (AGSBL) scheme for uplink channel estimation. Specifically, for the channel vectors to be estimated, we judiciously design a hierarchical prior model controlled by a set of tunable hyperparameters. Then, we develop a variational Bayesian algorithm to infer the posterior probability of the channel vectors and the hyperparameters associated with the prior, thereby obtaining the channel estimates. Due to the designed prior, we are able to adaptively divide the channel vectors involved into several groups, each group bearing a similar sparsity pattern. In this way, the AGSBL can efficiently exploit the partial joint sparsity shared by each group of channel vectors, and therefore significantly improves the channel estimation performance. The simulation results are provided to verify the advantages of the proposed AGSBL over the related counterparts.

Hyper-power zero forcing detector for massive MIMO systems

In massive multiple-input multiple-output (MIMO) systems when the number of base station antennas is much higher than the number of users, linear detectors, such as zero forcing (ZF) and minimum mean-square error (MMSE), are able to achieve the near-optimal performance due to the favorable massive MIMO channel propagation. But, these detectors employ, in general, exact matrix inversion which is computationally complex for such systems. In this paper, we affirm that computing the exact matrix inversion by direct methods is not necessary to find ZF or MMSE solution. An iterative matrix inversion procedure would yield similar performance. Thus, an efficient iterative matrix inversion based on the hyper-power (HP) method is proposed for massive MIMO detection. The computing efficiency of the iterative matrix inversion is further improved by optimizing the number of terms from the infinite series used in the HP method. Analytical results show that the optimum choice for the number of terms is three from the HP method. Simulation results show that the HP method with the optimum number of terms achieves the near-optimal ZF performance in a small number of iterations. Finally, the Coppersmith–Winograd algorithm for matrix multiplication is employed in order to reduce the computational complexity from \(O(K^{3})\) to \(O(K^{2.373})\), where K represents the number of users.

Compressive Sensing-Based Adaptive Active User Detection and Channel Estimation: Massive Access Meets Massive MIMO

This paper considers massive access in massive multiple-input multiple-output (MIMO) systems and proposes an adaptive active user detection and channel estimation scheme based on compressive sensing. By exploiting the sporadic traffic of massive connected user equipments and the virtual angular domain sparsity of massive MIMO channels, the proposed scheme can support massive access with dramatically reduced access latency. Specifically, we design non-orthogonal pseudo-random pilots for uplink broadband massive access, and formulate the active user detection and channel estimation problems as a generalized multiple measurement vector compressive sensing problem. Furthermore, by leveraging the structured sparsity of the uplink channel matrix, we propose an efficient generalized multiple measurement vector approximate message passing (GMMV-AMP) algorithm to realize simultaneous active user detection and channel estimation based on a spatial domain or an angular domain channel model. To jointly exploit the channel sparsity presented in both the spatial and the angular domains for enhanced performance, a Turbo-GMMV-AMP algorithm is developed for detecting the active users and estimating their channels in an alternating manner. Finally, an adaptive access scheme is proposed, which adapts the access latency to guarantee reliable massive access for practical systems with unknown channel sparsity level. Additionally, the state evolution of the proposed GMMV-AMP algorithm is derived to predict its performance. Simulation results demonstrate the superiority of the proposed active user detection and channel estimation schemes compared to several baseline schemes.

Compressive Sensing Based Channel Estimation for Massive MIMO Communication Systems

Massive multiple-input multiple-output (MIMO) is believed to be a key technology to get 1000x data rates in wireless communication systems. Massive MIMO occupies a large number of antennas at the base station (BS) to serve multiple users at the same time. It has appeared as a promising technique to realize high-throughput green wireless communications. Massive MIMO exploits the higher degree of spatial freedom, to extensively improve the capacity and energy efficiency of the system. Thus, massive MIMO systems have been broadly accepted as an important enabling technology for 5th Generation (5G) systems. In massive MIMO systems, a precise acquisition of the channel state information (CSI) is needed for beamforming, signal detection, resource allocation, etc. Yet, having large antennas at the BS, users have to estimate channels linked with hundreds of transmit antennas. Consequently, pilot overhead gets prohibitively high. Hence, realizing the correct channel estimation with the reasonable pilot overhead has become a challenging issue, particularly for frequency division duplex (FDD) in massive MIMO systems. In this paper, by taking advantage of spatial and temporal common sparsity of massive MIMO channels in delay domain, nonorthogonal pilot design and channel estimation schemes are proposed under the frame work of structured compressive sensing (SCS) theory that considerably reduces the pilot overheads for massive MIMO FDD systems. The proposed pilot design is fundamentally different from conventional orthogonal pilot designs based on Nyquist sampling theorem. Finally, simulations have been performed to verify the performance of the proposed schemes. Compared to its conventional counterparts with fewer pilots overhead, the proposed schemes improve the performance of the system.

Joint Channel Parameter Estimation in Multi-Cell Massive MIMO System

In this paper, we consider the uplink channel parameter estimation problem in the presence of pilot contamination for massive multiple-input-multiple-output (MIMO) systems. We propose a parallel factor (PARAFAC)-based estimation scheme, which exploits the low-rank property of massive MIMO channels caused by the finite scattering in a physical environment. Specifically, we first parameterize the channel in terms of three parameters, i.e., fading coefficients, directions of arrival (DOAs), and delays; thereby, the channel is characterized via three equivalent PARAFAC models. Then, the proposed PARAFAC-based scheme is developed, which jointly estimates these three channel parameters using an alternating least squares (ALS) algorithm. Therein, we certify the identifiability of the three channel parameters of the PARAFAC models to mitigate the pilot contamination and state the convergence of the ALS algorithm, which guarantees that the three channel parameters can be uniquely determined with the proposed scheme. Moreover, to further reduce the computational complexity, two advanced schemes are proposed by antenna selection and reducing the estimation frequency of DOAs and delays, respectively. Simulation results show that the proposed schemes can achieve both low computational complexities and close to optimal Cramer–Rao Bound performance.

Downlink Channel Estimation for Massive MIMO Systems Relying on Vector Approximate Message Passing

To reduce the pilot overhead of downlink channel estimation in massive multiple-input-multiple-output (MIMO) systems, a sparse recovery algorithm relying on the vector approximate message passing (VAMP) technique is proposed. More specifically, an a-priori channel model characterized by a multivariate Bernoulli-Gaussian distribution is invoked for exploiting the common sparsity of massive MIMO channels, and the VAMP technique is used for jointly estimating the spatially correlated channels. Moreover, the hyperparameters of the a-priori model are learned by invoking the expectation maximization algorithm. Our numerical results demonstrate that the proposed algorithm is capable of reducing the pilot overhead by 50% in massive MIMO systems.

Deep Learning-Based CSI Feedback Approach for Time-Varying Massive MIMO Channels

Massive multiple-input multiple-output (MIMO) systems rely on channel state information (CSI) feedback to perform precoding and achieve performance gain in frequency division duplex networks. However, the huge number of antennas poses a challenge to the conventional CSI feedback reduction methods and leads to excessive feedback overhead. In this letter, we develop a real-time CSI feedback architecture, called CsiNet-long short-term memory (LSTM), by extending a novel deep learning (DL)-based CSI sensing and recovery network. CsiNet-LSTM considerably enhances recovery quality and improves tradeoff between compression ratio (CR) and complexity by directly learning spatial structures combined with time correlation from training samples of time-varying massive MIMO channels. Simulation results demonstrate that CsiNet-LSTM outperforms existing compressive sensing-based and DL-based methods and is remarkably robust to CR reduction.

Compressed channel estimation for FDD massive MIMO systems without prior knowledge of sparse channel model

In this study, a new greedy-based algorithm for sparse channel estimation in frequency-division duplexing massive multiple-input multiple-output (MIMO) systems is introduced. The proposed algorithm is able to acquire the channel with no information about the channel model such as the sparsity order, statistical bound on sparsity support, and special features of the channel. In other words, the authors assume that the massive channel is totally unknown and then exploit the inherent property of correlation between measurements and the sensing matrix to estimate the channel, which is available at the user side. By utilising this property, a halting parameter is defined as the halting threshold instead of known prior information assumed in the conventional greedy algorithms. Furthermore, the lower and upper bounds of the halting parameter are obtained that helps the algorithm to take the suitable values of this parameter and by considering the lower bound as the values of the halting parameter, the algorithm can prevent from missing the original channel bins. Simulation results demonstrate that the proposed algorithm outperforms its counterparts in terms of normalised mean square error while it faces a completely unknown massive MIMO channel.

Massive MIMO Channel Estimation Over the mmWave Systems Through Parameters Learning

In this letter, we formulate an off-grid channel model to characterize spatial sample mismatching in the discrete Fourier transform (DFT) based massive multiple-input-multiple-output (MIMO) channel estimation over the millimeter-wave (mmWave) band. Then, we decompose the off-grid mmWave massive MIMO channel estimation into the learning of model parameters and virtual channel estimation. Specifically, an expectation maximization (EM) based sparse Bayesian learning framework is first developed to learn the model parameters, such as bias parameters and spatial signatures, with unknown noise. With the learned model parameters, we resort to the linear minimum mean square error method to estimate the instantaneous virtual channel with less pilot overhead. Finally, we corroborate the validity of the proposed method through numerical simulations.

Data Detection in Single User Massive MIMO Using Re-Transmissions

Background:Single user Massive Multiple Input Multiple Output (MIMO) can be used to increase the spectral efficiency since the data is transmitted simultaneously from a large number of antennas located at both the base station and mobile. It is feasible to have a large number of antennas in the mobile, in the millimeter wave frequencies. However, the major drawback of single user massive MIMO is the high complexity of data recovery at the receiver.Methods:In this work, we propose a low complexity method of data detection with the help of re-transmissions. A turbo code is used to improve the Bit-Error-Rate (BER).Results and Conclusion:Simulation results indicate a significant improvement in BER with just two re-transmissions as compared to the single transmission case. We also show that the minimum average SNR per bit required for error-free propagation over a massive MIMO channel with re-transmissions is identical to that of the Additive White Gaussian Noise (AWGN) channel, which is equal to -1.6 dB.

Efficient Evaluation of Massive MIMO Channel Capacity

Massive multiple-input multiple-output (MIMO) is a key promising technology for 5G wireless networks that allows significant increase in spectral and energy efficiency without increasing the spectrum and/or the number of cell sites. However, the computational time and resources required to rigorously analyze the capacity offered by a base station (BS) equipped with a large number of antenna elements increase with the increase of the number of antenna elements in the array. In this paper, we present a novel approximation approach for modeling large microstrip antenna arrays in BSs of massive MIMO systems. The approach subdivides an M × N array into columns, rows, rectangular, or square subarrays, each consisting of a group of elements. The coupling is rigorously taken into account within each subarray, but it is ignored between subarrays, using just an array factor instead. Results are demonstrated for an 8 × 8 = 64 element patch array. It is shown that the difference in the capacity evaluated using rigorous electromagnetic simulations and the proposed approach is less than 0.79% using the 2 × (8 × 4) approach for both the suburban macrocell model of the Extended Spatial Channel Model (SCME/suburban macro cell (SMa)) outdoor propagation model and three-dimensional independent identically distributed model with a significant reduction of 44% and 50%, respectively, in computational time as compared to the full-wave antenna array modeling approach.

Robust beamforming and spatial precoding for quasi-OSTBC massive MIMO communications

This paper considers the problem of massive multiple-input-multiple-output (MIMO) wireless communication systems with quasi-orthogonal space-time block code (QOSTBC) transmission in the presence of spatial correlation effect (SCE) and mutual coupling effect (MCE). Conventional MIMO channels with QOSTBC transmission suffer from several drawbacks. The number of transmit antennas is restricted to a few in order to achieve full transmission rate. Therefore, it is difficult to make a quasi-orthogonal space time block coded massive MIMO system to achieve full transmission rate. Moreover, MIMO channel with QOSTBC transmission is usually considered for the case where the number of user equipments (UEs) is one. We present a joint beamforming and spatial precoding method to deal with the above drawbacks. The proposed method incorporates a beamforming scheme and spatial precoding to formulate an appropriate optimization process to effectively alleviate the considered problems. The resulting optimization problem will be solved by using a cooperative coevolutionary particle swarm optimization algorithm under two proposed fitness functions. During the optimization process, the proposed method finds the optimal beamforming coefficients of the precoding matrix, the optimal normalized positions of transmit and receive antenna elements for the case of using linear antenna arrays, and the optimal angle differences of transmit and receive antenna elements for the case of using circular arrays. Based on the proposed method, we are able to cure the performance degradation of a quasi-orthogonal space time block coded massive MIMO system due to the SCE and MCE. Moreover, the proposed method makes QOSTBC MIMO communications with full transmission rate for any number of transmit antennas achievable. Several simulation examples are presented to show the superior bit error rate (BER) performances of QOSTBC wireless MIMO scenarios with linear as well as circular antenna arrays by using the proposed method as compared to the existing methods.

Nonlinear Hybrid Precoding for Coordinated Multi-Cell Massive MIMO Systems

This paper examines nonlinear hybrid precoding with minimum mean square error (MMSE)-vector perturbation (VP) for multi-cell massive multiple-input multiple-output (MIMO) systems. Two-timescale channel state information (CSI) is assumed, which consists of short-term noisy observations of the RF-precoded MIMO channel, and perfect knowledge of the long-term channel temporal and spatial correlation. By exploiting the low-dimensional effective CSI, we propose to estimate the instantaneous realization of the high-dimensional CSI via Kalman filtering. The CSI estimate is then utilized for RF precoding in consideration of centralized and distributed MMSE-VP at baseband. By abstracting the effect of nonlinear baseband precoding, RF precoding is separately formulated as a solution to balance the error performance of signal detection with the accuracy of channel tracking. To solve such nonconvex problems, we develop Cayley transformation-based gradient descent algorithms. Numerical results demonstrate the benefits of incorporating CSI tracking into hybrid precoding from its superior bit error rate to other transmit spatial correlation-based baselines, and its improved resilience to the channel estimation errors over the fully digital counterpart.

On Modeling of Dense Multipath Component for Indoor Massive MIMO Channels

Elaborate channel modeling is an essential prerequisite for design, testing, and improvement of the massive multiple-input–multiple-output (MIMO) system. In this letter, dense multipath component (DMC) modeling for massive MIMO channels is presented based on measurement campaigns in three different indoor scenarios. The parameters for DMC are extracted by applying a RiMAX-based estimator. The distance-dependence and the variance behaviors of the DMC parameters across the large-scale array are analyzed and modeled. Moreover, the model validation is performed by using an empirical cluster-based massive MIMO channel model. Entropy capacity, condition number, channel ellipticity, and root-mean-square delay spread, which reflect the spatial structure and multipath richness of the channel, are used as the validation metrics. The validation shows that the incorporation of DMC can significantly improve the accuracy of channel modeling.

Non-Uniform Burst-Sparsity Learning for Massive MIMO Channel Estimation

We address the downlink channel estimation problem for massive multiple-input multiple-output (MIMO) systems in this paper, where the inherit burst-sparsity structure is exploited to improve the channel estimation performance. In the literature, the commonly used burst-sparsity model assumes a uniform burst-sparse structure in which all bursts have similar sizes. However, such assumption is oversimplified to hold in practice. Outliers deviated from such uniform burst structures can significantly degrade the accuracy of the existing burst-sparsity models, which may result in a reduced recovery performance. To capture a more general burst-sparsity structure in practice, we propose a novel non-uniform burst-sparsity model and introduce an improved pattern-coupled prior to account for more realistic non-uniform burst structures. A generic sparse Bayesian learning based framework to exploit the non-uniform burst-sparsity and to enhance massive MIMO channel estimation performance is then developed. We further prove that our solution converges to a stationary point of the associated optimization problem, and our framework includes the state-of-the-art pattern-coupled method as a special case. Simulation results verify the robust performance of the devised method.

Channel estimation for FDD massive MIMO system by exploiting the sparse structures in angular domain

Massive multiple-input multiple-output (MIMO) is a powerful supporting technology to meet the energy/spectral efficiency and reliability requirement of Internet of Things (IoT) network. However, the gain of massive MIMO relies on the availability of channel state information (CSI). In this paper, we investigate the channel estimation problem for frequency division duplex (FDD) massive MIMO system. By analyzing the sparse property of the downlink massive MIMO channel in the angular domain, a structured prior-based sparse Bayesian learning (SP-SBL) approach is proposed to estimate the downlink channels between base station (BS) and users reliably. The scheme can be implemented without the knowledge of channel statistics and angular information of users. The simulation results show that the proposed scheme outperforms the reference schemes significantly in terms of normalized mean square error (NMSE) for a variety of scenarios with different lengths of pilot sequence, transmit signal-to-noise ratios (SNRs), and angular spreads.

Pilot Decontamination in Noncooperative Massive MIMO Cellular Networks Based on Spatial Filtering

Pilot contamination has been known as one of the most challenging issues in massive multiple-input multiple-output (MIMO) systems. Every user will experience interferences from users in adjacent cells who employ the same pilot sequence. For cell-edge users, pilot contamination is particularly detrimental, because their signals might be overwhelmed by the interference. In this paper, we propose a pilot decontamination method based on a spatial filter, which exploits the spatial sparsity of massive MIMO channels. In massive MIMO systems, the communication protocols are generally divided into four phases: pilot transmission, processing, uplink data transmission, and downlink data transmission. In the first phase, the base station (BS) receives both the desired signal and the pilot contaminated signal. In the second phase, all users in the target cell stay silent for one symbol period, and the BS only receives interference from adjacent cells. The fast Fourier transform can then be employed to analyze the spatial spectrums of the received signals. The spatial sparsity of the massive MIMO channels makes it possible to identify the pilot contamination components by comparing the two spectrums on different spatial signatures (or angles of arrival). A spatial filter can then be constructed to eliminate pilot contamination. Both the theoretical analysis and simulation results demonstrate the effectiveness of the proposed method, whose complexity is comparable to that of the traditional matched filter-based channel estimator.

Efficient Channel Estimator With Angle-Division Multiple Access

Massive multiple-input multiple-output (M-MIMO) is an enabling technology of 5G wireless communication. The performance of an M-MIMO system is highly dependent on the speed and accuracy of obtaining the channel state information (CSI). The computational complexity of channel estimation for an M-MIMO system can be reduced by making use of the sparsity of the M-MIMO channel. In this paper, we propose the hardware-efficient channel estimator based on angle-division multiple access (ADMA) for the first time. Preamble, uplink (UL) and downlink (DL) training are also implemented. For further hardware-efficiency consideration, optimization regarding quantization and approximation strategies have been discussed. Implementation techniques such as pipelining and systolic processing are also employed for hardware regularity. Numerical results and FPGA implementation have demonstrated the advantages of the proposed channel estimator.