Massive MIMO Channel Research Articles

Compressive Channel Estimation Based on Weighted IRLS in FDD Massive MIMO

In this letter a weighted iteratively reweighted least-square (IRLS) algorithm is proposed for FDD massive MIMO channel estimation. The priori support information is merged into the weighted IRLS to improve the recovery performance. The priori support information is obtained from the uplink channel by reciprocity in angle domain, and a support estimation algorithm is proposed from the analysis of basis mismatch and angle deviation between uplink and downlink which is more practical in the real scenario. A brief convergence analysis of weighted IRLS is given out. Simulations show that the proposed weighted IRLS outperforms the standard IRLS, subspace pursuit (SP) and weighted SP.

Spatial-Wideband Effect in Massive MIMO with Application in mmWave Systems

Massive MIMO, especially in the millimeter- wave frequency bands, has been recognized as a promising technique to enhance spectrum and energy efficiency, as well as network coverage for wireless communications. Most research in massive MIMO just uses the extended conventional MIMO channel model by directly assuming that the channel dimensionality becomes large. With massive numbers of antennas, however, there exists a non-negligible propagation delay across the large array aperture, which then causes a transmitted symbol to reach different antennas with different delays, thereby rendering conventional MIMO channel models inapplicable. Such a phenomenon is known as the spatial-wideband effect in the areas of array signal processing and radar signal processing, and introduces the beam squint effect in beamforming. However, the spatial-wideband effect and the related beam squint issue are seldom studied in massive MIMO communications. To design a practical massive MIMO system, it is important to understand when the spatial-wideband effect appears and how it affects signal transmission, how the spatial-wideband effect interacts with the frequency-wideband effect (frequency selectivity), especially for multi-carrier modulations such as orthogonal frequency- division multiplexing (OFDM), and how we should re-design the transceiver. In this article we suggest a new massive MIMO channel model that embraces both the spatial- and frequency- wideband effects, and discuss these issues.

CNN-Based LOS/NLOS Identification in 3-D Massive MIMO Systems

In this letter, we propose to identify line-of-sight (LOS) and non-line-of-sight (NLOS) conditions based on a convolutional neural network (CNN) in urban 3-D massive MIMO systems. The proposed method includes two parts. In the first part, given that the paths spread differently in time domain, we combine the normalized tap energy distribution on each antenna utilizing sounding reference signals and construct the coordinated tap energy matrix. In the second part, we train a CNN to analyze the matrix and identify the LOS/NLOS conditions. A 3-D massive MIMO channel model is considered in our simulation. Results show that error rates of the worst performance using proposed identification algorithm are lower than 2.4%, and a remarkable improvement is achieved compared with schemes that exploit the space–time–frequency channel correlation features.

Statistical MIMO beam codebook design for mmWave transmissions

We propose a novel method for constructing beam codebooks, i.e., a set of beamforming weights, to be used for beam sweeping and data transmission in mmWave massive MIMO channels. The proposed beam codebooks are designed according to the statistical distribution of the channel’s angles of departure in order to efficiently sectorize the angular space covered by the beams. In particular, the cumulative distribution function of these angles is used to sectorize the angular beam space in order to design the beams. We first present a general closed-form construction of beam codebooks for an arbitrary distribution and then tailor the results to the Laplace distribution. We consider both narrow and broad beams. The resulting beams are a priori better adapted to the channel statistics and thus enhance the spectral efficiency of the transmission as compared to the state-of-the-art beam designs. Finally, we investigate the performance of the design and also present some analytical bounds quantifying the inherent loss of a directional beamforming compared to the optimal beamforming with perfect channel state information at the transmitter.

Alternative direction for 3D orthogonal frequency division multiplexing massive MIMO FDD channel estimation and feedback

In this study, downlink channel estimation of three-dimensional massive multiple-input multiple-output (3D-MIMO) system operating in the frequency division duplexing (FDD) mode is considered. Inspired by the channel sparsity property, this study proposes a compressive sensing algorithm to exploit the channel sparsity structure in the angle-time domain. The proposed algorithm, named AMP-ADM, combines the multiple approximate message passing (M-AMP) algorithm with the alternative direction of multiplier (ADM) technique to efficiently exploit the sparsity structure of the 3D massive MIMO channel. First, the proposed AMP-ADM is implemented in the case of the conventional estimation for the FDD protocol where the channel is estimated individually at each user equipment. Then, building on this algorithm, a low complexity feedback AMP-ADM-T scheme at the transmitting base station (BS) side is proposed. In the proposed feedback AMP-ADM-T technique the users' channels are jointly estimated at the BS to fully exploit the common sparsity basis. Complexity and convergence analyses are provided for both the AMP-ADM and feedback AMP-ADM-T algorithms. Simulation results prove the improved performance of the proposed feedback AMP-ADM-T algorithm compared to different state-of-the-art joint channel estimation techniques.

Blind Estimation of Sparse Broadband Massive MIMO Channels With Ideal and One-bit ADCs

We study the maximum likelihood problem for the blind estimation of massive mmWave MIMO channels while taking into account their underlying sparse structure, the temporal shifts across antennas in the broadband regime, and ultimately one-bit quantization at the receiver. The sparsity in the angular domain is exploited as a key property to enable the unambiguous blind separation between user's channels. The main advantage of this approach is the fact that the overhead due to pilot sequences can be dramatically reduced especially when operating at low SNR per antenna. In addition, as sparsity is the only assumption made about the channel, the proposed method is robust with respect to the statistical properties of the channel and data and allows the channel estimation and the separation of interfering users from adjacent base stations to be performed in rapidly time-varying scenarios. For the case of one-bit receivers, a blind channel estimation is proposed that relies on the Expectation Maximization (EM) algorithm. Additionally, performance limits are derived based on the clairvoyant Cramer Rao lower bound. Simulation results demonstrate that this maximum likelihood formulation yields superior estimation accuracy in the narrowband as well as the wideband regime with reasonable computational complexity and limited model assumptions.

Structured Turbo Compressed Sensing for Massive MIMO Channel Estimation Using a Markov Prior

Accurate channel estimation with small pilot overhead is vital to improve the capacity and reliability of massive MIMO systems. Recently, compressed sensing has been applied to reduce the pilot overhead in such systems by exploiting the underlying structured channel sparsity. In this paper, we propose a structured turbo compressed sensing (Turbo-CS) framework for the design and analysis of structured sparse channel estimation algorithms. In this framework, a Markov prior is used to model the structured sparsity in massive MIMO channels. Then we extend the Turbo-CS algorithm for independent and identically distributed priors to propose a structured Turbo-CS algorithm to solve the resulting sparse channel estimation problem with the Markov chain prior. We also accurately characterize the performance of the algorithm using state evolution. As compared to the existing algorithms, both the state evolution analysis and simulations show that the structured Turbo-CS algorithm can substantially enhance the channel estimation performance.

On the Amount of Downlink Training in Correlated Massive MIMO Channels

In this paper, we study the effect of downlink (DL) training on the achievable sum rate of multiuser massive MIMO channels with spatial correlations, and derive sufficient conditions of the DL channel estimation error covariance matrices that maintain the full multiplexing gain at high data signal-to-noise-ratios (SNRs). Given the derived conditions, a simple asymptotic upper bound on the average sum rate loss due to channel estimation is obtained. We derive, in closed-form, training sequences of limited duration that satisfy these conditions. The training duration is variable and increases with the data SNR, while the sequences lie in a subspace spanned by a variable number of user spatial covariance matrices’ eigenvectors. We additionally study the problem of sequence codebook design and find solutions to this problem for uniform linear and rectangular arrays using asymptotic results. For the aforementioned training structure, the designed codebooks are observed numerically to be near-optimal for a moderate number of base station antennas. Due to their ability to identify a sufficient limited number of channel directions to train, the proposed solutions can substantially reduce DL training overheads while providing achievable rates that are comparable with the rates achieved with perfect channel state information.

Novel 3-D Non-Stationary Wideband Models for Massive MIMO Channels

In this paper, a novel 3-D non-stationary wideband geometry-based stochastic theoretical channel model for massive multiple-input multiple-output communication systems is proposed. First, a second-order approximation to the spherical wavefront in space and time domains, i.e., parabolic wavefront , is proposed to efficiently model near-field effects . Second, environment evolution effects are modeled by spatial-temporal cluster (re)appearance and shadowing processes. We propose (re)appearance processes to model the visibility of clusters with enhanced spatial-temporal consistency. Shadowing processes are used to capture smooth spatial-temporal variations of the clusters’ average power. In addition, a corresponding simulation model is derived along with a 3-D extension of the Riemann sum method for parameters computation. Key statistical properties of the proposed model, e.g., the spatial-temporal cross-correlation function, are derived and analyzed. Finally, we present numerical and simulation results showing an excellent agreement between the theoretical and simulation models and validating the proposed parameter computation method. The accuracy and flexibility of the proposed simulation model are demonstrated by comparing simulation results and measurements of the delay spread, slope of cluster power variations, and visibility regions’ size.

3D MIMO for 5G NR: Several Observations from 32 to Massive 256 Antennas Based on Channel Measurement

By placing active antennas in a 2D grid at a BS, 3D MIMO is considered as a promising and practical technique for 5G New Radio (NR). So far, 3D MIMO studies reported are mostly done with antenna elements from 32 up to 128 in the limited scenario at one frequency. To gain further insights into the 3D massive MIMO channel and performance, field measurements from 32 to 256 antenna elements at the transmitter and 16 antenna elements at the receiver are performed in three typical deployment scenarios, including outdoor to indoor, urban microcell, and urban macrocell at both 3.5 and 6 GHz frequencies with 200 MHz bandwidth. Based on the extracted channel information from measured data, power angle spectrum, root mean square angle spread, channel capacity, and eigenvalue spread have been studied. Several observations, including 3D MIMO channel spatial dispersive properties and multi-user performance varying with antenna number, scenario, and frequency are given. These findings can provide valuable experimental insights for efficient utilization of 3D MIMO with massive antenna elements.

Opportunistic Multicast NOMA with Security Concerns in a 5G Massive MIMO System

This article concentrates on the multicast service in massive MIMO systems, and develops a hierarchical security model-based opportunistic NOMA scheme for 3D massive MIMO channel. In the considered scenario, the base station communicates with different security level users, where eavesdroppers are randomly deployed. Different security level users are classified into NOMA users and non-NOMA users, where NOMA users employ successive interference cancellation to cancel the low security multicast interference and separate their own data streams. The proposed scheme employs multicast beamforming in the multicast group, and applies null-space-based interference cancellation to eliminate the signal leakage generated by other groups. Numerical results revealed that hierarchical security model-based opportunistic NOMA schemes can significantly improve the network throughput and secrecy capacity in typical massive MIMO scenarios.

Blind Signal Detection in Massive MIMO: Exploiting the Channel Sparsity

In practical massive MIMO systems, a substantial portion of system resources are consumed to acquire channel state information (CSI), leading to a drastically lower system capacity compared with the ideal case where perfect CSI is available. In this paper, we show that the overhead for CSI acquisition can be largely compensated by the potential gain due to the sparsity of the massive MIMO channel in a certain transformed domain. To this end, we propose a novel blind detection scheme that simultaneously estimates the channel and data by factorizing the received signal matrix. We show that by exploiting the channel sparsity, our proposed scheme can achieve a DoF very close to the ideal case, provided that the channel is sufficiently sparse. Specifically, the achievable degree of freedom (DoF) has a fractional gap of only $1/T$ from the ideal DoF, where $T$ is the channel coherence time. This is a remarkable advance for understanding the performance limit of the massive MIMO system. We further show that the performance advantage of our proposed scheme in the asymptotic SNR regime carries over to the practical SNR regime. Numerical results demonstrate that our proposed scheme significantly outperforms its counterpart schemes in the practical SNR regime under various system configurations.

Line-of-Sight Massive MIMO Channel Characteristics in an Indoor Scenario at 94 GHz

The fading and correlation characteristics of virtual, yet realistic, line-of-sight (LOS) $4\times 2500$ millimetric (mmW) massive MIMO channels are investigated at 94 GHz in an indoor office environment for three different Tx–Rx distance scenarios. The capability of the mmW massive MIMO channel to spatially decorrelate the users is evaluated with the computation of the channel correlation and other channel metrics, such as power-to-interference ratio and condition number. In particular, the correlation between channel vectors for a given user and its influence on receiving correlation is discussed. The results clearly demonstrate the capability of mmW massive MIMO systems to reach orthogonal Tx–Rx streams even for a small $7\times 7$ antenna array subset with correlation between users <0.2. Moreover, strong phase variations at Tx side at this frequency range are highlighted through channel phase correlation studies and were shown to contribute to the decorrelation at Rx side between close users, paving the way for further massive MIMO system enhancements.

Accurate Approximation of ZF Massive MIMO Channel Rate With a Finite Antenna Over Ricean Fading Channel

In a typical downlink massive multiple-input and multiple-output (massive MIMO) system, the available degree of freedom (DoF) and multiplexing gain improve the channel rate. However, while a finite base station (BS) antenna limits the DoF, the line of sight (LoS) component decreases the multiplexing gain as a result of reducing the rank of the Ricean channel matrix. This paper provides the simple and tight approximations of the massive MIMO channel rate using the zero-forcing (ZF) precoding over the Ricean fading channel and with a finite antenna. We derive an accurate approximation of the ZF Ricean channel covariance matrix by exploiting the arbitrary-rank channel mean. This allows the ZF precoding to focus on the nonzero eigenmode of the correlation matrix in order to improve the channel gain. Subsequently, we deduce the first-, second- and third-eigenvalue moments. We then obtain an asymptotic series expansion in the closed-form expressions of the ZF achievable rates. Numerical results confirm the accuracy of the approximations, as the approximated ZF achievable rates converge to the ideal channel rate. In particular, the convergence shows a dependence on the Ricean factor and effective signal-to-noise ratio (SNR), while a finite BS antenna in ZF massive MIMO channel offers the required diversity order.

Combined Message Passing Based SBL With Dirichlet Process Prior for Sparse Signal Recovery With Multiple Measurement Vectors

This paper concerns the problem of sparse signal recovery with multiple measurement vectors, where the sparse signal vectors share multiple supports (i.e., the signal vectors can be clustered and the vectors in a cluster share a common support) and the prior knowledge on the supports of the vectors is unknown. This problem can be solved using sparse Bayesian learning (SBL) with Dirichlet process (DP) as hyper-prior, which is named DP-SBL in this paper. This paper aims to design efficient inference algorithms. The variational inference for DP mixtures, in particular mean field (MF) inference, has been studied, and applying it to the problem in this paper leads to an MF-DP-SBL algorithm. In this paper, we propose a combined message passing (CMP) approach, where a factor graph representation is designed to enable a more efficient implementation with both the MF and approximate message passing (AMP), leading to a CMP-DP-SBL algorithm. It is shown that, compared with MF-DP-SBL and CMP-DP-SBL delivers the same or even better performance with significantly lower complexity. As an example, we apply it to massive MIMO channel estimation where, due to the large number of antennas deployed at the base station, the channel impulse responses measured at receive antennas can share multiple supports. It is shown that CMP-DP-SBL delivers considerably better performance than existing algorithms.

On the Uplink Achievable Rate for Massive MIMO With 1-Bit ADC and Superimposed Pilots

In this work, we consider a 1-bit quantized massive MIMO channel with superimposed pilot (SP) scheme, dubbed QSP. With linear minimum mean square error (LMMSE) channel estimator and maximum ratio combining (MRC) receiver at the BS, we derive an approximate lower bound on the achievable rate. When optimizing pilot and data powers, the optimal power allocation maximizing the data rate is obtained in a closed-form solution. Although there is a performance gap between the quantized and unquantized systems, it is shown that this gap diminishes as the number of BS antennas is asymptotically large. Moreover, we show that pilot removal from the received signal by using the channel estimate doesn't result in a significant increase in information, especially in the cases of low signal-to-noise ratio (SNR) and a large number of users. We present some numerical results to corroborate our analytical findings and insights are provided for further exploration of the quantized systems with SP.

Fast iterative WSVT algorithm in WNN minimization problem for multiuser massive MIMO channel estimation

SummaryIn this paper, channel estimation for multiuser massive MIMO system is addressed for the scenario, where the number of scatterers is small compared to the base station antennas and single antenna users in the cell. If the number of scatterers is limited, then the corresponding angle of arrivals are finite. Moreover, if all the users share the same angle of arrivals, then the correlation among the channel vector increases. Thus, the high‐dimensional channel is approximated to the low‐rank matrix. This rank minimization problem is formulated as the weighted nuclear norm problem and is estimated using iterative weighted singular value thresholding (IWSVT) algorithm. To increase the convergence rate, fast IWSVT algorithm is proposed and the performance is measured based on mean square error and uplink and downlink achievable sum‐rate. The simulation study shows that the proposed weighted nuclear norm minimization method with fast IWSVT algorithm performs better than the conventional least square and the nuclear norm minimization method for various finite scatterers in different signal‐to‐noise ratio levels.

Physical-Layer Cryptography Through Massive MIMO

We propose the new technique of physical-layer cryptography based on using a massive MIMO channel as a key between the sender and desired receiver, which need not be secret. The goal is for low-complexity encoding and decoding by the desired transmitter-receiver pair, whereas decoding by an eavesdropper is hard in terms of prohibitive complexity. The decoding complexity is analyzed by mapping the massive MIMO system to a lattice. We show that the eavesdropper's decoder for the MIMO system with M-PAM modulation is equivalent to solving standard lattice problems that are conjectured to be of exponential complexity for both classical and quantum computers. Hence, under the widely-held conjecture that standard lattice problems are hard to solve in the worst-case, the proposed encryption scheme has a more robust notion of security than that of the most common encryption methods used today such as RSA and Diffie-Hellman. Additionally, we show that this scheme could be used to securely communicate without a pre-shared secret and little computational overhead. Thus, by exploiting the physical layer properties of the radio channel, the massive MIMO system provides for low-complexity encryption commensurate with the most sophisticated forms of application-layer encryption that are currently known.

Optimum and quasi‐optimum relaxation parameters for low‐complexity massive MIMO detector based on Richardson method

The low-complexity minimum mean square error detector based on Richardson method for massive MIMO systems was proposed, where the very important relaxation parameter was obtained by intensive simulations for each given massive MIMO channel matrix. Thus, a simple approach is developed to determine the optimum relaxation parameter of Richardson method for any massive MIMO system configuration. Furthermore, by exploiting the massive MIMO channel property of asymptotic orthogonality, a simple way to obtain the quasi-optimum relaxation parameter is proposed, which is given as a function of the number of users and the received base station antennas of a massive MIMO system.

On the Performance of Channel-Statistics-Based Codebook for Massive MIMO Channel Feedback

The channel feedback overhead for massive multiple-input multiple-output systems with a large number of base station (BS) antennas is very high since the number of feedback bits of traditional codebooks scales linearly with the number of BS antennas. To reduce the feedback overhead, an effective codebook based on channel statistics has been designed, where the required number of feedback bits only scales linearly with the rank of the channel correlation matrix. However, this attractive conclusion was only proved under a particular channel assumption in the literature. To provide a rigorous theoretical proof under a general channel assumption, in this paper, we quantitatively analyze the performance of the channel-statistics-based codebook. Specifically, we first introduce the rate gap between the ideal case of perfect channel state information at the transmitter and the practical case of limited channel feedback, where we find that the rate gap depends on the quantization error of the codebook. Then, we derive an upper bound of the quantization error, based on which we prove that the required number of feedback bits to ensure a constant rate gap only scales linearly with the rank of the channel correlation matrix. Finally, numerical results are provided to verify this conclusion.