Massive Massive Multiple-input Multiple-output Channel Research Articles

Overcoming the Channel Estimation Barrier in Massive MIMO Communication via Deep Learning

A new wave of wireless services, including virtual reality, autonomous driving and Internet of Things, is driving the design of new generations of wireless systems to deliver ultra-high data rates, massive numbers of connections and ultra-low latency. Massive multiple-input multiple-output (MIMO) is one of the critical underlying technologies that allow future wireless networks to meet these service needs. This article discusses the application of deep learning (DL) for massive MIMO channel estimation in wireless networks by integrating the underlying characteristics of channels in future high-speed cellular deployment. We develop important insights derived from the physical radio frequency (RF) channel properties and present a comprehensive overview on the application of DL for accurately estimating channel state information (CSI) with low overhead. We provide examples of successful DL application in CSI estimation for massive MIMO wireless systems and highlight several promising directions for future research.

A Novelty Massive MIMO Channel Model Based on the Birth‐and‐Death Process of Spatial Multipath Cluster

AbstractIn this paper a novelty Massive Multiple Input Multiple Output (MIMO) channel model based on the birth‐and‐death process of multipath clusters is proposed. First, Massive MIMO measurements are conducted in typical outdoSor scenarios with the bandwidth of 100 MHz at frequencies of 1.4725 and 6 GHz, respectively, following with the investigation of radio propagation characteristics over antenna array. Then we research on the subchannel correlation and nonstationary based on the channel sounding experiments. Furthermore, we build up a Markov chain to characterize the birth‐and‐death process of the multipath clusters over the array, which is helpful to bring deeply insight into the cluster evolution over the antenna array axis. And the analysis results are consistent with the theory of the cluster's visible region. At last, the paper systematically demonstrates how does the spatial correlation influence the capacity of the communication system. The whole research work aims to contribute the radio channel modeling of the fifth‐generation (5G) Massive MIMO communication system.

The Design of a Trimodal Broadside Antenna Element for Compact Massive MIMO Arrays: Utilizing the Theory of Characteristic Modes

Massive multiple-input, multiple-output (MIMO) arrays are becoming critical elements in cellular base station infrastructure. We utilize the theory of characteristic modes (TCM) to design a novel trimodal broadside antenna element that is suitable for constructing compact massive MIMO arrays. The proposed antenna element consists of three ports, formed by reviewing an existing compact two-port Y-shaped patch antenna from a TCM perspective. Using this perspective, the Y-shaped antenna is modified into a snowflake-shaped patch antenna and excited by three ports via capacitive coupling. The advantage of this design approach is that the size of the three-port antenna is approximately the same as a conventional dual-polarized patch antenna, hence allowing 50% more antenna elements for the same array aperture. By cutting the ground plane into a hexagonal shape, a multiple of the proposed three-port canonical antennas are concatenated together to form 21- and 102-port massive MIMO arrays with all radiation patterns pointing in the broadside direction. Key performance characteristics of the massive MIMO arrays, i.e., the Hermitian product of the simulated massive MIMO channel and mutual coupling, validate the effectiveness of the compact design.

Learning the Time-Varying Massive MIMO Channels: Robust Estimation and Data-Aided Prediction

The quasi-static assumption of channels becomes invalid in a number of emerging applications of massive multiple-input multiple-output (MIMO) systems with high base station (BS)/user mobility, such as high speed train and unmanned aerial vehicle communications. In these situations, the time variation of channels shortens the channel coherence time and decreases the efficiency of traditional channel estimation schemes significantly. This paper focuses on the time-varying channel estimation problem in massive MIMO systems, where the mobility of BS/user is assumed to be high. The sparse property of the time-varying massive MIMO channels is analyzed, which reveals that the angular domain channels exhibit two kinds of spatial-temporal sparse (STS) structures, namely the temporal-common sparse structure and spatial-clustered sparse structure. By exploiting the STS structures, a novel structured variational Bayesian inference (VBI) framework is formulated to make a robust channel estimation during the training phase. A data-aided channel predication scheme is further proposed to combat the time variation of the channels during the data transmission phase without increasing the pilot consumption. The simulation results demonstrate the superiority of the proposed scheme in the time-varying scenarios with different BS/user mobilities.

Networked Optical Massive MIMO Communications

The low cost and versatility of optical devices make it possible to pack a large number of optical transceivers into arrays and exploit massive multiple-input multiple-output (MIMO) transmission in optical wireless communications. Nevertheless, optical massive MIMO presents several distinct challenges such as, the line-of-sight propagation and intensity modulation, incompatible with existing radio frequency massive MIMO techniques. This paper presents a networked optical massive MIMO system that consists of multiple base stations (BSs), each equipped with a transmit lens and an optical transmitter array, cooperatively serving a number of user terminals (UTs), each equipped with a receive lens and a photodetector array. We establish the optical massive MIMO channel model, analyze its asymptotic behavior, and evaluate the potential of networked optical massive MIMO on system throughput improvement. To achieve high throughput, we propose optical beam division multiple access (BDMA) transmission schemes under the total and per transmitter power constraints with the asymptotic optimality. Our results show that the system sum rate increases proportionally to the number of BSs and UTs using the optical BDMA transmission. Further numerical results show that the proposed optical massive MIMO system along with the optical BDMA transmission is able to achieve high throughput with low complexity.

Uplink-Aided High Mobility Downlink Channel Estimation Over Massive MIMO-OTFS System

Although it is often used in the orthogonal frequency division multiplexing (OFDM) systems, application of massive multiple-input multiple-output (MIMO) over the orthogonal time frequency space (OTFS) modulation could suffer from enormous training overhead in high mobility scenarios. In this paper, we propose one uplink-aided high mobility downlink channel estimation scheme for the massive MIMO-OTFS networks. Specifically, we firstly formulate the time domain massive MIMO-OTFS signal model along the uplink and adopt the expectation maximization based variational Bayesian (EM-VB) framework to recover the uplink channel parameters including the angle, the delay, the Doppler frequency, and the channel gain for each physical scattering path. Correspondingly, with the help of the fast Bayesian inference, one low complex approach is constructed to overcome the bottleneck of the EM-VB. Then, we fully exploit the angle, delay and Doppler reciprocity between the uplink and the downlink and reconstruct the angles, the delays, and the Doppler frequencies for the downlink massive channels at the base station. Furthermore, we examine the downlink massive MIMO channel estimation over the delay-Doppler-angle domain. The channel dispersion of the OTFS over the delay-Doppler domain is carefully analyzed and is utilized to associate one given path with one specific delay-Doppler grid if different paths of any user have distinguished delay-Doppler signatures. Moreover, when all the paths of any user could be perfectly separated over the angle domain, we design the effective path scheduling algorithm to map different users' data into the orthogonal delay-Doppler-angle domain resource and achieve the parallel and low complex downlink 3D channel estimation. For the general case, we adopt the least square estimator with reduced dimension to capture the downlink delay-Doppler-angle channels. Various numerical examples are presented to confirm the validity and robustness of the proposed scheme.

Angular-Domain Massive MIMO Detection: Algorithm, Implementation, and Design Tradeoffs

In massive multiple-input multiple-output (MIMO) systems, the large size of channel state information (CSI) matrix significantly increases the computational complexity of uplink detection and size of required memory to store the channel data. To address these challenges, we propose to perform detection in the angular domain, where the channel information can be presented in a more condensed way. The underlying idea is to exploit the sparsity of massive MIMO channel in the angular domain to reduce the size of CSI matrix by selecting dominant beams. Then, an angular-domain linear detector followed by a non-linear post-processing scheme is proposed to perform detection using the reduced-size CSI. Evaluated using measured massive MIMO channels, our method results in 35%-73% reduction in complexity and required memory compared to traditional detectors while it achieves better performance. Moreover, this paper provides a framework, which trades between performance, complexity, and size of required memory. As a proof of concept, we implement the angular-domain detector in a 28 nm FD-SOI CMOS for a massive MIMO with 128 antennas communicating with up to 16 users. Synthesis result shows that our design attains a throughput of 2240 Mbps with an area of 829 k gates.

Data-Driven Deep Learning to Design Pilot and Channel Estimator for Massive MIMO

In this paper, we propose a data-driven deep learning (DL) approach to jointly design the pilot signals and channel estimator for wideband massive multiple-input multiple-output (MIMO) systems. By exploiting the angular-domain compressibility of massive MIMO channels, the conceived DL framework can reliably reconstruct the high-dimensional channels from the under-determined measurements. Specifically, we design an end-to-end deep neural network (DNN) architecture composed of dimensionality reduction network and reconstruction network to respectively mimic the pilot signals and channel estimator, which can be acquired by data-driven deep learning. For the dimensionality reduction network, we design a fully-connected layer by compressing the high-dimensional massive MIMO channel vector as input to low-dimensional received measurements, where the weights are regarded as the pilot signals. For the reconstruction network, we design a fully-connected layer followed by multiple cascaded convolutional layers, which will reconstruct the high-dimensional channel as the output. By defining the mean square error between input and output as loss function, we leverage Adam algorithm to train the end-to-end DNN aforementioned with extensive channel samples. In this way, both the pilot signals and channel estimator can be simultaneously obtained. The simulation results demonstrate that the superiority of the proposed solution over state-of-the-art compressive sensing approaches.

Towards Massive MIMO Channel Emulation: Channel Accuracy Versus Implementation Resources

Channel emulation is widely used to control wireless channels and replay scenarios for repeatable experimentation and evaluation. Characterizing the propagation of massive Multiple-Input Multiple-Output (MIMO) systems, is challenging due to the rapid scaling of the number of channels needed to create representative scenarios as well as accurately modeling complex interdepedencies that exist within the channel matrix. Nonetheless, having the ability to emulate massive MIMO channels is critical for the development and testing of next-generation cellular protocols and algorithms. To achieve such scale for massive MIMO channel emulation solutions, in this paper, we study the tradeoff in channel emulation fidelity versus the hardware resources consumed using both analytical modeling and FPGA-based implementations. To reduce the memory footprint of our design, we optimize our channel emulation using an iterative structure to generate geometry-based channels at scale. In addition, the effects of varying the channel update rate and word length selection are evaluated in the paper and can significantly improve the implementation efficiency on an FPGA.

Double-Sparsity Learning-Based Channel-and-Signal Estimation in Massive MIMO With Generalized Spatial Modulation

In this paper, we study joint antenna activity detection, channel estimation, and multiuser detection for massive multiple-input multiple-output (MIMO) systems with general spatial modulation (GSM). We first establish a double-sparsity massive MIMO model by considering the channel sparsity of the massive MIMO channel and the signal sparsity of GSM. Based on the double-sparsity model, we formulate a blind detection problem. To solve the blind detection problem, we develop message-passing based blind channel-and-signal estimation (BCSE) algorithm. The BCSE algorithm basically follows the affine sparse matrix factorization technique, but with critical modifications to handle the double-sparsity property of the model. We show that the BCSE algorithm significantly outperforms the existing blind and training-based algorithms, and is able to closely approach the genie bounds (with either known channel or known signal). In the BCSE algorithm, short pilots are employed to remove the phase and permutation ambiguities after sparse matrix factorization. To utilize the short pilots more efficiently, we further develop the semi-blind channel-and-signal estimation (SBCSE) algorithm to incorporate the estimation of the phase and permutation ambiguities into the iterative message-passing process. We show that the SBCSE algorithm substantially outperforms the counterpart algorithms including the BCSE algorithm in the short-pilot regime.

Pilot Reuse for Vehicle-to-Vehicle Underlay Massive MIMO Transmission

Pilot overhead constitutes a bottleneck in vehicle-to-vehicle (V2V) underlay massive multiple-input multiple-output (MIMO) cellular networks. To decrease the pilot overhead and further improve the spectral efficiency, we propose pilot reuse for V2V underlay massive MIMO transmission. First, based on the angle domain sparsity of massive MIMO channels, we derive the channel angle domain condition under which the channel estimation mean-square-error for cellular and V2V links can be both minimized. Motivated by this condition, we then develop an angle information assisted pilot assignment (AIAPA) algorithm. Numerical results indicate that the proposed angle information assisted pilot reuse scheme can significantly improve the performance of spectral efficiency compared with the conventional orthogonal pilot scheme for both cellular and V2V links.

Robust massive MIMO channel estimation for 5G networks using compressive sensing technique

The pilot overhead provides fundamental limits on the performance of massive multiple-input multiple-output (MIMO) systems. This is because the performance of such systems is based on the failure of the presentation of accurate channel state information (CSI). Based on the theory of compressive sensing, this paper presents a novel channel estimation technique as the mean of minimizing the problems associated with pilot overhead. The proposed technique is based on the combination of the compressive sampling matching and sparsity adaptive matching pursuit techniques. The sources of the signals in MIMO systems are sparsely distributed in terms of spatial correlations. This distribution pattern enables then use of compressive sampling techniques to solve the channel estimation problem in MIMO systems. Simulation results demonstrate that the proposed channel estimation outperforms the conventional compressive sensing (CS)-based channel estimation algorithms in terms of the normalized mean square error (NMSE) performance at high signal-to-noise ratios (SNRs). Furthermore, it reduces the computational complexity of the channel estimation compared to conventional methods. In addition to the achieved performance gain in terms of NMSE, the presented method significantly reduces pilot overhead compared to conventional channel estimation techniques.

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.

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.

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.

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).