Multi-user Massive Multi-input Multi-output Research Articles

Joint Channel Estimation and Mixed-ADCs Allocation for Massive MIMO via Deep Learning

Millimeter wave (mmWave) multi-user massive multi-input multi-output (MIMO) is a promising technique for the next generation communication systems. However, the hardware cost and power consumption grow significantly as the number of radio frequency (RF) components increases, which hampers the deployment of practical massive MIMO systems. To address this issue and further facilitate the commercialization of massive MIMO, mixed analog-to-digital converters (ADCs) architecture has been considered, where parts of conventionally assumed full-resolution ADCs are replaced by one-bit ADCs. In this paper, we first propose a deep learning-based (DL) joint pilot design and channel estimation method for mixed-ADCs mmWave massive MIMO. Specifically, we devise a pilot design neural network whose weights directly represent the optimized pilots, and develop a Runge-Kutta model-driven densely connected network as the channel estimator. Instead of randomly assigning the mixed-ADCs, we then design a novel antenna selection network for mixed-ADCs allocation to further improve the channel estimation accuracy. Moreover, we adopt an autoencoder-inspired end-to-end architecture to jointly optimize the pilot design, channel estimation and mixed-ADCs allocation networks. Simulation results show that the proposed DL-based methods have advantages over the traditional channel estimators as well as the state-of-the-art networks.

Uplink Signal Detection via Look-Up Table-Based AMP for Massive MIMO Systems

We propose a novel look-up table (LUT)-based multi-user detection (MUD) algorithm to imitate approximate message passing (AMP) for uplink signal detection in massive multi-user multi-input multi-output (MU-MIMO) systems. When AMP is implemented with double-precision arithmetic, the dramatic increase in power consumption and process latency becomes a major barrier to practical application, as the system scale expands. To circumvent this issue, we design a novel referential AMP detector composed of many small LUTs cascaded hierarchically, where only informative integer-valued messages are exchanged on a factor graph (FG). Our method tracks the discrete distribution of the LUT outputs according to the multi-layer structure, and successively determines non-uniform quantization thresholds of the LUTs, using an unsupervised learning approach. Specifically, the thresholds at each level of the hierarchy, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e</i> ., layer, are optimized by clustering with the Lloyd-Max algorithm with initial values given by the k-means++ method, in order to minimize the performance degradation caused by quantization errors. The efficacy of the proposed referential AMP detector is confirmed by numerical simulations, which show that the proposed method significantly outperforms the state-of-the-art (SotA) in terms of the bit error rate (BER) performance in various channel models. The results also indicate the referential AMP is robust to changes in wireless channels, and then clarify the reason in terms of the algorithmic structure.

Optimal Zero-Forcing Hybrid Downlink Precoding for Sum-Rate Maximization

This letter studies zero-forcing (ZF) hybrid precoding for maximizing the sum-rate of a downlink multi-user massive multi-input multi-output (mMIMO) system. Assuming the water-filling power allocation across different users, we derive the optimal digital precoder based on the Karush-Kuhn-Tucker (KKT) condition. We then formulate the optimization of the analog precoder as an unconstrained nonlinear problem, which can be efficiently solved by the conjugate gradient method. The resultant hybrid precoder is optimal in the sense that it uses no approximation to the objective function of sum-rate. Therefore, it outperforms the state-of-the-art methods as verified by the numerical simulations.

Energy Efficiency Optimization of Massive MIMO Systems Based on the Particle Swarm Optimization Algorithm

As one of the key technologies in the fifth generation of mobile communications, massive multi‐input multioutput (MIMO) can improve system throughput and transmission reliability. However, if all antennas are used to transmit data, the same number of radiofrequency chains is required, which not only increases the cost of system but also reduces the energy efficiency (EE). To solve these problems, in this paper, we propose an EE optimization based on the particle swarm optimization (PSO) algorithm. First, we consider the base station (BS) antennas and terminal users and analyze their impact on EE in the uplink and downlink of a single‐cell multiuser massive MIMO system. Second, a dynamic power consumption model is used under zero‐forcing processing, and it obtains the expression of EE that is used as the fitness function of the PSO algorithm under perfect and imperfect channel state information (CSI) in single‐cell scenarios and imperfect CSI in multicell scenarios. Finally, the optimal EE value is obtained by updating the global optimal positions of the particles. The simulation results show that compared with the traditional iterative algorithm and artificial bee colony algorithm, the proposed algorithm not only possesses the lowest complexity but also obtains the highest optimal value of EE under the single‐cell perfect CSI scenario. In the single‐cell and multicell scenarios with imperfect CSI, the proposed algorithm is capable of obtaining the same or slightly lower optimal EE value than that of the traditional iterative algorithm, but the running time is at most only 1/12 of that imposed by the iterative algorithm.

A User Cooperation Approach for Interference Cancellation in FDD Massive MIMO Systems

The performance of a massive multi-user Multi-Input Multi-Output (MIMO) system, operating in Frequency Division Duplex (FDD) mode, severely degrades under imperfect Channel State Information (CSI). Among the main challenges toward the acquisition of sufficiently accurate CSI at the transmitter is the issue of enormous CSI feedback overhead. In this paper, a novel interference cancellation strategy is proposed to alleviate the overhead. The concept of a device-to-device based interference cancellation strategy was hinted in some prior works but has not been fully exploited in the multi-user MIMO systems, especially when the number of antennas becomes large. Hence, this paper aims to exploit the potential of User Equipment (UE) cooperation to reduce the dependency of precoder at the transmitter to the accuracy of CSI. To do so, adjacent pieces of UE that experience correlated CSI are clustered in a similar group, jointly adjusting their receive antenna combining the weight vector to maximize the channel vector orthogonality. Simulation results show that the proposed strategy reduces the dependency of system performance on the accuracy of CSI feedback; moreover, compared to the conventional limited feedback strategy, a larger number of antennas can be deployed at the transmitter.

Experimental Investigation of Frequency Domain Channel Extrapolation in Massive MIMO Systems for Zero-Feedback FDD

Estimating downlink (DL) channel state information (CSI) in frequency division duplex (FDD) massive multi-input multi-output (MIMO) systems generally requires downlink pilots and feedback overheads. Accordingly, this paper investigates the feasibility of zero-feedback FDD massive MIMO systems based on channel extrapolation. We use the high-resolution parameter estimation (HRPE), specifically the space-alternating generalized expectation-maximization (SAGE) algorithm, to extrapolate the DL CSI based on the extracted parameters of multipath components in the uplink channel. We apply the HRPE to two different channel models: the vector spatial signature (VSS) model and the direction of arrival (DOA) model. We verify these methods through real-world channel data acquired from channel measurement campaigns with two different types of channel sounders: a) a switched array-based, real-time, time-domain, outdoors setup at 3.5 GHz, and b) a virtual array-based, high-accuracy, frequency-domain, indoors setup at 2.4 and 5-7 GHz. The performance metrics of the extrapolated channels that we evaluate include the mean squared error, beamforming efficiency, and spectral efficiency in multiuser MIMO scenarios. The results show that the HRPE-based channel extrapolation performs best under the simple VSS model, which does not require array calibration, and if the BS is in an open outdoor environment having line-of-sight (LOS) paths to well-separated users.

A Machine Learning Approach to Blind Multi-Path Classification for Massive MIMO Systems

This paper concerns the problem of the multi-path classification in a multi-user multi-input multi-output (MIMO) system. We propose a machine learning approach to achieve a blind multi-path classification in the uplink (UL) scheme of a multi-user massive MIMO system. Note that the “blind” term in our approach represents the achievement of the multi-path classification without different pilot sequences on different users, without prior channel state information (CSI) at each user, and without any exploiting the special properties of the received signal. Specifically, our approach consists of two phases. In the first phase, multiple users transmit communication-requests to the base station (BS) for message transmission. The BS only estimates the scaled large-scale path loss of each user, which is determined by the distance between the transmitter and the receiver and is independent of the number of multi-path. Then, the BS compares the difference of the scaled large-scale path loss between any two users. If the difference is sufficiently large, the BS notifies all users to permit their simultaneous message transmissions. However, if the difference is small, the BS notifies each user to slightly adjust their transmission power and then permits their simultaneous message transmissions as well. In the second phase, all users simultaneously transmit their messages using the same radio resource. Then the BS selects one predetermined constellation point from the received pilot symbols as the input of clustering algorithms. According to the clustering results, the BS classifies each multi-path into a specific user. The key intuition of our approach is that the clustering algorithms can generate multiple cluster centroids and each cluster centroid represents the average reception power of each user. Moreover, we use a weighted ensemble clustering algorithm to further improve the performance of our approach. We implemented our approach and conducted extensive performance comparison. Our experimental results show that, when the received signal-to-noise ratio (SNR) is more than 13 dB, our approach with the weighted ensemble clustering algorithm can correctly classify all multi-path to the corresponding user and the output SNR can be improved by 3.2 dB, where we consider three users in an 8PSK system and each user possess 50 multi-path.

Multi-User Differential Spatial Modulation scheme for massive MIMO uplink communications

Spatial Modulation (SM) is a Multi-Input Multi-Output (MIMO) transmission technique where only one antenna transmits data in each transmission interval, leading to a reduction in the number of RF chains and transmission power. The application of SM in Massive MIMO systems relies on perfect channel estimation, which is a fundamental challenge in these systems. Differential Spatial Modulation (DSM) is a method proposed to avoid channel estimation challenges. However, the conventional square DSM cannot easily be applied to multi-user communication applications. In this paper, a novel Multi-User Differential Spatial Modulation (MU-DSM) transmission scheme is proposed for multi-user massive MIMO uplink communications. Moreover, for the proposed transmission scheme, a non-coherent MU-DSM detector is presented. As demonstrated in the analytical and simulation results, the proposed MU-DSM scheme performs very close to its coherent counterpart where perfect channel information is available.

SE Analysis for Mixed-ADC Massive MIMO Uplink With ZF Receiver and Imperfect CSI

This letter is on the multi-user massive multi-input multi-output (MIMO) uplink with the mixed analog-to-digital converter (ADC) architecture and the zero-forcing (ZF) receiver at the base station (BS). Under imperfect channel state information (CSI), a closed-form approximation of the spectral efficiency (SE) is derived for a general resolution profile. Further, simplified SE results are provided for two common asymptotic massive MIMO scenarios. In the SE analysis, to overcome the difficulty induced by the mixed-ADC structure, new techniques are developed in calculating the average noise powers caused by the CSI error and the quantization.

Performance analysis of mixed‐ADC receiver multiuser massive MIMO relaying system under imperfect CSI

In this paper, the authors investigate a multiuser massive multi-input-multi-output (MIMO) relay system with mixed analog-todigitalconverter (ADC) architecture. It is assumed that the channel state information (CSI) is imperfect between the relay and the user. Sum Spectral efficiency (SE) and Energy efficiency (EE) with the maximum-ratio combining (MRC) detector are derived. In addition, the authors have studied the trade-off between achievable Spectral efficiency and energy efficiency. it is revealed that the trade-off between the sum SE and EE with respect to key system parameters, including number of BS antennas, user transmit power, the power of the CSI error, and the quantization bits. Finally, numerical results show that the mixed-ADC structure can obtain a better energy-rate trade-off than low-precision ADC structure.

Pilot decontamination in massive multiuser MIMO systems based on low‐rank matrix approximation

In multi-cell massive multiuser multi-input multi-output (MU-MIMO) systems, the channel estimation performance is degraded by the pilot contamination problem. This effect occurs when non-orthogonal pilot sequences are reused by other users in the adjacent cells. In this study, two channel estimation methods based on low-rank matrix approximation technique are proposed to mitigate pilot contamination problem in time division duplex multi-cell massive MU-MIMO systems. In the first method, the massive MU-MIMO channel estimation is formulated as the nuclear norm (NN) optimisation problem and solved by using a novel estimation algorithm proposed in this study. In the second method, the iterative weighted NN (IWNN) is proposed to improve the NN estimation performance. Consequently, the regularisation parameter of both optimisation methods is selected based on the cross-validation curve method. The simulation results show that both proposed methods outperform the traditional least square method in terms of the normalised mean square error. Moreover, the IWNN estimation method demonstrates substantial improvement over the NN estimation method in the presence of strong pilot contamination problem.

Channel Sounding for Multi-User Massive MIMO in Distributed Antenna System Environment

We propose a generation scheme for a sounding reference signal (SRS) suitable for supporting a large number of users in massive multi-input multi-output (MIMO) system with a distributed antenna system (DAS) environment. The proposed SRS can alleviate the pilot contamination problem which occurs inherently in the multi-user system due to the limited number of orthogonal sequences. The proposed SRS sequence is generated by applying a well-chosen phase rotation to the conventional LTE/LTE-A SRS sequences without requiring an increased amount of resource usage. We also propose using the correlation-aided channel estimation algorithm as a supplemental scheme to obtain more reliable and refined channel estimation. It is shown that the proposed SRS sequence and the supplemental channel estimation scheme improve significantly the channel estimation performance in multi-user massive MIMO systems.

Full Dimension MIMO (FD-MIMO): Demonstrating Commercial Feasibility

Massive multi-input multi-output (MIMO) is shown to significantly increase spectral efficiency by exploiting a large number of antennas to support high-order multiuser MIMO. In 3GPP Release-13, a full-dimension MIMO (FD-MIMO) technology was introduced to address practical aspects for massive MIMO in cellular systems; extensive simulations show 2–4 times capacity gain compared with current LTE systems. FD-MIMO has been identified as one of the key 5G technologies and is being continuously improved in 3GPP new radio standards. However, several practical challenges such as interference mitigation among MIMO streams for a large number of users with limited channel feedback, hardware limitations, such as calibration errors that limit the precoding capabilities need to be addressed carefully. A proof of concept (PoC) base-station and user equipment (UE) prototype has been designed to validate the potential of FD-MIMO technology and demonstrate commercial implementation feasibility. In this paper, we present theory and architecture behind an FD-MIMO prototype and share the field test results with LTE-based UEs in a multi-user MIMO setup. We also analyze the impact of transmitter and receiver calibration errors on the performance of the FD-MIMO system.

Spectral Efficiency of Massive MIMO Systems With Low-Resolution ADCs and MMSE Receiver

This letter considers an uplink multi-user massive multi-input multi-output (MIMO) system with non-uniform low-resolution analog-to-digital converters (ADCs) and minimum mean-square error receivers at the base station side. Additive quantization noise model is utilized to measure the effect of finite ADC resolution. Non-uniform quantization brings difficulty in obtaining the asymptotic equivalent expression of the spectral efficiency. Based on the random matrix theory, a closed-form asymptotic equivalent expression is derived. Numerical results show the tightness of the asymptotic equivalent. It also shows that massive antennas are able to compensate for the loss of low-resolution quantization, implying the capability of low-resolution ADCs in massive MIMO systems.

Secure Massive MIMO Systems With Limited RF Chains

In future practical deployments of massive multi-input multi-output (MIMO) systems, the number of radio frequency (RF) chains at the base stations (BSs) may be much smaller than the number of BS antennas to reduce the overall expenditure. In this paper, we propose a novel design framework for joint data and artificial noise (AN) precoding in a multiuser massive MIMO system with limited number of RF chains, which improves the wireless security performance. With imperfect channel state information (CSI), we analytically derive an achievable lower bound on the ergodic secrecy rate of any mobile terminal (MT), for both analog and hybrid precoding schemes. The closed-form lower bound is used to determine optimal power splitting between data and AN that maximizes the secrecy rate through simple one-dimensional search. Analytical and numerical results together reveal that the proposed hybrid precoder, although suffers from reduced secrecy rate compared with theoretical full-dimensional precoder, is free of the high computational complexity of large-scale matrix inversion and null-space calculations, and largely reduces the hardware cost.

Multi-User Massive MIMO Communication Systems Based on Irregular Antenna Arrays

In practical mobile communication engineering applications, surfaces of antenna array deployment regions are usually uneven. Therefore, massive multi-input–multi-output (MIMO) communication systems usually transmit wireless signals by irregular antenna arrays. To evaluate the performance of irregular antenna arrays, the matrix correlation coefficient and the ergodic received gain are defined for massive MIMO communication systems with mutual coupling effects. Furthermore, the lower bound of the ergodic achievable rate, symbol error rate, and average outage probability is first derived for multi-user massive MIMO communication systems using irregular antenna arrays. Asymptotic results are also derived when the number of antennae approaches infinity. Numerical results indicate that there exists a maximum achievable rate when the number of antennae keeps increasing in massive MIMO communication systems using irregular antenna arrays. Moreover, the irregular antenna array outperforms the regular antenna array in the achievable rate of massive MIMO communication systems when the number of antennae is larger than or equal to a given threshold.

Interference and Outage Probability Analysis for Massive MIMO Downlink with MF Precoding

This letter analyzes the user-interference and outage probability for single-cell multi-user massive multi-input-multi-output (MIMO) systems with matched-filter (MF) precoding. Existing performance studies on massive MIMO systems have focused on the sum-rate by deriving the asymptotic deterministic equivalence. In this work, we treat the user-interference as random, and derive a tight closed-form approximation for the distribution of the interference power. This enables the analysis of the outage probability. The derived results are shown to have accurate match with the simulation.

Spectral Efficiency of Mixed-ADC Receivers for Massive MIMO Systems

This paper investigates the uplink of multi-user massive multi-input multioutput (MIMO) systems with a mixed analog-to-digital converter (ADC) receiver architecture, in which some antennas are equipped with costly full-resolution ADCs and others with less expensive low-resolution ADCs. A closed-form approximation of the achievable spectral efficiency (SE) with the maximum-ratio combining detector is derived. Based on this approximated result, the effects of the number of base station (BS) antennas, the transmit power, the proportion of full-resolution ADCs in the mixed-ADC structure, and the number of quantization bits of the low-resolution ADCs are revealed. Results show case that the achievable SE increases with the number of BS antennas and quantization bits, and it converges to a saturated value in the high user power regime or the full ADC resolution case. Most important, this work efficiency verifies that for a massive MIMO, the mixed-ADC receiver with a small fraction of full-resolution ADCs can have comparable SE performance with the receiver with all full-resolution ADCs but at a considerably lower hardware cost.

Semi-Blind Pilot Decontamination for Massive MIMO Systems

In multicell multiuser massive multi-input multi-output (MIMO) systems, pilot contamination degrades the uplink (UL) channel estimation performance. To mitigate the effect of pilot contamination, we propose a semiblind channel estimation method that does not require cell cooperation or statistical information of the channels. In the proposed method, we first sequentially estimate the UL data from different users in the target cell. To do that, for each user, we solve a constrained minimization problem to obtain an extracting vector and then use it to extract the desired data source from the observed mixture signal. An efficient algorithm is presented to solve the optimization problem. After the ambiguities in the extracted source are corrected with the aid of the pilot sequence, the estimates of the user UL data can be obtained. Based on the demodulated UL data of all users in the target cell, we finally obtain the least squares (LS) estimate of the channel. The pilot contamination effect is shown to be reduced as the UL data length grows. Simulation results demonstrate that the proposed method significantly outperforms some existing channel estimation methods that do not require cell cooperation or channel statistics.