Cell-free Massive Multiple-input Multiple-output Research Articles

Stochastic Geometry Based Performance Characterization of SWIPT in Cell-Free Massive MIMO

This paper investigates the integration of wireless information and power transfer (SWIPT) and cell-free massive multiple-input multiple-output (MIMO) technologies for a cell-free spatially random network, where the access points (APs) are located randomly and modeled using a Poisson point process, and the users' energy and data transfers are separated in time. For the time-division-duplexing mode of operation, the uplink channel state information is acquired locally at the distributed APs via user pilots, and the APs utilize conjugate beamforming for downlink transmissions by exploiting channel reciprocity. In addition, line-of-sight and non-line-of-sight scenarios, which arise from link blockages due to objects are considered along with the corresponding path loss and fading parameters in our performance analysis of the above system set-up. We characterize the harvested energy at a user for both linear and non-linear energy harvesting models, and derive expressions for the average achievable downlink rate for the energy harvesting users. Subsequently, we propose a multi-slot energy storing scheme, and thereby, derive the probability of a user being fully charged at any given time. The throughput and the harvested energy are investigated under different system parameters. We show that a higher mean energy can be harvested by energy users with limited impact on non-energy users through allocating a higher portion of power for the energy users. Furthermore, we reveal that increasing the AP power level has diminishing effect on the probability of being within the fully charged state.

Energy-Efficient Non-Orthogonal Multicast and Unicast Transmission of Cell-Free Massive MIMO Systems With SWIPT

This work investigates the energy-efficient resource allocation for layered-division multiplexing (LDM) based non-orthogonal multicast and unicast transmission in cell-free massive multiple-input multiple-output (MIMO) systems, where each user equipment (UE) performs wireless information and power transfer simultaneously. To begin with, the achievable data rates for multicast and unicast services are derived in closed form, as well as the received radio frequency (RF) power at each UE. Based on the analytical results, a nonsmooth and nonconvex optimization problem for energy efficiency (EE) maximization is formulated, which is however a challenging fractional programming problem with complex constraints. To suit the massive access setting, a first-order algorithm is developed to find both initial feasible point and the nearly optimal solution. Moreover, an accelerated algorithm is designed to improve the convergence speed. Numerical results demonstrate that the proposed first-order algorithms can achieve almost the same EE as that of second-order approaches yet with much lower computational complexity, which provides insight into the superiority of the proposed algorithms for massive access in cell-free massive MIMO systems.

Structured Massive Access for Scalable Cell-Free Massive MIMO Systems

How to meet the demand for increasing number of users, higher data rates, and stringent quality-of-service (QoS) in the beyond fifth-generation (B5G) networks? Cell-free massive multiple-input multiple-output (MIMO) is considered as a promising solution, in which many wireless access points cooperate to jointly serve the users by exploiting coherent signal processing. However, there are still many unsolved practical issues in cell-free massive MIMO systems, whereof scalable massive access implementation is one of the most vital. In this paper, we propose a new framework for structured massive access in cell-free massive MIMO systems, which comprises one initial access algorithm, a partial large-scale fading decoding (P-LSFD) strategy, two pilot assignment schemes, and one fractional power control policy. New closed-form spectral efficiency (SE) expressions with maximum ratio (MR) combining are derived. The simulation results show that our proposed framework provides high SE when using local partial minimum mean-square error (LP-MMSE) and MR combining. Specifically, the proposed initial access algorithm and pilot assignment schemes outperform their corresponding benchmarks, P-LSFD achieves scalability with a negligible performance loss compared to the conventional optimal large-scale fading decoding (LSFD), and scalable fractional power control provides a controllable trade-off between user fairness and the average SE.

On the Spectral and Energy Efficiencies of Full-Duplex Cell-Free Massive MIMO

In-band full-duplex (FD) operation is practically more suited for short-range communications such as WiFi and small-cell networks, due to its current practical limitations on the self-interference cancellation. In addition, cell-free massive multiple-input multiple-output (CF-mMIMO) is a new and scalable version of MIMO networks, which is designed to bring service antennas closer to end user equipments (UEs). To achieve higher spectral and energy efficiencies (SE-EE) of a wireless network, it is of practical interest to incorporate FD capability into CF-mMIMO systems to utilize their combined benefits. We formulate a novel and comprehensive optimization problem for the maximization of SE and EE in which power control, access point-UE (AP-UE) association and AP selection are jointly optimized under a realistic power consumption model, resulting in a difficult class of mixed-integer nonconvex programming. To tackle the binary nature of the formulated problem, we propose an efficient approach by exploiting a strong coupling between binary and continuous variables, leading to a more tractable problem. In this regard, two low-complexity transmission designs based on zero-forcing (ZF) are proposed. Combining tools from inner approximation framework and Dinkelbach method, we develop simple iterative algorithms with polynomial computational complexity in each iteration and strong theoretical performance guaranteed. Furthermore, towards a robust design for FD CF-mMIMO, a novel heap-based pilot assignment algorithm is proposed to mitigate effects of pilot contamination. Numerical results show that our proposed designs with realistic parameters significantly outperform the well-known approaches (i.e., small-cell and collocated mMIMO) in terms of the SE and EE. Notably, the proposed ZF designs require much less execution time than the simple maximum ratio transmission/combining.

Cell-Free Massive MIMO for Wireless Federated Learning

This paper proposes a novel scheme for cell-free massive multiple-input multiple-output (CFmMIMO) networks to support any federated learning (FL) framework. This scheme allows each instead of all the iterations of the FL framework to happen in a large-scale coherence time to guarantee a stable operation of an FL process. To show how to optimize the FL performance using this proposed scheme, we consider an existing FL framework as an example and target FL training time minimization for this framework. An optimization problem is then formulated to jointly optimize the local accuracy, transmit power, data rate, and users' processing frequency. This mixed-timescale stochastic nonconvex problem captures the complex interactions among the training time, and transmission and computation of training updates of one FL process. By employing the online successive convex approximation approach, we develop a new algorithm to solve the formulated problem with proven convergence to the neighbourhood of its stationary points. Our numerical results confirm that the presented joint design reduces the training time by up to 55% over baseline approaches. They also show that CFmMIMO here requires the lowest training time for FL processes compared with cell-free time-division multiple access massive MIMO and collocated massive MIMO.

Local Partial Zero-Forcing Precoding for Cell-Free Massive MIMO

Cell-free Massive MIMO (multiple-input multiple-output) is a promising distributed network architecture for 5G-and-beyond systems. It guarantees ubiquitous coverage at high spectral efficiency (SE) by leveraging signal co-processing at multiple access points (APs), aggressive spatial user multiplexing and extraordinary macro-diversity gain. In this study, we propose two distributed precoding schemes, referred to as \textit{local partial zero-forcing} (PZF) and \textit{local protective partial zero-forcing} (PPZF), that further improve the spectral efficiency by providing an adaptable trade-off between interference cancelation and boosting of the desired signal, with no additional front-hauling overhead, and implementable by APs with very few antennas. We derive closed-form expressions for the achievable SE under the assumption of independent Rayleigh fading channel, channel estimation error and pilot contamination. PZF and PPZF can substantially outperform maximum ratio transmission and zero-forcing, and their performance is comparable to that achieved by regularized zero-forcing (RZF), which is a benchmark in the downlink. Importantly, these closed-form expressions can be employed to devise optimal (long-term) power control strategies that are also suitable for RZF, whose closed-form expression for the SE is not available.

Max-Min Optimal Beamforming for Cell-Free Massive MIMO

This letter develops an optimum beamforming method for downlink transmissions in cell-free massive multiple-input multiple-output (MIMO) systems, which employ a massive number of distributed access points to provide concurrent services to multiple users. The optimum design is formulated as a max-min problem that maximizes the minimum signal-to-interference-plus-noise ratio of all users. It is shown analytically that the problem is quasi-concave, and the optimum solution is obtained with the second-order cone programming. The proposed method identifies the best achievable beamforming performance in cell-free massive MIMO systems. The results can be used as benchmarks for the design of practical low complexity beamformers.

Spectral and Energy Efficiency in Cell-Free Massive MIMO Systems Over Correlated Rician Fading

In this article, we investigate the downlink (DL) of a cell-free massive multiple-input multiple-output (MIMO) system over spatially correlated Rician fading, in which many distributed access points (APs) equipped with multiple antennas serve single-antenna users. The APs apply minimum mean-square error channel estimation to obtain the uplink channel state information (CSI). Furthermore, in order to obtain DL CSI at users, this article considers the use of maximum-ratio transmission to beamform DL pilots in the DL beamforming training (BT) phase. For such a system, we derive the closed-form expressions of the sum spectral efficiency (SE) and total energy efficiency (EE). Based on the obtained closed-form expressions, we develop two successive approximation algorithms to improve the sum SE and total EE by optimizing the power control coefficients of DL data and pilot. Numerical results are provided to demonstrate the superiority of the proposed algorithms in improving the sum SE and total EE. In addition, the numerical results also show that the sum SE of a cell-free massive MIMO system with exploiting the BT scheme can be significantly improved over the system without employing the BT scheme.

Scalable Cell-Free Massive MIMO Systems

Imagine a coverage area with many wireless access points that cooperate to jointly serve the users, instead of creating autonomous cells. Such a cell-free network operation can potentially resolve many of the interference issues that appear in current cellular networks. This ambition was previously called Network MIMO (multiple-input multiple-output) and has recently reappeared under the name Cell-Free Massive MIMO. The main challenge is to achieve the benefits of cell-free operation in a practically feasible way, with computational complexity and fronthaul requirements that are scalable to large networks with many users. We propose a new framework for scalable Cell-Free Massive MIMO systems by exploiting the dynamic cooperation cluster concept from the Network MIMO literature. We provide a novel algorithm for joint initial access, pilot assignment, and cluster formation that is proved to be scalable. Moreover, we adapt the standard channel estimation, precoding, and combining methods to become scalable. A new uplink and downlink duality is proved and used to heuristically design the precoding vectors on the basis of the combining vectors. Interestingly, the proposed scalable precoding and combining outperform conventional maximum ratio processing and also performs closely to the best unscalable alternatives.

On the Performance of Cell-Free Massive MIMO Relying on Adaptive NOMA/OMA Mode-Switching

The downlink (DL) of a non-orthogonal-multiple-access (NOMA)-based cell-free massive multiple-input multiple-output (MIMO) system is analyzed, where the channel state information (CSI) is estimated using pilots. It is assumed that the users are grouped into multiple clusters. The same pilot sequences are assigned to the users within the same clusters whereas the pilots allocated to all clusters are mutually orthogonal. First, a user's bandwidth efficiency (BE) is derived based on his/her channel statistics under the assumption of employing successive interference cancellation (SIC) at the users' end with no DL training. Next, the classic max-min optimization framework is invoked for maximizing the minimum BE of a user under per-access point (AP) power constraints. The max-min user BE of NOMA-based cell-free massive MIMO is compared to that of its orthogonal multiple-access (OMA) counter part, where all users employ orthogonal pilots. Finally, our numerical results are presented and an operating mode switching scheme is proposed based on the average per-user BE of the system, where the mode set is given by Mode = { OMA, NOMA }. Our numerical results confirm that the switching point between the NOMA and OMA modes depends both on the length of the channel's coherence time and on the total number of users.

Effective Channel Gain-Based Access Point Selection in Cell-Free Massive MIMO Systems

In this paper, we investigate the selection problem of access points (APs) in cell-free massive multiple-input multiple-output (MIMO) systems, where APs equipped with a large number of antennas are geographically distributed over a wide area with no cell border. These APs simultaneously serve many users, which are randomly distributed all over the area. We first derive formulas to calculate two proposed metrics used to measure the effective channel gain from all users to all APs and the channel quality of each user. Moreover, these metrics are only based on large-scale fading coefficients, which change very slowly in time. Next, we propose an algorithm to effectively sort and connect users to each AP in a sequential manner using these proposed metrics. Simulation results show that cell-free massive MIMO systems using proposed scheme have better performance compared to existing schemes.

Energy-Efficient Access-Point Sleep-Mode Techniques for Cell-Free mmWave Massive MIMO Networks With Non-Uniform Spatial Traffic Density

Cell-free massive multiple-input multiple-output (MIMO) is a novel beyond 5G (B5G) and 6G paradigm that, through the use of a common central processing unit (CPU), coordinates a large number of distributed access points (APs) to coherently serve mobile stations (MSs) on the same time/frequency resource. By exploiting the characteristics of new less-congested millimeter wave (mmWave) frequency bands, these networks can improve the overall system spectral and energy efficiencies by using low-complexity hybrid precoders/decoders. For this purpose, the system must be correctly dimensioned to provide the required quality of service (QoS) to MSs under different traffic load conditions. However, only heavy traffic load conditions are usually taken into account when analysing these networks and, thus, many APs might be underutilized during low traffic load periods, leading to an inefficient use of resources and waste of energy. Aiming at the implementation of energy-efficient AP switch on/off strategies, several approaches have been proposed in the literature that only consider rather unrealistic uniform spatial traffic distribution in the whole coverage area. Unlike prior works, this paper proposes energy efficient AP sleep-mode techniques for cell-free mmWave massive MIMO networks that are able to capture the inhomogeneous nature of spatial traffic distribution in realistic wireless networks. The proposed framework considers, analyzes and compares different AP switch ON-OFF (ASO) strategies that, based on the use of goodness-of-fit (GoF) tests, are specifically designed to dynamically turn on/off APs to adapt to both the number and the statistical distribution of MSs in the network. Numerical results show that the use of properly designed GoF-based ASO strategies under a non-uniform spatial traffic distribution can serve to considerably improve the achievable energy efficiency.

Optimal Downlink Transmission for Cell-Free SWIPT Massive MIMO Systems With Active Eavesdropping

This paper considers secure simultaneous wireless information and power transfer (SWIPT) in cell-free massive multiple-input multiple-output (MIMO) systems. The system consists of a large number of randomly (Poisson-distributed) located access points (APs) serving multiple information users (IUs) and an information-untrusted dual-antenna active energy harvester (EH). The active EH uses one antenna to legitimately harvest energy and the other antenna to eavesdrop information. The APs are networked by a centralized infinite backhaul which allows the APs to synchronize and cooperate via a central processing unit (CPU). Closed-form expressions for the average harvested energy (AHE) and a tight lower bound on the ergodic secrecy rate (ESR) are derived. The obtained lower bound on the ESR takes into account the IUs' knowledge attained by downlink effective precoded-channel training. Since the transmit power constraint is per AP, the ESR is nonlinear in terms of the transmit power elements of the APs and that imposes new challenges in formulating a convex power control problem for the downlink transmission. To deal with these nonlinearities, a new method of balancing the transmit power among the APs via relaxed semidefinite programming (SDP) which is proven to be rank-one globally optimal is derived. A fair comparison between the proposed cell-free and the colocated massive MIMO systems shows that the cell-free MIMO outperforms the colocated MIMO over the interval in which the AHE constraint is low and vice versa. Also, the cell-free MIMO is found to be more immune to the increase in the active eavesdropping power than the colocated MIMO.

Downlink Training in Cell-Free Massive MIMO: A Blessing in Disguise

Cell-free Massive MIMO (multiple-input multiple-output) refers to a distributed Massive MIMO system where all the access points (APs) cooperate to coherently serve all the user equipments (UEs), suppress inter-cell interference and mitigate the multiuser interference. Recent works demonstrated that, unlike co-located Massive MIMO, the \textit{channel hardening} is, in general, less pronounced in cell-free Massive MIMO, thus there is much to benefit from estimating the downlink channel. In this study, we investigate the gain introduced by the downlink beamforming training, extending the previously proposed analysis to non-orthogonal uplink and downlink pilots. Assuming single-antenna APs, conjugate beamforming and independent Rayleigh fading channel, we derive a closed-form expression for the per-user achievable downlink rate that addresses channel estimation errors and pilot contamination both at the AP and UE side. The performance evaluation includes max-min fairness power control, greedy pilot assignment methods, and a comparison between achievable rates obtained from different capacity-bounding techniques. Numerical results show that downlink beamforming training, although increases pilot overhead and introduces additional pilot contamination, improves significantly the achievable downlink rate. Even for large number of APs, it is not fully efficient for the UE relying on the statistical channel state information for data decoding.

Channel Estimation for Cell-Free mmWave Massive MIMO Through Deep Learning

The combination of cell-free massive multiple-input multiple-output (MIMO) systems along with millimeter-wave (mmWave) bands is indeed one of most promising technological enablers of the envisioned wireless Gbit/s experience. However, both massive antennas at access points and large bandwidth at mmWave induce high computational complexity to exploit an accurate estimation of channel state information. Considering the sparse mmWave channel matrix as a natural image, we propose a practical and accurate channel estimation framework based on the fast and flexible denoising convolutional neural network (FFDNet). In contrast to previous deep learning based channel estimation methods, FFDNet is suitable a wide range of signal-to-noise ratio levels with a flexible noise level map as the input. More specifically, we provide a comprehensive investigation to optimize the FFDNet based channel estimator. Extensive simulation results validate that the training speed of FFDNet is faster than state-of-the-art channel estimators without sacrificing normalized mean square error performance, which makes FFDNet as an practical channel estimator for cell-free mmWave massive MIMO systems.

Cell-Free Massive MIMO Systems With Low Resolution ADCs

This paper investigates the achievable performance of cell-free massive multiple-input multiple-output (MIMO) systems with low resolution analog-to-digital converters (ADCs) at both the access points (APs) and users. A closed-form expression for the achievable rate is derived, which enables the study of the effects of AP number, antenna number per AP, user number, and ADC resolution on the achievable rate. In addition, a simple asymptotic approximation for the individual user rate is presented, which shows that the user rate is mainly constrained by the ADC resolution at the user. Moreover, we propose an ADC resolution bits allocation scheme aiming at maximizing the sum rate subject to the total ADC resolution bits constraint, which substantially outperforms the equal ADC resolution bits allocation scheme. Furthermore, a max–min power control scheme is proposed, which not only ensures user fairness, but also improves the achievable rate. Finally, simulation results are provided to corroborate the analytical results.

Pilot Allocation and Power Control in Cell-Free Massive MIMO Systems

In this paper we consider a cell-free massive multiple-input multiple-output (MIMO) system which is composed of a large number of access points (APs) and a much smaller number of users. Each AP obtains the channel estimate from the uplink pilot and apply maximum ratio transmission in the downlink communication. Under the assumptions that the channels between the APs and users are Rician fading and the number of users is larger than that of orthogonal pilots, we derive the closed-form expression for the downlink achievable rate. Then, in order to maximize the achievable rate, we propose pilot allocation and power control algorithms for cell-free massive MIMO. Simulation results show that the proposed algorithms can achieve good system performance.

Max–Min Rate of Cell-Free Massive MIMO Uplink With Optimal Uniform Quantization

Cell-free Massive multiple-input multiple-output (MIMO) is considered, where distributed access points (APs) multiply the received signal by the conjugate of the estimated channel, and send back a quantized version of this weighted signal to a central processing unit (CPU). For the first time, we present a performance comparison between the case of perfect fronthaul links, the case when the quantized version of the estimated channel and the quantized signal are available at the CPU, and the case when only the quantized weighted signal is available at the CPU. The Bussgang decomposition is used to model the effect of quantization. The max-min problem is studied, where the minimum rate is maximized with the power and fronthaul capacity constraints. To deal with the non-convex problem, the original problem is decomposed into two sub-problems (referred to as receiver filter design and power allocation). Geometric programming (GP) is exploited to solve the power allocation problem whereas a generalized eigenvalue problem is solved to design the receiver filter. An iterative scheme is developed and the optimality of the proposed algorithm is proved through uplink-downlink duality. A user assignment algorithm is proposed which significantly improves the performance. Numerical results demonstrate the superiority of the proposed schemes.

Energy Efficiency of the Cell-Free Massive MIMO Uplink With Optimal Uniform Quantization

A cell-free Massive multiple-input multiple-output (MIMO) uplink is considered, where the access points (APs) are connected to a central processing unit (CPU) through limited-capacity wireless microwave links. The quantized version of the weighted signals are available at the CPU, by exploiting the Bussgang decomposition to model the effect of quantization. A closed-form expression for spectral efficiency is derived taking into account the effects of channel estimation error and quantization distortion. The energy efficiency maximization problem is considered with per-user power, backhaul capacity and throughput requirement constraints. To solve this non-convex problem, we decouple the original problem into two sub-problems, namely, receiver filter coefficient design, and power allocation. The receiver filter coefficient design is formulated as a generalized eigenvalue problem whereas a successive convex approximation (SCA) and a heuristic sub-optimal scheme are exploited to convert the power allocation problem into a standard geometric programming (GP) problem. An iterative algorithm is proposed to alternately solve each sub-problem. Complexity analysis and convergence of the proposed schemes are investigated. Numerical results indicate the superiority of the proposed algorithms over the case of equal power allocation.

Secure Communications Over Cell-Free Massive MIMO Networks With Hardware Impairments

This paper investigates the effect of hardware impairments on the physical layer security for a cell-free massive multiple-input multiple-output (MIMO) network in the presence of pilot spoofing attack. By employing a classical additive hardware distortion model, the joint hardware impairment effects brought by both access points (APs) and user equipments have been taken into account, whereas the eavesdropper is assumed to be equipped with perfect hardware. Thereby, we derive a closed-form lower bound for the ergodic secrecy rate in the presence of imperfect channel state information. To obtain further insights, we investigate asymptotic secrecy performance under different hardware scaling factors. It proves that the hardware-quality scaling effect vanishes as the number of APs increases in the considered secure cell-free massive MIMO system with active attack. Furthermore, by using continuous approximation and path-following algorithms, the optimal power allocation scheme is obtained to maximize the achievable secrecy rate. Numerical results validate the derived results and the efficiency of the proposed power allocation scheme.