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

Joint beamforming and power splitting design for MISO downlink communication with SWIPT: a comparison between cell-free massive MIMO and small-cell deployments

Simultaneous wireless information and power transfer (SWIPT) has been advocated as a highly promising technology for enhancing the capabilities of 5G and 6G devices. However, the challenge of dealing with large propagation path loss poses a significant hurdle. To address this issue, massive multiple-input multiple-output (MIMO) is employed to enhance the efficiency of SWIPT in cellular-based networks with multiple small cells, and especially increase the energy for cell-edge users. In addition, by leveraging a large set of spatially distributed base stations to collaboratively serve SWIPT-enabled user equipment, the cell-free massive MIMO has the potential to provide even better performance than the conventional small-cell systems. In this work, we extend the investigation to include the application of SWIPT technology with alternating current (AC) logic in the cell-free networks and the small-cell networks and propose joint beamforming and power splitting optimization frameworks to maximize the system sum-rate, subject to the constraints on harvested energy, AC logic energy supply, and total transmit power. The optimization problem is shown to be non-convex, posing a significant challenge. To address this challenge, we resort to a two-stage decomposition approach. Specifically, we first introduce quadratic transform-based fractional programming (FP) algorithms to iteratively solve the non-convex optimization problems in the first stage, achieving near-optimal solutions with low time complexities. To further reduce the complexities, we also incorporate conventional schemes such as zero forcing, maximum ratio transmission, and signal-to-leakage-and-noise ratio for the design of beamforming vectors. Second, to determine the optimal power splitting ratio within the framework, we develop a one-dimensional (1-D) search algorithm to tackle the single variable optimization problem reduced in the second stage. These algorithms are then evaluated in the context of cell-free MIMO and small-cell networks with numerical experiments. The results show that the FP-based algorithms can consistently outperform those utilizing the conventional beamforming schemes, and the solutions of this work can achieve up to fivefold improvement in the system sum-rate than the small-cell counterpart while providing different but comparable performance trends in energy harvesting (EH).

Learning to optimize power allocation in cell-free massive MIMO networks with hybrid green energy

In cell-free (CF) massive multiple-input multiple-output (MIMO) networks, many access points (APs) simultaneously serve user equipment (UEs) using the same time and frequency resources. The resource allocation algorithm in such networks needs to handle many calculations within a limited time frame to determine the power allocation from each AP to each UE. Further, the dispersion and large number of APs in CF massive MIMO networks pose challenges in terms of energy supply. As access to the power grid may be limited, renewable energies are often required as a supplement. However, due to the non-deterministic nature of the charging process, the resource allocation algorithm needs to consider the dynamic and uncertain amount of energy available at the APs. In this article, we propose a scalable machine learning algorithmbased on the emerging Learning to Optimize (L2O) paradigm that utilizes neural networks (NNs) for resource allocation in CF massive MIMO networks powered by electrical and renewable energies. Our objective is to minimize energy consumption from the power grid while satisfying the spectral efficiency (SE) constraints of the UEs. Additionally, our algorithm adopts a forward-looking approach and employs a green energy budgeting mechanism to prevent service interruption at green APs during energy shortages. Our algorithm design approach involves formulating the offline version of the problem as a second-order cone program (SOCP). Subsequently, we train an NN using the solutions obtained from solving the online variant of the SOCP. Our results indicated that our L2O-based algorithm can accurately mimic the solutions of the optimization problem with significantly reduced computational complexity.

A New Framework of RIS-Aided User-Centric Cell-Free Massive MIMO System for IoT Networks

With its merit of inter-cell interference elimination and enhanced throughput, cell-free (CF) massive multiple-input multiple-output (MIMO) system, has attracted considerable interests in evolution of 6G Internet-of-Things (IoT) networks. Meanwhile, reconfigurable intelligent surface (RIS) has shown its potential benefit in enhancing both capacity and energy efficiency (EE). In this paper, a new framework of RIS-aided CF massive MIMO system is proposed for IoT networks, in which extra active APs are deployed closely to the passive RISs, in that way, the RIS-user channels can be approximately obtained by parameters estimated at those extra APs with acceptable loss. To avoid extra power consumption, user-centric AP selection strategy in CF system is suggested, on the basis of which, an optimization problem related to power control, precoding and RIS phase shift is formulated to maximize the sum rate. To deal with this tough three-variable optimization, a Lagrangian dual transformation and fractional programming based algorithm is proposed. In particular, the proposed algorithm can extend to optimize EE and well adapt to other RIS-aided CF systems. Simulation results reveal that the proposed algorithm can achieve superior performance in terms of both sum rate (SR) and EE.

Cell-Free Massive MIMO for URLLC: A Finite-Blocklength Analysis

We present a general framework for the characterization of the packet error probability achievable in cell-free Massive multiple-input multiple output (MIMO) architectures deployed to support ultra-reliable low-latency (URLLC) traffic. The framework is general and encompasses both centralized and distributed cell-free architectures, arbitrary fading channels and channel estimation algorithms at both network and user-equipment (UE) sides, as well as arbitrary combing and precoding schemes. The framework is used to perform numerical experiments on specific scenarios, which illustrate the superiority of cell-free architectures compared to cellular architectures in supporting URLLC traffic in uplink and downlink. Also, these numerical experiments provide the following insights into the design of cell-free architectures for URLLC: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> ) minimum mean square error (MMSE) spatial processing must be used to achieve the URLLC targets; <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii</i> ) for a given total number of antennas per coverage area, centralized cell-free solutions involving single-antenna access points (APs) offer the best performance in the uplink, thereby highlighting the importance of reducing the average distance between APs and UEs in the URLLC regime; <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">iii</i> ) this observation applies also to the downlink, provided that the APs transmit precoded pilots to allow the UEs to estimate accurately the precoded channel.

Performance Analysis of Cell-Free Massive MIMO Network With Large-Scale-Fading Decoding and Low-Resolution ADCs

Concentrating on cell-free massive multiple-input multiple-output (MIMO) networks with low-resolution analog-to-digital converters (ADCs), we derive the theoretical achievable uplink spectral efficiency (SE) for the minimum mean-squared error (MMSE)-based large-scale fading decoding (LSFD). Moreover, we investigate the bit allocation (BA) among access points (APs) to maximize the asymptotic sum SE under the constraint of total ADC quantization bits. Simulation results confirm that our theoretical analysis is accurate and validate that the proposed BA technique is preferable to the random and fixed counterparts.

Performance of Cell-Free Massive MIMO Under Imperfect Channel State Information and Reciprocity Calibration

This article studies the downlink performance of a cell-free massive multiple-input–multiple-output (MIMO) system with imperfect channel estimation and reciprocity calibration. We present the statistical characteristics of the calibration error with the Argos algorithm and a relay-based calibration algorithm to obtain the calibration parameters of the whole network. Then, we derive approximate expressions of the downlink spectral efficiency for a cell-free massive MIMO system with imperfect channel state information and calibration error. The numerical results show the advantage of the proposed calibration algorithm and validate the accuracy of the theoretical expressions.

Distributed Learning for Uplink Cell-Free Massive MIMO Networks

Cell-free massive multiple-input multiple-output (MIMO) can resolve the inter-cell interference issue in cellular networks through cooperative beamforming of the distributed access points (APs). This paper focuses on an uplink cell-free massive MIMO network and investigates novel methods to train the central processing unit (CPU), the APs, and the users in the network. To reduce the communication burden posed on the fronthaul, each AP applies receive beamforming to compress the vector signals into scalar ones before passing them to the CPU for centralized processing. By drawing analogies between an uplink cell-free network and a quasi-neural network and borrowing the idea of backpropagation algorithm, we propose a novel scheme named the distributed learning for uplink cell-free massive MIMO beamforming (DLCB), which can achieve the multi-AP cooperation without explicit estimation of their channel state information (CSI). The DLCB has low computational complexity and is applicable to various objective functions, such as the minimum mean squared error criterion and the maximum sum rate criterion. Extensive simulations verify that the proposed scheme achieves superior performance over the state-of-the-art methods.

Robust Energy-Efficient Transmission for Cell-Free Massive MIMO Systems with Imperfect CSI

In this paper, we investigate a long-term power minimization problem of cell-free massive multiple-input multiple-output (MIMO) systems. To address this issue and to ensure the system queue stability, we formulate a dynamic optimization problem aiming to minimize the average total power cost in a time-varying system under imperfect channel conditions. The problem is then converted into a real-time weighted sum rate maximization problem for each time slot using the Lyapunov optimization technique. We employ approximation techniques to design robust sparse beamforming, which enables energy savings of the network and mitigates channel uncertainty. By applying direct fractional programming (DFP) and alternating optimization, we can obtain a locally optimal solution. Our DFP-based algorithm minimizes the average total power consumption of the network while satisfying the quality of service requirements for each user. Simulation results demonstrate the rapid convergence of the proposed algorithm and illustrate the tradeoff between average network power consumption and queue latency.

On Scalability of FDD-Based Cell-Free Massive MIMO Framework.

Cell-free massive multiple-input multiple-output (MIMO) systems have the potential of providing joint services, including joint initial access, efficient clustering of access points (APs), and pilot allocation to user equipment (UEs) over large coverage areas with reduced interference. In cell-free massive MIMO, a large coverage area corresponds to the provision and maintenance of the scalable quality of service requirements for an infinitely large number of UEs. The research in cell-free massive MIMO is mostly focused on time division duplex mode due to the availability of channel reciprocity which aids in avoiding feedback overhead. However, the frequency division duplex (FDD) protocol still dominates the current wireless standards, and the provision of angle reciprocity aids in reducing this overhead. The challenge of providing a scalable cell-free massive MIMO system in an FDD setting is also prevalent, since computational complexity regarding signal processing tasks, such as channel estimation, precoding/combining, and power allocation, becomes prohibitively high with an increase in the number of UEs. In this work, we consider an FDD-based scalable cell-free network with angular reciprocity and a dynamic cooperation clustering approach. We have proposed scalability for our FDD cell-free and performed a comparative analysis with reference to channel estimation, power allocation, and precoding/combining techniques. We present expressions for scalable spectral efficiency, angle-based precoding/combining schemes and provide a comparison of overhead between conventional and scalable angle-based estimation as well as combining schemes. Simulations confirm that the proposed scalable cell-free network based on an FDD scheme outperforms the conventional matched filtering scheme based on scalable precoding/combining schemes. The angle-based LP-MMSE in the FDD cell-free network provides 14.3% improvement in spectral efficiency and 11.11% improvement in energy efficiency compared to the scalable MF scheme.

Spanning Tree Method for Over-the-Air Channel Calibration in 6G Cell-Free Massive MIMO

Cell-free massive multiple-input multiple-output (MIMO) is an attractive network in 6G communications that significantly increases the spectral efficiency. Operating in time-division duplex (TDD) mode, the downlink beamforming is achieved by the estimated uplink channel, which is equal to the downlink channel due to the property of channel reciprocity. However, the involvement of different radio frequency (RF) gains in transceiver antennas renders the whole channel non-reciprocal. Therefore, it is of great necessity to calibrate the bi-directional channel. In this paper, we focus on the issue of over-the-air channel calibration in cell-free system. Taking a toy scenario as an example, we examine the performance differences between the calibration methods of ‘Direct Process’ and ‘Indirect Process’. A novel low-cost calibration method based on spanning tree model is proposed specifically for this distributed AP scenario, where a calibration tree is established to calculate calibration coefficients. Numerical results manifest that higher accuracy of our method is achieved compared to the existing calibration methods in the literatures. Our method is less sensitive to the location of master AP compared to Argos, and practical applications under the impact of phase noise show the priority of our method compared to LS method.

Task-Oriented Delay-Aware Multi-Tier Computing in Cell-Free Massive MIMO Systems

Multi-tier computing can enhance the task computation by multi-tier computing nodes. In this paper, we propose a cell-free massive multiple-input multiple-output (MIMO) aided computing system by deploying multi-tier computing nodes to improve the computation performance. At first, we investigate the computational latency and the total energy consumption for task computation, regarded as total cost. Then, we formulate a total cost minimization problem to design the bandwidth allocation and task allocation, while considering realistic heterogenous delay requirements of the computational tasks. Due to the binary task allocation variable, the formulated optimization problem is non-convex. Therefore, we solve the bandwidth allocation and task allocation problem by decoupling the original optimization problem into bandwidth allocation and task allocation subproblems. As the bandwidth allocation problem is a convex optimization problem, we first determine the bandwidth allocation for given task allocation strategy, followed by conceiving the traditional convex optimization strategy to obtain the bandwidth allocation solution. Based on the asymptotic property of received signal-to-interference-plus-noise ratio (SINR) under the cell-free massive MIMO setting and bandwidth allocation solution, we formulate a dual problem to solve the task allocation subproblem by relaxing the binary constraint with Lagrange partial relaxation for heterogenous task delay requirements. At last, simulation results are provided to demonstrate that our proposed task offloading scheme performs better than the benchmark schemes, where the minimum-cost optimal offloading strategy for heterogeneous delay requirements of the computational tasks may be controlled by the asymptotic property of the received SINR in our proposed cell-free massive MIMO-aided multi-tier computing systems.

An Interference Aware User-Group Pilot Assignment for Cell-Free Massive MIMO Systems

Cell-free (CF) massive multiple-input multiple-output (MIMO) system is introduced to fulfill the requirement of higher data rates by serving a user through multiple access points (APs). However, due to a large number of users and a limited number of pilot sequences, the CF network suffers from severe inter-user interference, which deteriorates the achievable throughput. In this work, we propose an interference aware user-group (IA-UG) pilot assignment scheme that addresses the issue of inter-user interference while supporting a large number of users. In the proposed IA-UG scheme, we count the number of common APs between two user pairs and use it as a likely measure of the number of interferers. Subsequently, we focuses on creating the user-groups by minimizing the number of interferers in the group having the maximum count. Numerical results show that the proposed pilot assignment scheme outperforms the existing schemes and yields a superior quality of channel estimates as well as the throughput.

Learning Decentralized Power Control in Cell-Free Massive MIMO Networks

This paper studies learning-based decentralized power control methods for cell-free massive multiple-input multiple-output (MIMO) systems where a central processor (CP) controls access points (APs) through fronthaul coordination. To determine the transmission policy of distributed APs, it is essential to develop a network-wide collaborative optimization mechanism. To address this challenge, we design a cooperative learning (CL) framework which manages computation and coordination strategies of the CP and APs using dedicated deep neural network (DNN) modules. To build a versatile learning structure, the proposed CL is carefully designed such that its forward pass calculations are independent of the number of APs. To this end, we adopt a parameter reuse concept which installs an identical DNN module at all APs. Consequently, the proposed CL trained at a particular configuration can be readily applied to arbitrary AP populations. Numerical results validate the advantages of the proposed CL over conventional non-cooperative approaches.

A Left-Null-Space-Based Massive Access Method for Cell-Free Massive MIMO IoT Systems.

Cell-free massive multiple-input multiple-output (MIMO) is a promising technology for the Internet of Things (IoT) because it can increase connectivity and provide considerable energy efficiency (EE) and spectral efficiency (SE). However, pilot contamination caused by pilot reuse severely limits the performance of the system. In this paper, we propose a left-null-space-based massive access method that can significantly reduce interference among users. The proposed method includes three stages: initial orthogonal access, left-null-space-based opportunistic access and data detection of all accessed users. The simulation results show that the proposed method can achieve much higher spectral efficiency than the existing massive access methods.

Joint User Clustering and Graph Coloring Based Pilot Assignment for Cell-Free Massive MIMO Systems.

Pilot contamination due to pilot reuse seriously mitigates the performance of the cell-free massive multiple-input multiple-output (MIMO) systems. In this paper, we propose a joint pilot assignment scheme that employs user clustering and graph coloring (UC-GC) to reduce pilot contamination. The proposed method consists of two steps: firstly, we utilize AP selection to classify all users; secondly, we assign pilots to users with more severe pilot contamination using the graph coloring algorithm and then assign pilots to the remaining users. The numerical simulation results show that the proposed scheme outperforms existing pilot assignment schemes and significantly improves throughout with low complexity.

Asynchronous Cell-Free Massive MIMO With Rate-Splitting

In practical cell-free (CF) massive multiple-input multiple-output (MIMO) networks with distributed and low-cost access points, the asynchronous arrival of signals at the user equipments increases multi-user interference that degrades the system performance. Meanwhile, rate-splitting (RS), exploiting the transmission of both common and private messages, has demonstrated to offer considerable spectral efficiency (SE) improvements and its robustness against channel state information (CSI) imperfection. The signal performance of a CF massive MIMO system is first analyzed for asynchronous reception capturing the joint effects of propagation delays and oscillator phases of transceivers. Taking into account the imperfect CSI caused by asynchronous phases and pilot contamination, we derive novel and closed-form downlink SE expressions for characterizing the performance of both the RS-assisted and conventional non-RS-based systems adopting coherent and non-coherent data transmission schemes, respectively. Moreover, we formulate the design of robust precoding for the common messages as an optimization problem that maximizes the minimum individual SE of the common message. To address the non-convexity of the design problem, a bisection method is proposed to solve the problem optimally. Simulation results show that asynchronous reception indeed destroys both the orthogonality of the pilots and the coherent data transmission resulting in poor system performance. Besides, thanks to the uniform coverage properties of CF massive MIMO systems, RS with a simple low-complexity precoding for the common message obtained by the equal ratio sum of the private precoding is able to achieve substantial downlink sum SE gains, while the application of robust precoding to the common message is shown to be useful in some extreme cases, e.g., serious oscillator mismatch and unknown delay phase.

Optimal User Pairing Approach for NOMA-Based Cell-Free Massive MIMO Systems

This study investigates a non-orthogonal multiple access (NOMA)-assisted cell-free massive multiple-input multiple-output (MIMO) system, considering the impact of both individual and linear-combination channel estimations. To make the best use of NOMA as an enabler for cell-free massive MIMO systems, user pairing should be employed effectively. Random user pairing naturally leads to a non-optimal solution, whereas an exhaustive search approach is unfavorable for practical systems owing to the high complexity. In this study, we propose an optimal user pairing strategy to group users that jointly optimize the minimum downlink rate per user and power allocation at an acceptable cost of complexity. To address this problem, we first relax the binary variables to continuous variables and then develop an iterative algorithm based on the inner approximation method, yielding at least one locally optimal solution. Numerical results show that the proposed user pairing algorithm outperforms existing counterparts, such as conventional beamforming, random pairing, far pairing, and close-pairing strategies, while it can be performed dynamically, that is, two arbitrary users satisfying the formulated problem can be paired regardless of geographical distance. Finally, our approach demonstrates that the combination channel estimation-based NOMA-assisted cell-free massive MIMO achieves the best result in terms of the downlink rate per user when associated with the proposed algorithm.

Asynchronous Activity Detection for Cell-Free Massive MIMO: From Centralized to Distributed Algorithms

Device activity detection in the emerging cell-free massive multiple-input multiple-output (MIMO) systems has been recognized as a crucial task in machine-type communications, in which multiple access points (APs) jointly identify the active devices from a large number of potential devices based on the received signals. Most of the existing works addressing this problem rely on the impractical assumption that different active devices transmit signals synchronously. However, in practice, synchronization cannot be guaranteed due to the low-cost oscillators, which brings additional discontinuous and nonconvex constraints to the detection problem. To address this challenge, this paper reveals an equivalent reformulation to the asynchronous activity detection problem, which facilitates the development of a centralized algorithm and a distributed algorithm that satisfy the highly nonconvex constraints in a gentle fashion as the iteration number increases, so that the sequence generated by the proposed algorithms can get around bad stationary points. To reduce the capacity requirements of the fronthauls, we further design a communication-efficient accelerated distributed algorithm. Simulation results demonstrate that the proposed centralized and distributed algorithms outperform state-of-the-art approaches, and the proposed accelerated distributed algorithm achieves close detection performance to that of the centralized algorithm but with a much smaller number of bits to be transmitted on the fronthaul links.

Energy Efficient AP Selection for Cell-Free Massive MIMO Systems: Deep Reinforcement Learning Approach

The problem of access point (AP) to device association in a cell-free massive multiple-input multiple-output (MIMO) system is investigated. Utilizing energy efficiency (EE) as our main metric, we determine the optimal association parameters subject to minimum rate constraints for all devices. We incorporate all existing practical concerns in our formulation, including training errors, pilot contamination, and central processing unit access to only statistical channel state information (CSI). This EE maximization problem is highly non-convex and possibly NP-hard. We propose to solve this challenging problem by model-free deep reinforcement learning (DRL) methods. Due to the very large discrete action space of our posed optimization problem, existing DRL approaches can not be directly applied. Thus, we approximate the large discrete action space with either a continuous set or a smaller discrete set, and modify existing DRL methods accordingly. Our novel approximations offer a framework with tolerable complexity and satisfactory performance that can be readily applied to other challenging optimization problems in wireless communication. Simulation results corroborate the superior performance of the modified DRL methods over conventional approaches.

Rate analysis of ZF receiver for uplink cell-free massive MIMO systems with D2D communications

This paper proposes a transmission structure of zero forcing (ZF) receiver for uplink cell-free massive multiple-input multiple-output (MIMO) systems with device-to-device (D2D) communications, followed by a rate analysis. We assumed that D2D users (DUEs) can utilize orthogonal radio resources to improve the efficiency of the scarce utilization or repurpose the time–frequency-spectrum resources currently used by the cell-free users (CFUEs). Assuming that the imperfect channel state information (CSI) is realizable, after that, the use-and-forget bounding technique is then used to respectively obtain the closed-form expressions of the CFUEs and DUEs, which provide the lower bounds on the ergodic approximate realizable rate of both communication links. First, we calculate the minimum-mean-square error (MMSE) estimation for all channels. Then, the derived results of the achievable uplink sum rate provide us with a tool that enables us to explain how some important parameters, such as the number of access points (APs)/CFUEs, each AP/CFUE/antenna, and the density of DUEs, affect system performance, highlighting the significance of cooperation between cell-free massive MIMO and D2D communication.