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

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.

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.

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.

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.

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.

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.

Decentralized Coordinated Precoding Design in Cell-Free Massive MIMO Systems for URLLC

Cell-free massive multiple-input multiple-output (MIMO) is a promising network to offer huge improvement of the achievable rate compared with conventional cellular massive MIMO systems. However, the commonly adopted Shannon-type achievable rate is only valid in the long block length regime that is not applicable to the emerging short-packet communication. To realize ultra-reliable and low-latency communication (URLLC) in cell-free massive MIMO systems, we optimize the precoding vector at the access points (APs) to maximize the minimum user rate in both the centralized and decentralized fashion. The design takes into account the impact of URLLC and we propose path-following algorithms (PFA) to address the considered problem which generates a sequence of advanced feasible points and converges to at least a locally optimal solution of the design problem. Moreover, we investigate the requirement of the precoding schemes, the length of the transmission duration, the number of antennas equipped at each AP, and the size of each AP cluster on the URLLC rate. Numerical results show that the decentralized PFA precoding can achieve 80% of the 95%-likely URLLC rate of the centralized precoding and 89% of the average URLLC rate with only 12% computational complexity of the centralized precoding.

Edge-Assisted Massive Video Delivery Over Cell-Free Massive MIMO

Massive Multiple-Input Multiple-Output (MIMO), with its spatial multiplexing and channel hardening, has the potential to provide high capacity and reliability for massive video services. In spite of this, massive MIMO in the physical layer does not fully showcase its abilities in video applications unless it is specifically designed to do so. In this paper, we consider a cell-free massive MIMO system as an edge node for scheduling massive streams, and thus the standard server-to-client transmission is split into server-to-edge and edge-to-client. When the server-to-edge transmission is ideal, edge schedules massive streams to alleviate user conflicts in cell-free massive MIMO. Moreover, we propose a novel edge-to-client grouping algorithm for assigning the streams with severe interference to different time slots. The proposed algorithm achieves an innovative.7-approximation ratio while keeping the group sizes within a certain range. When the server-to-edge transmission is non-ideal, we design a special transmission framework called Aggressive, wherein the server sends the next video chunk when the current chunk reaches the edge rather than the client. Thus, the proposed framework saves considerable server-to-edge latency compared with the traditional framework. Simulation results show that the proposed user grouping algorithm improves the achievable rate by around 18% and the Aggressive framework improves the average bitrate.

Learning-Based Downlink Power Allocation in Cell-Free Massive MIMO Systems

This paper considers a cell-free massive multiple-input multiple-output (MIMO) system that consists of a large number of geographically distributed access points (APs) serving multiple users via coherent joint transmission. The downlink performance of the system is evaluated, with maximum ratio and regularized zero-forcing precoding, under two optimization objectives for power allocation: sum spectral efficiency (SE) maximization and proportional fairness. We present iterative centralized algorithms for solving these problems. Aiming at a less computationally complex and also distributed scalable solution, we train a deep neural network (DNN) to approximate the same network-wide power allocation. Instead of training our DNN to mimic the actual optimization procedure, we use a heuristic power allocation, based on large-scale fading (LSF) parameters, as the pre-processed input to the DNN. We train the DNN to refine the heuristic scheme, thereby providing higher SE, using only local information at each AP. Another distributed DNN that exploits side information assumed to be available at the central processing unit is designed for improved performance. Further, we develop a clustered DNN model where the LSF parameters of a small number of APs, forming a cluster within a relatively large network, are used to jointly approximate the power coefficients of the cluster.

Time-Sequential Cooperative Localization for Moving Sensor in Millimeter-Wave Cell-Free Massive MIMO System

To address the moving-sensor localization problem in millimeter-wave (mm-wave) cell-free massive multiple-input multiple-output (MIMO) systems, a novel cooperative localization framework is proposed in this article. First, the angle of arrival (AoA) of the target sensor is extracted by each access point (AP) in the angle domain. Then, for the purpose of establishing the motion equation that is used to predict the location of the target sensor in the next period, a two-step velocity estimation algorithm is proposed to estimate the velocity and corresponding variance of the moving sensor simultaneously. Furthermore, based on horizontal dilution of precision (HDOP), an AP selection scheme is proposed to decide the subset of APs that participate in localization. On this basis, a time-sequential cooperative localization (TSCL) framework is constructed by jointly utilizing the estimated AoAs and the motion equation. The location estimation is converted to a joint posterior probability problem. The solution that maximizes the posterior probability is obtained through factor graph theory. The simulation results show that the proposed algorithm improves localization accuracy and robustness in time-varying environments.

A Gradual Method for Channel Non-Reciprocity Calibration in Cell-Free Massive MIMO

This letter proposes a method for gradually calibrating channel non-reciprocity in an ultra-dense cell-free massive multiple-input multiple-output (MIMO) system. Many studies assume perfect channel reciprocity in time division duplex (TDD) systems. However, reciprocity is not valid in actual channels. Therefore, determining the reciprocity-calibrated precoding matrix is important for the performance of the network. In a cell-free massive MIMO system, user equipment (UE) is served by many access nodes (ANs). Since there are many nodes, it is difficult to calibrate the matrix simultaneously. Using the proposed method, the network sequentially calibrates the precoding matrix in order of influence. Thus, the proposed method can obtain a large gain compared to a system without calibration by performing only minimal channel calibration. To show the capacity gain of the proposed method, a simulation was performed considering the overhead required for channel calibration.

Mitigation pilot contamination based on matching technique for uplink cell-free massive MIMO systems

In this paper, the cell-free massive multiple input multiple output (MIMO) network is affected by the pilot contamination phenomenon when a large number of users and a small number of available pilots exists, the quality of service (QoS) will deteriorate due to the low accuracy of the channel estimation because some of users will use the same pilot. Therefore, we address this problem by presenting two novel schemes of pilot assignment and pilot power control design based on the matching technique for the uplink of cell-free massive MIMO systems to maximize spectral efficiency. We first formulate an assignment optimization problem in order to find the best possible pilot sequence to be used by utilizing genetic algorithm (GA) and then propose a Hungarian matching algorithm to solve this formulated problem. Regarding the power control design, we formulate a minimum-weighted assignment problem to assign pilot power control coefficients to the estimated channel’s minimum mean-squared error by considering the access point (AP) selection. Then, we also propose the Hungarian algorithm to solve this problem. Simulation results show that our proposed schemes outperform the state-of-the-art techniques concerning both the pilot assignment and the pilot power control design by achieving a 15% improvement in the spectral efficiency. Finally, the computational complexity analysis is provided for the proposed schemes compared with the state-of-the-art techniques.

Spatially Correlated RIS-Aided CF Massive MIMO Systems With Generalized MR Combining

In this correspondence, we study the uplink ergodic net throughput of a spatially correlated reconfigurable intelligent surface (RIS)-aided cell-free (CF) massive multiple-input multiple-output (MIMO) system over Rayleigh fading channels. We investigate the impact of the generalized maximum ratio (GMR) combining and obtain the closed-form expression for characterizing the uplink net throughput revealing that the GMR can double the system performance compared with the maximum ratio (MR) in our system. Then, we compare the performance and complexity of the MR, GMR, and large-scale fading decoding (LSFD). Moreover, we consider a practical fractional power control to mitigate the inter-user interference. The obtained interesting results show that the system performance decreases with the increasing number of RIS elements. It reveals that efficient interference cancellation processing is needed to cope with severer pilot contamination brought by the large number of RIS elements to improve the system performance. Finally, the accuracy of our derived analytical results has been verified by Monte-Carlo simulations.

Location-aided uplink transmission for user-centric cell-free massive MIMO systems: a fairness priority perspective

In this paper, we investigate the uplink transmission for user-centric cell-free massive multiple-input multiple-output (MIMO) systems. The largest-large-scale-fading-based access point (AP) selection method is adopted to achieve a user-centric operation. Under this user-centric framework, we propose a novel inter-cluster interference-based (IC-IB) pilot assignment scheme to alleviate pilot contamination. Considering the local characteristics of channel estimates and statistics, we propose a location-aided distributed uplink combining scheme to balance the relationship among the spectral efficiency (SE), user equipment (UE) fairness and complexity, in which local partial minimum mean-squared error (LP-MMSE) combining is adopted for some APs, while maximum-ratio (MR) combining is adopted for the remaining APs. A corresponding AP selection scheme based on a novel proposed metric representing inter-user interference is proposed. We also propose a new fairness coefficient taking SE performance into account to indicate the UE fairness. Moreover, the performance of the proposed scheme is investigated under fractional power control and max–min fairness (MMF) power control. Simulation results demonstrate that the channel estimation accuracy of our proposed IC-IB pilot assignment scheme outperforms that of the conventional pilot assignment schemes. It is also shown that compared with the benchmark LP-MMSE combining, the proposed location-aided combining trades 13.45% average SE loss for 26.61% UE fairness improvement and 28.58% complexity reduction when gamma = 0.6. And by adjusting the threshold gamma, a good trade-off between the average SE, UE fairness and computational complexity can be provided by the proposed scheme. Furthermore, the proposed scheme with fractional power control can better demonstrate the advantages of trade-off performance than MMF power control and full power transmission.

User-Centric Access Point Selection in Cell-Free Massive MIMO Systems: A Game-Theoretic Approach

In this letter, we investigate user-centric access point (AP) selection for cell-free massive multiple-input multiple-output (MIMO) systems. In contrast to existing works, we study this problem from the perspective of game theory and model user-centric AP service cluster formation as a local altruistic game, which is proven to be an exact potential game (EPG) and to have at least one pure Nash equilibrium (NE). Then, an improved maximum non-neighbor-set-based concurrent spatial adaptive play (MNSB-C-SAP) algorithm is proposed to achieve the NE. Simulation results show that the proposed algorithm outperforms existing algorithms in terms of convergence speed and verify the superiority of the game-theoretic AP selection method compared with some existing approaches.