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

Energy-efficient power allocation in cell-free massive MIMO with zero-forcing: First order methods

In this paper, the downlink of cell-free massive multiple-input multiple-output (MIMO) with zero-forcing processing is considered. To maximize the system energy efficiency (EE), we design power allocation algorithms taking into account imperfect channel state information, hardware, and backhaul power consumption. The total EE optimization problem is nonconvex, which traditionally is solved by the successive convex approximation framework which involves second order cone programs (SOCPs). As such methods have high complexity, the run time is extremely long, especially in large-scale systems with thousands of access points (APs) and users. To overcome this problem, in this paper, we propose to apply two computationally efficient methods, namely proximal gradient (PG) method and accelerated proximal gradient (APG) method to solve the considered problem. Numerical results show that, compared to the conventional SOCPs approximation methods, our proposed methods achieve the same performance while the run time is much smaller.

Cell-Free Massive MIMO for 6G Wireless Communication Networks

The recently commercialized fifth-generation (5G) wireless networks have achieved many improvements, including air interface enhancement, spectrum expansion, and network intensification by several key technologies, such as massive multiple-input multiple-output (MIMO), millimeter-wave communications, and ultra-dense networking. Despite the deployment of 5G commercial systems, wireless communications is still facing many challenges to enable connected intelligence and a myriad of applications such as industrial Internet-of-things, autonomous systems, brain-computer interfaces, digital twin, tactile Internet, etc. Therefore, it is urgent to start research on the sixth-generation (6G) wireless communication systems. Among the candidate technologies for 6G, cell-free massive MIMO, which combines the advantages of distributed systems and massive MIMO, is a promising solution to enhance the wireless transmission efficiency and provide better coverage. In this paper, we present a comprehensive study on cell-free massive MIMO for 6G wireless communication networks with a special focus on the signal processing perspective. Specifically, we introduce enabling physical layer technologies for cell-free massive MIMO, such as user association, pilot assignment, transmitter, and receiver design, as well as power control and allocation. Furthermore, some current and future research problems are described.

Local Partial Zero-Forcing Combining for Cell-Free Massive MIMO Systems

Cell-free massive multiple-input multiple-output (MIMO) provides more uniform spectral efficiency (SE) for users (UEs) than cellular technology. The main challenge to achieve the benefits of cell-free massive MIMO is to realize signal processing in a scalable way. In this paper, we consider scalable fullpilot zero-forcing (FZF), partial FZF (PFZF), protective weak PFZF (PWPFZF), and local regularized ZF (LRZF) combining by exploiting channel statistics. We derive closed-form expressions of the uplink SE for FZF, PFZF, and PWPFZF combining with large-scale fading decoding over independent Rayleigh fading channels, taking channel estimation errors and pilot contamination into account. Moreover, we investigate the impact of the number of pilot sequences, antennas per AP, and APs on the performance. Numerical results show that LRZF provides the highest SE. However, PWPFZF is preferable when the number of pilot sequences is large and the number of antennas per AP is small. The reason is that PWPFZF has lower computational complexity and the SE expression can be computed in closed-form. Furthermore, we investigate the performance of PWPFZF combining with fractional power control and the numerical results show that it improves the performance of weak UEs and realizes uniformly good service for all UEs in a scalable fashion.

The Downlink Performance for Cell-Free Massive MIMO with Instantaneous CSI in Slowly Time-Varying Channels.

In centralized massive multiple-input multiple-output (MIMO) systems, the channel hardening phenomenon can occur, in which the channel behaves as almost fully deterministic as the number of antennas increases. Nevertheless, in a cell-free massive MIMO system, the channel is less deterministic. In this paper, we propose using instantaneous channel state information (CSI) instead of statistical CSI to obtain the power control coefficient in cell-free massive MIMO. Access points (APs) and user equipment (UE) have sufficient time to obtain instantaneous CSI in a slowly time-varying channel environment. We derive the achievable downlink rate under instantaneous CSI for frequency division duplex (FDD) cell-free massive MIMO systems and apply the results to the power control coefficients. For FDD systems, quantized channel coefficients are proposed to reduce feedback overhead. The simulation results show that the spectral efficiency performance when using instantaneous CSI is approximately three times higher than that achieved using statistical CSI.

Improving Cell-Free Massive MIMO Networks Performance: A User Scheduling Approach

Cell-Free (CF) massive multiple-input multiple-output (MIMO) system is a distributed antenna system, wherein a large number of access points wish to simultaneously communicate with a relatively small number of users. Similar to co-located massive MIMO system, pilot contamination and multi-user interference are two major impediments to CF massive MIMO network performance improvement. One can mitigate the detrimental effect of pilot contamination and multi-user interference through judicious resource allocation. In this work, we formulate and investigate the problem of frequency assignment for a CF massive MIMO. The formulated optimization problem is proven to be generally NP-hard. Local optima can be found by approaches such as the Lagrangian method that however, has considerably slow rates of convergence. To circumvent this issue, we propose an alternative solution being of two-folds. Firstly, we reformulate the problem as a grouping strategy which enables to attenuate the effect of intra-group multi-user interference. In the second fold, frequencies are assigned in a non-overlapping fashion to each scheduled group to palliate the effect of inter-group interference and pilot contamination. To further improve the performance of the proposed approach, power coefficients are allocated to the users via a sequential convex approximation (SCA)-based framework. The effectiveness of the proposed algorithms is then verified through extensive numerical simulations which demonstrate a non-negligible improvement in the performance of the studied scenario.

2D Fingerprinting-Based Localization for mmWave Cell-Free Massive MIMO Systems

In this letter, fingerprinting-based cooperative localization for millimeter-wave (mmWave) cell-free massive multiple-input multiple-output (MIMO) systems is investigated. For the purpose of robust localization in line-of-sight (LOS) or non-LOS (NLOS) environments, a dynamic two-dimensional (2D) fingerprint training scheme employing maximum likelihood (ML) estimation and information entropy theory is proposed. This scheme regularly extracts link state matrix and confidence factor-aided AOA vectors from uplink channels. Then, a dynamic AP select scheme along with an anchor node (AN) filtering scheme is used to rapidly lock the range of the user location. Based on this, a weighted mean square error (WMSE)-based AOA fingerprinting scheme is developed to estimate the user location. Numerical results are provided to validate the localization accuracy of the proposed scheme.

Optimization of Duplex Mode Selection for Network-Assisted Full-Duplex Cell-Free Massive MIMO Systems

Network-assisted full-duplex enable simultaneous uplink (UL) and downlink (DL) communications by allocating remote antenna units (RAUs) to perform either UL reception of DL transmission at each time slot, which improve the spectral efficiency (SE) of cell-free massive multiple-input multiple-output (MIMO) systems. However, previous studies mainly focus on analyzing the system performance under given duplex mode of RAUs. In this letter, we propose to dynamically optimize the duplex mode of RAUs to further improve the SE. An algorithm based on parallel successive convex approximation is proposed to solve the non-convex duplex mode optimization problem. To reduce algorithm complexity and achieve higher SE, a reinforcement learning algorithm based on enhanced Q-learning is also proposed. Simulation results show that the proposed algorithms improve the SE of cell-free massive MIMO systems greatly with lower complexity.

Exploiting Underlay Spectrum Sharing in Cell-Free Massive MIMO Systems

We investigate the coexistence of underlay spectrum sharing in cell-free massive multiple-input multiple-output (MIMO) systems. A primary system with geographically distributed primary access points (P-APs) serves a multitude of primary users (PUs), while a secondary system serves a large number of secondary users (SUs) in the same primary/licensed spectrum by exploiting the underlay spectrum sharing. To mitigate the secondary co-channel interference inflected at PUs, stringent secondary transmit power constraints are defined for the secondary access points (S-APs). A generalized pilots sharing scheme is used to locally estimate the uplink channels at P-APs/S-APs, and thereby, conjugate precoders are adopted to serve PUs/SUs in the same time-frequency resource element. Moreover, the effect of a user-centric AP clustering scheme is investigated by assigning a suitable set of APs to a particular user. The impact of estimated downlink (DL) channels at PUs/SUs via DL pilots beamformed by P-APs/S-APs is investigated. The achievable primary/secondary rates at PUs/SUs are derived for the statistical DL and estimated DL CSI cases. User-fairness for PUs/SUs is achieved by designing efficient transmit power control policies based on a multi-objective optimization problem formulation of joint underlay spectrum sharing and max-min criteria. The proposed orthogonal multiple-access based analytical framework is also extended to facilitate non-orthogonal multiple-access. Our analysis and numerical results manifest that the primary/secondary performance of underlay spectrum sharing can be boosted by virtue of the average reduction of transmit powers/path-losses, uniform coverage/service, and macro-diversity gains, which are inherent to distributed transmissions/receptions of cell-free massive MIMO.

Full-Duplex Cell-Free Massive MIMO With Low-Resolution ADCs

This paper studies the sum spectral/energy efficiency (SE/EE) of a full-duplex (FD) cell-free (CF) massive multiple-input multiple-output (MIMO) system with low-resolution analog-to-digital converters (ADCs) at the access points (APs) and the downlink (DL) users. We characterize the joint impact of the residual self-interference, inter-AP interference, uplink (UL)-to-DL interference, pilot contamination and quantization noise (QN) by deriving closed-form solutions for the UL/DL SE. It is shown that the UL SE loss due to the QN can be compensated by increasing the receiving antenna arrays. By contrast, in the DL, increasing the transmit antennas is ineffective in compensating for the DL SE loss. Furthermore, the analysis shows that the operating region of the FD CF massive MIMO is reduced as the ADCs’ resolution declines. We investigate the EE/SE trade-offs.

UAV Communications With WPT-Aided Cell-Free Massive MIMO Systems

Cell-free (CF) massive multiple-input multiple-output (MIMO) is a promising solution to provide uniform good performance for unmanned aerial vehicle (UAV) communications. In this paper, we propose the UAV communication with wireless power transfer (WPT) aided CF massive MIMO systems, where the harvested energy (HE) from the downlink WPT is used to support both uplink data and pilot transmission. We derive novel closed-form downlink HE and uplink spectral efficiency (SE) expressions that take hardware impairments of UAV into account. UAV communications with current small cell (SC) and cellular massive MIMO enabled WPT systems are also considered for comparison. It is significant to show that CF massive MIMO achieves two and five times higher 95%-likely uplink SE than the ones of SC and cellular massive MIMO, respectively. Besides, the large-scale fading decoding receiver cooperation can reduce the interference of the terrestrial user. Moreover, the maximum SE can be achieved by changing the time-splitting fraction. We prove that the optimal time-splitting fraction for maximum SE is determined by the number of antennas, altitude and hardware quality factor of UAVs. Furthermore, we propose three UAV trajectory design schemes to improve the SE. It is interesting that the angle search scheme performs best than both AP search and line path schemes. Finally, simulation results are presented to validate the accuracy of our expressions.

Cell-Free Massive MIMO Systems With Oscillator Phase Noise: Performance Analysis and Power Control

Cell-free massive multiple-input multiple-output (MIMO) is considered as a promising technology for satisfying higher rate requirement of users in beyond-5G networks. This paper investigates the impact of phase noise on the performance of cell-free MIMO systems which employ a large number of multi-antenna access points (APs). For both downlink and uplink transmissions, we derive the tractable closed-form achievable rate expressions when signal detection with channel state information (CSI) and channel distribution information (CDI), respectively, by utilizing the extended deterministic equivalence method in random matrix theory. The closed-form achievable rate expressions provide efficient evaluation for the impact of phase noise on system performance. The analytical results indicate that the phase noise influences the power of the desired signal, the beamforming uncertainty gain, and the inter-user interference increment caused by the pilot contamination. In addition, the special cases that only APs have phase noise and only users have phase noise are discussed. It is found that the impact of phase noise at users is more severe than that at APs. Besides, we discuss the system performance at low and high SNR regimes. It demonstrates that the phase noise is the major limitation of the system performance in high SNR regime while it can be neglected in low SNR regime. Furthermore, we formulate the max-min power control problem for both downlink and uplink transmissions to guarantee the users’ fairness and prove that the downlink max-min problem is a quasi-concave problem while the uplink max-min problem is a geometric programming (GP) problem. Then, the phase noise-aware max-min power control schemes for both downlink and uplink transmissions are proposed to ensure the users’ fairness. Finally, numerical results are provided to validate the analytical results and the proposed phase noise-aware power control scheme.

Utility Maximization for Large-Scale Cell-Free Massive MIMO Downlink

We consider utility maximization problems in the downlink cell-free massive multiple-input multiple-output (MIMO) whereby a large number of access points (APs) simultaneously serve a group of users. Four fundamental maximization objectives are of interest: (i) average spectral efficiency (SE), (ii) proportional fairness, (iii) harmonic-rate, and (iv) minimum SE of all users, subject to a sum power constraint at each AP. As considered problems are non-convex, existing solutions normally rely on successive convex approximation (SCA) and use off-the-shelf convex solvers, which implement an interior-point algorithm, to solve derived convex problems. The complexity of such methods scales quickly with the problem size. Therefore, we propose an accelerated projected gradient method to solve the considered problems. Particularly, each iteration of the proposed solution is given in a closed form and only requires the first order oracle of the objective, rather than the Hessian matrix as in known solutions, and thus is much more memory efficient. Numerical results demonstrate that our proposed solution achieves the same utility performance but with far less run-time, compared to the SCA method. Simulation results show that large-scale cell-free massive MIMO has the intrinsic user fairness, i.e. the four utility functions can deliver nearly uniformed services to all users.

Exploiting Cell-Free Massive MIMO for Enabling Simultaneous Wireless Information and Power Transfer

The performance of simultaneous wireless information and power transfer (SWIPT) in downlink (DL) cell-free massive multiple-input multiple-output (MIMO) is investigated. Tight approximations to the DL harvested energy and the DL/uplink (UL) achievable rates are derived for two practical channel state information (CSI) cases by using a non-linear energy harvesting model for time-switching and power-splitting protocols. Max-min fairness-based transmit power control policies are employed to mitigate the deleterious near-far effects caused by distributed transmissions/receptions in cell-free massive MIMO. The achievable common DL energy-rate trade-off is derived, and thereby, it is shown that the proposed max-min power control guarantees user-fairness regardless of near-far effects in terms of both harvested energy and achievable rate. The benefits of user estimated DL CSI to boost the SWIPT performance are explored. These performance metrics are compared against those of the conventional co-located massive MIMO, and thereby, it is revealed that the reduction of path-losses and lower average transmit powers offered by cell-free massive MIMO can be exploited to boost the energy-rate trade-off of SWIPT at the expense of increased backhaul requirements.

Limited-Fronthaul Cell-Free Massive MIMO With Local MMSE Receiver Under Rician Fading and Phase Shifts

A cell-free Massive multiple-input multiple-output (MIMO) system is considered, where the access points (APs) are linked to a central processing unit (CPU) via the limited-capacity fronthaul links. It is assumed that only the quantized version of the weighted signals are available at the CPU. The achievable rate of a limited fronthaul cell-free massive MIMO with local minimum mean square error (MMSE) detection is studied. We study the assumption of uncorrelated quantization distortion, which is commonly used in literature. We show that this assumption will not affect the validity of the insights obtained in our work. To investigate this, we compare the uplink per-user rate with different system parameters for two different scenarios; 1) the exact uplink per-user rate and 2) the uplink per-user rate while ignoring the correlation between the inputs of the quantizers. Finally, we present the conditions which imply that the quantization distortions across APs can be assumed to be uncorrelated.

Limiting Doppler Shift Effect on Cell-Free Massive MIMO Systems: A Stochastic Geometry Approach

Cell-free (CF) massive multiple-input multiple-output (MIMO) system is currently considered as a promising network architecture to satisfy the anticipated rate requirements of beyond-5G networks. However, in practical scenarios with the presence of high-velocity users, the network experiences an inevitable performance degradation due to the Doppler shift effect. This paper analyzes the potential of frame length optimization in limiting the Doppler shift effect on the performance of time-division duplexing CF massive MIMO under different mobility conditions. In doing so, we derive novel expressions for tight lower bound of the average downlink (DL) and uplink (UL) rates. Capitalizing on the derived analytical results, we provide an analytical framework to determine the optimal frame length that limits the Doppler shift effect on DL and UL rates according to some criterion. Our results show perfect match of both analytical and simulated results under different system settings. Also, we reveal that the optimal frame lengths for maximizing the DL and UL rates are different and depend mainly on the transmission criterion and the users' velocities. Besides, our results demonstrate the high potential of adapting the frame length according to the velocity conditions in limiting the Doppler shift effect compared to applying a fixed frame length.

Aerial intelligent reflecting surface-enhanced cell-free massive MIMO for high-mobility communication: joint Doppler compensation and power optimization

Intelligent reflecting surfaces (IRSs) are considered one of the core technologies in sixth-generation (6G) mobile communication. In this paper, we investigate an aerial IRS (AIRS)-enhanced cell-free (CF) massive multiple-input-multiple-output (MIMO)system where multiple APs serve a high-speed mobile user simultaneously. The mobility of the user leads to fast time-varying and nonnegligible Doppler frequency offsets (DFOs), which cause a serious threat to link performance. To overcome the influence of the Doppler effect and reduce the energy consumption of the system, we propose a Doppler compensation and transmission method by using the AIRS. Specifically, we divide the AIRS reflection phase shift vector into two parts: one part is used for Doppler compensation, and the other is used for transmission. First, we propose an angle-sensing algorithm to obtain the user angle in each coherent time (CT) and use it to design a Doppler compensation vector. Then, we propose an angle information-aided transmission strategy to design the transmission reflecting vector, the beamforming vector, and the power allocation coefficient of each AP to minimize the transmission power of all APs at a required achievable rate. The simulation results show that we can significantly reduce the total transmission power by using the proposed method.

Cell-Free Massive MIMO: Joint Maximum-Ratio and Zero-Forcing Precoder With Power Control

Cell-free massive multiple-input multiple-output (MIMO) system is a promising architecture for next generation wireless systems by deploying a very large number of distributed access points (APs), which simultaneously serve a smaller number of user equipments (UEs) over the same time-frequency resources. It guarantees uniformly good service at high spectral efficiency with simple linear precoding techniques and max-min power control. In this article, we propose a new joint maximum-ratio and zero-forcing (JMRZF) precoding scheme, where part of APs are combined to perform centralized zero-forcing (ZF), while other APs apply simple maximum-ratio transmission (MRT). Our proposed precoder offers an adaptable trade-off between the spectral efficiency and front-haul signalling overhead. A corresponding AP subset selection scheme is also proposed which is based on large-scale fading coefficients. A closed-form expression for the achievable spectral efficiency of our proposed scheme is derived, which represents a generalized result including both fully distributed MRT and fully centralized ZF cases. Based on this closed-form expression, max-min power control is formulated and solved via the second order cone and first order methods. The former can obtain the global optimal solution, but its computational complexity is very high. On the other hand, the latter technique is sub-optimal, yet, it has very low computational complexity. Hence, it is suitable for large-scale cell-free massive MIMO systems with hundreds or thousands of APs and users. Numerical results show that our proposed JMRZF scheme can substantially outperform the local precoding schemes, even when a small part of APs are combined to deploy ZF and is implementable even when each AP has very few antennas. In addition, it is shown that our max-min power controls improves the spectral efficiency significantly, compared to the uniform power control scheme.

Robust MMSE Precoding and Power Allocation for Cell-Free Massive MIMO Systems

We consider the downlink of a cell-free massive multiple-input multiple-output (MIMO) system with single-antenna access points (APs) and single-antenna users. An iterative robust minimum mean-square error (RMMSE) precoder based on generalized loading is developed to mitigate interference in the presence of imperfect channel state information (CSI). An achievable rate analysis is carried out and optimal and uniform power allocation schemes are developed based on the signal-to-interference-plus-noise ratio. An analysis of the computational costs of the proposed RMMSE and existing schemes is also presented. Numerical results show the improvement provided by the proposed RMMSE precoder against linear minimum mean-square error, zero-forcing and conjugate beamforming precoders in the presence of imperfect CSI.

Impact of Channel Aging on Cell-Free Massive MIMO Over Spatially Correlated Channels

In this paper, we investigate the impact of channel aging on the performance of cell-free (CF) massive multiple-input multiple-output (MIMO) systems with both spatial correlation and pilot contamination. We derive novel closed-form uplink and downlink spectral efficiency (SE) expressions that take imperfect channel estimation into account. More specifically, we consider large-scale fading decoding and matched-filter receiver cooperation in the uplink. The uplink performance of a small-cell (SC) system is derived for comparison. The CF massive MIMO system achieves higher 95%-likely uplink SE than the SC system. In the downlink, the coherent transmission has four times higher 95%-likely per-user SE than the non-coherent transmission. Statistical channel cooperation power control (SCCPC) is used to mitigate the inter-user interference. SCCPC performs better than full power transmission, but the benefits are gradually weakened as the channel aging becomes stronger. Furthermore, strong spatial correlation reduces the SE but degrades the effect of channel aging. Increasing the number of antennas can improve the SE while decreasing the energy efficiency. Finally, we use the maximum normalized Doppler shift to design the SE-improved length of the resource block. Simulation results are presented to validate the accuracy of our expressions and prove that the CF massive MIMO system is more robust to channel aging than the SC system.

Pilot Assignment for Cell Free Massive MIMO Systems Using a Weighted Graphic Framework

Pilot contamination resulting from pilot reuse seriously restricts the communication performance of the cell-free massive multiple-input multiple-output (MIMO) networks. To deal with this problem, an efficient pilot assignment scheme using a weighted graphic framework is proposed in this correspondence paper. Specifically, a novel metric is first introduced for capturing the severity of potential mutual pilot contamination in cell-free topology. On this basis, the weighted pilot contamination graph is constructed to depict the dynamic interference relationship corresponding to the network. Then, the pilot assignment optimization is mapped to the Max k-Cut problem, and a heuristic algorithm is exploited to realize pilot decontamination. Numerical simulation results reveal the superior performance of the proposed scheme, which is capable of achieving a significant improvement in throughput with low complexity.