Cell-Free Massive MIMO Systems Research Articles

Power Allocation in Smart Grid Aided Cell Free Massive MIMO Systems for URLLC Applications

This paper investigates power allocation in cell-free massive MIMO for URLLC applications, where each access point is powered by smart grid or solar panels/wind-turbines. In particular, the closed-form achievable rate for URRLC is derived. By exploiting the derived results, a non-convex and non-smooth optimization problem is formulated for maximizing the minimum URRLC rate of all multicast group, and is NP-hard. To deal with this problem, the formulated optimization problem is transformed into a tractable version, then the classical CVX tool is adopted to solve the resultant problem. Numerical simulation verifies the practicability of the derived theoretical results and the proposed algorithm.

Structured Tensor CP Decomposition-Aided Pilot Decontamination for UAV Communication in Cell-Free Massive MIMO Systems

This letter proposes a structured CANDECOMP/PARAFAC (CP) decomposition-aided (SCPD) pilot decontamination (PDC) scheme for UAV communication in cell-free massive MIMO systems. We design a two-stage pilot transmission scheme and intentionally generate pilot contamination for pilot decontamination. At first, we formulate the received signals as a second-order tensor. Then we turn the PDC problem into a joint channel parameter estimation problem. By exploiting the Vandermonde structure of the factor matrix, we propose a SCPD-aided scheme for channel estimation, which only leverages standard linear algebra and avoids numerous iterations. The simulation results demonstrate the effectiveness of the proposed SCPD scheme in terms of accuracy and complexity.

Uplink Performance of Cell-Free Massive MIMO With Multi-Antenna Users Over Jointly-Correlated Rayleigh Fading Channels

In this paper, we investigate a cell-free massive MIMO system with both access points (APs) and user equipments (UEs) equipped with multiple antennas over jointly-correlated Rayleigh fading channels. We study four uplink implementations, from fully centralized processing to fully distributed processing, and derive their achievable spectral efficiency (SE) expressions with minimum mean-squared error successive interference cancellation (MMSE-SIC) detectors and arbitrary combining schemes. Furthermore, the global and local MMSE combining schemes are derived based on full and local channel state information (CSI) obtained under pilot contamination, which can maximize the achievable SE for the fully centralized and distributed implementation, respectively. We study a two-layer decoding implementation with an arbitrary combining scheme in the first layer and optimal large-scale fading decoding (LSFD) in the second layer. Besides, we compute novel closed-form SE expressions for the two-layer decoding implementation with maximum ratio (MR) combining. In the numerical results, we compare the SE performance for different implementation levels, combining schemes, and channel models. It is important to note that increasing the number of antennas per UE may degrade the SE performance.

Uplink Channel Estimation With Reduced Fronthaul Overhead in Cell-Free Massive MIMO Systems

This letter focuses on the problem of uplink channel estimation with the reduced fronthaul overhead in cell-free massive multiple-input multiple-output (mMIMO) systems. First, we propose a sub-sampling scheme to reduce the dimension of fronthaul. Then, we exploit the inherent channel sparsity and model the underdetermined channel estimation problem as an off-grid sparse signal recovery problem. Finally, an enhanced sparse Bayesian learning (ESBL) channel estimation algorithm is proposed to refine the sampled grid points and recover the sparse channel iteratively. Simulation results demonstrate that the proposed algorithm achieves a significant reduction on the fronthaul overhead and offers a better channel estimation performance.

Secure Downlink Transmission in Cell-Free Massive MIMO System Enhanced by Intelligent Reflecting Surfaces

This paper presents the application of intelligent reflecting surfaces (IRSs) in a cell-free massive MIMO network to enhance secure transmission in the system. Multiantenna access points (APs) need to transmit information to users safely and reliably via IRSs without fully knowing the channel state information (CSI) of a multiantenna eavesdropper (Eve) or the accurate beamforming information of a jammer. Specifically, through joint optimization of the AP active beamforming (ABF) and IRS passive beamforming (PBF), the information leaked to the Eve is limited by a set threshold, and restrictions on the IRS reflection phase are considered to maximize the weighted sum rate of the system’s downlink transmission. To solve this multivariate-coupled nonconvex problem, we propose a joint precoding framework under imperfect CSI, using the generalized S-procedure, fractional programming (FP), and multidimensional complex quadratic transformation (MCQT) to transform the original complex nonconvex problem into an easily solvable convex optimization problem, and an alternating algorithm to obtain the optimal solution for precoding and IRS phase shifting. Simulation results show that the proposed scheme can significantly increase the weighted sum rate of the system compared to conventional antijamming methods while revealing that the scheme is effective in enhancing secure system transmission.

Resource Allocation for TDD Cell-Free Massive MIMO Systems

In this paper, we investigate a joint resource allocation algorithm in a time-division duplex (TDD)-based cell-free massive MIMO (CFMM) system, which has great potential to improve spectrum efficiency and throughput. Because the throughput of the system is a bottleneck due to the sharing of the pilot, we attempted to alleviate pilot contamination. We propose a pilot assignment approach called user-distance-ordering-based pilot assignment (UDOPA) based on the distance between users and the center, which can be calculated by the K-means method. Then, using an access point (AP) selection algorithm, only the APs having a major impact on the macro diversity gain of a user are selected as the serving APs. In contrast to the existing AP selection algorithms, users with the same pilot are not allowed to share the same serving AP in the proposed AP selection algorithm, which also significantly reduces the complexity of data processing. Finally, a modified max–min power control scheme with teaching–learning-based optimization (TLBO) is proposed to further improve the performance of the systems and guarantee the minimum user rate. Simulation results show that the proposed joint resource allocation scheme can effectively enhance CFMM systems’ performance.

Secure transmission in one-bit cell-free massive MIMO system with multiple non-colluding eavesdroppers

Secure transmission in one-bit cell-free massive MIMO system with multiple non-colluding eavesdroppers

Partial Cooperative Zero-Forcing Decoding for Uplink Cell-Free Massive MIMO

We propose a partial cooperative zero-forcing (PCZF) decoding scheme for the uplink cell-free massive MIMO system, wherein the neighboring access points (APs) around each user equipment (UE) share the channel state information (CSI) and jointly suppress the interference using the zero-forcing technique. Using asymptotic analysis, we derive a closed-form asymptotic expression for a lower bound on the achievable rates. Considering the unique and complex form of the achievable rates, we propose power control schemes according to two criteria. The first criterion is to maximize the minimum achievable rate. For this criterion, we propose a target-SINR-tracking (TST)-based bisection algorithm. Since the power control update functions are standard interference functions, the TST-based bisection method always converges to the optimal solution. The second criterion is to maximize the sum rate, for which we propose two power control algorithms: 1) randomization and scaling algorithm (RSA) and 2) fractional programming algorithm (FPA). In each iteration of the RAS algorithm, we first exploit the randomization technique to transform the sum-rate maximization problem into a series of power minimization problems, and then improve the sum rate by scaling. In the FP algorithm, we derive a lower bound on the sum rate, and then propose an iterative approach based on the Lagrangian dual transform and fractional programming to maximize the sum-rate lower bound. Numerical results validate the theoretical analysis and verify the efficiency of the proposed power control algorithms.

Performance Analysis of Cell-Free Massive MIMO Systems in LoS/ NLoS Channels

In cellular communication systems, it is conventional to assume the absence of a line of sight (LoS) path between the users and theirassociated access points (APs). This assumption however becomes questionable in the context of recent developments in the direction of cell-free (CF) massive MIMO systems. In the CF massive MIMO, the AP density is assumed to be comparable with the user density, which increases probability of existence of an LoS path between the users and their associated APs. In this paper, we analyze the performance of an uplink CF massive MIMO system, with a probabilistic LoS channel model. Here, we first derive the effective statistics of this channel model, and argue that their behaviour is fundamentally different from that of the conventional rich scattering channels. Utilizing these statistics, we next compare the rates achievable by CF massive MIMO systems, under both stream-wise and joint decoding at the central processing unit. Following this, we also discuss the centralized MMSE based data detection to obtain a complexity/ performance trade-off. Finally, using detailed Monte-Carlo simulations, we validate our analytical results, and evaluate the performance of the three data detection schemes.

Scalable Cell-Free Massive MIMO with Multiple CPUs

In this paper, we consider the uplink of a scalable cell-free massive MIMO (CF-M-MIMO) system where user equipments (UEs) are served only by a subset of access points (APs). All APs are physically divided into predetermined “real clusters”, which are linked to different cooperative central processing units (CPUs). Based on the cooperative nature of the considered communications framework, we assume that each UE is affiliated with a “virtual cluster”, which is associated with some APs coming from different real clusters. Thanks to the degrees of cooperation among multiple CPUs, the uplink spectral efficiencies (SEs) of four different levels are analyzed. To achieve system scalability, the CF-M-MIMO system with multiple CPUs is introduced, which leads to lower SE. To this end, we design a joint combining method based on statistical channel state informations (CSIs), which not only has low complexity but also improves the SE of the system. Simulation results indicate that the average rate of our proposed method can be improved by about 30%.

On the spectral efficiency of cell‐free massive MIMO system in irregular 5G mobile networks

SummarySpectral efficiency (SE) is one of the eminent requirements in 5G mobile networks. Cell‐free (CF) massive MIMO is deemed a key technology to provide substantial SE in 5G compared with the cellular and small cell approaches. Most of the prior studies have been focusing on the access points (APs) uniform distribution to assess the SE performance. However, 5G networks are typically dense, irregularly distributed, and mostly constrained by channel impairments. Therefore, considering a uniform distribution of APs is unrealistic. This paper considers a practical network distribution by taking into account the irregular and adaptive APs distribution based on the Poisson point process approach and over the Rician fading channels. Therein, the downlink (DL) SE of CF massive MIMO system is accurately investigated bearing in mind the AP's irregular distribution and fast channel variation for both perfect and imperfect channel state information (CSI) cases. The simulation results have shown that the DL SE of the CF massive MIMO system is considerably affected when considering the irregular deployment of APs compared with the uniform distribution, especially when the phase noise effect is tense. The SE gain performance is reduced by 37.9% in the DL transmissions, compared with the uniform model. Besides, the results have proven that the DL SE gain is remarkably improved when the APs are largely distributed within the network. However, the gained DL SE is affected when increasing the user's density and length of the uplink training period.

Decentralized Beamforming for Cell-Free Massive MIMO With Unsupervised Learning

Cell-free massive MIMO (CF-mMIMO) systems represent a promising approach to increase the spectral efficiency of wireless communication systems. However, near-optimal beamforming solutions require a large amount of signaling exchange between access points (APs) and the network controller (NC). In this letter, we propose two unsupervised deep neural networks (DNN) architectures, fully and partially distributed, that can perform decentralized coordinated beamforming with zero or limited communication overhead between APs and NC, for both fully digital and hybrid precoding. The proposed DNNs achieve near-optimal sum-rate while also reducing complexity by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10-24\times $ </tex-math></inline-formula> compared to conventional near-optimal solutions.

Improved Pilot Designs for Enhancing Connectivity in Multicarrier Massive MIMO Systems

This letter proposes improved pilot designs to enhance the connectivity of multicarrier massive MIMO systems. Exploiting the fact that orthogonal frequency-division multiplexing (OFDM) training symbols end with zero samples, the proposed pilot designs reduce pilot overhead by truncating the zero samples and/or intentionally using them for a guard interval without affecting the channel estimation quality. The proposed designs allow a massive MIMO system either to serve more users with a fixed amount of training time, or requires less training time for a fixed number of users. Numerical results obtained for a cell-free massive MIMO system (as an application use case) demonstrate significant improvements in connectivity and spectral efficiency by the proposed designs over the conventional designs.

UAV-Enabled Hardware-Impaired Spatially Correlated Cell-Free Massive MIMO Systems: Analysis and Energy Efficiency Optimization

We consider a cell-free (CF) massive multi-input multi-output (mMIMO) system, where multi-antenna access points (APs) serve single-antenna unmanned aerial vehicles (UAVs) and ground users (GUEs). We assume, unlike the existing CF mMIMO literature, hardware-impaired UAVs and GUEs, which observe a mixture of spatially-correlated Rician- and Rayleigh-faded channels while communicating with hardware-impaired APs. We derive a closed-form downlink spectral efficiency (SE) expression by using practical models for the channel mixture, and by considering channel estimation errors. We propose a novel block quadratic transformation (block-QT) technique to optimize non-convex network-centric global energy efficiency (GEE) by appropriately modeling circuit, UAV propulsion and fronthaul powers. The novel block-QT approach combines block optimization and quadratic transformation technique to decompose GEE optimization into simpler convex sub-problems. We numerically show that i) it is better to operate a UAV at a larger height when it has severe hardware impairments; and ii) when UAVs operate at a lower height, they do not significantly affect the SE of GUEs.

Joint optimization of spectral efficiency and energy efficiency with low-precision ADCs in cell-free massive MIMO systems

Joint optimization of spectral efficiency and energy efficiency with low-precision ADCs in cell-free massive MIMO systems

Downlink transmission and channel estimation for cell-free massive MIMO-OFDM with DSDs

In a cell-free massive MIMO system, multiple users arrive at multiple access points at separate times, while in an OFDM system, different delays can be equivalent to delay spread differences (DSDs). Since DSDs are not all the same, in the downlink transmission process, it is necessary to consider its impact on transmission techniques, such as channel estimation and downlink precoding. In this paper, aiming at the performance loss caused by DSDs in cell-free massive MIMO-OFDM system, we propose a multi-RB precoding optimization algorithm that maximizes the downlink sum rate. We derive the sum rate maximization problem into an iterative second-order cone programming form to achieve convex approximation. Then, considering the impact of DSDs on the accuracy of cell-free massive MIMO-OFDM channel estimation, we propose a downlink channel estimation method, which jointly uses channel state information reference signal and demodulation reference signal. The simulation results show that the proposed multi-RB optimal precoding can effectively improve the downlink sum rate, and the proposed downlink channel estimation can obtain accurate multi-RB frequency-domain channel parameters.

Coexistence of D2D Communications and Cell-Free Massive MIMO Systems With Low Resolution ADC for Improved Throughput in Beyond-5G Networks

In this paper, uplink transmission of a cell-free massive multiple-input multiple-output (CF-mMIMO) system coexisting with device-to-device (D2D) communication links is investigated, under the assumption that access points (APs) are equipped with low resolution analog-to-digital converters (ADCs). Lower bounds of achievable rates for both D2D users (DUEs) and CF-mMIMO users (CFUEs) are derived in closed-form, with perfect and imperfect channel state information. Next, in order to reduce pilot contamination, greedy and graph coloring-based pilot allocation algorithms are proposed and analyzed for the considered scenario. Furthermore, to control interference and improve the performance, two power control strategies are designed and their complexity and convergence are also discussed. The first power control strategy aims at maximizing CFUEs’ sum spectral efficiency (SE) subject to quality of service constraints on DUEs, while the second one maximizes the weighted product of CFUEs’ and DUEs’ signal-to-interference-plus-noise-ratios (SINRs). Numerical results show that the proposed pilot and power allocations bring a considerable improvement to the network SE. Also, it is revealed that the activation of D2D links has a positive effect on the system throughput, i.e. the network offloading ensured by the D2D links overcomes the increased interference brought by D2D communications.

Millimeter Wave Cell-Free Massive MIMO Systems: Joint Beamforming and AP-User Association

We consider the problem of joint beamforming and access point (AP)-user association for downlink millimeter Wave (mmWave) cell-free (CF) massive MIMO systems. Such a problem is formulated into an integer-constrained optimization problem which aims at maximizing the minimum average received signal power among users. Directly solving this problem is NP-hard due to its combinatorial nature. To address this difficulty, we first transform the problem into a feasibility checking problem within a bisection framework. Then an alternating average reflection algorithm (AARA)-based method is developed to solve the feasibility checking problem. Simulation results show that the proposed algorithm achieves a considerable performance improvement over existing methods.

Joint Activity Detection and Channel Estimation in Cell-Free Massive MIMO Networks With Massive Connectivity

Cell-free massive MIMO is one of the key technologies for future wireless communications, in which users are simultaneously and jointly served by all access points (APs). In this paper, we investigate the minimum mean square error (MMSE) estimation of effective channel coefficients in cell-free massive MIMO systems with massive connectivity. To facilitate the theoretical analysis, only single measurement vector (SMV) based MMSE estimation is considered in this paper, i.e., the MMSE estimation is performed based on the received pilot signals at each AP separately. Inspired by the decoupling principle of replica symmetric postulated MMSE estimation of sparse signal vectors with independent and identically distributed (i.i.d.) non-zero components, we develop the corresponding decoupling principle for the SMV based MMSE estimation of sparse signal vectors with independent and non-identically distributed (i.n.i.d.) non-zero components, which plays a key role in the theoretical analysis of SMV based MMSE estimation of the effective channel coefficients in cell-free massive MIMO systems with massive connectivity. Subsequently, based on the obtained decoupling principle of MMSE estimation, likelihood ratio test and the optimal fusion rule, we perform user activity detection based on the received pilot signals at only one AP, or cooperation among the entire set of APs for centralized or distributed detection. Via theoretical analysis, we show that the error probabilities of both centralized and distributed detection tend to zero when the number of APs tends to infinity while the asymptotic ratio between the number of users and pilots is kept constant. We also investigate the asymptotic behavior of oracle estimation in cell-free massive MIMO systems with massive connectivity via random matrix theory. Moreover, in order to demonstrate the potential performance loss of SMV based MMSE estimation, which does not employ the correlation between the received pilot signals at different APs, the multiple measurement vector (MMV) based MMSE estimation, i.e., joint MMSE estimation with pilot signals from all APs, is analyzed via numerical results. Numerical analysis shows that the theoretical analyze with our decoupling principle for the SMV based MMSE estimation of sparse signal vectors with i.n.i.d. non-zero components matches well with the numerical results.

Secure performance analysis and pilot spoofing attack detection in cell-free massive MIMO systems with finite-resolution ADCs

In this article, the secure communication in cell-free massive multiple-input multiple-output system with low-resolution analog-to-digital converters is investigated in the presence of an active eavesdropper. Specifically, in this article, the deterioration caused by the analog-to-digital converter imperfections on the accuracy of the channel estimation and secure transmission performance is studied. Besides, the additive quantization noise model is utilized to analyze the impacts of the low-resolution analog-to-digital converters. The minimum mean square error channel estimation results show that there is a nonzero floor caused by the coarse analog-to-digital converters. Then, the closed-form expressions for both the legitimate users achievable ergodic rate and the information leakage to the eavesdropper are derived, respectively. Moreover, tight approximated ergodic secrecy rate expression is also presented with respect to analog-to-digital converters quantization bits, number of antennas, pilot power, and so on. To degrade the impacts of the pilot spoofing attack, an active attack detection approach based on random matrix theory is proposed which can only be operated at one access point. Simulation results are provided to corroborate the obtained results and analyze the impacts of various parameters on system secrecy performance. Also, the superiority of the proposed active attacks detection method is confirmed via simulation results.