Cell-free (CF) massive multiple-input multiple-output (MIMO) has recently emerged as a highly promising technology for supporting future six-generation (6G) networks, owing to its unique ability to provide high data rates and reliable connectivity. However, a primary challenge in CF massive MIMO is severe inter-user interference, which is caused by densely located user equipments (UEs) and the presence of imperfect channel state information (CSI). Fortunately, the rate-splitting (RS) strategy offers significant benefits by enabling partially interference decoding, thereby greatly enhancing overall system performance. In this paper, we investigate the performance of uplink RS in CF massive MIMO systems. Considering the inevitable channel estimation errors caused by pilot contamination, we first derive a novel closed-form expression for characterizing spectral efficiency (SE). Moreover, we propose two innovative decoding strategies tailored to the 6G scenario, highlighting their role in enhancing the interference management capabilities of RS, while balancing decoding performance with computational complexity. To ensure successful decoding of each sub-message to the greatest extent possible, we devise an optimization-based power control scheme to maximize the minimum SE of the sub-messages, and propose a low-complexity scheme for comparative analysis. Additionally, we investigate the total energy efficiency (EE) of the system and propose a power control scheme for maximizing EE by exploiting fractional programming (FP) theory. Simulation results corroborate our theoretical expressions and demonstrate that both RS and the proposed power control schemes can significantly improve both SE and EE.

Cell-free (CF) massive multiple-input multiple-output (MIMO) has emerged as a promising technique to deliver uniform signal coverage and high data rates. However, employing low-precision hardware in user equipment introduces susceptibility to hardware impairments (HI), resulting in significantly degraded channel state information (CSI) accuracy. Fortunately, rate-splitting multiple access (RSMA) has been proposed as a robust solution to mitigate the adverse effects of imperfect CSI by performing message splitting at the transmitter and successive interference cancellation (SIC) at the receiver. In this paper, we incorporate RSMA into CF massive MIMO systems to tackle the problem posed by imperfect CSI. Taking into account inevitable pilot contamination, we first derive a novel and closed-form expression for the spectral efficiency (SE) to analytically characterize the performance of RSMA-enabled CF massive MIMO systems under spatially correlated Rician fading channels. Subsequently, we focus on optimizing the decoding order, power allocation, and fronthaul weights to maximize the system’s sum SE. To address this mixed-integer nonlinear programming (MINLP) problem, we initially propose an alternating optimization (AO)-based optimization method that decomposes the original intractable problem into three manageable subproblems, which are iteratively handled until convergence. Considering the significant computational complexity associated with the AO-based approach, we further propose a proximal policy optimization (PPO)-based method to establish an effective and low-complexity optimization framework. Simulation results unveil the detrimental impact of HI on both CSI accuracy and the overall sum SE performance. In particular, the presence of HI introduces residual interference that limits the performance gains achievable through additional RSMA layers, especially in strong line-of-sight scenarios, highlighting the trade-off between these gains and the SIC-related costs in terms of computational complexity and decoding latency.

The distributed deployment of communication infrastructure is a promising evolutionary trend in the next-generation wireless communication systems, as exemplified by the novel cell-free massive multiple-input multiple-output (CF mMIMO) technology. In user-centric CF mMIMO systems, synchronization among access points (APs) is a critical challenge that significantly impacts the effectiveness of coherent joint processing gains. In this paper, we investigate a CF mMIMO system featuring distributed AP deployments and low-resolution analog-to-digital converters (ADCs). To guarantee precise phase synchronization, we first propose two double-layer AP clustering approaches for rapid synchronization using the Leader-Follower paradigm: one based on the K-means algorithm and the other utilizing classical graph theory with geographical distance metrics in AP deployment. Specifically, in the first layer, a designated Leader AP keeps synchronization with its serving secondary Follower-1 APs, while in the second layer, each Follower-1 AP communicates with its neighboring Follower-2 APs. Next, we propose novel phase synchronization and carrier frequency synchronization strategies among APs based on an over-the-air synchronization signal transmission mechanism, which enables mutual calibration without transmitting any measurements to the central processing unit via fronthaul links. Furthermore, we consider the effect of quantization accuracy of radio frequency hardware on synchronization performance, thereby facilitating the adoption of low-cost components. Finally, simulation results demonstrate that synchronization precision can be significantly improved, reaching values on the order of$10^{-5}$. Additionally, even with moderately coarse ADC quantization, near-optimal performance can be achieved in practical scenarios.

The integration of reconfigurable intelligent surfaces (RIS) with cell-free massive MIMO (CF mMIMO) represents a compelling paradigm for satisfying the stringent reliability and latency demands of ultra-reliable low-latency communication (URLLC). In this framework, distributed access points (APs) provide substantial macro-diversity gains, while dynamically controllable RIS elements facilitate enhanced signal propagation. This paper investigates a practical RIS-aided CF mMIMO system designed for URLLC applications, where communications occur through RIS-reflected links under realistic spatially correlated Rayleigh fading channels, with practical impairments such as RIS phase estimation errors and electromagnetic interference explicitly considered. To evaluate reliability in the short-packet regime, we adopt the decoding error probability (DEP) as the performance metric and derive its analytical expression based on user-side SINR. We formulate a non-convex optimization problem to minimize the maximum DEP among users by jointly optimizing AP beamforming, RIS phase shifts, and blocklength allocation. A hybrid solution framework is proposed, combining deep reinforcement learning for continuous variables with a differential evolution (DE) algorithm for discrete blocklength optimization. Simulation results demonstrate the superior performance of the proposed method over alternating optimization and genetic algorithm (GA) baselines. Notably, increasing the number of AP antennas and transmission blocklength improves network availability, although gains saturate due to inter-user interference and diminishing returns. Moreover, the proposed DE-based algorithm for blocklength optimization consistently outperforms the GA method in terms of both solution quality and computational efficiency.

Reconfigurable intelligent surfaces (RIS) are emerging as a crucial technology to address the energy consumption challenges posed by the widespread deployment of access points (APs) in cell-free massive multiple-input multiple-output (CF mMIMO) systems within future sixth-generation (6G) networks. However, most existing studies on RIS-aided CF mMIMO systems assume ideal hardware and static channel conditions, which deviate from practical deployment scenarios. This work analyzes the performance of a RIS-aided CF mMIMO system by incorporating the combined effects of hardware impairments from non-ideal transceivers and channel aging caused by user mobility. We first characterize both direct and cascaded channels between APs and user equipment, modeling them using correlated Rician fading to capture realistic propagation effects. The overall channel is then estimated via the minimum mean square error method under perfect and imperfect line-of-sight phase knowledge, and we derive an analytical expression for the instantaneous spectral efficiency (SE). We also derive the closed-form expressions of the use-and-then-forget bound with the maximum-ratio transmission precoding method. Building on these insights, we establish an efficient joint optimization framework for beamforming in the AP and phase-shift adaptations in the RIS, exploring an alternating optimization method and a deep-reinforcement learning (DRL)-based algorithm. The numerical results validate our theoretical analysis, illustrating the impact of hardware impairments and channel aging on SE. Although the DRL-based method is scalable and adapts well to dynamic environments, its high computational and memory demands pose challenges for real-time deployment, highlighting a trade-off between performance and feasibility.

In this paper, we investigate the downlink distributed transmit beamforming problem in partially connected cell-free massive multiple-input multiple-output (CF mMIMO) systems, specifically designed to satisfy the stringent requirements of ultra-reliable and low-latency communication (URLLC) services. First, we propose a scalable framework that incorporates partial access points (APs) to serve active user equipment (UE), with a reduced energy consumption and computational complexity. To this end, a min-max optimization problem is formulated for minimizing the decoding error probability (DEP) among URLLC services. Then, a graph neural network (GNN)-based strategy called G4PCF is proposed for partially connected CF mMIMO, which takes into account the underlying characteristics of the problem. Furthermore, by leveraging the temporal correlation in channel state information acquired from the previous frame, we develop a parallel G4PCF (P-G4PCF) scheme that significantly reduces both the signaling overhead and computation delay for minimizing DEP of the worst UE. Simulation results demonstrate that the proposed G4PCF and P-G4PCF architectures exhibit excellent scalability for CF mMIMO networks, offering superior performance over existing methods in terms of quality of service outage probability. Notably, P-G4PCF excels in supporting URLLC services with short frame durations and highly correlated channels, while G4PCF performs better under lower channel correlation. Moreover, the proposed algorithms can significantly enhance the application of GNNs into CF mMIMO systems with a reduced complexity compared with the classical weighted minimum mean-squared error algorithm, especially with delay sensitive services.

Cell-free (CF) massive multiple-input multiple-output (MIMO) provides a ubiquitous coverage to user equipments (UEs) but it is also susceptible to interference. Rate-splitting (RS) effectively extracts data by decoding interference, yet its effectiveness is limited by the weakest UE. In this paper, we investigate an RS-based CF massive MIMO system, which combines strengths and mitigates weaknesses of both approaches. Considering imperfect channel state information (CSI) resulting from both pilot contamination and noise, we derive a closed-form expression for the sum spectral efficiency (SE) of the RS-based CF massive MIMO system under a spatially correlated Rician channel. Moreover, we propose low-complexity heuristic algorithms based on statistical CSI for power-splitting of common messages and power-control of private messages, and genetic algorithm is adopted as a solution for upper bound performance. Furthermore, we formulate a joint optimization problem, aiming to maximize the sum SE of the RS-based CF massive MIMO system by optimizing the power-splitting factor and power-control coefficient. Importantly, we improve a generative AI (GAI) algorithm to address this complex and non-convexity problem by using a diffusion model to obtain solutions. Simulation results demonstrate its effectiveness and practicality in mitigating interference, especially in dynamic environments.

The use of predictor antennas (PAs) has significant potential to enhance wireless channel prediction performance in high-speed railway (HSR) communications. The PA system features two sets of antennas installed on the roof of a vehicle. The PA is located at the front of the vehicle and is used to predict the channel observed by the receive antenna (RA), which is located behind the PA. The PAs can be integrated with dense pilots spatially, but the prediction performance decreases when channel estimations are sparse. Therefore, this paper first proposes a multiple PAs (mPAs) system combined with interpolation for sparse channel estimations. Subsequently, recognizing the need for PAs to measure all antenna channels in the estimation interval, we propose an informer-based mPAs system. This system predicts future RA channels in parallel, effectively solving the problem of error propagation in sequential prediction methods. Simulation results demonstrate that as the prediction horizon extends, the proposed informer-based mPAs system outperforms others. Finally, we investigate how varying velocities impact prediction accuracy. It was found that the prediction accuracy of a single PA system performs well at low speeds but drops rapidly at high speeds. Moreover, our proposed informer-based mPAs system achieves higher prediction horizons and maintains efficiency at high speeds.

Cell-free (CF) massive multiple-input multiple-output (MIMO) system has emerged as a highly promising technology, primarily due to its ability to improve coverage and performance. However, one of the key challenges is their reliance on perfect channel state information (CSI). To address this issue, we propose the incorporation of a rate-splitting (RS) strategy, which has been proven to effectively mitigate the negative impact of imperfect CSI. In this paper, we investigate CF massive MIMO systems that utilize the RS strategy. We derive a closed-form expression for the RS-assisted CF massive MIMO system in the uplink, while accounting for pilot contamination. We also present four decoding schemes that can be implemented in practical systems. Our extensive simulations reveal that CF massive MIMO systems utilizing the RS strategy outperform those that do not in terms of sum spectral efficiency (SE). These findings emphasize the effectiveness of RS technology in mitigating the negative effects of imperfect CSI in CF massive MIMO systems. The insights gained from this research can serve as a basis for the design and optimization of future CF massive MIMO systems, ultimately improving their performance and expanding their applicability in diverse scenarios.

The reconfigurable intelligent surface (RIS) technology holds great promise for the advancement of future sixth-generation networks. However, existing research on RIS-assisted communication systems often relies on ideal hardware and static channel conditions, which are impractical in real-world scenarios. In this study, we assess the performance of a RIS-assisted communication system, considering the combined effects of hardware impairments caused by imperfect transceivers and channel aging resulting from user mobility. To achieve this, we analyze the direct and cascade channels between the base station and the user, assuming correlated Rician distributions. We employ the linear minimum mean square estimation method to estimate the overall channel and derive a closed-form expression for the uplink spectral efficiency (SE). By formulating an optimization problem for RIS phase shift, we maximize SE using the projected gradient ascent algorithm. Monte Carlo simulations reveal the impact of channel aging and hardware impairments on system performance. While practical RIS implementations may introduce phase estimation error in the reflected signal, these errors can be mitigated through phase shift optimization. Overall, our results highlight the significant potential of RIS technology in addressing challenges posed by imperfect hardware and users’ mobility.

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.

Cell-free (CF) massive multiple-input multiple-output (MIMO) systems are expected to implement advanced cooperative communication techniques to let geographically distributed access points jointly serve user equipments. Building on the Team Theory, we design the uplink team minimum mean-squared error (TMMSE) combining under limited data and flexible channel state information (CSI) sharing. Taking into account the effect of both channel estimation errors and pilot contamination, a minimum MSE problem is formulated to derive unidirectional TMMSE, centralized TMMSE and statistical TMMSE combining functions, where CF massive MIMO systems operate in unidirectional CSI, centralized CSI and statistical CSI sharing schemes, respectively. We then derive the uplink spectral efficiency (SE) of the considered system. The results show that, compared to centralized TMMSE, the unidirectional TMMSE only needs nearly half the cost of CSI sharing burden with neglectable SE performance loss. Moreover, the performance gap between unidirectional and centralized TMMSE combining schemes can be effectively reduced by increasing the number of APs and antennas per AP.

High-speed train (HST) communications with orthogonal frequency division multiplexing (OFDM) techniques have received significant attention in recent years. Besides, cell-free (CF) massive multiple-input multiple-output (MIMO) is considered a promising technology to achieve the ultimate performance limit. In this paper, we focus on the performance of CF massive MIMO-OFDM systems with both matched filter and large-scale fading decoding (LSFD) receivers in HST communications. HST communications with small cell and cellular massive MIMO-OFDM systems are also analyzed for comparison. Considering the bad effect of Doppler frequency offset (DFO) on system performance, exact closed-form expressions for uplink spectral efficiency (SE) of all systems are derived. According to the simulation results, we find that the CF massive MIMO-OFDM system with LSFD achieves both larger SE and lower SE drop percentages than other systems. In addition, increasing the number of access points (APs) and antennas per AP can effectively compensate for the performance loss from the DFO. Moreover, there is an optimal vertical distance between APs and HST to achieve the maximum SE.

Cell-free (CF) massive multiple-input multiple-output (MIMO) systems show great potentials in low-mobility scenarios, due to cell boundary disappearance and strong macro diversity. However, the great Doppler frequency offset (DFO) leads to serious inter-carrier interference in orthogonal frequency division multiplexing (OFDM) technology, which makes it difficult to provide high-quality transmissions for both high-speed train (HST) operation control systems and passengers. In this paper, we focus on the performance of CF massive MIMO-OFDM systems with both fully centralized and local minimum mean square error (MMSE) combining in HST communications. Considering the local maximum ratio (MR) combining, the large-scale fading decoding (LSFD) cooperation and the practical effect of DFO on system performance, exact closed-form expressions for uplink spectral efficiency (SE) expressions are derived. We observe that cooperative MMSE combining achieves better SE performance than uncooperative MR combining. In addition, HST communications with small cell and cellular massive MIMO-OFDM systems are compared in terms of SE. Numerical results reveal that the CF massive MIMO-OFDM system achieves a larger and more uniform SE than the other systems. Finally, the train antenna centric (TA-centric) CF massive MIMO-OFDM system is designed for practical implementation in HST communications, and three power control schemes are adopted to optimize the propagation of TAs for reducing the impact of the DFO.

Recently, unmanned aerial vehicle (UAV) communications have drawn significant research interests. Meanwhile, cell-free (CF) massive multiple-input multiple-output (MIMO) is proposed as a promising technology to achieve the ultimate performance limits. In this paper, we investigate 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. Take hardware impairments of UAV into account, novel closed-form downlink HE and uplink spectral efficiency (SE) expressions are derived. UAV communications with small cell (SC) and cellular massive MIMO enabled WPT systems are also considered for comparison. Our results reveal that CF massive MIMO achieves two and four times higher 95%-likely uplink SE than the ones of SC and cellular massive MIMO, respectively. To this end, SE is a concave function of the time-splitting fraction, and the optimal time-splitting fraction for maximizing SE is determined by the altitude and hardware impairment factor of the UAV.

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.

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.

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 pilot contamination. To take into account the channel aging effect due to user mobility, we first compute a channel estimate. We use it to derive novel closed-form expressions for the uplink spectral efficiency (SE) of CF massive MIMO systems with large-scale fading decoding and matched-filter receiver cooperation. The performance of a small-cell system is derived for comparison. It is found that CF massive MIMO systems achieve higher 95%-likely uplink SE in both low-and high-mobility conditions, and CF massive MIMO is more robust to channel aging. Fractional power control (FPC) is considered to compensate to limit the inter-user interference. The results show that, compared with full power transmission, the benefits of FPC are gradually weakened as the channel aging grows stronger.

To reduce the hardware cost and power consumption in millimeter wave (mmWave) multiuser massive multiple-input multiple-output (MIMO) systems, a quantized hybrid transmit model with low-resolution digital-to-analog converters (DACs) is introduced. A correlation-based hybrid precoding algorithm is proposed as an attractive low-complexity approach for the considered system. Using the Bussgang theorem and the additive quantization noise model (AQNM), we derive the asymptotic downlink achievable rate expressions. The rate loss caused by low-resolution DACs shows negligible quantization distortion at low power regime. Numerical results demonstrate the superiority of the proposed algorithm over other algorithms in terms of the rate performance.

High-speed railway (HSR) wireless communications are required to support high data rate with seamless connectivity. In this paper, we investigate the outage performance of a downlink single-cell non-orthogonal multiple access (NOMA) based wireless network in HSR scenarios, where it is challenging to derive the perfect channel state information (CSI) and the distribution of the users are quite different from the traditional cellular scenarios. More specifically, the performance of NOMA over composite large-scale and Rician fading channel is studied with two kinds of partial CSI, e.g., imperfect small-scale CSI and no small-scale CSI. We derive the exact closed-form expression of the outage probability based on partial CSI, respectively, by using the Gauss-Chebyshev quadrature method. Finally, simulation results evidence the validity of the derived results and show that the average outage probability of NOMA systems outperforms conventional orthogonal multiple access systems.