This paper presents the first experimental validation of reflective near-field beamfocusing using a reconfigurable intelligent surface (RIS). While beamfocusing has been theoretically established as a key feature of large-aperture RISs, its practical realization has remained unexplored. We derive new analytical expressions for the array gain achieved with a $b$-bit RIS in near-field line-of-sight scenarios, characterizing both the finite depth and angular width of the focal region. The theoretical results are validated through a series of measurements in an indoor office environment at 28 GHz using a one-bit 1024-element RIS. The experiments confirm that beamfocusing can be dynamically achieved and accurately predicted by the proposed simplified analytical model, despite the presence of hardware imperfections and multipath propagation. These findings demonstrate that near-field beamfocusing is a robust and practically viable feature of RIS-assisted wireless communications.

We investigate the problem of maximizing the sum-rate performance of a beyond-diagonal reconfigurable intelligent surface (BD-RIS)-aided multi-user (MU)-multiple-input single-output (MISO) system using fractional programming (FP) techniques. More specifically, we leverage the Lagrangian Dual Transform (LDT) and Quadratic Transform (QT) to derive an equivalent objective function which is then solved iteratively via a manifold optimization framework. It is shown that these techniques reduce the complexity of the optimization problem for the scattering matrix solution, while also providing notable performance gains compared to state-of-the-art (SotA) methods under the same system conditions. Simulation results confirm the effectiveness of the proposed method in improving sum-rate performance.

We propose a novel low-complexity receiver design for multicarrier continuous aperture array (CAPA) systems operating over doubly-dispersive (DD) channels. The receiver leverages a Gaussian Belief Propagation (GaBP)-based framework that hinges only on element-wise scalar operations for the detection of the transmitted symbols. Simulation results for the orthogonal frequency division multiplexing (OFDM), orthogonal time frequency space (OTFS), and affine frequency division multiplexing (AFDM) waveforms demonstrate significant performance improvements in terms of uncoded bit error rate (BER) compared to conventional discrete antenna array systems, while maintaining very low computational complexity.

Rydberg atomic quantum receivers (RAQRs) have emerged as highly sensitive receivers for future communication and sensing systems. However, conventional RAQRs are primarily effective for single-carrier and narrowband reception, typically with an operational bandwidth of only a few hundred kilohertz. To enable the reception of multi-carrier signals with larger bandwidth, we propose a multi-carrier Rydberg atomic quantum receiver (MC-RAQR) architecture based on a five-level quantum system model. We analyze the amplitude and phase of the output laser in MC-RAQR and extract the baseband electrical signal for signal processing. Furthermore, we quantify the performance of MC-RAQR in multi-carrier communication and sensing by studying the channel capacity and distance estimation, respectively. Numerical results show that the MC-RAQR is capable of achieving a bandwidth of $7.2$ MHz, which is an order of magnitude larger than conventional RAQRs. Besides, compared to conventional receivers, MC-RAQR can improve the capacity and distance estimation by $18$-fold and $10^3$-fold, respectively. This validates the superiority of MC-RAQR in receiving multi-carrier signal, and demonstrates its compatibility in detecting waveforms such as orthogonal frequency‐division multiplexing.

With the deployment of large antenna arrays at high-frequency bands, future wireless communication systems are likely to operate in the radiative near-field. Unlike far-field beam steering, near-field beams can be focused on a spatial region with a finite depth, enabling spatial multiplexing in the range dimension. Moreover, in the line-of-sight MIMO near-field, multiple spatial degrees of freedom (DoF) are accessible, akin to a scattering-rich environment. In this paper, we derive the beamdepth for a generalized uniform rectangular array (URA) and investigate how the array geometry influences near-field beamdepth and its limits. We define the effective beamfocusing Rayleigh distance (EBRD), to present a near-field boundary with respect to beamfocusing and spatial multiplexing gains for the generalized URA. Our results demonstrate that under a fixed element count constraint, the array geometry has a strong impact on beamdepth, whereas this effect diminishes under a fixed aperture length constraint. Moreover, compared to uniform square arrays, elongated configurations such as uniform linear arrays (ULAs) yield narrower beamdepth and extend the effective near-field region defined by the EBRD. Building on these insights, we design a polar codebook for compressed-sensing-based channel estimation that leverages our findings. Simulation results show that the proposed polar codebook achieves a 2 dB NMSE improvement over state-of-the-art methods. Additionally, we present an analytical expression to quantify the effective spatial DoF in the near-field, revealing that they are also constrained by the EBRD. Notably, the maximum spatial DoF is achieved with a ULA configuration, outperforming a square URA in this regard.

We consider a cell-free massive multiple-input multiple-output (MIMO) system with multiple antennas on the users and access points (APs). In previous works, the downlink spectral efficiency (SE) has been evaluated using the hardening bound that requires no downlink pilots. This approach works well for single-antenna users. In this paper, we show that much higher SEs can be achieved if downlink pilots are sent when having multi-antenna users. The reason is that the effective channel matrix does not harden. We propose a pilot-based downlink estimation scheme, derive a new SE expression, and show numerically that it yields substantially higher performance when having correlated Rayleigh fading channels. In cases with multi-antenna users, the APs can either coherently transmit the same data streams, or alternatively they transmit separate data streams non-coherently. The latter approach reduces the fronthaul signaling overhead, albeit with a potential SE penalty. For both strategies, we propose novel precoding and combining schemes. Specifically, we develop precoders based on the minimum mean square error (MMSE) criterion and investigate receive combining methods, including an MMSE combiner. Furthermore, we consider sharing different levels of channel knowledge between the APs. Finally, we present a comprehensive numerical analysis to validate our findings, evaluating the performance trade-offs associated with the number of users, APs, and antennas, as well as the choice of transmission strategy and the level of CSI sharing among APs.

Beyond-diagonal reconfigurable intelligent surfaces (BD-RISs) are emerging as a transformative technology in wireless communications, enabling enhanced performance and quality of service (QoS) of wireless systems in harsh urban environments due to their relatively low cost and advanced signal processing capabilities. Generally, BD-RIS systems are employed to improve robustness, increase achievable rates, and enhance energy efficiency of wireless systems in both direct and indirect ways. The direct way is to produce a favorable propagation environment via the design of optimized scattering matrices, while the indirect way is to reap additional improvements via the design of multiple-input multiple-output (MIMO) beamformers that further exploit the latter "engineered" medium. In this article, the problem of sum-rate maximization via BD-RIS is examined, with a focus on feasibility, namely low-complexity physical implementation, by enforcing reciprocity in the BD-RIS design in a manner that adheres to the geometry of the manifold of symmetric matrices. To that end, the sum-rate objective is transformed into a quadratic function via fractional programming (FP), augmented via the also quadratic reciprocity constraint in the form of a regularization term, while the unitary constraint is dealt with via a manifold optimization framework. Simulation results demonstrate the effectiveness of the proposed method in outperforming current state-of-the-art (SotA) approaches in terms of sum-rate maximization.

This paper investigates how near-field beamfocusing can be achieved using a modular linear array (MLA), composed of multiple widely spaced uniform linear arrays (ULAs). The MLA architecture extends the aperture length of a standard ULA without adding additional antennas, thereby enabling near-field beamfocusing without increasing processing complexity. Unlike conventional far-field beamforming, near-field beamfocusing enables simultaneous data transmission to multiple users at different distances in the same angular interval, offering significant multiplexing gains. We present a detailed mathematical analysis of the beamwidth and beamdepth achievable with the MLA and show that by appropriately selecting the number of antennas in each constituent ULA, ideal near-field beamfocusing can be realized. In addition, we propose a computationally efficient localization method that fuses estimates from each ULA, enabling efficient parametric channel estimation. Simulation results confirm the accuracy of the analytical expressions and that MLAs achieve near-field beamfocusing with a limited number of antennas, making them a promising solution for next-generation wireless systems.

In the design of a metasurface-assisted system for indoor environments, it is essential to take into account not only the performance gains and coverage extension provided by the metasurface but also the operating costs brought by its reconfigurability, such as powering and cabling. These costs can present challenges, particularly in indoor dense spaces (IDSs). A self-sustainable reconfigurable intelligent surface (ssRIS), which retains reconfigurability unlike a static metasurface (SMS), achieves a lower operating cost than a reconfigurable intelligent surface (RIS) by being self-sustainable through power harvesting. In this paper, in order to find a better trade-off between metasurface gain, coverage, and operating cost, the design and performance of an ssRIS-assisted indoor mmWave communication system are investigated. We simplify the use of the ssRIS by considering a preset-based element splitting scheme for maintaining self-sustainability and the formation of coverage groups by associating ssRISs with the closest user equipments (UEs). We propose a two-stage iterative algorithm to maximize the minimum data rate by jointly deciding the association between the UEs and the ssRISs, the phase shifts of the ssRISs, and allocating time resources for each UE. The non-convex optimization problem is tackled using the feasible point pursuit successive convex approximation method. To understand the best scenario for using ssRIS, the resulting performance is compared with that achieved with RIS and SMS. Our numerical results indicate that ssRISs are best utilized in a small environment where self-sustainability is easier to achieve when the budget for operating costs is tight.

We address the modeling and optimal beamforming (BF) design for multiple-input multiple-output (MIMO) continuous aperture array (CAPA) systems operating over doubly-dispersive (DD) channels. First, a comprehensive DD continuous MIMO (DDC MIMO) channel model that incorporates CAPAs at both the transmitter (TX) and receiver (RX) is derived, which is used to obtain explicit input-output (I/O) relations for various waveforms well suited to integrated sensing and communications (ISAC) and robust to DD channels, namely orthogonal frequency division multiplexing (OFDM), orthogonal time frequency space (OTFS), and affine frequency division multiplexing (AFDM). Then, functional optimization problems are formulated for the design of TX and RX BF matrices that maximize received power, in which novel low-complexity, closed-form solutions are obtained via the calculus of variations (CoV) method, yielding expressions closely related to the classical matched filter commonly used in conventional MIMO systems. Simulation results confirm that the proposed TX/RX BF designs with CAPAs provide significant performance and computational complexity gains over conventional MIMO systems in DD channels.

We propose a novel resource-efficient over-the-air (OTA) computation framework to address the huge fronthaul computational and control overhead requirements in cell-free massive multiple-input multiple-output (MIMO) networks. We show that the global sufficient statistics to decode the data symbols can be computed OTA using the locally available information at the access points (APs). We provide the essential signal processing aspects at the APs and the central processing unit (CPU) to facilitate the OTA computation of sufficient statistics. The proposed framework scales effectively with an increase in the number of APs. We also make a comprehensive study of the benefits of an OTA framework compared to a conventional digital fronthaul in terms of the overhead associated in transferring the sufficient statistics from the APs to the CPU. To evaluate the performance of the OTA framework, we give closed-form expressions for the mean-square error (MSE) of the estimators of sufficient statistics and the overall data estimator. Furthermore, we assess the symbol error rate (SER) and bit error rate (BER) of the user equipment (UEs) data to demonstrate the efficacy of our method, and benchmark them against the state-of-the-art wired fronthaul networks.

The growing demand for efficient delivery of common content to multiple user equipments (UEs) has motivated significant research in physical-layer multicasting. By exploiting the beamforming capabilities of massive MIMO, multicasting provides a spectrum-efficient solution that avoids unnecessary intra-group interference. A key challenge, however, is solving the max-min fair (MMF) and quality-of-service (QoS) multicast beamforming optimization problems, which are NP-hard due to the non-convex structure and the requirement for rank-1 solutions. Traditional approaches based on semidefinite relaxation (SDR) followed by randomization exhibit poor scalability with system size, while state-of-the-art successive convex approximation (SCA) methods only guarantee convergence to stationary points. In this paper, we propose an alternating direction method of multipliers (ADMM)-based framework for MMF and QoS multicast beamforming in cell-free massive MIMO networks. The algorithm leverages SDR but incorporates a novel iterative elimination strategy within the ADMM updates to efficiently obtain near-global optimal rank-1 beamforming solutions with reduced computational complexity compared to standard SDP solvers and randomization methods. Numerical evaluations demonstrate that the proposed ADMM-based procedure not only achieves superior spectral efficiency but also scales favorably with the number of antennas and UEs compared to state-of-the-art SCA-based algorithms, making it a practical tool for next-generation multicast systems.

In many wireless communication applications, it is desirable to transmit the same data to multiple user equipments (UEs). Physical layer multicasting presents an efficient transmission topology to exploit the beamforming capabilities at the transmitting nodes and broadcast nature of the wireless channel to satisfy the demand for the same content from several UEs. An advantage of multicasting is to avoid unnecessary co-channel interference between UEs requesting the same data. The difficulty is to find the suitable beamforming configuration that guarantees an acceptable minimum data rate, among the receiving UE group, to the multicast transmission. This paper addresses the max-min fair multigroup multicast optimization problem and proposes a novel iterative elimination procedure coupled with semidefinite relaxation (SDR) to find the near-optimal rank-1 beamforming vectors in a cell-free massive MIMO (multiple-input multiple-output) network. The proposed optimization procedure significantly improves computational complexity and spectral efficiency compared to common methods that use SDR followed by some randomization procedure and the state-of-the-art difference-of-convex approximation algorithm. The importance of the proposed procedure is that it is applicable to any SDR problem where a low-rank solution is desirable. Further, we propose a low-complexity algorithm that achieves 87% of the optimal rank-1 solution at orders-of-magnitude lower computational time.

Terahertz (THz) communication is envisioned as a key technology for 6G and beyond wireless systems owing to its multi-GHz bandwidth. To maintain the same aperture area and the same link budget as the lower frequencies, ultra-massive multi-input and multi-output (UM-MIMO) with hybrid beamforming is promising. Nevertheless, the hardware imperfections particularly at THz frequencies, can degrade spectral efficiency and lead to a high symbol error rate (SER), which is often overlooked yet imperative to address in practical THz communication systems. In this paper, the hybrid beamforming is investigated for THz UM-MIMO systems accounting for comprehensive hardware imperfections, including DAC and ADC quantization errors, in-phase and quadrature imbalance (IQ imbalance), phase noise, amplitude and phase error of imperfect phase shifters and power amplifier (PA) nonlinearity. Then, a two-stage hardware imperfection compensation algorithm is proposed. In the first stage, a deep neural network (DNN) based unified hardware imperfection model is developed to represent the combined hardware imperfections. Furthermore, to balance the performance and model complexity, a tailored network slimming framework is proposed using three slimming methods including pruning, parameter sharing, and power-aware scheme to slim the network in the first stage. In the second stage, the digital precoder in the transmitter (Tx) or the combiner in the receiver (Rx) is designed using neural network (NN) to effectively compensate for these imperfections. Numerical results show that the Tx compensation can perform better than the Rx compensation. Additionally, using the combined slimming methods can reduce parameters by 97.2% and running time by 39.2% while maintaining nearly the same performance in both uncoded and coded systems.

The extremely short wavelength of terahertz (THz) communications leads to an extended radiative near-field region, in which some canonical far-field assumptions fail. Existing near-field boundary formulations (Fraunhofer distance) for uniform linear/planar array (ULA/UPA) configurations assume ideal alignment between transceivers, overlooking practical misalignments caused by mobility or mechanical imperfections. This paper addresses this critical gap by analyzing the impact of spatial misalignment on near-field distance calculations in THz systems. We derive exact analytical expressions and simplified approximations for the near-field boundary in both ULA–ULA and UPA–UPA configurations under arbitrary misalignment off-sets. Through numerical simulations, we validate our theoretical models and quantify how misalignment reshapes the near-field region. These findings provide essential guidelines for optimizing THz system deployment in realistic scenarios.

This study seeks to utilize large language models (LLMs) to forecast the moving ports of fluid antenna (FA). By repositioning the antenna to the locations identified by our proposed model, we intend to address the mobility challenges faced by user equipment (UE). To the best of our knowledge, this paper introduces, for the first time, the application of LLMs in the prediction of FA ports, presenting a novel model termed Port-LLM. The architecture of our model is based on the pre-trained GPT-2 framework. We designed specialized data preprocessing, input embedding, and output projection modules to effectively bridge the disparities between the wireless communication data and the data format utilized by the pre-trained LLM. Simulation results demonstrate that our model exhibits superior predictive performance under different numbers of base station (BS) antennas and varying UE speeds, indicating strong generalization and robustness ability. Furthermore, the spectral efficiency (SE) attained by our model surpasses that achieved by traditional methods in both medium and high-speed mobile environments.

Reconfigurable intelligent surfaces (RISs) can greatly improve the signal quality of future communication systems by reflecting transmitted signals toward the receiver. However, even when the base station (BS) has perfect channel knowledge and can compute the optimal RIS phase-shift configuration, implementing this configuration requires feedback signaling over a control channel from the BS to the RIS. This feedback must be kept minimal, as it is transmitted wirelessly every time the channel changes. In this paper, we examine how the feedback load, measured in bits, affects the performance of an RIS-aided system. Specifically, we investigate the trade-offs between codebook-based and element-wise feedback schemes, and how these influence the signal-to-noise ratio (SNR). We propose a novel quantization codebook tailored for line-of-sight (LoS) that guarantees a minimal SNR loss using a number of feedback bits that scale logarithmically with the number of RIS elements. We demonstrate the codebook's usefulness over Rician fading channels and how to extend it to handle a non-zero static path. Numerical simulations and analytical analysis are performed to quantify the performance degradation that results from a reduced feedback load, shedding light on how efficiently RIS configurations can be fed back in practical systems.

In massive MIMO systems, fully digital precoding offers high performance but has significant implementation complexity and energy consumption, particularly at millimeter frequencies and beyond. Hybrid analog-digital architectures provide a practical alternative by reducing the number of radio frequency (RF) chains while retaining performance in spatially sparse multipath scenarios. However, most hybrid precoder designs assume ideal, infinite-resolution analog phase shifters, which are impractical in real-world scenarios. Another practical constraint is the limited fronthaul capacity between the baseband processor and array, implying that each entry of the digital precoder must be picked from a finite set of quantization labels. To minimize the sum rate degradation caused by quantized analog and digital precoders, we propose novel designs inspired by the sphere decoding (SD) algorithm. We demonstrate numerically that our proposed designs outperform traditional methods, ensuring minimal sum rate loss in hybrid precoding systems with lowresolution phase shifters and limited fronthaul capacity.

Integrated sensing and communication (ISAC) has already established itself as a promising solution to the spectrum scarcity problem, even more so when paired with a reconfigurable intelligent surface (RIS), as RISs can shape the propagation environment by adjusting their phase-shift coefficients. Albeit the potential performance gain, a RIS is also a potential security threat to the system. In this paper, we explore both the positive and negative sides of having a RIS in a multi-user multiple-input multiple-output (MIMO) ISAC network. We first develop an alternating optimization algorithm, obtaining the active and passive beamforming vectors that maximize the sensing signal-to-noise ratio (SNR) under minimum signal-to-interference-plus-noise ratio (SINR) constraints for the communication users and finite power budget. We also investigate the destructive potential of the RIS by devising a RIS phase-shift optimization algorithm that minimizes the sensing SNR while preserving the same minimum communication SINR previously guaranteed by the system. We further investigate the impact of the RIS's individual element failures on the system performance. The simulation results show that the RIS performance-boosting potential is as good as its destructive one and that both of our optimization strategies are hindered by the investigated impairments.

Sensing emerges as a critical challenge in 6G networks, which require simultaneous communication and target sensing capabilities. State-of-the-art super-resolution techniques for the direction of arrival (DoA) estimation encounter significant performance limitations when the number of targets exceeds antenna array dimensions. This paper introduces a novel sensing parameter estimation algorithm for orthogonal frequencydivision multiplexing (OFDM) multiple-input multiple-output (MIMO) radar systems. The proposed approach implements a strategic two-stage methodology: first, discriminating targets through delay and Doppler domain filtering to reduce the number of effective targets for super-resolution DoA estimation, and second, introducing a fusion technique to mitigate sidelobe interferences. The algorithm enables robust DoA estimation, particularly in high-density target environments with limitedsize antenna arrays. Numerical simulations validate the superior performance of the proposed method compared to conventional DoA estimation approaches.

Extremely large-scale antenna arrays (ELAAs) enable high spatial resolution and multiplexing, especially for user equipments (UEs) in the radiative near-field. To reduce hardware cost, modular ELAA architectures with distributed baseband units (BBUs) are gaining traction. This paper addresses near-field line-of-sight (LOS) channel estimation under low noise amplifier (LNA)-induced hardware impairments in such modular systems. We propose computationally efficient estimators that exploit the array geometry and constant-modulus structure of near-field LOS channels, including a novel two-dimensional (2D) discrete Fourier transform (DFT) masking technique that improves estimation accuracy and significantly reduces fronthaul signaling. Numerical results show that the proposed methods significantly outperform the conventional least squares (LS) method.

This paper introduces a sensing management method for integrated sensing and communications (ISAC) in cell-free massive multiple-input multiple-output (MIMO) systems. Conventional communication systems employ channel estimation procedures that impose significant overhead during data transmission, consuming resources that could otherwise be utilized for data. To address this challenge, we propose a state-based approach that leverages sensing capabilities to track the user when there is no communication request. Upon receiving a communication request, predictive beamforming is employed based on the tracked user position, thereby reducing the need for channel estimation. Our framework incorporates an extended Kalman filter (EKF) based tracking algorithm with adaptive sensing management to perform sensing operations only when necessary to maintain high tracking accuracy. The simulation results demonstrate that our proposed sensing management approach provides uniform downlink communication rates that are higher than with existing methods by achieving overhead-free predictive beamforming.

This paper considers a millimeter-wave wideband point-to-point MIMO system with fully digital transceivers at the base station and the user equipment (UE), focusing on mobile UE scenarios. A main challenge when building a digital UE combining is the large volume of baseband samples to handle. To mitigate computational and hardware complexity, we propose a novel two-stage digital combining scheme at the UE. The first stage reduces the Nrreceived signals to Ncstreams before baseband processing, leveraging channel geometry for dimension reduction and updating at the beam coherence time, which is longer than the channel coherence time of the small-scale fading. By contrast, the second-stage combining is updated per fading realization. We develop a pilot-based channel estimation framework for this hardware setup based on maximum likelihood estimation in both uplink and downlink. Digital precoding and combining designs are proposed, and a spectral efficiency expression that incorporates imperfect channel knowledge is derived. The numerical results demonstrate that the proposed approach outperforms hybrid beamforming, showcasing the attractiveness of using two-stage fully digital transceivers in future systems.

In this paper, we introduce a novel amplitude and phase reciprocity calibration protocol for distributed multi-antenna systems to enable coherent transmission from multiple access points (APs). The proposed scheme significantly enhances reciprocity calibration by resolving both phase and amplitude mismatches between APs, achieving near-optimal synchronization performance at practical signal-to-noise ratio (SNR) regimes. The protocol provides a closed-form solution for reciprocity calibration performed locally at each AP, maintaining low computational complexity while ensuring scalability and high-fidelity coherent transmission in large and dense distributed networks. The numerical results validate the robustness of the proposed technique, demonstrating accurate calibration and efficient transmission across various system configurations, including variations in the number of antennas and SNR values.

In the context of the joint radar and communications (JRC) framework, reconfigurable intelligent surfaces (RISs) emerged as a promising technology for their ability to shape the propagation environment by adjusting their phase-shift coefficients. However, achieving perfect synchronization and effective collaboration between access points (APs) and RISs is crucial to successful operation. This paper investigates the performance of a bistatic JRC network operating in the millimeter-wave (mmWave) frequency band, where the receiving AP is equipped with an RIS-integrated array. This system simultaneously serves multiple UEs while estimating the position of a target with limited prior knowledge of its position. To achieve this, we optimize both the power allocation of the transmitted waveform and the RIS phase-shift matrix to minimize the position error bound (PEB) of the target. At the same time, we ensure that the UEs achieve an acceptable level of spectral efficiency. The numerical results show that an RIS-integrated array, even with a small number of receiving antennas, can achieve high localization accuracy. Additionally, optimized phase-shifts significantly improve the localization accuracy in comparison to a random phase-shift configuration.

Cell-free massive MIMO (multiple-input multiple-output) is a promising infrastructure for 6G and beyond, offering significantly higher spectral efficiency than traditional cellular systems. In cell-free massive MIMO, a large number of low-cost access points (APs) are densely deployed, making hardware impairments inevitable due to cost-effective radio hardware. While the impact of quantization and other impairments has been extensively studied for narrowband channels, their effects in wideband scenarios remain relatively unexamined. This paper presents the first analysis of how low-resolution analog-to-digital converters (ADCs) affect the uplink performance of a cell-free massive MIMO system using an orthogonal frequency division multiplexing (OFDM) waveform. Both quantization-impaired channel estimation and data detection are considered, and the quantization-unaware and quantization-aware linear receivers are developed. To further mitigate the adverse effects of quantization at the bit level, an alternating direction method of multipliers (ADMM)-based receiver is proposed. Simulation results demonstrate that the ADMM-based receiver outperforms conventional linear receivers by orders of magnitude.

Massive multiple-input multiple-output (mMIMO) has been the core of 5G due to its ability to improve spectral efficiency and spatial multiplexing significantly; however, cell-edge users still experience performance degradation due to intercell interference and uneven signal distribution. While cell-free mMIMO (cfmMIMO) addresses this issue by providing uniform coverage through distributed antennas, it requires significantly more deployment cost due to the fronthaul and tight synchronization requirements. Alternatively, repeater-assisted massive MIMO (RA-MIMO) has recently been proposed to extend the coverage of cellular mMIMO by densely deploying low-cost single-antenna repeaters capable of amplifying and forwarding signals. In this work, we investigate amplification control for the repeaters for two different goals: (i) providing a fair performance among users, and (ii) reducing the extra energy consumption by the deployed repeaters. We propose a max-min amplification control algorithm using the convex-concave procedure for fairness and a joint sleep mode and amplification control algorithm for energy efficiency, comparing long- and short-term strategies. Numerical results show that RA-MIMO, with maximum amplification, improves signal-to-interference-plus-noise ratio (SINR) by over 20 dB compared to mMIMO and performs within 1 dB of cfmMIMO when deploying the same number of repeaters as access points in cfmMIMO. Additionally, our majority-rule-based long-term sleep mechanism reduces repeater power consumption by 70 % while maintaining less than 1 % spectral efficiency outage.

There is a demand for the same data content from several user equipments (UEs) in many wireless communication applications. Physical-layer multicasting combines the beamforming capability of massive MIMO (multiple-input multiple-output) and the broadcast nature of the wireless channel to efficiently deliver the same data to a group of UEs using a single transmission. This paper tackles the max-min fair (MMF) multicast beamforming optimization, which is an NP-hard problem. We develop an efficient semidefinite program-alternating direction method of multipliers (SDP-ADMM) algorithm to find the near-global optimal rank-1 solution to the MMF multicast problem in a massive MIMO system. Numerical results show that the proposed SDP-ADMM algorithm exhibits similar spectral efficiency performance to state-of-the-art algorithms running on standard SDP solvers at a vastly reduced computational complexity. We highlight that the proposed ADMM elimination procedure can be employed as an effective low-complexity rank reduction method for other problems utilizing semidefinite relaxation.

Neural networks (NNs) are pivotal in enhancing data processing tasks such as classification, generation, and restoration. A crucial consideration in these applications is the signal-to-noise ratio (SNR), which serves as a measure of the quality of the data. In this paper, we hypothesize that optimizing NNs in some tasks can be more effective when all samples in the dataset are clustered based on quantized SNR levels regarding the statistical similarity between training/test dataset. Hence, we introduce two novel techniques, i.e., 1) a linear algebraic method with a single-shot data sample and 2) an NN-based method with few-shot data samples, for estimating the SNR of a sparse signal. The proposed techniques are based on the mathematical fact that the dominant singular values contain the information of a signal space when signals are Hankelized in matrix form. Both algorithms achieve over 93% clustering accuracy, and almost 100% accuracy in high SNR scenarios and increased signal length. Furthermore, we provide an example of signal denoising as practical validation of the benefits of these clustering results for optimizing NN in a task. The proposed approaches show a superior denoising performance while requiring an extremely small training dataset compared to conventional methods, which can be interpreted as an improvement in the learnability of the NN.

This paper considers a multi-user multiple-input multiple-output (MU-MIMO) system where the downlink communication between a base station (BS) and multiple user equipments (UEs) is aided by a reconfigurable intelligent surface (RIS). We study the sum rate maximization problem with the objective of finding the optimal precoding vectors and RIS configuration. Due to fronthaul limitation, each entry of the precoding vectors must be picked from a finite set of quantization labels. Furthermore, two scenarios for the RIS are investigated, one with continuous infinite-resolution reflection coefficients and another with discrete finite-resolution reflection coefficients. A novel framework is developed which, in contrast to the common literature that only offers sub-optimal solutions for optimization of discrete variables, is able to find the optimal solution to problems involving discrete constraints. Based on the classical weighted minimum mean square error (WMMSE), we transform the original problem into an equivalent weighted sum mean square error (MSE) minimization problem and solve it iteratively. We compute the optimal precoding vectors via an efficient algorithm inspired by sphere decoding (SD). For optimizing the discrete RIS configuration, two solutions based on the SD algorithm are developed: An optimal SD-based algorithm and a low-complexity heuristic method that can efficiently obtain RIS configuration without much loss in optimality. The effectiveness of the presented algorithms is corroborated via numerical simulations where it is shown that the proposed designs are remarkably superior to the commonly used benchmarks.

This article provides a comprehensive analysis aimed at addressing the impact of power amplifier nonlinearities on massive multiple-input multiple-output (MIMO) communication systems. Specifically, we derive a closed-form expression for the received distortion power, a critical aspect that has not been explored in literature. Our derived expression takes into account the combined influence of spatial diversity and frequency-selectivity on received distortion, with a particular emphasis on the slowly varying parameters, primarily the locations of users and delay spread. In the context of massive MIMO systems, characterized by an exceptionally large number of antennas, our work highlights the crucial role of distortion correlation among antennas. Neglecting distortion correlation can result in significant inaccuracies in system evaluation and algorithmic design. Utilizing the analytical framework we have developed, we formulate a power allocation problem that explicitly exploits the distortion correlation. The proposed solution outperforms methods that neglect the spatial distortion correlation, particularly in terms of spectral efficiency (SE). This superior performance is crucial in optimizing the overall system performance and ensuring desirable power allocation decisions.

The objective of this study is to address the mobility challenges faced by user equipment (UE) through the implementation of fluid antenna (FA) on the UE side. This approach aims to maintain the time-varying channel in a relatively stable state by strategically relocating the FA to an appropriate port. To the best of our knowledge, this paper introduces, for the first time, the application of large language models (LLMs) in the prediction of FA ports, presenting a novel model termed Port-LLM. Our proposed method for predicting the moving port of the FA is a two-step prediction method. To enhance the learning efficacy of our proposed Port-LLM model, we integrate low-rank adaptation (LoRA) fine-tuning technology. Additionally, to further exploit the natural language processing capabilities of pre-trained LLMs, we propose a framework named Prompt-Port-LLM, which is constructed upon the Port-LLM architecture and incorporates prompt fine-tuning techniques along with a specialized prompt encoder module. The simulation results show that our proposed models all exhibit strong generalization ability and robustness under different numbers of base station antennas and medium-to-high mobility speeds of UE. In comparison to existing methods, the performance of the port predicted by our models demonstrates superior efficacy. Moreover, both of our proposed models achieve millimeter-level inference speed.

Accurate estimation of the cascaded channel from a user equipment (UE) to a base station (BS) via each reconfigurable intelligent surface (RIS) element is critical to realizing the full potential of the RIS’s ability to control the overall channel. The number of parameters to be estimated is equal to the number of RIS elements, requiring an equal number of pilots unless an underlying structure can be identified. In this paper, we show how the spatial correlation inherent in the different RIS channels provides this desired structure. We first optimize the RIS phase-shift pattern using a much-reduced pilot length (determined by the rank of the spatial correlation matrices) to minimize the mean square error (MSE) in the channel estimation under electromagnetic interference. In addition to considering the linear minimum MSE (LMMSE) channel estimator, we propose a novel channel estimator that requires only knowledge of the array geometry while not requiring any user-specific statistical information. We call this the reduced-subspace least squares (RS-LS) estimator and optimize the RIS phase-shift pattern for it. This novel estimator significantly outperforms the conventional LS estimator. For both the LMMSE and RS-LS estimators, the proposed optimized RIS configurations result in significant channel estimation improvements over the benchmarks.

Extremely large aperture arrays (ELAAs) and reconfigurable intelligent surfaces (RISs) are candidate enablers to realize connectivity goals for the sixth-generation (6G) wireless networks. For instance, ELAAs can provide orders-of-magnitude higher area throughput compared to what massive multiple-input multiple-output (MIMO) can deliver through spatial multiplexing, while RISs can improve the propagation conditions over wireless channels but a passively reflecting RIS must be large to be effective. Active RIS with amplifiers can deal with this issue. In this paper, we analyze the distortion generated by nonlinear amplifiers in both ELAAs and active RIS. We derive analytical expressions for the angular directions and depth of nonlinear distortion in both near-field and far-field channels. These insights are then used in a distortion-aware scheduling scheme that predicts the beamforming directions of the distortion and strategically allocates users in frequency to minimize its impact. Numerical results validate our theoretical analysis and compare distortion-aware and distortion-unaware scheduling methods, highlighting the benefits of accounting for nonlinearities. We conclude that nonlinearities can both create in-band and out-of-band distortion that is beamformed in entirely new directions and distances from the transmitter.

The use of a reconfigurable intelligent surface (RIS) for aiding user-specific transmission has been widely explored. However, little attention has been devoted to utilizing RIS for assisting cell-specific transmission, where the RIS needs to reflect signals in a broad angular range. Furthermore, although modern communication systems operate in two polarizations, the majority of the works on RIS consider a uni-polarized surface, only reflecting the signals in one polarization. To fill these gaps, we study a downlink broadcasting scenario where a base station (BS) sends a cell-specific signal to all the users residing at unknown locations with the assistance of a dual-polarized RIS. We utilize the duality between the auto-correlation function and power spectrum in the space/spatial-frequency domain to design configurations for broad-beam reflection. We first consider a free-space line-of-sight BS-RIS channel and show that the RIS configuration matrices must form a Golay complementary array pair for broad-beam radiation. We also present how to form Golay complementary array pairs based on known Golay complementary sequence pairs. We then consider an arbitrary BS-RIS channel and propose an algorithm based on stochastic optimization to find RIS configurations that produce a practically broad beam by relaxing the requirement on uniform broadness. Numerical simulations are finally conducted to corroborate the analyses and evaluate the performance.

Millimeter-wave network deployment is an essential and ongoing problem due to the limited coverage and expensive network infrastructure. In this work, we solve a joint network deployment and resource allocation optimization problem for a mmWave cell-free massive MIMO network considering indoor environments. The objective is to minimize the number of deployed access points (APs) for a given environment, bandwidth, AP cooperation, and precoding scheme while guaranteeing the rate requirements of the user equipments (UEs). Considering coherent joint transmission (C-JT) and non-coherent joint transmission (NC-JT), we solve the problem of AP placement, UE-AP association, and power allocation among the UEs and resource blocks jointly. For numerical analysis, we model a mid-sized airplane cabin in ray-tracing as an exemplary case for IDS. Results demonstrate that a minimum data rate of 1Gbps can be guaranteed with less than 10 APs with C-JT. From a holistic network design perspective, we analyze the trade-off between the required fronthaul capacity and the processing capacity per AP, under different network functional split options. We observe an above 600Gbps fronthaul rate requirement, once all network operations are centralized, which can be reduced to 200Gbps under physical layer functional splits.

A large-scale MIMO (multiple-input multiple-output) system offers significant advantages in wireless communication, including potential spatial multiplexing and beamforming capabilities. However, channel estimation becomes challenging with multiple antennas at both the transmitter and receiver ends. The minimum mean-squared error (MMSE) estimator, for instance, requires a spatial correlation matrix whose dimensions scale with the square of the product of the number of antennas on the transmitter and receiver sides. This scaling presents a substantial challenge, particularly as antenna counts increase in line with current technological trends. Traditional MIMO literature offers alternative channel estimators that mitigate the need to fully acquire the spatial correlation matrix. In this paper, we revisit point-to-point MIMO channel estimation and introduce a reduced-subspace least squares (RS-LS) channel estimator designed to eliminate physically impossible channel dimensions inherent in uniform planar arrays. Additionally, we propose a cluster-aware RS-LS estimator that leverages both reduced and cluster-specific subspace properties, significantly enhancing performance over the conventional RS-LS approach. Notably, both proposed methods obviate the need for fully/partial knowledge of the spatial correlation matrix.

The reconfigurable intelligent surface (RIS) technology emerges as a highly useful component of the rapidly evolving integrated sensing and communications paradigm, primarily owing to its remarkable signal-to-noise ratio enhancement capabilities. In this paper, our focus is on mono-static target detection while considering the communication requirement of a user equipment. Both sensing and communication benefit from the presence of an RIS, which makes the channels richer and stronger. Diverging from prior research, we comprehensively examine three target echo paths: the direct (static) channel path, the path via the RIS, and a combination of these, each characterized by distinct radar cross sections (RCSs). We take both the line-of-sight (LOS) and the non-line-of-sight (NLOS) paths into account under a clutter for which the distribution is not known, but the low-rank subspace it resides. We derive the generalized likelihood ratio test (GLRT) detector and introduce a novel approach for jointly optimizing the configuration of RIS phase-shifts and precoding. Our simulation results underscore the paramount importance of this combined design in terms of enhancing detection probability. Moreover, it becomes evident that the derived clutter-aware target detection significantly enhances detection performance, especially when the clutter is strong.

Holographic multiple-input multiple-output (MIMO) systems represent a spatially constrained MIMO architecture with a massive number of antennas with small antenna spacing as a close approximation of a spatially continuous electromagnetic aperture. Accurate channel modeling is essential for realizing the full potential of this technology. In this paper, we investigate the impact of mutual coupling and spatial channel correlation on the estimation precision in holographic MIMO systems, as well as the importance of knowing their characteristics. We demonstrate that neglecting mutual coupling can lead to significant performance degradation for the minimum mean squared error estimator, emphasizing its critical consideration when designing estimation algorithms. Conversely, the least-squares estimator is resilient to mutual coupling but only yields good performance in high signal-to-noise ratio regimes. Our findings provide insights into how to design efficient estimation algorithms in holographic MIMO systems, aiding its practical implementation.

A reconfigurable intelligent surface (RIS) alters the reflection of incoming signals based on the phase-shift configuration assigned to its elements. This feature can be used to improve the signal strength for user equipments (UEs), expand coverage, and enhance spectral efficiency in wideband communication systems. Having accurate channel state information (CSI) is indispensable to realize the full potential of RIS-aided wideband systems. Unfortunately, CSI is challenging to acquire due to the passive nature of the RIS elements, which cannot perform transmit/receive signal processing. Recently, a parametric maximum likelihood (ML) channel estimator has been developed and demonstrated excellent estimation accuracy. However, this estimator is designed for narrowband systems with no non- line-of-sight (NLOS) paths. In this paper, we develop a novel parametric ML channel estimator for RIS-assisted wideband systems, which can handle line-of-sight (LOS) paths in the base station (BS)-RIS and RIS-UE links as well as NLOS paths between the UE, BS, and RIS. We leverage the reduced subspace representation induced by the array geometry to suppress noise in unused dimensions, enabling accurate estimation of the NLOS paths. Our proposed algorithm demonstrates superior estimation performance for the BS-UE and RIS-UE channels, outperforming the existing ML channel estimator.

In this paper, we consider a single-anchor localization system assisted by a reconfigurable intelligent surface (RIS), where the objective is to localize multiple user equipments (UEs) placed in the radiative near-field region of the RIS by estimating their azimuth angle-of-arrival (AoA), elevation AoA, and distance to the surface. The three-dimensional (3D) locations can be accurately estimated via the conventional MUltiple SIgnal Classification (MUSIC) algorithm, albeit at the expense of tremendous complexity due to the 3D grid search. In this paper, capitalizing on the symmetric structure of the RIS, we propose a novel modified MUSIC algorithm that can efficiently decouple the AoA and distance estimation problems and drastically reduce the complexity compared to the standard 3D MUSIC algorithm. Additionally, we introduce a spatial smoothing method by partitioning the RIS into overlapping sub-RISs to address the rank-deficiency issue in the signal covariance matrix. We corroborate the effectiveness of the proposed algorithm via numerical simulations and show that it can achieve the same performance as 3D MUSIC but with much lower complexity.

Physical layer multicasting is an efficient transmission technique that exploits the beamforming potential at the transmitting nodes and the broadcast nature of the wireless channel, together with the demand for the same content from several UEs. This paper addresses the max-min fair multigroup multicast beamforming optimization, which is an NP-hard problem. We propose a novel iterative elimination procedure coupled with semidefinite relaxation (SDR) to find the near-global optimum rank-1 beamforming vectors in a cell-free massive MIMO (multiple-input multiple-output) network setup. The proposed optimization procedure shows significant improvements in computational complexity and spectral efficiency performance compared to the SDR followed by the commonly used randomization procedure and the state-of-the-art difference-of-convex approximation algorithm. The significance of the proposed procedure is that it can be utilized as a rank reduction method for any problem in conjunction with SDR.

We propose a novel resource efficient analog over-the-air (OTA) computation framework to address the demanding requirements of the uplink (UL) fronthaul between the access points (APs) and the central processing unit (CPU) in cell-free massive multiple-input multiple-output (MIMO) systems. We discuss the drawbacks of the wired and wireless fronthaul solutions, and show that our proposed mechanism is efficient and scalable as the number of APs increases. We present the transmit precoding and two-phase power assignment strategies at the APs to coherently combine the signals OTA in a spectrally efficient manner. We derive the statistics of the APs' locally available signals which enable us to to obtain the analytical expressions for the Bayesian and classical estimators of the OTA combined signals. We empirically evaluate the normalized mean square error (NMSE), symbol error rate (SER), and the coded bit error rate (BER) of our developed solution and benchmark against the state-of-the-art wired fronthaul based system.

In this paper, we examine the energy efficiency (EE) of a base station (BS) with multiple antennas. We use a state-of-the-art power consumption model, taking into account the passive and active parts of the transceiver circuitry, including the effects of radiated power, signal processing, and passive consumption. The paper treats the transmit power, bandwidth, and number of antennas as the optimization variables. We provide novel closed-form solutions for the optimal ratios of power per unit bandwidth and power per transmit antenna. We present a novel algorithm that jointly optimizes these variables to achieve maximum EE, while fulfilling constraints on the variable ranges. We also discover a new relationship between the radiated power and the passive transceiver power consumption. We provide analytical insight into whether using maximum power or bandwidth is optimal and how many antennas a BS should utilize.

In this paper, we consider a downlink multi-user multiple-input multiple-output (MU-MIMO) communication assisted by a reconfigurable intelligent surface (RIS) and study the precoding and RIS configuration design under practical system constraints. These constraints include the limited-capacity fronthaul at the transmitter side and the finite resolution of RIS elements. We investigate the sum mean squared error (MSE) minimization problem and propose an algorithm based on the block coordinate descent method to optimize the precoding, RIS configuration, and receiver gains. We compute the precoding vectors and RIS configuration using the Schnorr-Euchner sphere decoding (SESD) method which delivers the optimal MSE-minimizing solution. We numerically evaluate the performance of the proposed SESD-based methods and corroborate their effectiveness in improving the system performance.

Extremely large aperture arrays can enable unprecedented spatial multiplexing in beyond 5G systems due to their extremely narrow beamfocusing capabilities. However, acquiring the spatial correlation matrix to enable efficient channel estimation is a complex task due to the vast number of antenna dimensions. Recently, a new estimation method called the “reduced-subspace least squares (RS-LS) estimator” has been proposed for densely packed arrays. This method relies solely on the geometry of the array to limit the estimation resources. In this paper, we address a gap in the existing literature by deriving the average spectral efficiency for a certain distribution of user equipments (UEs) and a lower bound on it when using the RS-LS estimator. This bound is determined by the channel gain and the statistics of the normalized spatial correlation matrices of potential UEs but, importantly, does not require knowledge of a specific UE's spatial correlation matrix. We establish that there exists a pilot length that maximizes this expression. Additionally, we derive an approximate expression for the optimal pilot length under low signal-to-noise ratio (SNR) conditions. Simulation results validate the tightness of the derived lower bound and the effectiveness of using the optimized pilot length.

We consider a cell-free massive MIMO system with multiple antennas on the users and access points. In previous works, the downlink spectral efficiency (SE) has been evaluated using the hardening bound that requires no downlink pilots. This approach works well when having single-antenna users. In this paper, we show that much higher SEs can be achieved if downlink pilots are sent since the effective channel matrix does not harden when having multi-antenna users. We propose a pilot-based downlink estimation scheme and derive a new SE expression that utilizes zero-forcing combining. We show numerically how the number of users and user antennas affects the SE.

Digital phased arrays have often been disregarded for millimeter-wave communications since the analog-to-digital converters (ADCs) are power-hungry. In this paper, we provide a different perspective on this matter by demonstrating analytically and numerically how the ADC resolution can be reduced when using digital phased arrays. We perform a theoretical analysis of the quantization noise characteristics for an OFDM signal received and processed by a digital phased array, using Gaussian approximation of the OFDM signal. In particular, we quantify the quantization noise suppression factor analytically and numerically. This factor describes how much the coherent combining reduces the quantization noise as a function of the number of antennas, which allows for reducing the ADC bit resolution. For instance in a 8–16 antenna digital phased array the ADC resolution can be reduced with 1–2 bits compared to the ADC required for an analog phased array.

In this paper, we investigate how metasurfaces can be deployed to deliver high data rates in a millimeter-wave (mmWave) indoor dense space with many blocking objects. These surfaces can either be static metasurfaces (SMSs) that reflect with fixed phase-shifts or reconfigurable intelligent surfaces (RISs) that can reconfigure their phase-shifts to the currently served user. The latter comes with an increased power, cabling, and signaling cost. To see how reconfigurability affects the network performance, we propose an iterative algorithm based on the feasible point pursuit successive convex approximation method. We jointly optimize the types and phase-shifts of the surfaces and the time portion allocated to each user equipment to maximize the minimum data rate achieved by the network. Our numerical results demonstrate that the minimum data rate improves as more RISs are introduced but the gain diminishes after some point. Therefore, introducing more reconfigurability is not always necessary. Another result shows that to reach the same data rate achieved by using 22 SMSs, at least 18 RISs are needed. This suggests that when it is costly to deploy many RISs, as an inexpensive alternative solution, one can reach the same data rate just by densely deploying more SMSs.

Federated learning (FL) is a distributed learning paradigm wherein users exchange FL models with a server instead of raw datasets, thereby preserving data privacy and reducing communication overhead. However, the increased number of FL users may hinder completing large-scale FL over wireless networks due to high imposed latency. Cell-free massive multiple-input multiple-output (CFmMIMO) is a promising architecture for implementing FL because it serves many users on the same time/frequency resources. While CFmMIMO enhances energy efficiency through spatial multiplexing and collaborative beamforming, it remains crucial to meticulously allocate uplink transmission powers to the FL users. In this paper, we propose an uplink power allocation scheme in FL over CFmMIMO by considering the effect of each user's power on the energy and latency of other users to jointly minimize the users' uplink energy and the latency of FL training. The proposed solution algorithm is based on the coordinate gradient descent method. Numerical results show that our proposed method outperforms the well-known max-sum rate by increasing up to 27% and max-min energy efficiency of the Dinkelbach method by increasing up to 21 % in terms of test accuracy while having limited uplink energy and latency budget for FL over CFmMIMO.

In this paper, we study a cell-free multiple-input multiple-output network equipped with integrated sensing and communication (ISAC) access points (APs). The distributed APs are used to jointly serve the communication needs of user equipments (UEs) while sensing a target, assumed to be an eavesdropper (Eve). To increase the system's robustness towards said Eve, we develop an ISAC waveform model that includes artificial noise (AN) aimed at degrading the Eve channel quality. The central processing unit receives the observations from each AP and calculates the optimal precoding and AN covariance matrices by solving a semi-definite relaxation of a constrained Cramer-Rao bound (CRB) minimization problem. Simulation results highlight an underlying trade-off between sensing and communication performances: in particular, the UEs signal-to-noise and interference ratio and the maximum Eve's signal to noise ratio are directly proportional to the CRB. Furthermore, the optimal AN covariance matrix is rank-1 and has a peak in the eve's direction, leading to a surprising inverse-proportionality between the UEs-Eve distance and optimal-CRB magnitude.

Co-channel interference poses a challenge in any wireless communication network where the time-frequency resources are reused over different geographical areas. The interference is particularly diverse in cell-free massive multiple-input multiple-output (MIMO) networks, where a large number of user equipments (UEs) are multiplexed by a multitude of access points (APs) on the same time-frequency resources. For realistic and scalable network operation, only the interference from UEs belonging to the same serving cluster of APs can be estimated in real-time and suppressed by precoding/combining. As a result, the unknown interference arising from scheduling variations in neighboring clusters makes the rate adaptation hard and can lead to outages. This paper aims to model the unknown interference power in the uplink of a cell-free massive MIMO network. The results show that the proposed method effectively describes the distribution of the unknown interference power and provides a tool for rate adaptation with guaranteed target outage.

For the energy-efficient deployment of cell-free massive MIMO functionality in a practical wireless network, the end-to-end (from radio site to the cloud) energy-aware operation is essential. In line with the cloudification and virtualization in the open radio access networks (O-RAN), it is indisputable to envision prospective cell-free infrastructure on top of the O-RAN architecture. In this paper, we explore the performance and power consumption of cell-free massive MIMO technology in comparison with traditional small-cell systems, in the virtualized O-RAN architecture. We compare two different functional split options and different resource orchestration mechanisms. In the end-to-end orchestration scheme, we aim to minimize the end-to-end power consumption by jointly allocating the radio, optical fronthaul, and virtualized cloud processing resources. We compare end-to-end orchestration with two other schemes: 1) “radio-only” where radio resources are optimized independently from the cloud; and 2) “local cloud coordination” where orchestration is only allowed among a local cluster of radio units. We develop several algorithms to solve the end-to-end power minimization and sum spectral efficiency maximization problems. The numerical results demonstrate that end-to-end resource allocation with fully virtualized fronthaul and cloud resources provides a substantial additional power saving than the other resource orchestration schemes.

In this paper, we study a new kind of pilot contamination appearing in multi-operator reconfigurable intelligent surfaces (RIS) assisted networks, where multiple operators provide services to their respective served users. The operators use dedicated frequency bands, but each RIS inadvertently reflects the transmitted uplink signals of the user equipment devices in multiple bands. Consequently, the concurrent reflection of pilot signals during the channel estimation phase introduces a new inter-operator pilot contamination effect. We investigate the implications of this effect in systems with either deterministic or correlated Rayleigh fading channels, specifically focusing on its impact on channel estimation quality, signal equalization, and channel capacity. The numerical results demonstrate the substantial degradation in system performance caused by this phenomenon and highlight the pressing need to address inter-operator pilot contamination in multi-operator RIS deployments. To combat the negative effect of this new type of pilot contamination, we propose to use orthogonal RIS configurations during uplink pilot transmission, which can mitigate or eliminate the negative effect of inter-operator pilot contamination at the expense of some inter-operator information exchange and orchestration.

Energy harvesting can enable a reconfigurable intelligent surface (RIS) to self-sustain its operations without relying on external power sources. In this paper, we consider the problem of energy harvesting for RISs in the absence of coordination with the ambient RF source. We propose a series of sequential phase-alignment algorithms that maximize the received power based on only power measurements. We prove the convergence of the proposed algorithm to the optimal value for the noiseless scenario. However, for the noisy scenario, we propose a linear least squares estimator. We prove that within the class of linear estimators, the optimal set of measurement phases are equally-spaced phases. To evaluate the performance of the proposed method, we introduce a random phase update algorithm as a benchmark. Our simulation results show that the proposed algorithms outperform the random phase update method in terms of achieved power after convergence while requiring fewer measurements per phase update. Using simulations, we show that in a noiseless scenario with a discrete set of possible phase shifts for the RIS elements, the proposed method is sub-optimal, achieving a higher value than the random algorithm but not exactly the maximum feasible value that we obtained by exhaustive search.

This paper studies an integrated sensing and communication (ISAC) system within a centralized cell-free massive MIMO (multiple-input multiple-output) network for target detection. ISAC transmit access points serve the user equipments in the downlink and optionally steer a beam toward the target in a multi-static sensing framework. A maximum a posteriori ratio test detector is developed for target detection in the presence of clutter, so-called target-free signals. Additionally, sensing spectral efficiency (SE) is introduced as a key metric, capturing the impact of resource utilization in ISAC. A power allocation algorithm is proposed to maximize the sensing signal-to-interference-plus-noise ratio while ensuring minimum communication requirements. Two ISAC configurations are studied: utilizing existing communication beams for sensing and using additional sensing beams. The proposed algorithm’s efficiency is investigated in realistic and idealistic scenarios, corresponding to the presence and absence of the target-free channels, respectively. Despite performance degradation in the presence of target-free channels, the proposed algorithm outperforms the interference-unaware benchmark, leveraging clutter statistics. Comparisons with a fully communication-centric algorithm reveal superior performance in both cluttered and clutter-free environments. The incorporation of an extra sensing beam enhances detection performance for lower radar cross-section variances. Moreover, the results demonstrate the effectiveness of the integrated operation of sensing and communication compared to an orthogonal resource-sharing approach.

Ultra-massive multiple-input multiple-output (UM-MIMO) is the enabler of Terahertz (THz) communications in next-generation wireless networks. In THz UM-MIMO systems, a new paradigm of cross-field communications spanning from near-field to far-field is emerging, since the near-field range expands with higher frequencies and larger array apertures. Precise beam alignment in cross-field is critical but challenging. Specifically, unlike far-field beams that rely only on the angle domain, the incorporation of dual-domain (angle and distance) training significantly increases overhead. A natural question arises of whether far-field beam training can be deployed for cross-field beam alignment. In this paper, this question is answered, by demonstrating that the far-field training enables sufficient signal-to-noise ratio (SNR) in both far- and near-field scenarios, while exciting all channel dimensions. Based on that, we propose a subarray-coordinated hierarchical (SCH) training with greatly reduced overhead. To further obtain high-precision beam designs, we propose a two-phase angle and distance beam estimator (TPBE). Extensive simulations demonstrate the effectiveness of the proposed methods. Compared to near-field exhaustive search, the SCH possesses 0.2% training overhead. The TPBE achieves 0.16 degrees and 0.01 meters estimation root-mean-squared errors for angle and distance. Furthermore, with the estimated beam directions, a near-optimal SNR with 0.3 dB deviation is attained after beam alignment.

The design of Reconfigurable Intelligent Surfaces (RISs) is typically based on treating the RIS as an infinitely large surface that steers incident plane waves toward the desired direction. In practical implementations, however, the RIS has finite size and the incident wave is a beam of finite k-content, rather than a plane wave of$\delta $-like k-content. To understand the implications of the finite extent of both the RIS and the incident beam, here we treat the RIS as a spatial filter, the transfer function of which is determined by both the prescribed RIS operation and the shape of the RIS boundary. Following this approach, we study how the RIS transforms the incident k-content and we demonstrate how, by engineering the RIS shape, size, and response, it is possible to shape beams with nontrivial k-content to suppress unwanted interference, while concentrating the reflected power to desired directions. We also demonstrate how our framework, when applied in the context of near-field communications, provides the necessary insights into how the wavefront of the beam is tailored to enable focusing, propagation with invariant profile, and bending, beyond conventional beamforming.

This paper examines how to minimize the energy consumption of a user equipment (UE) when transmitting short data payloads. The receiving base station (BS) controls a reconfigurable intelligent surface (RIS), which requires additional pilot signals to be configured, to improve the channel conditions. The challenge is that the pilot signals increase the energy consumption and must be balanced against energy savings during data transmission. We derive a formula for the energy consumption, including both pilot and data transmission powers and the effects of imperfect channel state information and discrete phase-shifts. To shorten the pilot length, we propose dividing the RIS into subarrays of multiple elements using the same reflection coefficient. The pilot power and subarray size are tuned to the payload length to minimize the energy consumption. Analytical results show that there exists a unique energy-minimizing solution. For small payloads and when the direct path loss between the BS and UE is weak compared to the path loss via the RIS, the solution is using subarrays with many elements and low pilot power and vice versa. The optimal percentage of energy spent on pilot signaling is in the order of 10-40%.

Considering the dimensionality of a typical reconfigurable intelligent surface (RIS), channel state information acquisition in RIS-assisted systems requires lengthy pilot transmissions. Moreover, the large aperture of the RIS may cause transmitters/receivers to fall in its near-field region, where both distance and angles affect the channel structure. This paper proposes a parametric maximum likelihood estimation (MLE) framework for jointly estimating the direct channel between the user and the base station (BS) and the line-of-sight channel between the user and the RIS, in both far-field and near-field scenarios. The MLE framework is first developed for the case of single-antenna BS and later extended to the scenario where the BS is equipped with multiple antennas. A novel adaptive RIS configuration strategy is proposed to select the RIS configuration for the next pilot to actively refine the estimate. We design a minimal-sized codebook of orthogonal RIS configurations to choose from during pilot transmission with a dimension much smaller than the number of RIS elements. To further reduce the required number of pilots, we propose an initialization strategy with two wide beams. We demonstrate numerically that the proposed MLE method needs only a few pilots for achieving accurate channel estimates and further show that the presented framework performs well under Rician fading. We also showcase efficient user channel tracking in near-field and far-field scenarios.

Future wireless networks must provide ever higher data rates. The available bandwidth increases roughly linearly as we increase the carrier frequency, but the range shrinks drastically. This paper explores if we can instead reach massive capacities using spatial multiplexing over multiple-input multiple-output (MIMO) channels. In line-of-sight (LOS) scenarios, the rank of the MIMO channel matrix depends on the polarization and antenna arrangement. We optimize the rank and condition number by identifying the optimal antenna spacing in dual-polarized planar antenna arrays with imperfect isolation. The result is sparsely spaced antenna arrays that exploit radiative near-field properties. We further optimize the array geometry for minimum aperture length and aperture area, which leads to different configurations. Moreover, we prove analytically that for fixed-sized arrays, the MIMO rank grows quadratically with the carrier frequency in LOS scenarios, if the antennas are appropriately designed. Hence, MIMO technology contributes more to the capacity growth than the bandwidth. The numerical results show that massive data rates, far beyond 1 Tbps, can be reached both over fixed and mobile point-to-point links. It is also possible for a large base station to serve a practically-sized mobile device.

Most wireless communication systems operate in the far-field region of antennas and antenna arrays, where waves are planar and beams have infinite depth. When antenna arrays become electrically large, it is possible that the receiver is in the radiative near-field of the transmitter, and vice versa. Recent works have shown that near-field beamforming exhibits a finite depth, which enables a new depth-based spatial multiplexing paradigm. In this paper, we explore how the shape and size of an array determine the near-field beam behaviors. In particular, we investigate the 3 dB beam depth (BD), defined as the range of distances where the gain is greater than half of the peak gain. We derive analytical gain and BD expressions and prove how they depend on the aperture area and length. For non-broadside transmissions, we find that the BD increases as the transmitter approaches the end-fire direction of the array. Furthermore, it is sufficient to characterize the BD for a broadside transmitter, as the beam pattern with a non-broadside transmitter can be approximated by that of a smaller/projected array with a broadside transmitter. Our analysis demonstrates that the BD can be ordered from smallest to largest as ULA, circular, and square arrays.

This paper considers a mmWave cell-free massive MIMO (multiple-input multiple-output) network composed of a large number of geographically distributed access points (APs) simultaneously serving multiple user equipments (UEs) via coherent joint transmission. We address UE mobility in the downlink (DL) with imperfect channel state information (CSI) and pilot training. Aiming at extending traditional handover concepts to the challenging AP-UE association strategies of cell-free networks, distributed algorithms for joint pilot assignment and cluster formation are proposed in a dynamic environment considering UE mobility. The algorithms provide a systematic procedure for initial access and update of the serving APs and assigned pilot sequence to each UE. The principal goal is to limit the necessary number of AP and pilot changes, while limiting computational complexity. We evaluate the performance, in terms of spectral efficiency (SE), with maximum ratio and regularized zero-forcing precoding. Results show that our proposed distributed algorithms effectively identify the essential AP-UE association refinements with orders-of-magnitude lower computational time compared to the state-of-the-art. It also provides a significantly lower average number of pilot changes compared to an ultra-dense network (UDN). Moreover, we develop an improved pilot assignment procedure that facilitates massive access to the network in highly loaded scenarios.

Terahertz (THz) ultra-massive multiple-input multiple-output (UM-MIMO) systems are promising in enabling next-generation wireless communications, offering high data rates with tens of GHz of continuous bandwidth and high spectral efficiency. In THz UM-MIMO systems, a new paradigm of cross-field communications is emerging, since THz transmission distances span from near-field to far-field. To achieve the benefits of THz UM-MIMO, precise beam alignment implemented through beam training or beam scanning is required. However, different from the traditional far-field alignment in the angle domain, the near-field angle and distance alignment should be considered in the cross-field. The additional distance domain searching brings higher training overhead and thus limits the system's performance. In this paper, a far-field training with estimation (FTE) framework for cross-field beam alignment is proposed. The far-field training enables the received signal-to-noise ratio (SNR) in both the far- and near-field for successful control signal reception. Moreover, a three-phase beam estimator (TPBE) is proposed for high-precision alignment. Extensive simulations demonstrate the effectiveness of the proposed methods. Specifically, the FTE possesses a near-optimal signal-to-noise ratio with only 0.5 dB deviation, with 3.3% training overhead and low complexity compared to near-field exhaustive search.

Most wireless communication systems operate in the far-field region of antennas and antenna arrays, where waves are planar and beams have infinite depth. When antenna arrays become electrically large, it is possible that the receiver is in the radiative near-field of the transmitter, and vice versa. Recent works have shown that near-field beamforming exhibits a finite depth, which enables a new depth-based spatial multiplexing paradigm. In this paper, we explore how the shape and size of a rectangular array determine the near-field beam behaviors. In particular, we investigate the 3 dB beam depth (BD), defined as the range of distances where the gain is greater than half of the peak gain. We derive analytical gain and BD expressions and prove how they depend on the aperture area and length. The largest BD is obtained for a square array while the smallest BD is obtained by a uniform linear array.

Reconfigurable intelligent surface (RIS) is a newly-emerged technology that, with its unique features, is considered to be a game changer for future wireless networks. Channel estimation is one of the most critical challenges for the realization of RIS-assisted communications. Non-parametric channel estimation techniques are inefficient due to the huge pilot dimensionality that stems from the large number of RIS elements. The challenge becomes more serious if we consider the mobility of the users where the channel needs to be re-estimated whenever the user moves to a new location. This paper develops a novel maximum likelihood estimator (MLE) for jointly estimating the line-of-sight (LOS) channel from the user to the RIS and the direct channel between the user and the base station. By smartly refining the RIS configuration during the channel estimation procedure, we show that the channels can be accurately estimated with only a few pilot transmissions-much fewer than the number of RIS elements. The proposed scheme is also shown to be capable of effectively tracking the channel when the user moves around in a continuous but non-stationary manner with varying LOS angles,

This paper considers a multi-user multiple-input multiple-output (MU-MIMO) system where the precoding matrix is selected in a baseband unit (BBU) and then sent over a digital fronthaul to the transmitting antenna array. The fronthaul has a limited bit resolution with a known quantization behavior. We formulate a new sum rate maximization problem where the precoding matrix elements must comply with the quantizer. We solve this non-convex mixed-integer problem to local optimality by a novel iterative algorithm inspired by the classical weighted minimum mean square error (WMMSE) approach. The precoding optimization subproblem becomes an integer least-squares problem, which we solve with a new algorithm using a sphere decoding (SD) approach. We show numerically that the proposed precoding technique vastly outperforms the baseline of optimizing an infinite-resolution precoder and then quantizing it. We also develop a heuristic quantization-aware precoding that outperforms the baseline while having comparable complexity.

In this work, we consider the deployment of reconfigurable intelligent surfaces (RISs) to extend the coverage of a millimeter-wave (mmWave) network in indoor dense spaces. We first integrate RIS into ray-tracing simulations to realistically capture the propagation characteristics, then formulate a non-convex optimization problem that minimizes the number of RISs under rate constraints. We propose a feasible point pursuit and successive convex approximation-based algorithm, which solves the problem by jointly selecting the RIS locations, optimizing the RIS phase-shifts, and allocating time resources to user equipments (UEs). The numerical results demonstrate substantial coverage extension by using at least four RISs, and a data rate of 130 Mbit/s is guaranteed for UEs in the considered area of an airplane cabin.

We derive a novel uplink-downlink duality principle for optimal joint precoding design under per-transmitter power and information constraints. The main application is to cell-free networks, where each access point (AP) must typically satisfy an individual power constraint, and form its transmit signal on the basis of possibly partial data and channel state information sharing. By measuring performance using the popular hardening inner bound on the ergodic capacity, we show that optimal joint precoders can be interpreted as optimal joint combiners on a dual uplink channel with properly designed transmit and noise powers, and that they can be obtained using a variation of the recently developed team minimum mean-square error method. We finally apply our results to the numerical evaluation of optimal centralized and local precoding in a typical user-centric cell-free network subject to per-AP power constraints.

Nonlinear distortion stemming from low-cost power amplifiers may severely affect wireless communication performance through out-of-band (OOB) radiation and in-band distortion. The distortion is correlated between different transmit antennas in an antenna array, which results in a beamforming gain at the receiver side that grows with the number of antennas. In this paper, we investigate how the strength of the distortion is affected by the frequency selectivity of the channel. A closed-form expression for the received distortion power is derived as a function of the number of multipath components (MPCs) and the delay spread, which highlight their impact. The performed analysis, which is verified via numerical simulations, reveals that as the number of MPCs increases, distortion exhibits distinct characteristics for in-band and OOB frequencies. It is shown that the received in-band and OOB distortion power is inversely proportional to the number of MPCs, and it is reported that as the delay spread gets narrower, the in-band distortion power is beamformed towards the intended user, which yields higher received in-band distortion compared to the OOB distortion.

In this paper, we formulate and solve the optimization problem for joint access point placement and resource allocation for indoor mmWave communications with static users, with a particular focus on airplanes. The proposed scheme obtains the required number of access points (APs) and their locations, for a given data rate threshold and given radio resources such as bandwidth, antenna numbers, and AP co-operation. We first build an airplane cabin environment in a ray-tracing tool to realistically capture the propagation effects. Then, we cast optimal deployment problems considering the performance of different AP cooperation schemes, namely coordinated scheduling (CS), non-coherent joint transmission (NC-JT), and coherent joint transmission (C-JT). The results indicate that full cooperation among the APs with C-JT requires fewer APs, especially under high data rate requirements. Comparing the network deployments in the mmWave and sub-6GHz bands, we observe 9 times higher data rates in mmWave although more APs are required.

This paper addresses mobility management in the downlink of a mmWave cell-free massive MIMO (multiple-input multiple-output) network with imperfect channel knowledge obtained from pilot training. The network consists of a large number of geographically distributed access points (APs) simultaneously serving multiple user equipments (UEs) via coherent joint transmission. The objective is to extend traditional handover concepts to the challenging AP-UE association strategies of cell-free networks. To this end, we propose a distributed algorithm for joint pilot assignment and cluster formation in a dynamic environment considering UE mobility. The primary goal is to limit the necessary number of AP and pilot changes, with reasonable computational complexity. We evaluate the performance in terms of the spectral efficiency with maximum ratio and regularized zero-forcing precoding. Results show that our proposed distributed algorithm effectively identifies the essential AP-UE association refinements. Moreover, it provides a significantly lower average number of pilot changes compared to an ultra-dense network.

Cell-free massive multiple-input multiple-output (MIMO) networks, where a massive number of geographically distributed access points cooperate to jointly serve the users, have been proved to solve many of the interference related issues associated to cellular networks. One of the main challenges of cell-free massive MIMO networks, however, is to guarantee that the potential benefits this architecture entails can be achieved with signal processing computational complexities and fronthaul resource requirements that are scalable as the number of users goes to infinity. User-centric architectures have been proposed in the literature that potentially solve the scalability issues related to, first, the signal processing associated to channel estimation and massive MIMO combining/precoding, second, the power allocation algorithms and, third, the fronthaul signaling for data and channel state information sharing. One of the best centralized combiners/precoders that have been proposed in practice, however, which is termed as partial minimum mean square error (P-MMSE), does not allow obtaining expressions of its spectral efficiency in a scalable way except when using lower bounds based on the well-known use-and-then-forget (UatF) approach. These lower bounds, however, in addition to being rather inaccurate, are not suited for the design and analysis of non-linear combining/precoding schemes based on successive interference cancellation (SIC) when users are equipped with multiple antennas. In this paper, we propose novel linear and non-linear combining/precoding schemes, which we term improved P-MMSE (IP-MMSE), whose achievable spectral efficiency can be accurately analyzed in a scalable manner. The proposed IP-MMSE combiner/precoder achieves spectral efficiencies close to that provided by MMSE-based unscalable solutions, and outperforms to a great extent the P-MMSE-based counterparts.

Cell-free massive multiple-input multiple-output (CF mMIMO) systems serve the user equipments (UEs) by geographically distributed access points (APs) by means of joint transmission and reception. To limit the power consumption due to fronthaul signaling and processing, each UE should only be served by a subset of the APs, but it is hard to identify that subset. Previous works have tackled this combinatorial problem heuristically. In this paper, we propose a sparse distributed processing design for CF mMIMO, where the AP-UE association and long-term signal processing coefficients are jointly optimized. We formulate two sparsity-inducing mean-squared error (MSE) minimization problems and solve them by using efficient proximal approaches with block-coordinate descent. For the downlink, more specifically, we develop a virtually optimized large-scale fading precoding (V-LSFP) scheme using uplink-downlink duality. The numerical results show that the proposed sparse processing schemes work well in both uplink and downlink. In particular, they achieve almost the same spectral efficiency as if all APs would serve all UEs, while the energy efficiency is 2–4 times higher thanks to the reduced processing and signaling.

One of the first widespread uses of multi-user multiple-input multiple-output (MU-MIMO) is in 5G networks, where each base station has an advanced antenna system (AAS) that is connected to the baseband unit (BBU) with a capacity-constrained fronthaul. In the AAS configuration, multiple passive antenna elements and radio units are integrated into a single box. This paper considers precoded downlink transmission over a single-cell MU-MIMO system. We study optimized linear precoding for AAS with a limited-capacity fronthaul, which requires the precoding matrix to be quantized. We propose a new precoding design that is aware of the fronthaul quantization and minimizes the mean-squared error at the receiver side. We compute the precoding matrix using a sphere decoding (SD) approach. We also propose a heuristic low-complexity approach to quantized precoding. This heuristic is computationally efficient enough for massive MIMO systems. The numerical results show that our proposed precoding significantly outperforms quantization-unaware precoding and other previous approaches in terms of the sum rate. The performance loss for our heuristic method compared to quantization-aware precoding is insignificant considering the complexity reduction, which makes the heuristic method feasible for real-time applications. We consider both perfect and imperfect channel state information (CSI).

This paper considers a single-cell massive MIMO (multiple-input multiple-output) system with dual-polarized antennas at both the base station and users. We study a channel model that includes the key practical aspects that arise when utilizing dual-polarization: channel cross-polar discrimination (XPD) and cross-polar correlations (XPC) at the transmitter and receiver. We derive the achievable uplink and downlink spectral efficiencies (SE) with and without successive interference cancellation (SIC) when using the linear minimum mean squared error (MMSE), zero-forcing (ZF), and maximum ratio (MR) combining/precoding schemes. The expressions depend on the statistical properties of the MMSE channel estimator obtained for the dual-polarized channel model. Closed-form uplink and downlink SE expressions for MR combining/precoding are derived. Using these expressions, we propose power-control algorithms that maximize the uplink and downlink sum SEs under uncorrelated fading but can be used to enhance performance also with correlated fading. We compare the SEs achieved in dual-polarized and uni-polarized setups numerically and evaluate the impact of XPD and XPC conditions. The simulations reveal that dual-polarized setups achieve 40-60% higher SEs and the gains remain also under severe XPD and XPC. Dual-polarized also systems benefit more from advanced signal processing that compensates for imperfections.

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.

This paper studies a joint communication and sensing (JCAS) system with downlink communication and multi-static sensing for single-target detection in a cloud radio access network architecture. A centralized operation of cell-free massive MIMO is considered for communication and sensing purposes. The JCAS transmit access points (APs) jointly serve the user equipments (UEs) and optionally steer a beam towards the target. A maximum a posteriori ratio test detector is derived to detect the target using signals received at distributed APs. We propose a power allocation algorithm to maximize the sensing signal-to-noise ratio under the condition that a minimal signal-to-interference-plus-noise ratio value for each UE is guaranteed. Nu-merical results show that, compared to the fully communication-centric power allocation, the detection probability under a certain false alarm probability can be increased significantly by the proposed algorithm for both JCAS setups: i) using additional sensing symbols or ii) using only existing communication symbols.

Base stations in 5G and beyond use advanced antenna systems (AASs), where multiple passive antenna elements and radio units are integrated into a single box. A critical bottleneck of such a system is the digital fronthaul between the AAS and baseband unit (BBU), which has limited capacity. In this paper, we study an AAS used for precoded down-link transmission over a multi-user multiple-input multiple-output (MU-MIMO) channel. First, we present the baseline quantization-unaware precoding scheme created when a pre-coder is computed at the BBU and then quantized to be sent over the fronthaul. We propose a new precoding design that is aware of the fronthaul quantization. We formulate an optimization problem to minimize the mean squared error at the receiver side. We rewrite the problem to utilize mixed-integer programming to solve it. The numerical results manifest that our proposed precoding greatly outperforms quantization-unaware precoding in terms of sum rate.

Previous works on cell-free massive MIMO mostly consider physical-layer and fronthaul transport aspects. How to deploy cell-free massive MIMO functionality in a practical wireless system is an open problem. This paper proposes a new cell-free architecture that can be implemented on top of a virtualized cloud radio access network (V-CRAN). We aim to minimize the end-to-end power consumption by jointly considering the radio, optical fronthaul, virtualized cloud processing resources, and spectral efficiency requirements of the user equipments. The considered optimization problem is cast in a mixed binary second-order cone programming form and, thus, the global optimum can be found using a branch-and-bound algorithm. The optimal power-efficient solution of our proposed cell-free system is compared with conventional small-cell implemented using V-CRAN, to determine the benefits of cell-free networking. The numerical results demonstrate that cell-free massive MIMO increases the maximum rate substantially, which can be provided with almost the same energy per bit. We show that it is more power-efficient to activate cell-free massive MIMO already at low spectral efficiencies (above 1 bit/s/Hz).

In this paper, we examine the energy consumption of a user equipment (UE) when it transmits a finite-sized data packet. The receiving base station (BS) controls a reconfigurable intelligent surface (RIS) that can be utilized to improve the channel conditions, if additional pilot signals are transmitted to configure the RIS. We derive a formula for the energy consumption taking both the pilot and data transmission powers into account. By dividing the RIS into subarrays consisting of multiple RIS elements using the same reflection coefficient, the pilot overhead can be tuned to minimize the energy consumption while maintaining parts of the aperture gain. Our analytical results show that there exists an energy-minimizing subarray size. For small data blocks and when the channel conditions between the BS and UE are favorable compared to the path to the RIS, the energy consumption is minimized using large subarrays. When the channel conditions to the RIS are better and the data blocks are large, it is preferable to use fewer elements per subarray and potentially configure the elements individually.

An Intelligent Reflecting Surface (IRS) is an emerging technology for improving the data rate over wireless channels by controlling the underlying channel. In this paper, we describe a novel solution for IRS configuration to maximize the data rate over wideband channels. The optimization is obtained by online training of a deep generative neural network. Inspired by related works in image processing, this network is randomly initialized and acts as a regularization term for the optimization process since the structure of the generator is sufficient to capture a great deal of IRS statistics prior to any learning. In contrast to recent deep learning techniques for IRS configuration, the proposed technique does not require an offline training stage and can adapt quickly to any environment. Compared to the previous state-of-the-art algorithm, the proposed method is significantly faster and obtains IRS configurations that achieve higher data transmission rates.

Wireless power transfer (WPT) is an alternative technology to conventional batteries for powering Internet of things (IoT) devices. WPT is especially beneficial in situations when battery replacement is infeasible or expensive. It can also reduce battery-related e-waste. In this paper, we analyze the limits of adopting WPT technology for remote powering of IoT devices. We assume that an IoT device periodically harvests energy from a base station (BS) and transmits a data packet related to the sensor measurement under shadow fading channel conditions. Our goal is to characterize the ε-coverage range, where ε is the probability of the coverage. Our analysis shows a tradeoff between the coverage range and the rate of sensor measurements, where the maximal ε-coverage range is achieved as the sensor measurement rate approaches zero. We demonstrate that the weighted sum of the sleep power consumption and the harvesting sensitivity power of an IoT device limits the maximal ε-coverage range. Beyond that range, the IoT device cannot harvest enough energy to operate. The desired rate of the sensor measurements also significantly impacts the ε-coverage range. Our results suggest that for an IoT device designed using current technology, the maximal 0.95-coverage range is in the order of 120 m. When high measurement rates are required, the coverage range drops to 50–100 m. Compared to battery-powered IoT devices, WPT is well-suited for medium-range applications plus when battery replacement is costly.

In this paper, the indoor dense space (IDS) channel at 28 GHz is characterized through extensive Ray-Tracing (RT) simulations. We consider IDS as a specific type of indoor environment with confined geometry and packed with humans, such as aircraft cabins and train wagons. Based on RT simulations, we characterize path loss, shadow fading, root-mean-square delay spread, Rician K-factor, azimuth/elevation angular spread of arrival/departure considering different RT simulation scenarios of the fuselage geometry, material, and human presence. While the large-scale fading parameters are similar to the state-of-the-art channel models, the small-scale fading parameters demonstrate richer multipath scattering in IDS, resulting in poorer bit error rate performance in comparison to the 3GPP indoor channel model.

Massive multiple input multiple output (MIMO) emerged as the leading technology for supporting fifth generation (5G) and beyond 5G cellular communication systems. Due to the tremendous increase in data traffic in urban areas and to meet such a significant demand, most studies consider macro/micro cell deployments in urban environments. Internet service providers (ISPs) are less interested in providing communication services in rural areas considering the relatively low profits compared to the deployment and maintenance costs. In this paper, we investigate the massive MIMO performance in rural scenarios. In particular, we investigate different aspects to consider while designing a long-range communication system. We propose to use elevated base station (BS) with sectorized antennas with unusually large aperture and implement a user scheduling algorithm at the BS to provide full digital coverage. We analyze the coverage range of a massive MIMO system to provide high-rate services. Furthermore, we also analyze the link budget requirements and the rates users can achieve in such a SuperCell massive MIMO network.

In this paper, we examine the potential for a reconfigurable intelligent surface (RIS) to be powered by energy harvested from information signals. This feature might be key to reap the benefits of RIS technology’s lower power consumption compared to active relays. We first identify the main RIS power-consuming components and then propose an energy harvesting and power consumption model. Furthermore, we formulate and solve the problem of the optimal RIS placement together with the amplitude and phase response adjustment of its elements in order to maximize the signal-to-noise ratio (SNR) while harvesting sufficient energy for its operation. Finally, numerical results validate the autonomous operation potential and reveal the range of power consumption values that enables it.

Conventional Internet of things (IoT) devices are powered by batteries. However, batteries pose a risk of e-waste and chemical leakage to the environment. An alternative way to power remote IoT devices is to harvest ambient RF energy. It is especially beneficial when battery replacement is costly and could enable large-scale IoT deployments at net-zero energy cost. In this paper, we assume that the IoT devices periodically harvest energy from multiple surrounding base stations (BSs) and use the harvested energy to take sensor measurements and transmit related data packets. We propose an approximate method to analyze the feasibility of this approach in terms of which measurement rates can be supported. To this end, we assume a Poisson point process for the locations of the BSs. We derive mathematical expressions for the coverage probability (i.e., the probability that an IoT device harvests enough energy to operate at a given measurement rate) and the required BS site density in the presence of channel uncertainties, blockage, and harvesting nonlinearities. We derive the parameters of a Gamma distribution to approximate the distribution of the harvested power. For a coverage probability of 0.5, we derive a simplified approximate expression for the required site density that closely describes the one obtained empirically.

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.

We study downlink channel estimation in a multi-cell Massive multiple-input multiple-output (MIMO) system operating in time-division duplex. The users must know their effective channel gains to decode their received downlink data. Previous works have used the mean value as the estimate, motivated by channel hardening. However, this is associated with a performance loss in non-isotropic scattering environments. We propose two novel estimation methods that can be applied without downlink pilots. The first method is model-based and asymptotic arguments are utilized to identify a connection between the effective channel gain and the average received power during a coherence interval. The second method is data-driven and trains a neural network to identify a mapping between the available information and the effective channel gain. Both methods can be utilized for any channel distribution and precoding. For the model-aided method, we derive all expressions in closed form for the case when maximum ratio or zero-forcing precoding is used. We compare the proposed methods with the state-of-the-art using the normalized mean-squared error and spectral efficiency (SE). The results suggest that the two proposed methods provide better SE than the state-of-the-art when there is a low level of channel hardening, while the performance difference is relatively small with the uncorrelated channel model.

Reciprocity-based time-division duplex (TDD) Massive MIMO (multiple-input multiple-output) systems utilize channel estimates obtained in the uplink to perform precoding in the downlink. However, this method has been criticized of breaking down, in the sense that the channel estimates are not good enough to spatially separate multiple user terminals, at low uplink reference signal signal-to-noise ratios, due to insufficient channel estimation quality. Instead, codebook-based downlink precoding has been advocated for as an alternative solution in order to bypass this problem. We analyze this problem by considering a “grid-of-beams world” with a finite number of possible downlink channel realizations. Assuming that the terminal accurately can detect the downlink channel, we show that in the case where reciprocity holds, carefully designing a mapping between the downlink channel and the uplink reference signals will perform better than both the conventional TDD Massive MIMO and frequency-division duplex (FDD) Massive MIMO approach. We derive elegant metrics for designing this mapping, and further, we propose algorithms that find good sequence mappings.

Reconfigurable intelligent surfaces (RISs) consist of many passive elements of metamaterials whose impedance can be controllable to change the characteristics of wireless signals impinging on them. Channel estimation is a critical task when it comes to the control of a large RIS when having a channel with a large number of multipath components. In this paper, we derive Bayesian channel estimators for two RIS-assisted massive multiple-input multiple-output (MIMO) configurations: i) the short-term RIS configuration based on the instantaneous channel estimates; ii) the long-term RIS configuration based on the channel statistics. The proposed methods exploit spatial correlation characteristics at both the base station and the planar RISs, and other statistical characteristics of multi-specular fading in a mobile environment. Moreover, a novel heuristic for phase-shift selection at the RISs is developed. A computationally efficient fixed-point algorithm, which solves the max-min fairness power control optimally, is proposed. Simulation results demonstrate that the proposed uplink RIS-aided framework improves the spectral efficiency of the cell-edge mobile user equipments substantially in comparison to a conventional single-cell massive MIMO system. The impact of several channel effects are studied to gain insight about when the channel estimation, i.e., the short-term configuration, is preferable in comparison to the long-term RIS configuration to boost the spectral efficiency.

This article studies a novel distributed precoding design, coinedteam minimum mean-square error(TMMSE) precoding, which rigorously generalizes classical centralized MMSE precoding to distributed operations based on transmitter-specific channel state information (CSIT). Building on the so-calledtheory of teams, we derive a set of necessary and sufficient conditions for optimal TMMSE precoding, in the form of an infinite dimensional linear system of equations. These optimality conditions are further specialized to cell-free massive MIMO networks, and explicitly solved for two important examples, i.e., the classical case of local CSIT and the case of unidirectional CSIT sharing along a serial fronthaul. The latter case is relevant, e.g., for the recently proposedradio stripeconcept and the related advances on sequential processing exploiting serial connections. In both cases, our optimal design outperforms the heuristic methods that are known from the previous literature. Duality arguments and numerical simulations validate the effectiveness of the proposed team theoretical approach in terms of ergodic achievable rates under a sum-power constraint.

Reconfigurable intelligent surfaces (RISs) have attracted great attention as a potential beyond 5G technology. These surfaces consist of many passive elements of metamaterials whose impedance can be controllable to change the phase, amplitude, or other characteristics of wireless signals impinging on them. Channel estimation is a critical task when it comes to the control of a large RIS when having a channel with a large number of multipath components. In this paper, we propose a novel channel estimation scheme that exploits spatial correlation characteristics at both the massive multiple-input multiple-output (MIMO) base station and the planar RISs, and other statistical characteristics of multi-specular fading in a mobile environment. Moreover, a novel heuristic for phase-shift selection at the RISs is developed, inspired by signal processing methods that are effective in conventional massive MIMO. Simulation results demonstrate that the proposed uplink RIS-aided framework improves the spectral efficiency of the cell-edge mobile users substantially in comparison to a conventional single-cell massive MIMO system.

Reconfigurable intelligent surfaces (RISs) have recently received widespread attention in the field of wireless communication. An RIS can be controlled to reflect incident waves from the transmitter towards the receiver; a feature that is believed to fundamentally contribute to beyond 5G wireless technology. The typical RIS consists of entirely passive elements, which requires the high-dimensional channel estimation to be done elsewhere. Therefore, in this paper, we present a semipassive large-scale RIS architecture equipped with only a small fraction of simplified receiver units with only 1-bit quantization. Based on this architecture, we first propose an alternating direction method of multipliers (ADMM)-based approach to recover the training signals at the passive RIS elements, We then obtain the global channel by combining a channel sparsification step with the generalized approximate message passing (GAMP) algorithm. Our proposed scheme exploits both the sparsity and lowrankness properties of the channel in the joint spatial-frequency domain of a wideband mmWave multiple-input-multiple-output (MIMO) communication system. Simulation results show that the proposed algorithm can significantly reduce the pilot signaling needed for accurate channel estimation and outperform previous methods, even with fewer receiver units.

Caching popular contents at a large number of access points and edge-clouds is a promising solution to alleviate the increasing backhaul congestion in beyond fifth-generation (B5G) networks. By integrating with cell-free massive multiple-input multiple-output (CF mMIMO), wireless caching can harness their combined virtues, i.e., almost uniform service quality, strong macro-diversity, and reduction of the data traffic from the core network. In this paper, we consider an offline cache-aided scenario with two caching strategies to minimize the total energy consumption (TEC), which are evaluated from the cache hit probability (CHP). The TEC minimization is showed to be NP-complete and, hence, dealt with a proposed greedy algorithm. An adaptive power control policy is proposed to reduce the TEC. We compare CF mMIMO with small cells in terms of the successful content delivery probability (SCDP) and TEC, respectively. The numerical results show that CF mMIMO can offer a much more uniform service, significantly higher SCDP, and lower average TEC when compared to than SC.

How to meet the demand for increasing number of users, higher data rates, and stringent quality-of-service (QoS) in the beyond fifth-generation (B5G) networks? Cell-free massive multiple-input multiple-output (MIMO) is considered as a promising solution, in which many wireless access points cooperate to jointly serve the users by exploiting coherent signal processing. However, there are still many unsolved practical issues in cell-free massive MIMO systems, whereof scalable massive access implementation is one of the most vital. In this paper, we propose a new framework for structured massive access in cell-free massive MIMO systems, which comprises one initial access algorithm, a partial large-scale fading decoding (P-LSFD) strategy, two pilot assignment schemes, and one fractional power control policy. New closed-form spectral efficiency (SE) expressions with maximum ratio (MR) combining are derived. The simulation results show that our proposed framework provides high SE when using local partial minimum mean-square error (LP-MMSE) and MR combining. Specifically, the proposed initial access algorithm and pilot assignment schemes outperform their corresponding benchmarks, P-LSFD achieves scalability with a negligible performance loss compared to the conventional optimal large-scale fading decoding (LSFD), and scalable fractional power control provides a controllable trade-off between user fairness and the average SE.

In this paper, we investigate optimal downlink power allocation in massive multiple-input multiple-output (MIMO) networks with distributed antenna arrays (DAAs) under correlated and uncorrelated channel fading. In DAA massive MIMO, a base station (BS) consists of multiple antenna sub-arrays. Notably, the antenna sub-arrays are deployed in arbitrary locations within a DAA massive MIMO cell. Consequently, the distance-dependent large-scale propagation coefficients are different from a user to these different antenna sub-arrays, which makes power control a challenging problem. We assume that the network operates in time-division duplex mode, where each BS obtains the channel estimates via uplink pilots. Based on the channel estimates, the BSs perform maximum-ratio transmission in the downlink. We then derive a closed-form signal-to-interference-plus-noise ratio (SINR) expression, where the channels are subject to correlated fading. Based on the SINR expression, we propose a network-wide max-min power control algorithm to ensure that each user in the network receives a uniform quality of service. Numerical results demonstrate the performance advantages offered by DAA massive MIMO. For some specific scenarios, DAA massive MIMO can improve the average per-user throughput up to 55%. Furthermore, we demonstrate that channel fading covariance is an important factor in determining the performance of DAA massive MIMO.

This paper investigates the performance of limited-fronthaul cell-free massive multiple-input multiple-output (MIMO) taking account the fronthaul quantization and imperfect channel acquisition. Three cases are studied, which we refer to as Estimate & Quantize, Quantize & Estimate, and Decentralized, according to where channel estimation is performed and exploited. Maximum-ratio combining (MRC), zero-forcing (ZF), and minimum mean-square error (MMSE) receivers are considered. The Max algorithm and the Bussgang decomposition are exploited to model optimum uniform quantization. Exploiting the optimal step size of the quantizer, analytical expressions for spectral and energy efficiencies are presented. Finally, an access point (AP) assignment algorithm is proposed to improve the performance of the decentralized scheme. Numerical results investigate the performance gap between limited fronthaul and perfect fronthaul cases, and demonstrate that exploiting relatively few quantization bits, the performance of limited-fronthaul cell-free massive MIMO closely approaches the perfect-fronthaul performance.

Future wireless networks need to support massive machine type communication (mMTC) where a massive number of devices accesses the network and massive MIMO is a promising enabling technology. Massive access schemes have been studied for co-located massive MIMO arrays. In this paper, we investigate the activity detection in grant-free random access for mMTC in cell-free massive MIMO networks using distributed arrays. Each active device transmits a non-orthogonal pilot sequence to the access points (APs) and the APs send the received signals to a central processing unit (CPU) for joint activity detection. The maximum likelihood device activity detection problem is formulated and algorithms for activity detection in cell-free massive MIMO are provided to solve it. The simulation results show that the macro diversity gain provided by the cell-free architecture improves the activity detection performance compared to co-located architecture when the coverage area is large.

In this paper, we evaluate the uplink spectral efficiency (SE) of a single-cell massive multiple-input-multiple-output (MIMO) system with distributed jammers. We define four different attack scenarios and compare their impact on the massive MIMO system as well as on a conventional single-input-multiple-output (SIMO) system. More specifically, the jammers attack the base station (BS) during both the uplink training phase and data phase. The BS uses either least squares (LS) or linear minimum mean square error (LMMSE) estimators for channel estimation and utilizes either maximum-ratio-combining (MRC) or zero-forcing (ZF) decoding vectors. We show that ZF gives higher SE than MRC but, interestingly, the performance is unaffected by the choice of the estimators. The simulation results show that the performance loss percentage of massive MIMO is less than that of the SIMO system. Moreover, we consider two types of power control algorithms: jamming-aware and jamming-ignorant. In both cases, we consider the max-min and proportional fairness criteria to increase the uplink SE of massive MIMO systems. We notice numerically that max-min fairness is not a good option because if one user is strongly affected by the jamming, it will degrade the other users' SE as well. On the other hand, proportional fairness improves the sum SE of the system compared with the full power transmission scenario.

The prospects of using a Reconfigurable Intelligent Surface (RIS) to aid wireless communication systems have recently received much attention from academia and industry. Most papers make theoretical studies based on elementary models, while the prototyping of RIS-aided wireless communication and real-world field trials are scarce. In this paper, we describe a new RIS prototype consisting of 1100 controllable elements working at 5.8 GHz band. We propose an efficient algorithm for configuring the RIS over the air by exploiting the geometrical array properties and a practical receiver-RIS feedback link. In our indoor test, where the transmitter and receiver are separated by a 30 cm thick concrete wall, our RIS prototype provides a 26 dB power gain compared to the baseline case where the RIS is replaced by a copper plate. A 27 dB power gain was observed in the short-distance outdoor measurement. We also carried out long-distance measurements and successfully transmitted a 32 Mbps data stream over 500 m. A 1080p video was live-streamed and it only played smoothly when the RIS was utilized. The power consumption of the RIS is around 1 W. Our paper is vivid proof that the RIS is a very promising technology for future wireless communications.

Cell-free massive multiple-input-multiple-output (mMIMO) is an emerging technology for beyond 5G with its promising features such as higher spectral efficiency and superior spatial diversity as compared to conventional multiple-input-multiple-output (MIMO) technology. The main working principle of cell-free mMIMO is that many distributed access points (APs) cooperate simultaneously to serve all the users within the network without creating cell boundaries. This paper considers the uplink of a cell-free mMIMO system utilizing the radio stripe network architecture with a sequential fronthaul between the APs. A novel uplink sequential processing algorithm is developed, which is proved to be optimal in both the maximum spectral efficiency (SE) and the minimum mean square error (MSE) sense. A detailed quantitative analysis of the fronthaul requirement or signaling of the proposed algorithm and its comparison with competing sub-optimal algorithms is provided. Key conclusions and implications are summarized in the form of corollaries. Based on the analytical and numerical simulation results, we conclude that the proposed scheme can significantly reduce the fronthaul signaling, without compromising the communication performance.

In Massive MIMO base stations (BSs), the hardware design needs to balance high spectral efficiency (SE) with low complexity. The level of hardware impairments (HWIs) indicates how strong the signal distortion introduced by hardware imperfections is. In particular, the analog-to-digital converters (ADCs) have an important impact on signal distortion and power consumption. This article addresses the fundamental problem of selecting the optimal hardware quality in the Massive MIMO space. In particular, we examine the optimal HWI and ADC bit allocation per BS antenna to maximize the SE. The results show that in co-located arrays with low channel gain variations across antennas, equal ADC bit allocation is optimal. In contrast, cell-free Massive MIMO systems benefit the most from optimizing the ADC bit allocation achieving improvements in the order of 2 [bit-per-channel-use] per user equipment when using regularized zero-forcing (RZF). In addition, when including the impact of power consumption in cell-free Massive MIMO with RZF, allocating low values of mixed ADC bit resolutions across the BS antennas can increase the energy efficiency up to 30% compared to equal ADC bit allocation.

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 full-pilot 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.

This paper considers wireless uplink information and downlink power transfer in cell-free massive multiple-input multiple-output systems. The single-antenna user equipments (UEs) utilize the energy harvested in the downlink to transmit uplink pilot and information signals to the multiple-antenna access points (APs). We consider Rician fading and maximum ratio processing based on either linear minimum mean-squared error (LMMSE) or least-squares (LS) channel estimation. We derive the average harvested energy by using a practical non-linear energy harvesting circuit model for both coherent and non-coherent transmission schemes. Furthermore, the uplink spectral efficiency (SE) is derived for all the considered methods and the max-min fairness problem is cast where the optimization variables are the AP and UE power control coefficients together with the large-scale fading decoding vectors. The objective is to maximize the minimum SE of the UEs' under APs' and UEs' transmission power constraints. A novel alternating optimization algorithm with guaranteed convergence and improvement at each step is proposed to solve the highly-coupled non-convex problem.

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.

A large-scale distributed antenna system that serves the users by coherent joint transmission is called Cell-free Massive MIMO (multiple input multiple output). For a given user set, only a subset of the access points (APs) is likely needed to satisfy the users' performance demands. To find a flexible and energy-efficient implementation, we minimize the total power consumption at the APs in the downlink, considering both the hardware and transmit powers, where APs can be turned off. Even though this is a non-convex optimization problem, a globally optimal solution is obtained by solving a mixed-integer second-order cone program. We also propose a low-complexity algorithm that exploits group-sparsity in the problem formulation. Numerical results manifest that our optimization framework can greatly reduce the power consumption compared to keeping all APs turned on and only minimizing the transmit powers.

This paper considers the large-scale fading precoding design for mitigating the pilot contamination in the downlink of multi-cell massive MIMO (multiple-input multiple-output) systems. Rician fading with spatially correlated channels are considered where the line-of-sight (LOS) components of the channels are randomly phase-shifted in each coherence block. The large-scale fading precoding weights are designed based on maximizing the product of the signal-to-interference-plus-noise ratios (SINRs) of the users, which provides a good balance between max-min fairness and sum rate maximization. The spectral efficiency (SE) is derived based on the scaled least squares (LS) estimates of the channels, which only utilize the despreaded pilot signals without any matrix inversion. Simulation results show that the two-layer large-scale fading precoding improves the SE of almost all users compared to the conventional single-layer precoding.

This paper considers signal detection in massive multiple-input multiple-output (MIMO) systems with general additive hardware impairments and one-bit quantization. First, we present the quantization-unaware and Bussgang decomposition-based linear receivers by generalizing them for the considered hardware impairment model. We propose an optimization problem to estimate the uplink data signals by choosing a suitable cost function that treats the unquantized received signal at the base station as the variable. We exploit the additional structure of the one-bit quantization and signal modulation by including proper constraints. To solve the non-convex quadratically-constrained quadratic programming (QCQP) problem, we propose an ADMM-based algorithm with closed-form update equations. Then, we replace the harsh projectors in the updates with their soft versions to improve the detection performance. We show that the proposed ADMM-based algorithm outperforms the state-of-the-art linear receivers significantly in terms of bit error rate (BER) and the performance gain increases with the number of antennas and users.

An intelligent reflecting surface (IRS), consisting of reconfigurable metamaterials, can be used to partially control the radio environment and thereby bring new features to wireless communications. Previous works on IRS have particularly studied the range extension use case and under what circumstances the new technology can beat relays. In this paper, we study another use case that might have a larger impact on the channel capacity: rank improvement. One of the classical bottlenecks of point-to-point MIMO communications is that the capacity gains provided by spatial multiplexing are only large at high SNR, and high SNR channels are mainly appearing in line-of-sight (LoS) scenarios where the channel matrix has low rank and therefore does not support spatial multiplexing. We demonstrate how an IRS can be used and optimized in such scenarios to increase the rank of the channel matrix, leading to substantial capacity gains.

In this paper, we analyze the uplink spectral efficiency (SE) of an arbitrary user in a single-cell massive multiple-input-multiple-output (MIMO) system in which there are jammers randomly distributed. We compare this SE with that of a user in a single-input-multiple-output (SIMO) system. We utilize two types of receivers that are widely used in massive MIMO literature: Maximum-ratio-combining (MRC) and zero-forcing (ZF). The jammers attack the base station (BS) during the training and data transmission phases. In order to estimate the channel vectors of the legitimate users, the BS uses either the linear minimum mean square error (LMMSE) estimator which requires information about the jamming power or the least squares (LS) estimator which does not require any knowledge about the jamming signals. We show that ZF gives higher SE than MRC, but interestingly the performance is unaffected by the choice of the estimators. Moreover, we derive the closed form signal-to-interference-noise ratio (SINR) for the MRC receiver when the jammers attack to the BS and based on this SINR expression we utilize power control algorithms that achieve max-min fairness and proportional fairness.

Despite the deleterious effect of hardware impairments (HWIs) on wireless systems, most prior works in cell-free (CF) massive multiple-input-multiple-output (mMIMO) systems have not accounted for their impact. In particular, the effect of phase noise (PN) has not been investigated at all in CF systems. Moreover, there is no work investigating HWIs in scalable CF (SCF) mMIMO systems, encountering the prohibitively demanding fronthaul requirements of large networks with many users. Hence, we derive the uplink spectral efficiency (SE) under HWIs with minimum mean-squared error (MMSE) combining in closed-form by means of the deterministic equivalent (DE) analysis. Notably, previous works, accounted for MMSE decoding, studied the corresponding SE only by means of simulations. Numerical results illustrate the performance loss due to HWIs and result in insightful conclusions.

This paper considers cell-free massive multiple-input multiple-output systems where the multiple-antenna access points (APs) assist the single-antenna user equipments (UEs) by wireless power transfer. The UEs utilize the energy harvested in the downlink to transmit uplink pilot and information signals to the APs. We consider practical Rician fading with the line-of-sight components of the channels being phase-shifted in each coherence block. The uplink spectral efficiency (SE) is derived for this model and the max-min fairness problem is considered where the optimization variables are the AP and UE power control coefficients together with the large-scale fading decoding vectors. The objective is to maximize the minimum SE of the users under APs' and UEs' transmission power constraints. An alternating optimization algorithm is proposed for the solution of the highly-coupled non-convex problem.

Recently, the first version of the fifth-generation (5G) new radio (NR) standard with massive multiple-input multiple-output (MIMO) has been finished by the 3rd Generation Partnership Project (3GPP), with initial deployments occurring in 2018. Despite the major advances in 5G, there are still many challenges remaining. 6G and beyond will require even higher data rates, lower latencies, better energy efficiency, and improved robustness.Multiple antenna technologies,which have played important roles in nearly all recent wireless standards, will be key to addressing these challenges. MIMO research continues to evolve, and new MIMO research topics such as enhanced massive MIMO techniques and array architectures hold much potential for 6G and beyond. Cell-free massive MIMO utilize a large number of distributed access points (APs) that jointly serve users in a coordinated fashion, using only local channel state information at each AP. While the performance of cell-free massive MIMO can be analyzed using a similar methodology as in cellular massive MIMO, the fundamental limits, signal processing, and resource allocation are substantially different. In order to reduce the hardware cost and energy consumption in millimeter wave (mmWave) massive MIMO systems, beamspace MIMO has been proposed to significantly reduce the number of required radio-frequency (RF) chains by using lens antenna arrays or phase shifters. Alternatively, the intelligent reflecting surface (IRS) concept involves electromagnetically controllable surfaces that can be integrated into large-scale infrastructure such as building walls, airports, and stadiums. There are active and partially passive forms of large intelligent surface (LIS), and variants with either large antenna spacing or continuous aperture. There are also some substantial differences between the new multiple antenna technologies and traditional MIMO systems, such as transceiver design and propagation models. This special issue aims to highlight recent research on multiple antenna technologies.

Multiple antenna technologies have attracted much research interest for several decades and have gradually made their way into mainstream communication systems. Two main benefits are adaptive beamforming gains and spatial multiplexing, leading to high data rates per user and per cell, especially when large antenna arrays are adopted. Since multiple antenna technology has become a key component of the fifth-generation (5G) networks, it is time for the research community to look for new multiple antenna technologies to meet the immensely higher data rate, reliability, and traffic demands in the beyond 5G era. Radically new approaches are required to achieve orders-of-magnitude improvements in these metrics. There will be large technical challenges, many of which are yet to be identified. In this paper, we survey three new multiple antenna technologies that can play key roles in beyond 5G networks: cell-free massive MIMO, beamspace massive MIMO, and intelligent reflecting surfaces. For each of these technologies, we present the fundamental motivation, key characteristics, recent technical progresses, and provide our perspectives for future research directions. The paper is not meant to be a survey/tutorial of a mature subject, but rather serve as a catalyst to encourage more research and experiments in these multiple antenna technologies.

Recently, the first version of the fifth-generation (5G) new radio (NR) standard with massive multiple-input multiple-output (MIMO) has been finished by the 3rd Generation Partnership Project (3GPP), with initial deployments occurring in 2018. Despite the major advances in 5G, there are still many challenges remaining. 6G and beyond will require even higher data rates, lower latencies, better energy efficiency, and improved robustness.Multiple antenna technologies,which have played important roles in nearly all recent wireless standards, will be key to addressing these challenges. MIMO research continues to evolve, and new MIMO research topics such as enhanced massive MIMO techniques and array architectures hold much potential for 6G and beyond. Cell-free massive MIMO utilize a large number of distributed access points (APs) that jointly serve users in a coordinated fashion, using only local channel state information at each AP. While the performance of cell-free massive MIMO can be analyzed using a similar methodology as in cellular massive MIMO, the fundamental limits, signal processing, and resource allocation are substantially different. In order to reduce the hardware cost and energy consumption in millimeter wave (mmWave) massive MIMO systems, beamspace MIMO has been proposed to significantly reduce the number of required radio-frequency (RF) chains by using lens antenna arrays or phase shifters. Alternatively, the intelligent reflecting surface (IRS) concept involves electromagnetically controllable surfaces that can be integrated into large-scale infrastructure such as building walls, airports, and stadiums. There are active and partially passive forms of large intelligent surface (LIS), and variants with either large antenna spacing or continuous aperture. There are also some substantial differences between the new multiple antenna technologies and traditional MIMO systems, such as transceiver design and propagation models. This special issue aims to highlight recent research on multiple antenna technologies.

Imagine a coverage area with many wireless access points that cooperate to jointly serve the users, instead of creating autonomous cells. Such a cell-free network operation can potentially resolve many of the interference issues that appear in current cellular networks. This ambition was previously called Network MIMO (multiple-input multiple-output) and has recently reappeared under the name Cell-Free Massive MIMO. The main challenge is to achieve the benefits of cell-free operation in a practically feasible way, with computational complexity and fronthaul requirements that are scalable to large networks with many users. We propose a new framework for scalable Cell-Free Massive MIMO systems by exploiting the dynamic cooperation cluster concept from the Network MIMO literature. We provide a novel algorithm for joint initial access, pilot assignment, and cluster formation that is proved to be scalable. Moreover, we adapt the standard channel estimation, precoding, and combining methods to become scalable. A new uplink and downlink duality is proved and used to heuristically design the precoding vectors on the basis of the combining vectors. Interestingly, the proposed scalable precoding and combining outperform conventional maximum ratio (MR) processing and also performs closely to the best unscalable alternatives.

This paper studies the transmit power optimization in multi-cell Massive multiple-input multiple-output (MIMO) systems. Network-wide max-min fairness (NW-MMF) and network-wide proportional fairness (NW-PF) are two well-known power control schemes in the literature. The NW-MMF focus on maximizing the fairness among users at the cost of penalizing users with good channel conditions. On the other hand, the NW-PF focuses on maximizing the sum SE, thereby ignoring fairness, but gives some extra attention to the weakest users. However, both of these schemes suffer from a scalability issue which means that for large networks, it is highly probable that one user has a very poor channel condition, pushing the spectral efficiency (SE) of all users towards zero. To overcome the scalability issue of NW-MMF and NW-PF, we propose a novel power control scheme that is provably scalable. This scheme maximizes the geometric mean (GM) of the per-cell max-min SE. To solve this new optimization problem, we prove that it can be rewritten in a convex optimization form and then solved using standard tools. The simulation results highlight the benefits of our model which is balancing between NW-PF and NW-MMF.

We consider backward crosstalk in 2 × 2 transmitters, which is caused by crosstalk from the outputs of the transmitter to the inputs or by the combination of output crosstalk and impedance mismatch. We analyze its impact via feedback networks together with third-order power amplifier non-linearities. We utilize the Bussgang decomposition to express the distorted output signals of the transmitter as a linear transformation of the input plus uncorrelated distortion. The normalized mean-square errors (NMSEs) between the distorted and desired amplified signals are expressed analytically and the optimal closed-form power back-off that minimizes the worst NMSE of the two branches is derived. In the second part of the paper, an achievable spectral efficiency (SE) is presented for the communication from this “dirty” transmitter to another single-antenna receiver. The SE-maximizing precoder is optimally found by exploiting the hardware characteristics. Furthermore, the optimal power back-off is analyzed for two sub-optimal precoders, which either do not exploit any hardware knowledge or only partial knowledge. The simulation results show that the performance of these sub-optimal precoders is close-to-optimal. We also discuss how the analysis in this paper can be extended to transmitters with an arbitrary number of antenna branches.

Since the seminal paper by Marzetta from 2010, Massive MIMO has changed from being a theoretical concept with an infinite number of antennas to a practical technology. The key concepts are adopted into the 5G New Radio Standard and base stations (BSs) with M = 64 fully digital transceivers have been commercially deployed in sub-6GHz bands. The fast progress was enabled by many solid research contributions of which the vast majority assume spatially uncorrelated channels and signal processing schemes developed for single-cell operation. These assumptions make the performance analysis and optimization of Massive MIMO tractable but have three major caveats: 1) practical channels are spatially correlated; 2) large performance gains can be obtained by multicell processing, without BS cooperation; 3) the interference caused by pilot contamination creates a finite capacity limit, as M → ∞. There is a thin line of papers that avoided these caveats, but the results are easily missed. Hence, this tutorial article explains the importance of considering spatial channel correlation and using signal processing schemes designed for multicell networks. We present recent results on the fundamental limits of Massive MIMO, which are not determined by pilot contamination but the ability to acquire channel statistics. These results will guide the journey towards the next level of Massive MIMO, which we call “Massive MIMO 2.0”.

Massive multiple-input multiple-output (MIMO) systems have attracted much attention lately due to the many advantages they provide over single-antenna systems. Owing to the many antennas, low-cost implementation and low power consumption per antenna are desired. To that end, massive MIMO structures with low-resolution analog-to-digital converters (ADC) have been investigated in many studies. However, the effect of a strong interferer in the adjacent band on quantized massive MIMO systems have not been examined yet. In this study, we analyze the performance of uplink massive MIMO with low-resolution ADCs under frequency selective fading with orthogonal frequency division multiplexing (OFDM) in the perfect and imperfect receiver channel state information cases. We derive analytical expressions for the bit error rate and ergodic capacity. We show that the interfering band can be suppressed by increasing the number of antennas or the oversampling rate when a zero-forcing receiver is employed.

Massive MIMO uses a large number of antennas to increase the spectral efficiency (SE) through spatial multiplexing of users, which requires accurate channel state information. It is often assumed that regular pilots (RP), where a fraction of the time-frequency resources is reserved for pilots, suffices to provide high SE. However, the SE is limited by the pilot overhead and pilot contamination. An alternative is superimposed pilots (SP) where all resources are used for pilots and data. This removes the pilot overhead and reduces pilot contamination by using longer pilots. However, SP suffers from data interference that reduces the SE gains. This paper proposes the Massive-MIMO Iterative Channel Estimation and Decoding (MICED) algorithm where partially decoded data is used as side-information to improve the channel estimation and increase SE. We show that users with precise data estimates can help users with poor data estimates to decode. Numerical results with QPSK modulation and LDPC codes show that the MICED algorithm increases the SE and reduces the block-error-rate with RP and SP compared to conventional methods. The MICED algorithm with SP delivers the highest SE and it is especially effective in scenarios with short coherence blocks like high mobility or high frequencies.

Cell-free Massive MIMO is considered as a promising technology for satisfying the increasing number of users and high rate expectations in beyond-5G networks. The key idea is to let many distributed access points (APs) communicate with all users in the network, possibly by using joint coherent signal processing. The aim of this paper is to provide the first comprehensive analysis of this technology under different degrees of cooperation among the APs. Particularly, the uplink spectral efficiencies of four different cell-free implementations are analyzed, with spatially correlated fading and arbitrary linear processing. It turns out that it is possible to outperform conventional Cellular Massive MIMO and small cell networks by a wide margin, but only using global or local minimum mean-square error (MMSE) combining. This is in sharp contrast to the existing literature, which advocates for maximum-ratio combining. Also, we show that a centralized implementation with optimal MMSE processing not only maximizes the SE but largely reduces the fronthaul signaling compared to the standard distributed approach. This makes it the preferred way to operate Cell-free Massive MIMO networks. Non-linear decoding is also investigated and shown to bring negligible improvements.

Large-scale distributed antenna systems with many access points (APs) that serve the users by coherent joint transmission is being considered for 5G-and-beyond networks. The technology is called Cell-free Massive MIMO and can provide a more uniform service level to the users than a conventional cellular topology. For a given user set, only a subset of the APs is likely needed to satisfy the users' performance demands, particularly outside the peak traffic hours. To find achieve an energy-efficient load balancing, we minimize the total downlink power consumption at the APs, considering both the transmit powers and hardware dissipation. APs can be temporarily turned off to reduce the latter part. The formulated optimization problem is non-convex but, nevertheless, a globally optimal solution is obtained by solving a mixed-integer second-order cone program. Since the computational complexity is prohibitive for real-time implementation, we also propose two low-complexity algorithms that exploit the inherent group-sparsity and the optimized transmit powers in the problem formulation. Numerical results manifest that our optimization algorithms can greatly reduce the power consumption compared to keeping all APs turned on and only minimizing the transmit powers. Moreover, the low-complexity algorithms can effectively handle the power allocation and AP activation for large-scale networks.

This paper considers the sum spectral efficiency (SE) optimization problem in multi-cell Massive MIMO systems with a varying number of active users. This is formulated as a joint pilot and data power control problem. Since the problem is non-convex, we first derive a novel iterative algorithm that obtains a stationary point in polynomial time. To enable real-time implementation, we also develop a deep learning solution. The proposed neural network, PowerNet, only uses the large-scale fading information to predict both the pilot and data powers. The main novelty is that we exploit the problem structure to design a single neural network that can handle a dynamically varying number of active users; hence, PowerNet is simultaneously approximating many different power control functions with varying number inputs and outputs. This is not the case in prior works and thus makes PowerNet an important step towards a practically useful solution. Numerical results demonstrate that PowerNet only loses 2% in sum SE, compared to the iterative algorithm, in a nine-cell system with up to 90 active users per in each coherence interval, and the runtime was only 0.03 ms on a graphics processing unit (GPU). When good data labels are selected for the training phase, PowerNet can yield better sum SE than by solving the optimization problem with one initial point.

Cell-free Massive MIMO (multiple-input multiple-output) is a promising distributed network architecture for 5G-and-beyond systems. It guarantees ubiquitous coverage at high spectral efficiency (SE) by leveraging signal co-processing at multiple access points (APs), aggressive spatial user multiplexing and extraordinary macro-diversity gain. In this study, we propose two distributed precoding schemes, referred to as local partial zero-forcing (PZF) and local protective partial zero-forcing (PPZF), that further improve the spectral efficiency by providing an adaptable trade-off between interference cancelation and boosting of the desired signal, with no additional front-hauling overhead, and implementable by APs with very few antennas. We derive closed-form expressions for the achievable SE under the assumption of independent Rayleigh fading channel, channel estimation error and pilot contamination. PZF and PPZF can substantially outperform maximum ratio transmission and zero-forcing, and their performance is comparable to that achieved by regularized zero-forcing (RZF), which is a benchmark in the downlink. Importantly, these closed-form expressions can be employed to devise optimal (long-term) power control strategies that are also suitable for RZF, whose closed-form expression for the SE is not available.

Massive multiple-input multiple-output (MIMO) systems have attracted much attention lately due to the many advantages they provide over single- antenna systems. Owing to the many antennas, low- cost implementation and low power consumption per antenna are desired. To that end, massive MIMO structures with one-bit analog-to-digital converters (ADC) have been investigated in many studies. However, the effect of a strong interferer in the adjacent band on one-bit quantized massive MIMO systems have not been examined yet. In this study, we analyze the performance of uplink massive MIMO with one-bit ADCs under frequency selective fading with orthogonal frequency division multiplexing (OFDM) in the perfect and imperfect receiver channel state information cases. We derive analytical expressions for the bit error rate and ergodic rate. We show that the interfering band can be suppressed by increasing the number of antennas or the oversampling rate when a zero-forcing receiver is employed.

In this paper, we study an active user detection problem for massive machine type communications (mMTC). The users transmit pilot-hopping sequences and detection of active users is performed based on the received energy. We utilize the channel hardening and fa-vorable propagation properties of massive multiple-input multiple-output (MIMO) to simplify the user detection. We propose and compare a number of different user detection methods and find that using non-negative least squares (NNLS) is well suited for the task at hand as it achieves good results as well as having the benefit of not having to specify further parameters.

This paper studies the transmit power optimization in a multi-cell massive multiple-input multiple-output (MIMO) system. To over-come the scalability issue of network-wide max-min fairness (NW-MMF), we propose a novel power control (PC) scheme. This scheme maximizes the geometric mean (GM) of the per-cell max-min spectral efficiency (SE). To solve this new optimization problem, we prove that it can be rewritten in a convex form and then solved using standard tools. To provide a fair comparison with the available utility functions in the literature, we solve the network-wide proportional fairness (NW-PF) PC as well. The NW-PF focuses on maximizing the sum SE, thereby ignoring fairness, but gives some extra attention to the weakest users. The simulation results highlight the benefits of our model which is balancing between NW-PF and NW-MMF.

In this paper, we study the joint power control and scheduling in uplink massive multiple-input multiple-output (MIMO) systems with random data arrivals. The data is generated at each user according to an individual stochastic process. Using Lyapunov optimization techniques, we develop a dynamic scheduling algorithm (DSA), which decides at each time slot the amount of data to admit to the transmission queues and the transmission rates over the wireless channel. The proposed algorithm achieves nearly optimal performance on the long-term user throughput under various fairness policies. Simulation results show that the DSA can improve the time-average delay performance compared to the state-of-the-art power control schemes developed for Massive MIMO with infinite backlogs.

This paper investigates the joint data and pilot power optimization for maximum sum spectral efficiency (SE) in multi-cell Massive MIMO systems, which is a non-convex problem. We first propose a new optimization algorithm, inspired by the weighted minimum mean square error (MMSE) approach, to obtain a stationary point in polynomial time. We then use this algorithm together with deep learning to train a convolutional neural network to perform the joint data and pilot power control in sub-millisecond runtime, making it suitable for online optimization in real multi-cell Massive MIMO systems. The numerical result demonstrates that the solution obtained by the neural network is 1% less than the stationary point for four-cell systems, while the sum SE loss is 2% in a nine-cell system.

This paper studies a two-layer decoding method that mitigates inter-cell interference in multi-cell Massive MIMO systems. In layer one, each base station (BS) estimates the channels to intra-cell users and uses the estimates for local decoding on each BS, followed by a second decoding layer where the BSs cooperate to mitigate inter-cell interference. An uplink achievable spectral efficiency (SE) expression is computed for arbitrary two-layer decoding schemes, while a closed-form expression is obtained for correlated Rayleigh fading channels, maximum-ratio combining (MRC), and large-scale fading decoding (LSFD) in the second layer. We formulate a non-convex sum SE maximization problem with both the data power and LSFD vectors as optimization variables and develop an algorithm based on the weighted MMSE (minimum mean square error) approach to obtain a stationary point with low computational complexity.

Cell-free massive multiple-input multiple-output (MIMO) is a promising network architecture for future wireless systems. This paper investigates the uplink performance of cell-free massive MIMO systems employing the least-square (LS) estimator over spatially correlated fading channels. We first derive a generalized closed-form expression of the spectral efficiency as a function of the number of access point (AP) antennas and the spatial correlation matrices. We use this result to analyze the impact that the fronthaul, number of users and number of APs have on the energy efficiency. Compared to traditional co-located massive MIMO using maximum ratio combining (MRC), our analysis shows that the large performance gain of cell-free massive MIMO with low-complexity linear LS estimators.

This paper takes a new look at Cell-free Massive MIMO (multiple-input multiple-output) through the lens of the dynamic cooperation cluster framework from the Network MIMO literature. The purpose is to identify and address scalability issues that appear in prior work. We provide distributed algorithms for initial access, pilot assignment, cluster formation, precoding, and combining that are scalable in the sense of being implementable with arbitrarily many users. Interestingly, the suggested precoding and combining outperform conjugate beamforming and matched filtering, respectively, while also being fully distributed.

In overloaded Massive MIMO systems, wherein the number K of user equipments (UEs) exceeds the number of base station antennas M, it has recently been shown that non-orthogonal multiple access (NOMA) can increase performance. This paper aims at identifying cases of the classical operating regime K <; M, where code-domain NOMA can also improve the spectral efficiency of Massive MIMO. Particular attention is given to use cases in which poor favorable propagation conditions are experienced. Numerical results show that Massive MIMO with planar antenna arrays can benefit from NOMA in practical scenarios where the UEs are spatially close to each other.

This paper analyzes how the distortion created by hardware impairments in a multiple-antenna base station affects the uplink spectral efficiency (SE), with a focus on massive multiple input multiple output (MIMO). This distortion is correlated across the antennas but has been often approximated as uncorrelated to facilitate (tractable) SE analysis. To determine when this approximation is accurate, basic properties of distortion correlation are first uncovered. Then, we separately analyze the distortion correlation caused by third-order non-linearities and by quantization. Finally, we study the SE numerically and show that the distortion correlation can be safely neglected in massive MIMO when there are sufficiently many users. Under independent identically distributed Rayleigh fading and equal signal-to-noise ratios (SNRs), this occurs for more than five transmitting users. Other channel models and SNR variations have only minor impact on the accuracy. We also demonstrate the importance of taking the distortion characteristics into account in the receive combining.

Massive multiple-input-multiple-output (MIMO) systems can suffer from coherent intercell interference due to the phenomenon of pilot contamination. This paper investigates a two-layer decoding method that mitigates both coherent and non-coherent interference in multi-cell Massive MIMO. To this end, each base station (BS) first estimates the channels to intra-cell users using either minimum mean-squared error (MMSE) or element-wise MMSE estimation based on uplink pilots. The estimates are used for local decoding on each BS followed by a second decoding layer where the BSs cooperate to mitigate inter-cell interference. An uplink achievable spectral efficiency (SE) expression is computed for arbitrary two-layer decoding schemes. A closed form expression is then obtained for correlated Rayleigh fading, maximum-ratio combining, and the proposed large-scale fading decoding (LSFD) in the second layer. We also formulate a sum SE maximization problem with both the data power and LSFD vectors as optimization variables. Since this is an NP-hard problem, we develop a low-complexity algorithm based on the weighted MMSE approach to obtain a local optimum. The numerical results show that both data power control and LSFD improve the sum SE performance over single-layer decoding multi-cell Massive MIMO systems.

In this paper, we consider device-to-device (D2D) communication that is underlaid in a multi-cell massive multiple-input multiple-output (MIMO) system and proposes a new framework for power control and pilot allocation. In this scheme, the cellular users (CUs) in each cell get orthogonal pilots which are reused with reuse factor one across cells, while all the D2D pairs share another set of orthogonal pilots. We derive a closed-form capacity lower bound for the CUs with different receive processing schemes. In addition, we derive a capacity lower bound for the D2D receivers and a closed-form approximation of it. We provide power control algorithms to maximize the minimum spectral efficiency (SE) and to maximize the product of the signal-to-interference-plus-noise ratios in the network. Different from prior works, in our proposed power control schemes, we consider joint pilot and data transmission optimization. Finally, we provide a numerical evaluation, where we compare our proposed power control schemes with the maximum transmit power case and the case of conventional multi-cell massive MIMO without D2D communication. Based on the provided results, we conclude that our proposed scheme increases the sum SE of multi-cell massive MIMO networks.

We consider transmission of system information in a cell-free massive MIMO system, when the transmitting access points do not have any channel state information and the receiving terminal has to estimate the channel based on downlink pilots. We analyze the system performance in terms of outage rate and coverage probability and use space-time block codes to increase performance. We propose a heuristic method for pilot/data power optimization that can be applied without any channel state information at the access points. We also analyze the problem of grouping the access points, which is needed when the single-antenna access points jointly transmit a space-time block code.

This paper considers multi-cell massive multiple-input multiple-output systems, where the channels are spatially correlated Rician fading. The channel model is composed of a deterministic line-of-sight path and a stochastic non-line-of-sight component describing a practical spatially correlated multipath environment. We derive the statistical properties of the minimum mean squared error (MMSE), element-wise MMSE, and least-square channel estimates for this model. Using these estimates for maximum ratio combining and precoding, rigorous closed-form uplink (UL) and downlink (DL) achievable spectral efficiency (SE) expressions are derived and analyzed. The asymptotic SE behavior, when using the different channel estimators, are also analyzed. The numerical results show that the SE is higher when using the MMSE estimator than that of the other estimators, and the performance gap increases with the number of antennas.

In this paper, we study the uplink (UL) and downlink (DL) spectral efficiency (SE) of a cell-free massive multiple-input-multiple-output (MIMO) system over Rician fading channels. The phase of the line-of-sight (LoS) path is modeled as a uniformly distributed random variable to take the phase-shifts due to mobility and phase noise into account. Considering the availability of prior information at the access points (APs), the phase-aware minimum mean square error (MMSE), non-aware linear MMSE (LMMSE), and least-square (LS) estimators are derived. The MMSE estimator requires perfectly estimated phase knowledge whereas the LMMSE and LS are derived without it. In the UL, a two-layer decoding method is investigated in order to mitigate both coherent and non-coherent interference. Closed-form UL SE expressions with phase-aware MMSE, LMMSE, and LS estimators are derived for maximum-ratio (MR) combining in the first layer and optimal large-scale fading decoding (LSFD) in the second layer. In the DL, two different transmission modes are studied: coherent and non-coherent. Closed-form DL SE expressions for both transmission modes with MR precoding are derived for the three estimators. Numerical results show that the LSFD improves the UL SE performance and coherent transmission mode performs much better than non-coherent transmission in the DL. Besides, the performance loss due to the lack of phase information depends on the pilot length and it is small when the pilot contamination is low.

In this paper, we consider the downlink of a multi-cell multiple-input multiple-output system and find the jointly optimal number of base station (BS) antennas and transmission powers that minimize the power consumption while satisfying each user's effective signal-to-interference-and-noise-ratio constraint and the BSs' power constraints. Different from prior work, we consider a power consumption model that takes both transmitted and hardware-consumed power into account. We formulate the joint optimization problem for both single-cell and multi-cell systems. The closed-form expressions for the optimal number of BS antennas and transmission powers are derived for the single-cell case. The analysis for the multi-cell case reveals that increasing the number of BS antennas in any cell always improves the performance of the overall system in terms of both feasibility and total radiated power. A key contribution of this paper is to show that the joint optimization problem can be relaxed as a geometric programming problem that can be solved efficiently. The solution can be utilized in practice to turn on and off antennas depending on the traffic load variations. The substantial power savings are demonstrated by simulation.

This paper considers the uplink of a distributed Massive MIMO network where N base stations (BSs), each equipped with M antennas, receive data from K = 2 users. We study the asymptotic spectral efficiency (as M → ∞) with spatial correlated channels, pilot contamination, and different degrees of channel state information (CSI) and statistical knowledge at the BSs. By considering a two-user setup, we can simply derive fundamental asymptotic behaviors and provide novel insights into the structure of the optimal combining schemes. In line with [1], when global CSI is available at all BSs, the optimal minimum-mean squared error combining has an unbounded capacity as M → ∞, if the global channel covariance matrices of the users are asymptotically linearly independent. This result is instrumental to derive a suboptimal combining scheme that provides unbounded capacity as M → ∞ using only local CSI and global channel statistics. The latter scheme is shown to outperform a generalized matched filter scheme, which also achieves asymptotic unbounded capacity by using only local CSI and global channel statistics, but is derived following [2] on the basis of a more conservative capacity bound.

This work introduces a new approach to solve the joint precoding and power allocation for sum rate maximization problem in the downlink multiuser MIMO by a combination of random matrix theory and optimization theory. The new approach results in a simplified problem that, though non-convex, obeys a simple separable structure. The sum rate maximization problem is decomposed into different single-variable optimization problems that can be solved in parallel. A water-filling-like solution is found, which can be applied under some mild conditions on the SNRs of the users. The proposed scheme provides large gains over heuristic solutions when the number of users in the cell is large, which suggests the applicability in massive MIMO systems.

We study joint unicast and multigroup multicast transmission in single-cell massive multiple-input-multiple-output (MIMO) systems, under maximum ratio transmission. For the unicast transmission, the objective is to maximize the weighted sum spectral efficiency (SE) of the unicast user terminals (UTs) and for the multicast transmission the objective is to maximize the minimum SE of the multicast UTs. These two problems are coupled to each other in a conflicting manner, due to their shared power resource and interference. To address this, we formulate a multiobjective optimization problem (MOOP). We derive the Pareto boundary of the MOOP analytically and determine the values of the system parameters to achieve any desired Pareto optimal point. Moreover, we prove that the Pareto region is convex, hence the system should serve the unicast and multicast UTs at the same time-frequency resource.

Future cellular networks are expected to support new communication paradigms such as machine-type communication (MTC) services along with human-type communication (HTC) services. This requires base stations to serve a large number of devices in relatively short channel coherence intervals which renders allocation of orthogonal pilot sequence per-device approaches impractical. Furthermore, the stringent power constraints, place-and-play type connectivity and various data rate requirements of MTC devices make it impossible for the traditional cellular architecture to accommodate MTC and HTC services together. Massive multiple-input-multiple-output (MaMIMO) technology has the potential to allow the coexistence of HTC and MTC services, thanks to its inherent spatial multiplexing properties and low transmission power requirements. In this work, we investigate the performance of a single cell under a shared physical channel assumption for MTC and HTC services and propose a novel scheme for sharing the time-frequency resources. The analysis reveals that MaMIMO can significantly enhance the performance of such a setup and allow the inclusion of MTC services into the cellular networks without requiring additional resources.

In this paper, we investigate downlink power control in massive multiple-input multiple-output (MIMO) networks with distributed antenna arrays. The base station (BS) in each cell consists of multiple antenna arrays, which are deployed in arbitrary locations within the cell. Due to the spatial separation between antenna arrays, the large-scale propagation effect is different from a user to different antenna arrays in a cell, which makes power control a challenging problem as compared to conventional massive MIMO. We assume that the BS in each cell obtains the channel estimates via uplink pilots. Based on the channel estimates, the BSs perform maximum ratio transmission for the downlink. We then derive a closed-form spectral efficiency (SE) expression, where the channels are subject to correlated fading. Utilizing the derived expression, we propose a max-min power control algorithm to ensure that each user in the network receives a uniform quality of service. Numerical results demonstrate that, for the network considered in this work, optimizing for max-min SE through the max-min power control improves the sum SE of the network as compared to equal power allocation.

Large-scale massive MIMO network deployments can provide higher spectral efficiency and better coverage for future communication systems like 5G. Due to the large number of antennas at the base station, the system achieves stable channel quality and spatially separable channels to the different users. In this paper, linear, planar, circular and cylindrical arrays are used in the evaluation of a large-scale multi-cell massive MIMO network. The system-level performance is predicted using two different kinds of channel models. First, a ray-based deterministic tool is utilized in a real North American city environment. Second, an independent and identically distributed (i.i.d.) Rayleigh fading channel model is considered, as often used in previously published massive MIMO studies. The analysis is conducted in a 16-macro-cell network with outdoor and randomly distributed users. It is shown that the array configuration has a large impact on the throughput statistics. Although the system-level performance with i.i.d. Rayleigh fading can be close to the deterministic prediction in some situations (e.g., with large linear arrays), significant differences are noticed when considering other types of arrays.

In this work, we consider the downlink of a multi-user multiple-input multiple-output (MIMO) system and aim to find the jointly optimal number of base station (BS) antennas and transmission powers that minimize the power consumption while satisfying each user's signal-to-interference-and-noise-ratio (SINR) constraint and the BS's power constraint. Different from prior work, we consider a power consumption model that takes both transmitted and hardware-consumed power into account. We formulate the joint optimization problem for a single-cell system and derive closed-form expressions for the optimal number of BS antennas and transmission powers. The solution can be utilized in practice to turn on and off antennas depending on the traffic load variations. Substantial power savings are demonstrated by simulation.

Cell-free (CF) massive multiple-input multiple-output (MIMO) is an alternative topology for future wireless networks, where a large number of single-antenna access points (APs) are distributed over the coverage area. There are no cells but all users are jointly served by the APs using network MIMO methods. Prior works have claimed that the CF massive MIMO inherits the basic properties of cellular massive MIMO, namely, channel hardening and favorable propagation. In this paper, we evaluate if one can rely on these properties when having a realistic stochastic AP deployment. Our results show that channel hardening only appears in special cases, for example, when the pathloss exponent is small. However, by using 5-10 antennas per AP, instead of one, we can substantially improve the hardening. Only spatially well-separated users will exhibit favorable propagation, but when adding more antennas and/or reducing the pathloss exponent, it becomes more likely for favorable propagation to occur. The conclusion is that we cannot rely on the channel hardening and the favorable propagation when analyzing and designing the CF massive MIMO networks, but we need to use achievable rate expressions and resource allocation schemes that work well also in the absence of these properties. Some options are reviewed in this paper.

This paper analyzes the performance of linearly precoded time division duplex based multi-user massive MIMO downlink system under joint impacts of channel non-reciprocity (NRC) and imperfect channel state information. We consider a generic and realistic NRC model that accounts for transceiver frequency-response as well as mutual coupling mismatches at both user equipment (UE) and base station (BS) sides. The analysis covers two most prominent forms of linear precoding schemes, namely, zero-forcing (ZF) and maximum-ratio transmission (MRT), and assumes that only the statistical properties of the beamformed channel are used at the UE side to decode the received signal. Under the approximation of i.i.d. Gaussian channels, closed-form analytical expressions are derived for the effective signal to interference and noise ratios (SINRs) and the corresponding capacity lower bounds. The expressions show that, in moderate to high SNR, the additional interference caused by imperfect NRC calibration can degrade the performance of both precoders significantly. Moreover, ZF is shown to be more sensitive to NRC than MRT. Numerical evaluations with practical NRC levels indicate that this performance loss in the spectral efficiency can be as high as 42% for ZF, whereas it is typically less than 13% for MRT. It is also shown that due to the NRC, the asymptotic large-antenna performance of both precoders saturate to an identical finite level. The derived analytical expressions provide useful tools and valuable technical insight, e.g., into calculating the NRC calibration requirements in BSs and UEs for any given specific performance targets in terms of effective SINR or the system capacity bound.

We design a jamming-resistant receiver scheme to enhance the robustness of a massive MIMO uplink system against jamming. We assume that a jammer attacks the system both in the pilot and data transmission phases. The key feature of the proposed scheme is that, in the pilot phase, the base station estimates not only the legitimate channel, but also the jamming channel by exploiting a purposely unused pilot sequence. The jamming channel estimate is used to construct linear receiver filters that reject the impact of the jamming signal. The performance of the proposed scheme is analytically evaluated using the asymptotic properties of massive MIMO. The best regularized zero-forcing receiver and the optimal power allocations for the legitimate system and the jammer are also studied. Numerical results are provided to verify our analysis and show that the proposed scheme greatly improves the achievable rates, as compared with conventional receivers. Interestingly, the proposed scheme works particularly well under strong jamming attacks, since the improved estimate of the jamming channel outweighs the extra jamming power.

The capacity of cellular networks can be improved by the unprecedented array gain and spatial multiplexing offered by Massive MIMO. Since its inception, the coherent interference caused by pilot contamination has been believed to create a finite capacity limit, as the number of antennas goes to infinity. In this paper, we prove that this is incorrect and an artifact from using simplistic channel models and suboptimal precoding/combining schemes. We show that with multicell MMSE precoding/combining and a tiny amount of spatial channel correlation or large-scale fading variations over the array, the capacity increases without bound as the number of antennas increases, even under pilot contamination. More precisely, the result holds when the channel covariance matrices of the contaminating users are asymptotically linearly independent, which is generally the case. If also the diagonals of the covariance matrices are linearly independent, it is sufficient to know these diagonals (and not the full covariance matrices) to achieve an unlimited asymptotic capacity.

This paper considers the use of non-orthogonal-multiple-access (NOMA) in multiuser MIMO systems in practical scenarios where channel state information (CSI) is acquired through pilot signaling. A new NOMA scheme that uses shared pilots is proposed. Achievable rate analysis is carried out for different pilot signaling schemes, including both uplink and downlink pilots. The achievable rate performance of the proposed NOMA scheme with shared pilot within each group is compared with the traditional orthogonal access scheme with orthogonal pilots. Our proposed scheme is a generalization of the orthogonal scheme, and can be reduced to the orthogonal scheme when appropriate power allocation parameters are chosen. Numerical results show that when downlink CSI is available at the users, our proposed NOMA scheme outperforms orthogonal schemes. However with more groups of users present in the cell, it is preferable to use multi-user beamforming instead of NOMA.

This paper considers pilot design to mitigate pilot contamination and provide good service for everyone in multi-cell massive multiple-input-multiple-output systems. Instead of modeling the pilot design as a combinatorial assignment problem, as in prior works, we express the pilot signals using a pilot basis and treat the associated power coefficients as continuous optimization variables. We compute a lower bound on the uplink capacity for Rayleigh fading channels with maximum ratio detection that applies with arbitrary pilot signals. We further formulate the max-min fairness problem under power budget constraints, with the pilot signals and data powers as optimization variables. Because this optimization problem is non-deterministic polynomial-time hard due to signomial constraints, we then propose an algorithm to obtain a local optimum with polynomial complexity. Our framework serves as a benchmark for pilot design in scenarios with either ideal or non-ideal hardware. Numerical results manifest that the proposed optimization algorithms are close to the optimal solution obtained by exhaustive search for different pilot assignments and the new pilot structure and optimization bring large gains over the state-of-the-art suboptimal pilot design.

We consider transmission of system information in massive multiple-input multiple-output (MIMO). This information needs to be reliably delivered to inactive users in the cell without any channel state information at the base station. Downlink transmission entails the use of downlink pilots and a special type of precoding that aims to reduce the dimension of the downlink channel and the pilot overhead, which would otherwise scale with the number of base station antennas. We consider a scenario in which the base station transmits over a small number of coherence intervals, providing little time/frequency diversity. The system information is transmitted with orthogonal space-time block codes to increase reliability and performance is measured using outage rates. Several different codes are compared, both for spatially correlated and uncorrelated channels and for varying amounts of time/frequency diversity. We show that a massive MIMO base station can outperform a single-antenna base station in all considered scenarios.

This paper considers a two-way half-duplex decode-and-forward relaying system, where multiple pairs of single-antenna users exchange information via a multiple-antenna relay. Assuming that the channel knowledge is nonideal and the relay employs maximum ratio processing, we derive a largescale approximation of the sum spectral efficiency (SE) that is tight when the number of relay antennas M becomes very large. Furthermore, we study how the transmit power scales with M to maintain a desired SE. In particular, three special powerscaling cases are discussed and the corresponding asymptotic SE is deduced with clear insights. Our elegant power-scaling laws reveal a tradeoff between the transmit powers of the user/relay and pilot symbol. Finally, we formulate a power allocation problem in terms of maximizing the sum SE and obtain a local optimum by solving a sequence of geometric programming problems.

This paper considers the downlink precoding for physical layer multicasting in massive multiple-input multiple-output (MIMO) systems. We study the max-min fairness (MMF) problem, where channel state information at the transmitter is used to design precoding vectors that maximize the minimum spectral efficiency (SE) of the system, given fixed power budgets for uplink training and downlink transmission. Our system model accounts for channel estimation, pilot contamination, arbitrary path-losses, and multi-group multicasting. We consider six scenarios with different transmission technologies (unicast and multicast), different pilot assignment strategies (dedicated or shared pilot assignments), and different precoding schemes (maximum ratio transmission and zero forcing), and derive achievable spectral efficiencies for all possible combinations. Then, we solve the MMF problem for each of these scenarios, and for any given pilot length, we find the SE maximizing uplink pilot and downlink data transmission policies, all in closed forms. We use these results to draw a general guideline for massive MIMO multicasting design, where for a given number of base station antennas, number of users, and coherence interval length, we determine the multicasting scheme that shall be used.

We study the joint unicast and multi-group multicast transmission in massive multiple-input multiple-output systems. We consider a system model that accounts for channel estimation and pilot contamination and derive achievable spectral efficiencies (SEs) for unicast and multicast user terminals (UTs) under maximum ratio transmission and zero-forcing precoding. For unicast transmission, our objective is to maximize the weighted sum SE of the unicast UTs, and for the multicast transmission, our objective is to maximize the minimum SE of the multicast UTs. These two objectives are coupled in a conflicting manner, due to their shared power resource. Therefore, we formulate a multiobjective optimization problem (MOOP) for the two conflicting objectives. We derive the Pareto boundary of the MOOP analytically. As each Pareto optimal point describes a particular efficient tradeoff between the two objectives of the system, we determine the values of the system parameters (uplink training powers, downlink transmission powers, and so on) to achieve any desired Pareto optimal point. Moreover, we prove that the Pareto region is convex, and hence, the system should serve the unicast and multicast UTs at the same time-frequency resource. Finally, we validate our results using numerical simulations.

Next-generation wireless networks aim at providing substantial improvements in spectral efficiency (SE) and energy efficiency (EE). Massive MIMO has been proved to be a viable technology to achieve these goals by spatially multiplexing several users using many base station (BS) antennas. A potential limitation of massive MIMO in multicell systems is pilot contamination, which arises in the channel estimation process from the interference caused by reusing pilots in neighboring cells. A standard method to reduce pilot contamination, known as regular pilot (RP), is to adjust the length of pilot sequences while transmitting data and pilot symbols disjointly. An alternative method, called superimposed pilot (SP), sends a superposition of pilot and data symbols. This allows use of longer pilots which, in turn, reduces pilot contamination. We consider the uplink of a multicell massive MIMO network, with i.i.d. Rayleigh fading channels, using maximum ratio combining and compare RP and SP in terms of SE and EE. To this end, we derive rigorous closed-form achievable rates with SP under a practical random BS deployment. We prove that the reduction of pilot contamination with SP is outweighed by the additional coherent and non-coherent interference. Numerical results show that when both methods are optimized, RP achieves comparable SE and EE to SP in practical scenarios.

This work aims to design a cellular network for maximal energy efficiency (EE). In particular, we consider the uplink with multi-antenna base stations and assume that zero- forcing (ZF) combining is used for data detection with imperfect channel state information. Using stochastic geometry and a new lower bound on the average per-user spectral efficiency of the network, we optimize the pilot reuse factor, number of antennas and users per base station. Closed- form expressions are computed from which valuable insights into the interplay between the optimization variables, hardware characteristics, and propagation environment are obtained. Numerical results are used to validate the analysis and make comparisons with a network using maximum ratio (MR) combining. The results show that a Massive MIMO setup arises as the EE-optimal network configuration. In addition, ZF provides higher EE than MR while allowing a smaller pilot reuse factor and a more dense network deployment.

Optimal physical layer multicasting (PLM) is an NP-hard problem that for simplicity has been studied under idealistic assumptions, e.g., availability of perfect channel state information (CSI), both at the base station (BS) and at the user terminals (UTs). With the advent of massive multiple-input-multiple-output (MIMO), PLM has become more challenging, as the computational complexity of the precoder design is proportional to the number of BS antennas. In this paper, we address these issues by introducing computationally efficient precoders that account for practical CSI acquisition. We derive achievable spectral efficiencies for the proposed precoders. Then we introduce a novel problem formulation for the max-min fairness power control that accounts the CSI acquisition overhead, uplink training and downlink transmission powers. We solve this problem and find the optimal uplink and downlink power control policies in closed form. Using numerical simulations, we verify the effectiveness of our proposed schemes comparing them with the state of the art PLM schemes for massive MIMO systems.

Massive multiple-input multiple-output (MIMO) is a viable technology to improve the spectral efficiency (SE) by spatially multiplexing several users. A potential limitation of Massive MIMO in multicell systems is pilot contamination, which arises from interference in the channel estimation due to the reuse of pilot sequences in neighboring cells. A standard method to reduce pilot contamination, referred to as regular pilot (RP), is to adjust the length of the pilot sequences while transmitting data and pilot symbols disjointly. Alternatively, the superimposed pilot (SP) method sends a superposition of pilot and data symbols, thereby allowing the use of longer pilots which can also reduce pilot contamination. This work considers the uplink of a general multicell Massive MIMO system with SP and maximum ratio combining and derives rigorous closed-form achievable rates, which are used to make comparisons with RP. Numerical results consider a realistic random base station deployment and show that with SP the reduction of pilot contamination is outweighed by the additional coherent and non-coherent interference from the data transmission. Moreover, it turns out that, when the pilot length is optimized, RP provides comparable SE as with SP.

We design jamming resistant receivers to enhance the robustness of a massive MIMO uplink channel against jamming. In the pilot phase, we estimate not only the desired channel, but also the jamming channel by exploiting purposely unused pilot sequences. The jamming channel estimate is used to construct the linear receive filter to reduce impact that jamming has on the achievable rates. The performance of the proposed scheme is analytically and numerically evaluated. These results show that the proposed scheme greatly improves the rates, as compared to conventional receivers. Moreover, the proposed schemes still work well with stronger jamming power.

In massive MIMO systems, which rely on uplink pilots to estimate the channel, the time interval between pilot transmissions constrains the length of the downlink. Since switching between up- and downlink takes time, longer downlink blocks increase the effective spectral efficiency. We investigate the use of low-complexity channel models and Kalman filters for channel prediction, to allow for longer intervals between the pilots. Specifically, we quantify how often uplink pilots have to be sent when the downlink rate is allowed to degrade by a certain percentage. To this end, we consider a time-correlated channel aging model, whose spectrum is rectangular, and use autoregressive moving average (ARMA) processes to approximate the time-variations of such channels. We show that ARMA-based predictors can increase the interval between pilots and the spectral efficiency in channels with high Doppler spreads. We also show that Kalman prediction is robust to mismatches in the channel statistics.

Consider the uplink transmission of a single-cell multi-user multiple-input multiple-output (MIMO) system with K single-antenna users and a base station (BS) equipped with a very large number of antennas denoted by M. Consider a jamming device with N > M distributed antennas attempting to deteriorate the communication between the users and the BS. We propose an asymptotic condition on the jamming power under which the jamming-plus-noise subspace overlaps with the signal subspace. Under this condition, existing blind jamming rejection methods, such as the one in [1], fail. The proposed results are based on the application of results from large-dimensional random matrix theory.

Massive MIMO (multiple-input multiple-output) provides great improvements in spectral efficiency over legacy cellular networks, by coherent combining of the signals over a large antenna array and by spatial multiplexing of many users. Since its inception, the coherent interference caused by pilot contamination has been believed to be an impairment that does not vanish, even with an unlimited number of antennas. In this work, we show that this belief is incorrect and an artifact from using simplistic channel models and suboptimal signal processing schemes. We focus on the uplink and prove that with multicell MMSE combining, the spectral efficiency grows without bound as the number of antennas increases, even under pilot contamination, under a condition of linear independence between the channel covariance matrices. This condition is generally satisfied, except in special cases that are hardly found in practice.

This paper optimizes the pilot assignment and pilot transmit powers to mitigate pilot contamination in Massive MIMO (multiple-input multiple-output) systems. While prior works have treated pilot assignment as a combinatorial problem, we achieve a more tractable problem formulation by directly optimizing the pilot sequences. To this end, we compute a lower bound on the uplink (UL) spectral efficiency (SE), for Rayleigh fading channels with maximum ratio (MR) detection and arbitrary pilot sequences. We optimize the max-min SE with respect to the pilot sequences and pilot powers, under power budget constraints. This becomes an NP-hard signomial problem, but we propose an efficient algorithm to obtain a local optimum with polynomial complexity. Numerical results manifest the near optimality of the proposed algorithm and show significant gains over existing suboptimal algorithms.

The phenomenon of pilot contamination (PC) in multi-cell Massive MIMO systems is investigated in the presence of imperfect timing synchronization (TS). In particular, a basic setup is considered, where a base station (BS) is perfectly synchronized with the user of its cell, but there is imperfect TS between the BS and the user in another cell, possibly due to different propagation distances. A discrete-time system model is derived based on the continuous-time system model. The discrete-time system model accurately captures the phenomenon of imperfect TS in terms of the timing mismatch and the pulse shaping filter impulse responses. The derived discrete-time system model is used to study the achievable rates of a two-cell Massive MIMO uplink. It is shown that the structure imposed to the pilot contaminating signal due to the imperfect TS can be leveraged to mitigate the effect of PC. The level of PC suppression is quantified as a function of the timing mismatch and the characteristics of the transmit/receive pulse shaping filters.

Millimeter wave (mmWave) communications have recently attracted large research interest, since the huge available bandwidth can potentially lead to the rates of multiple gigabit per second per user. Though mmWave can be readily used in stationary scenarios, such as indoor hotspots or backhaul, it is challenging to use mmWave in mobile networks, where the transmitting/receiving nodes may be moving, channels may have a complicated structure, and the coordination among multiple nodes is difficult. To fully exploit the high potential rates of mmWave in mobile networks, lots of technical problems must be addressed. This paper presents a comprehensive survey of mmWave communications for future mobile networks (5G and beyond). We first summarize the recent channel measurement campaigns and modeling results. Then, we discuss in detail recent progresses in multiple input multiple output transceiver design for mmWave communications. After that, we provide an overview of the solution for multiple access and backhauling, followed by the analysis of coverage and connectivity. Finally, the progresses in the standardization and deployment of mmWave for mobile networks are discussed.

For the potential of providing rates of multiple Giga-bps in a single channel, millimeter wave (mmWave) communications have recently attracted substantial research interest. While mmWave technology is already being used in stationary scenarios such as indoor hotspots or backhaul, it is challenging to use mmWave frequencies in mobile networks, where transmitting/receiving nodes may be moving, channels may have a complicated structure, and the coordination among multiple nodes is difficult. To fully exploit the high potential rates of mmWave in mobile networks, many significant technical challenges must be tackled. The main objective of this IEEE JSAC Special Issue on “Millimeter wave communications for future mobile networks” is to collect the most recent technical advances in mmWave for future mobile networks. The response from the community to the call has been overwhelming. We received 96 submissions with a call period short than 4 months. Many of the submissions are from the most well known research groups in the field. After a strict review process, we decided to accept 38 papers, which will be published in two issues. The papers were selected based on the technical relevance and merits. Unfortunately, due to space limitations, a number of interesting papers were not selected, despite the merits that they had. We sincerely hope those papers can find other publishing venues.

We present a method for jamming a time-division duplex link using a transceiver with a large number of antennas. By utilizing beamforming, a jammer with M antennas can degrade the spectral efficiency of the primary link more than conventional omnidirectional jammers under the same power constraint, or perform equally well with approximately 1/M of the output power. The jammer operates without any prior knowledge of channels to the legitimate transmitters, or the legitimate signals by relying on channel reciprocity.

The massive multiple-input multiple-output (MIMO) technology has great potential to manage the rapid growth of wireless data traffic. Massive MIMO achieves tremendous spectral efficiency by spatial multiplexing many tens of user equipments (UEs). These gains are only achieved in practice if many more UEs can connect efficiently to the network than today. As the number of UEs increases, while each UE intermittently accesses the network, the random access functionality becomes essential to share the limited number of pilots among the UEs. In this paper, we revisit the random access problem in the Massive MIMO context and develop a reengineered protocol, termedstrongest-user collision resolution(SUCRe). An accessing UE asks for a dedicated pilot by sending an uncoordinated random access pilot, with a risk that other UEs send the same pilot. The favorable propagation of massive MIMO channels is utilized to enable distributed collision detection at each UE, thereby determining the strength of the contenders’ signals and deciding to repeat the pilot if the UE judges that its signal at the receiver is the strongest. The SUCRe protocol resolves the vast majority of all pilot collisions in crowded urban scenarios and continues to admit UEs efficiently in overloaded networks.

A massive MIMO system, represented by a base station with hundreds of antennas, is capable of spatially multiplexing many devices and thus naturally suited to serve dense crowds of wireless devices in emerging applications, such as machine-type communications. Crowd scenarios pose new challenges in the pilot-based acquisition of channel state information and call for pilot access protocols that match the intermittent pattern of device activity. A joint pilot assignment and data transmission protocol based on random access is proposed in this paper for the uplink of a massive MIMO system. The protocol relies on the averaging across multiple transmission slots of the pilot collision events that result from the random access process. We derive new uplink sum rate expressions that take pilot collisions, intermittent device activity, and interference into account. Simplified bounds are obtained and used to optimize the device activation probability and pilot length. A performance analysis indicates how performance scales as a function of the number of antennas and the transmission slot duration.

Massive MIMO systems, where the base stations are equipped with hundreds of antenna elements, are an attractive way to attain unprecedented spectral efficiency in future wireless networks. In the "classical" massive MIMO setting, the terminals are assumed fully loaded and a main impairment to the performance comes from the inter-cell pilot contamination, i.e., interference from terminals in neighboring cells using the same pilots as in the home cell. However, when the terminals are active intermittently, it is viable to avoid inter-cell contamination by pre-allocation of pilots, while same-cell terminals use random access to select the allocated pilot sequences. This leads to the problem of intra-cell pilot contamination. We propose a framework for random access in massive MIMO networks and derive new uplink sum rate expressions that take intra-cell pilot collisions, intermittent terminal activity, and interference into account. We use these expressions to optimize the terminal activation probability and pilot length.

We consider a multi-pair two-way amplify-and-forward relaying system with a massive antenna array at the relay and estimated channel state information, assuming maximum-ratio combining/transmission processing. Closed-form approximations of the sum spectral efficiency are developed and simple analytical power scaling laws are presented, which reveal a fundamental trade-off between the transmit powers of each user/the relay and of each pilot symbol. Finally, the optimal power allocation problem is studied.

Consider a multicell multiuser MIMO (multiple-input multiple-output) system with a very large number of antennas at each base station (BS). The number of users in each cell is assumed to be fixed as the number of BS antennas grows large. Under certain conditions on the powers of the transmitting users, the signal eigenvalue spectrum is asymptotically separated from the interference-plus-noise spectrum as the number of BS antennas grows large. As it was observed in [1], this phenomenon allows to mitigate the pilot contamination problem. We provide the power limits for each user in the cell of interest above which such a separation occurs asymptotically. Unlike the approximative methods used in [1], we obtain these power limits by making use of the exact asymptotic characterizations of the interference-plus-noise spectrum. The results are based on the theory of small rank perturbations of large dimensional random matrices.

State-of-the-art algorithms for energy-efficient power allocation in wireless networks are based on fractional programming theory, and allow to find the global maximum of the energy efficiency only in noise-limited scenarios. In interference-limited scenarios, several sub-optimal solutions have been proposed, but an efficient framework to globally maximize energy-efficient metrics is lacking. The goal of this work is to fill this gap by making use of fractional programming theory jointly with monotonic optimization. The resulting optimization framework is useful for at least two main reasons. First, it sheds light on the ultimate energy-efficiency performance of wireless networks. Second, it provides the means to benchmark the energy efficiency of state-of-the-art, but sub-optimal, solutions.

Wireless networks with many antennas at the base stations and multiplexing of many users, known as Massive MIMO systems, are key to handle the rapid growth of data traffic. As the number of users increases, the random access in contemporary networks will be flooded by user collisions. In this paper, we propose a reengineered random access protocol, coined strongest-user collision resolution (SUCR). It exploits the channel hardening feature of Massive MIMO channels to enable each user to detect collisions, determine how strong the contenders' channels are, and only keep transmitting if it has the strongest channel gain. The proposed SUCR protocol can quickly and distributively resolve the vast majority of all pilot collisions.

This paper aims to minimize the total transmit power consumption for Massive MIMO (multiple-input multiple-output) downlink cellular systems when each user is served by the optimized subset of the base stations (BSs). We derive a lower bound on the ergodic spectral efficiency (SE) for Rayleigh fading channels and maximum ratio transmission (MRT) when the BSs cooperate using non-coherent joint transmission. We solve the joint user association and downlink transmit power minimization problem optimally under fixed SE constraints. Furthermore, we solve a max-min fairness problem with user specific weights that maximizes the worst SE among the users. The optimal BS-user association rule is derived, which is different from maximum signal-to-noise-ratio (max-SNR) association. Simulation results manifest that the proposed methods can provide good SE for the users using less transmit power than in small-scale systems and that the optimal user association can effectively balance the load between BSs when needed.

In high-density low-bitrate Internet-of-Things (IoT) use case of 5G networks, the terminals and sensors are to be of extremely low-cost and low energy-consuming. Typically, the analog-to-digital converters (ADCs) dominate the power-budget of receiver chains, in particular if the quantization resolution is high. Hence, receiver architectures deploying 1-bit ADCs are of high interest towards realizing low-cost, high energy-efficiency device solutions. In this paper, we study the waveform design and optimization for a narrowband low-bitrate massive MISO downlink targeting to achieve rates higher than 1 bits/sec (per real-dimension) where the terminal receivers adopt only simple 1-bit quantization (per real-dimension) with oversampling. In this respect, first we show that for a particular precoder structure, the overall link is equivalent to that of an AWGN SISO with controlled intersymbol interference (ISI). The filter design problem for generating the desired ISI in such SISO links has been studied in previous works, however, the only known method in literature is a computationally demanding brute force search method. As a novel contribution, we develop models and tools that elaborate on the conditions to be satisfied for unique detection and existence of solution for the filter coefficients. Then, as a concrete example, the developed models and tools are utilized to show that in the absence of noise, five-times oversampling is required for unique detection of 16-QAM input alphabet. Building on these findings, we then develop novel algorithms that can efficiently design the filter coefficients. Examples and simulations are provided to elaborate on filter coefficient design and optimization, and to illustrate good SER performance of the MISO link with 1-bit receiver even at SNRs down to 5 dB.

The continuous rise in wireless data traffic brings forth an increase in power consumption and static users constitute a large fraction of these traffic demands. This work focuses on designing cellular networks to deliver a given data rate per area and user, while minimizing the power consumption. In particular we are interested in optimizing the transmission power, density of access points (APs), number of AP antennas and number of users served in each cell. To this end, we consider a network model based on stochastic geometry and a detailed power consumption model to derive closed form expressions and obtain insights on the interplay of the aforementioned design parameters. The results show that, in contrast with previous works on optimal network design for energy efficiency, having exceedingly high AP density does not bring the most benefits in terms of power savings. Instead the AP density should be chosen according to the area data rate that we want to deliver. In addition numerical results show that the minimum power consumption is obtained in the Massive MIMO regime with many antennas and users per AP.

What would a cellular network designed for maximal energy efficiency look like? To answer this fundamental question, tools from stochastic geometry are used in this paper to model future cellular networks and obtain a new lower bound on the average uplink spectral efficiency. This enables us to formulate a tractable uplink energy efficiency (EE) maximization problem and solve it analytically with respect to the density of base stations (BSs), the transmit power levels, the number of BS antennas and users per cell, and the pilot reuse factor. The closed-form expressions obtained from this general EE maximization framework provide valuable insights on the interplay between the optimization variables, hardware characteristics, and propagation environment. Small cells are proved to give high EE, but the EE improvement saturates quickly with the BS density. Interestingly, the maximal EE is achieved by also equipping the BSs with multiple antennas and operate in a “massive MIMO” fashion, where the array gain from coherent detection mitigates interference and the multiplexing of many users reduces the energy cost per user.

The problem of maximum likelihood (ML) detection in training-assisted single-input multiple-output (SIMO) systems with phase noise impairments is studied for two different scenarios, i.e., the case when the channel is deterministic and known (constant channel) and the case when the channel is stochastic and unknown (fading channel). Furthermore, two different operations with respect to the phase noise sources are considered, namely, the case of identical phase noise sources and the case of independent phase noise sources over the antennas. In all scenarios, the optimal detector is derived for a very general parameterization of the phase noise distribution. Furthermore, a high signal-to-noise-ratio (SNR) analysis is performed to show that symbol-error-rate (SER) floors appear in all cases. The SER floor in the case of identical phase noise sources (for both constant and fading channels) is independent of the number of antenna elements. In contrast, the SER floor in the case of independent phase noise sources is reduced when increasing the number of antenna elements (for both constant and fading channels). Finally, the system model is extended to multiple data channel uses and it is shown that the conclusion is valid for these setups, as well.

Massive MIMO is a promising technique for increasing the spectral efficiency (SE) of cellular networks, by deploying antenna arrays with hundreds or thousands of active elements at the base stations and performing coherent transceiver processing. A common rule-of-thumb is that these systems should have an order of magnitude more antennas M than scheduled users K because the users' channels are likely to be near-orthogonal when M/K 10. However, it has not been proved that this rule-of-thumb actually maximizes the SE. In this paper, we analyze how the optimal number of scheduled users K* depends on M and other system parameters. To this end, new SE expressions are derived to enable efficient system-level analysis with power control, arbitrary pilot reuse, and random user locations. The value of K* in the large-M regime is derived in closed form, while simulations are used to show what happens at finite M, in different interference scenarios, with different pilot reuse factors, and for different processing schemes. Up to half the coherence block should be dedicated to pilots and the optimal M/K is less than 10 in many cases of practical relevance. Interestingly, K* depends strongly on the processing scheme and hence it is unfair to compare different schemes using the same K.

This paper investigates the joint power allocation and user association problem in multi-cell Massive MIMO (multiple-input multiple-output) downlink (DL) systems. The target is to minimize the total transmit power consumption when each user is served by an optimized subset of the base stations (BSs), using non-coherent joint transmission. We first derive a lower bound on the ergodic spectral efficiency (SE), which is applicable for any channel distribution and precoding scheme. Closed-form expressions are obtained for Rayleigh fading channels with either maximum ratio transmission (MRT) or zero forcing (ZF) precoding. From these bounds, we further formulate the DL power minimization problems with fixed SE constraints for the users. These problems are proved to be solvable as linear programs, giving the optimal power allocation and BS-user association with low complexity. Furthermore, we formulate a max-min fairness problem that maximizes the worst SE among the users, and we show that it can be solved as a quasi-linear program. Simulations manifest that the proposed methods provide good SE for the users using less transmit power than in small-scale systems and the optimal user association can effectively balance the load between BSs when needed. Even though our framework allows the joint transmission from multiple BSs, there is an overwhelming probability that only one BS is associated with each user at the optimal solution.

We illustrate potential benefits of using massive antenna arrays for wireless energy transfer (WET). Specifically, we analyze probability of outage in WET over fading channels when a base station (BS) with multiple antennas beamforms energy to a wireless sensor node (WSN). Our analytical results show that by using massive antenna arrays, the range of WET can be increased for a given target outage probability. We prove that by using multiple-antenna arrays at the BS, a lower downlink energy is required to get the same outage performance, resulting in savings of radiated energy. We show that for energy levels used in WET, the outage performance with least-squares or minimum mean-square-error channel estimates is the same as that obtained based on perfect channel estimates. We observe that a strong line-of-sight component between the BS and WSN lowers outage probability. Furthermore, by deploying more antennas at the BS, a larger energy can be transferred reliably to the WSN at a given target outage performance for the sensor to be able to perform its main tasks. In our numerical examples, the RF power received at the input of the sensor is assumed to be on the order of a mW, such that the rectenna operates at an efficiency in the order of 50%.

We consider the uplink of a cellular massive multiple-input multiple-output network. Acquiring channel state information at the base stations (BSs) requires uplink pilot signaling. Since the number of orthogonal pilot sequences is limited by the channel coherence, pilot reuse across cells is necessary to achieve high spectral efficiency. However, finding efficient pilot reuse patterns is non-trivial, especially in practical asymmetric BS deployments. We approach this problem using the coalitional game theory. Each BS has a few unique pilots and can form coalitions with other BSs to gain access to more pilots. The BSs in a coalition, thus, benefit from serving more users in their cells at the expense of higher pilot contamination and interference. Given that a cell's average spectral efficiency depends on the overall pilot reuse pattern, the suitable coalitional game model is in the partition form. We develop a low-complexity distributed coalition formation based on individual stability. By incorporating a BS intercommunication budget constraint, we are able to control the overhead in message exchange between the BSs and ensure the algorithm's convergence to a solution of the game called individually stable coalition structure. Simulation results reveal fast algorithmic convergence and substantial performance gains over the baseline schemes with no pilot reuse, full pilot reuse, or random pilot reuse pattern.

The development of 5G enabling technologies brings new challenges to the design of power amplifiers (PAs). In particular, there is a strong demand for low-cost, nonlinear PAs which, however, introduce nonlinear distortions. On the other hand, contemporary expensive PAs show great power efficiency in their nonlinear region. Inspired by this trade-off between nonlinearity distortions and efficiency, finding an optimal operating point is highly desirable. Hence, it is first necessary to fully understand how and how much the performance of multiple-input multiple-output (MIMO) systems deteriorates with PA nonlinearities. In this paper, we first reduce the ergodic achievable rate (EAR) optimization from a power allocation to a power control problem with only one optimization variable, i.e. total input power. Then, we develop a closed-form expression for the EAR, where this variable is fixed. Since this expression is complicated for further analysis, two simple lower bounds and one upper bound are proposed. These bounds enable us to find the best input power and approach the channel capacity. Finally, our simulation results evaluate the EAR of MIMO channels in the presence of nonlinearities. An important observation is that the MIMO performance can be significantly degraded if we utilize the whole power budget.

In this paper, a new multi-cell MMSE detector is proposed for massive MIMO systems. Let K and B denote the number of users in each cell and the number of available pilot sequences in the network, respectively, with B = βK, where β ≥ 1 is called the pilot reuse factor. The novelty of the multi-cell MMSE detector is that it utilizes all B channel directions that can be estimated locally at a base station, so that intra-cell interference, parts of the inter-cell interference and the noise can all be actively suppressed, while conventional detectors only use the K intra-cell channels. Furthermore, in the large- system limit, a deterministic equivalent expression of the uplink SINR for the proposed multi-cell MMSE is derived. The expression is easy to compute and accounts for power control for the pilot and payload, imperfect channel estimation and arbitrary pilot allocation. Numerical results show that significant sum spectral efficiency gains can be obtained by the multi-cell MMSE over the conventional single-cell MMSE and the recent multi-cell ZF, and the gains become more significant as β and/or K increases. Furthermore, the deterministic equivalent is shown to be very accurate even for relatively small system dimensions.

In this paper, a new multi-cell MMSE precoder is proposed for massive MIMO systems. We consider a multi-cell network where each cell has K users and B orthogonal pilot sequences are available, with B = βK and β ≥ 1 being the pilot reuse factor over the network. In comparison with conventional single-cell precoding which only uses the K intra-cell channel estimates, the proposed multi-cell MMSE precoder utilizes all B channel directions that can be estimated locally at a base station, so that the transmission is designed spatially to suppress both parts of the inter-cell and intra-cell interference. To evaluate the performance, a large-scale approximation of the downlink SINR for the proposed multi-cell MMSE precoder is derived and the approximation is tight in the large-system limit. Power control for the pilot and payload, imperfect channel estimation and arbitrary pilot allocation are accounted for in our precoder. Numerical results show that the proposed multi-cell MMSE precoder achieves a significant sum spectral efficiency gain over the classical single-cell MMSE precoder and the gain increases as K or β grows. Compared with the recent M-ZF precoder, whose performance degrades drastically for a large K, our M-MMSE can always guarantee a high and stable performance. Moreover, the large-scale approximation is easy to compute and shown to be accurate even for small system dimensions.

For both maximum ratio transmission (MRT) and zero forcing (ZF) precoding schemes and given any specific rate requirement the optimal transmit power, number of antennas to be used, number of users to be served and number of pilots spent on channel training are found with the objective to minimize the total consumed power at the base station. The optimization problem is solved by finding closed form expressions of the optimal transmit power and then search over the remaining discrete variables. The analysis consists of two parts, the first part investigates the situation when only power consumed in the RF amplifiers is considered. The second part includes both the power consumed in the RF amplifiers and in other transceiver circuits. In the former case having all antennas active while reducing the transmit power is optimal. Adaptive scheme to switch off some of the antennas at the base stations is found to be optimal in the latter case.

This paper considers the downlink of a heterogeneous network, where multiple base stations (BSs) can serve the users by non-coherent multiflow beamforming. We assume imperfect channel state information at both BSs and users. The objective is to jointly optimize the precoding, load balancing, and BS operation mode (active or sleep) for improving the energy efficiency of the network. The considered problem is to minimize the weighted total power consumption (both circuit power and dynamic transmit power), while satisfying per-user quality of service constraints and per-BS transmit power constraints. This problem is non-convex, but we prove that for each combination of BS modes, the considered problem has a hidden convexity structure. Thus, the global optimal solution is obtained by an exhaustive search over all possible BS mode combinations. Furthermore, by iterative convex approximations of the non-convex power consumption functions, a heuristic algorithm is proposed to obtain a local optimal solution with low complexity. Simulation results illustrate that our proposed algorithms significantly reduce the total power consumption, compared to the scheme where all BSs are continuously active. This implies that putting a BS into sleep mode by proper load balancing is an important solution for energy savings in heterogeneous networks.

In this paper, the problem of optimal maximum likelihood detection in a single user single-input multiple-output (SIMO) channel with phase noise at the receiver is considered. The optimal detection rules under training are derived for two operation modes, namely when the phase increments are fully correlated among the M receiver antennas (synchronous operation) and when they are independent (non-synchronous operation). The phase noise increments are parameterized by a very general distribution, which includes the Wiener phase noise model as a special case. It is proven that phase noise creates a symbol-error-rate (SER) floor for both operation modes. In the synchronous operation this error floor is independent of M, while it goes to zero exponentially with M in the non-synchronous operation.

Hardware non-idealities in wireless transmitter electronics cause distortion that is not captured by conventional linear channel models; in fact, error-vector magnitude (EVM) measurements in conformance testing conceptually reduce their collective effect to an additive noise component at each subcarrier. Motivated by the EVM, the present paper considers a `binoisy' multiple-input multiple-output (MIMO) channel model where the additional non-idealities manifest themselves as an additive distortion noise term at the transmit side. Through this extended MIMO relation, the effects of hardware impairments on the achievable rates of different digital modulation schemes are studied via large system analysis. The numerical results illustrate how tolerable EVM levels depend non-trivially on various factors, including the signal-to-noise ratio, modulation order and the level of asymmetry in antenna array configurations.

Hardware impairments in radio-frequency components of a wireless system cause unavoidable distortions to transmission that are not captured by the conventional linear channel model. In this paper, a “binoisy” single-user multiple-input multiple-output (SU-MIMO) relation is considered where the additional distortions are modeled via an additive noise term at the transmit side. Through this extended SU-MIMO channel model, the effects of transceiver hardware impairments on the achievable rate of multi-antenna point-to-point systems are studied. Channel input distributions encompassing practical discrete modulation schemes, such as, QAM and PSK, as well as Gaussian signaling are covered. In addition, the impact of mismatched detection and decoding when the receiver has insufficient information about the non-idealities is investigated. The numerical results show that for realistic system parameters, the effects of transmit-side noise and mismatched decoding become significant only at high modulation orders.

Radio-frequency (RF) impairments, which intimately exist in wireless communication systems, can severely limit the performance of multiple-input-multiple-output (MIMO) systems. Although we can resort to compensation schemes to mitigate some of these impairments, a certain amount of residual impairments always persists. In this paper, we consider a training-based point-to-point MIMO system with residual transmit RF impairments (RTRI) using spatial multiplexing transmission. Specifically, we derive a new linear channel estimator for the proposed model, and show that RTRI create an estimation error floor in the high signal-to-noise ratio (SNR) regime. Moreover, we derive closed-form expressions for the signal-to-noise-plus-interference ratio (SINR) distributions, along with analytical expressions for the ergodic achievable rates of zero-forcing, maximum ratio combining, and minimum mean-squared error receivers, respectively. In addition, we optimize the ergodic achievable rates with respect to the training sequence length and demonstrate that finite dimensional systems with RTRI generally require more training at high SNRs than those with ideal hardware. Finally, we extend our analysis to large-scale MIMO configurations, and derive deterministic equivalents of the ergodic achievable rates. It is shown that, by deploying large receive antenna arrays, the extra training requirements due to RTRI can be eliminated. In fact, with a sufficiently large number of receive antennas, systems with RTRI may even need less training than systems with ideal hardware.

Massive multiple-input multiple-output (MIMO) systems are cellular networks where the base stations (BSs) are equipped with unconventionally many antennas, deployed on co-located or distributed arrays. Huge spatial degrees-of-freedom are achieved by coherent processing over these massive arrays, which provide strong signal gains, resilience to imperfect channel knowledge, and low interference. This comes at the price of more infrastructure; the hardware cost and circuit power consumption scale linearly/affinely with the number of BS antennas N. Hence, the key to cost-efficient deployment of large arrays is low-cost antenna branches with low circuit power, in contrast to today's conventional expensive and power-hungry BS antenna branches. Such low-cost transceivers are prone to hardware imperfections, but it has been conjectured that the huge degrees-of-freedom would bring robustness to such imperfections. We prove this claim for a generalized uplink system with multiplicative phase-drifts, additive distortion noise, and noise amplification. Specifically, we derive closed-form expressions for the user rates and a scaling law that shows how fast the hardware imperfections can increase with N while maintaining high rates. The connection between this scaling law and the power consumption of different transceiver circuits is rigorously exemplified. This reveals that one can make √N the circuit power increase as N, instead of linearly, by careful circuit-aware system design.

Assume that a multi-user multiple-input multiple-output (MIMO) system is designed from scratch to uniformly cover a given area with maximal energy efficiency (EE). What are the optimal number of antennas, active users, and transmit power? The aim of this paper is to answer this fundamental question. We consider jointly the uplink and downlink with different processing schemes at the base station and propose a new realistic power consumption model that reveals how the above parameters affect the EE. Closed-form expressions for the EE-optimal value of each parameter, when the other two are fixed, are provided for zero-forcing (ZF) processing in single-cell scenarios. These expressions prove how the parameters interact. For example, in sharp contrast to common belief, the transmit power is found to increase (not to decrease) with the number of antennas. This implies that energy-efficient systems can operate in high signal-to-noise ratio regimes in which interference-suppressing signal processing is mandatory. Numerical and analytical results show that the maximal EE is achieved by a massive MIMO setup wherein hundreds of antennas are deployed to serve a relatively large number of users using ZF processing. The numerical results show the same behavior under imperfect channel state information and in symmetric multi-cell scenarios.

This paper considers a downlink heterogeneous network, where different types of multiantenna base stations (BSs) communicate with a number of single-antenna users. Multiple BSs can serve the users by spatial multiflow transmission techniques. Assuming imperfect channel state information at both BSs and users, the precoding, load balancing, and BS operation mode are jointly optimized for improving the network energy efficiency. We minimize the weighted total power consumption while satisfying quality-of-service constraints at the users. This problem is nonconvex, but we prove that for each BS mode combination, the considered problem has a hidden convexity structure. Thus, the optimal solution is obtained by an exhaustive search over all possible BS mode combinations. Furthermore, by iterative convex approximations of the nonconvex objective function, a heuristic algorithm is proposed to obtain a suboptimal solution of low complexity. We show that although multicell joint transmission is allowed, in most cases, it is optimal for each user to be served by a single BS. The optimal BS association condition is parameterized, which reveals how it is impacted by different system parameters. Simulation results indicate that putting a BS into sleep mode by proper load balancing is an important solution for energy savings.

Channel measurements show that significant spatially non-wide-sense-stationary characteristics rise in massive MIMO channels. Notable parameter variations are experienced along the base station array, such as the average received energy at each antenna, and the directions of arrival of signals impinging on different parts of the array. In this paper, a new channel model is proposed to describe this spatial non-stationarity in massive MIMO channels by incorporating the concepts of partially visible clusters and wholly visible clusters. Furthermore, a closed-form expression of an upper bound on the ergodic sum capacity is derived for the new model, and the influence of the spatial non-stationarity on the sum capacity is analyzed. Analysis shows that for non-identically-and-independent-distributed (i.i.d.) Rayleigh fading channels, the non-stationarity benefits the sum capacity by bringing a more even spread of channel eigenvalues. Specifically, more partially visible clusters, smaller cluster visibility regions, and a larger antenna array can all help to yield a well-conditioned channel, and benefit the sum capacity. This shows the advantage of using a large antenna array in a non-i.i.d. channel: the sum capacity benefits not only from a higher array gain, but also from a more spatially non-stationary channel. Numerical results demonstrate our analysis and the tightness of the upper bound.

In this work, we consider the downlink of a single-cell multi-user MIMO system in which the base station (BS) makes use of N antennas to communicate with K single-antenna user equipments (UEs). The UEs move around in the cell according to a random walk mobility model. We aim at determining the energy consumption distribution when different linear precoding techniques are used at the BS to guarantee target rates within a finite time interval T. The analysis is conducted in the asymptotic regime where N and K grow large with fixed ratio under the assumption of perfect channel state information (CSI). Both recent and standard results from large system analysis are used to provide concise formulae for the asymptotic transmit powers and beamforming vectors for all considered schemes. These results are eventually used to provide a deterministic approximation of the energy consumption and to study its fluctuations around this value in the form of a central limit theorem. Closed-form expressions for the asymptotic means and variances are given. Numerical results are used to validate the accuracy of the theoretical analysis and to make comparisons. We show how the results can be used to approximate the probability that a battery-powered BS runs out of energy and also to design the cell radius for minimizing the energy consumption per unit area. The imperfect CSI case is also briefly considered.

We consider the downlink of a single-cell multi-user MIMO system in which the base station makes use of N antennas to communicate with K single-antenna user equipments (UEs) randomly positioned in the coverage area. In particular, we focus on the problem of designing the optimal linear precoding for minimizing the total power consumption while satisfying a set of target signal-to-interference-plus-noise ratios (SINRs). To gain insights into the structure of the optimal solution and reduce the computational complexity for its evaluation, we analyze the asymptotic regime where N and K grow large with a given ratio and make use of recent results from large system analysis to compute the asymptotic solution. Then, we concentrate on the asymptotically design of heuristic linear precoding techniques. Interestingly, it turns out that the regularized zero-forcing (RZF) precoder is equivalent to the optimal one when the ratio between the SINR requirement and the average channel attenuation is the same for all UEs. If this condition does not hold true but only the same SINR constraint is imposed for all UEs, then the RZF can be modified to still achieve optimality if statistical information of the UE positions is available at the BS. Numerical results are used to evaluate the performance gap in the finite system regime and to make comparisons among the precoding techniques.

Massive multiple-input multiple-output (MIMO) systems are cellular networks where the base stations (BSs) are equipped with unconventionally many antennas. Such large antenna arrays offer huge spatial degrees-of-freedom for transmission optimization; in particular, great signal gains, resilience to imperfect channel knowledge, and small inter-user interference are all achievable without extensive inter-cell coordination. The key to cost-efficient deployment of large arrays is the use of hardware-constrained base stations with low-cost antenna elements, as compared to today's expensive and power-hungry BSs. Low-cost transceivers are prone to hardware imperfections, but it has been conjectured that the excessive degrees-of-freedom of massive MIMO would bring robustness to such imperfections. We herein prove this claim for an uplink channel with multiplicative phase-drift, additive distortion noise, and noise amplification. Specifically, we derive a closed-form scaling law that shows how fast the imperfections increase with the number of antennas.

Physical transceivers exhibit distortions from hardware impairments, of which traces remain even after compensation and calibration. Multicell MIMO coordinated beamforming methods that ignore these residual impairments may suffer from severely degraded performance. In this work, we consider a general model for the aggregate effect of the residual hardware impairments, and propose an iterative algorithm for finding locally optimal points to a weighted sum rate optimization problem. The importance of accounting for the residual hardware impairments is verified by numerical simulation, and a substantial gain over traditional time-division multiple access with impairments-aware resource allocation is observed.

In this work, we consider the downlink of a single-cell multi-user multiple-input multiple-output system in which zero-forcing precoding is used at the base station (BS) to serve a certain number of user equipments (UEs). A fixed data rate is guaranteed at each UE. The UEs move around in the cell according to a Brownian motion, thus the path losses change over time and the energy consumption fluctuates accordingly. We aim at determining the distribution of the energy consumption. To this end, we analyze the asymptotic regime where the number of antennas at the BS and the number of UEs grow large with a given ratio. It turns out that the energy consumption is asymptotically a Gaussian random variable whose mean and variance are derived analytically. These results can, for example, be used to approximate the probability that a battery-powered BS runs out of energy within a certain time period.

Radio-frequency (RF) impairments in the transceiver hardware of communication systems (e.g., phase noise (PN), high power amplifier (HPA) nonlinearities, or in-phase/quadrature-phase (I/Q) imbalance) can severely degrade the performance of traditional multiple-input multiple-output (MIMO) systems. Although calibration algorithms can partially compensate these impairments, the remaining distortion still has substantial impact. Despite this, most prior works have not analyzed this type of distortion. In this paper, we investigate the impact of residual transceiver hardware impairments on the MIMO system performance. In particular, we consider a transceiver impairment model, which has been experimentally validated, and derive analytical ergodic capacity expressions for both exact and high signal-to-noise ratios (SNRs). We demonstrate that the capacity saturates in the high-SNR regime, thereby creating a finite capacity ceiling. We also present a linear approximation for the ergodic capacity in the low-SNR regime, and show that impairments have only a second-order impact on the capacity. Furthermore, we analyze the effect of transceiver impairments on large-scale MIMO systems; interestingly, we prove that if one increases the number of antennas at one side only, the capacity behaves similar to the finite-dimensional case. On the contrary, if the number of antennas on both sides increases with a fixed ratio, the capacity ceiling vanishes; thus, impairments cause only a bounded offset in the capacity compared to the ideal transceiver hardware case.

Radio-frequency (RF) impairments, that exist intimately in wireless communications systems, can severely degrade the performance of traditional multiple-input multiple-output (MIMO) systems. Although compensation schemes can cancel out part of these RF impairments, there still remains a certain amount of impairments. These residual impairments have fundamental impact on the MIMO system performance. However, most of the previous works have neglected this factor. In this paper, a training-based MIMO system with residual transmit RF impairments (RTRI) is considered. In particular, we derive a new channel estimator for the proposed model, and find that RTRI can create an irreducible estimation error floor. Moreover, we show that, in the presence of RTRI, the optimal training sequence length can be larger than the number of transmit antennas, especially in the low and high signal-to-noise ratio (SNR) regimes. An increase in the proposed approximated achievable rate is also observed by adopting the optimal training sequence length. When the training and data symbol powers are required to be equal, we demonstrate that, at high SNRs, systems with RTRI demand more training, whereas at low SNRs, such demands are nearly the same for all practical levels of RTRI.

Assume that a multi-user multiple-input multiple-output (MIMO) communication system must be designed to cover a given area with maximal energy efficiency (bits/Joule). What are the optimal values for the number of antennas, active users, and transmit power? By using a new model that describes how these three parameters affect the total energy efficiency of the system, this work provides closed-form expressions for their optimal values and interactions. In sharp contrast to common belief, the transmit power is found to increase (not decrease) with the number of antennas. This implies that energy efficient systems can operate at high signal-to-noise ratio (SNR) regimes in which the use of interference-suppressing precoding schemes is essential. Numerical results show that the maximal energy efficiency is achieved by a massive MIMO setup wherein hundreds of antennas are deployed to serve relatively many users using interference-suppressing regularized zero-forcing precoding.

This paper considers the mode selection problem for network-assisted device-to-device (D2D) communications with multiple antennas at the base station. We study transmission in both dedicated and shared frequency bands. Given the type of resources (i.e., dedicated or shared), the user equipment (UE) decides to transmit in the conventional cellular mode or directly to its corresponding receiver in the D2D mode. We formulate this problem under two different objectives. The first problem is to maximize the quality-of-service (QoS) given a transmit power, and the second problem is to minimize the transmit power given a QoS requirement. We derive closed-form results for the optimal decision and show that the two problem formulations behave differently. Taking a geometrical approach, we study the area around the transmitter UE where the receiving UE should be to have D2D mode optimality, and how it is affected by the transmit power, QoS, and the number of base station antennas.

The use of large-scale antenna arrays can bring substantial improvements in energy and/or spectral efficiency to wireless systems due to the greatly improved spatial resolution and array gain. Recent works in the field of massive multiple-input multiple-output (MIMO) show that the user channels decorrelate when the number of antennas at the base stations (BSs) increases, thus strong signal gains are achievable with little interuser interference. Since these results rely on asymptotics, it is important to investigate whether the conventional system models are reasonable in this asymptotic regime. This paper considers a new system model that incorporates general transceiver hardware impairments at both the BSs (equipped with large antenna arrays) and the single-antenna user equipments (UEs). As opposed to the conventional case of ideal hardware, we show that hardware impairments create finite ceilings on the channel estimation accuracy and on the downlink/uplink capacity of each UE. Surprisingly, the capacity is mainly limited by the hardware at the UE, while the impact of impairments in the large-scale arrays vanishes asymptotically and interuser interference (in particular, pilot contamination) becomes negligible. Furthermore, we prove that the huge degrees of freedom offered by massive MIMO can be used to reduce the transmit power and/or to tolerate larger hardware impairments, which allows for the use of inexpensive and energy-efficient antenna elements.

Recently, it was shown that transceiver hardware impairments have a detrimental impact on the performance of communication systems, especially for high-rate systems. The vast majority of technical contributions in the area of relaying assume ideal transceiver hardware. This paper quantifies the impact of transceiver hardware impairments in dual-hop Amplify-and-Forward (AF) relaying, both for fixed and variable gain relays. The outage probability (OP) in this practical scenario is a function of the instantaneous end-to-end signal-to-noise-and-distortion ratio (SNDR). This paper derives closed-form expressions for the exact and asymptotic OPs under Rayleigh fading, accounting for hardware impairments at both the transmitter and the relay. The performance loss is small at low spectral efficiency, but can otherwise be very substantial. In particular, it turns out that for high signal-to-noise ratio (SNR), the instantaneous end-to-end SNDR converges to a deterministic constant, called the SNDR ceiling, which is inversely proportional to the level of impairments. This stands in stark contrast to the ideal hardware case for which the end-to-end SNDR grows without bound in the high SNR regime.

This work seeks to design a pilot signal, under a power constraint, such that the channel can be estimated with minimum mean square error. The procedure we derive does not assume Kronecker structure on the underlying covariance matrices, and the pilot signal is obtained in three main steps. Firstly, we solve a relaxed convex version of the original minimization problem. Secondly, its solution is projected onto the feasible set. Thirdly we use the projected solution as starting point for an augmented Lagrangian method. Numerical experiments indicate that this procedure may produce pilot signals that are far better than those obtained under the Kronecker structure assumption.

This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, also known as “massive MIMO”. Unlike previous works on this topic, which mainly considered the impact of inter-cell disturbance due to pilot reuse (so-called pilot contamination), we are concerned with the computational complexity. The conventional minimum mean square error (MMSE) and minimum variance unbiased (MVU) channel estimators rely on inverting covariance matrices, which has cubic complexity in the multiplication of number of antennas at each side. Since this is extremely expensive when there are hundreds of antennas, we propose to approximate the inversion by an L-order matrix polynomial. A set of low-complexity Bayesian channel estimators, coined Polynomial ExpAnsion CHannel (PEACH) estimators, are introduced. The coefficients of the polynomials are optimized to yield small mean square error (MSE). We show numerically that near-optimal performance is achieved with low polynomial orders. In practice, the order L can be selected to balance between complexity and MSE. Interestingly, pilot contamination is beneficial to the PEACH estimators in the sense that smaller L can be used to achieve near-optimal MSEs.

Physical transceivers have hardware impairments that create distortions which degrade the performance of communication systems. The vast majority of technical contributions in the area of relaying neglect hardware impairments and, thus, assume ideal hardware. Such approximations make sense in low-rate systems, but can lead to very misleading results when analyzing future high-rate systems. This paper quantifies the impact of hardware impairments on dual-hop relaying, for both amplify-and-forward and decode-and-forward protocols. The outage probability (OP) in these practical scenarios is a function of the effective end-to-end signal-to-noise-and-distortion ratio (SNDR). This paper derives new closed-form expressions for the exact and asymptotic OPs, accounting for hardware impairments at the source, relay, and destination. A similar analysis for the ergodic capacity is also pursued, resulting in new upper bounds. We assume that both hops are subject to independent but non-identically distributed Nakagami-m fading. This paper validates that the performance loss is small at low rates, but otherwise can be very substantial. In particular, it is proved that for high signal-to-noise ratio (SNR), the end-to-end SNDR converges to a deterministic constant, coined the SNDR ceiling, which is inversely proportional to the level of impairments. This stands in contrast to the ideal hardware case in which the end-to-end SNDR grows without bound in the high-SNR regime. Finally, we provide fundamental design guidelines for selecting hardware that satisfies the requirements of a practical relaying system.

Physical wireless transceivers suffer from a variety of impairments that distort the transmitted and received signals. Their degrading impact is particularly evident in modern systems with multiuser transmission, high transmit power, and low-cost devices, but their existence is routinely ignored in the optimization literature for multicell transmission. This paper provides a detailed analysis of coordinated beamforming in the multicell downlink. We solve two optimization problems under a transceiver impairment model and derive the structure of the optimal solutions. We show numerically that these solutions greatly reduce the impact of impairments, compared with beamforming developed for ideal transceivers. Although the so-called multiplexing gain is zero under transceiver impairments, we show that the gain of multiplexing can be large at practical SNRs.

Feedback of channel state information (CSI) is necessary to achieve high throughput and low outage probability in multiuser multi antenna systems. There are two types of CSI: directional and quality information. Many papers have analyzed the importance of these in asymptotic regimes. However, we show that such results should be handled with care, as very different conclusions can be drawn depending on the spatial correlation and number of users. There fore, we propose a quantization framework and evaluate the tradeoff between directional and quality feedback under practical conditions.

In this paper, we propose a multiple-state other-cell interference (OCI) model, which takes into account the interference variability and uncertainty created by scheduling and other fast resource allocation adaptivity. This situation is modeled by a set of states, each described by a spatial covariance matrix and a probability. In order to illustrate the usefulness of such a model, we study two receive beamforming design problems, one maximizing the average data rate and one maximizing the worst-case data rate. We compare the resulting performance with what can be obtained when state information is not available. We show theoretically and numerically that exploring the multiple-state OCI structure can improve the receive beamforming design efficiency, especially for cell-edge users in a interference-limited system.

Base station cooperative transmission is an effective strategy to mitigate inter-cell interference. Centralized multi-cell transmission provides considerable performance gains but is impractical in large cellular systems, due to its prohibitive complexity and large amount of overhead. Dividing cells into small clusters enables practical channel acquisition and coordination within each cluster but still suffers from out-of-cluster interference. In this paper, we propose a dynamic cooperative framework for large cellular systems, which divides cells into groups such that neighboring cells belong to different groups. Based on the cell-grouping, a distributed scheduling strategy is proposed which can effectively coordinate the interference between cell-groups. With limited signalling among BSs and lower complexity, the cell-grouping based distributed scheduling and beamforming shows performance advantages over the fixed clustering based centralized scheduling and beamforming.

Base station cooperation can theoretically improve the throughput of multicell systems by coordinating interference and serving cell edge terminals through multiple base stations. In practice, the extent of cooperation is limited by the increase in backhaul signaling and computational demands. To address these concerns, we propose a novel distributed cooperation structure where each base station has responsibility for the interference towards a set of terminals, while only serving a subset of them with data. Weighted sum rate maximization is considered, and conditions for beamforming optimality and the optimal transmission structure are derived using Lagrange duality theory. This leads to distributed low-complexity transmission strategies, which are evaluated on measured multiantenna channels in a typical urban multicell environment.

\boldmath The impact of transmission design and spatial correlation on the symbol error rate (SER) is analyzed for multi-antenna communication links. The receiver has perfect channel state information (CSI), while the transmitter has either statistical or no CSI. The transmission is based on orthogonal space-time block codes (OSTBCs) and linear precoding. The precoding strategy that minimizes the worst-case SER is derived for the case when the transmitter has no CSI. Based on this strategy, the intuitive result that spatial correlation degrades the SER performance is proved mathematically. In the case when the transmitter knows the channel statistics, the correlation matrix is assumed to be jointly-correlated (a generalization of the Kronecker model). The eigenvectors of the SER-optimal precoding matrix are shown to originate from the correlation matrix and the remaining power allocation is a convex problem. Equal power allocation is SER-optimal at high SNR. Beamforming is SER-optimal at low SNR, or for increasing constellation sizes, and its optimality range is characterized. A heuristic low-complexity power allocation is proposed and evaluated numerically. Finally, it is proved analytically that receive-side correlation always degrades the SER. Transmit-side correlation will however improve the SER at low to medium SNR, while its impact is negligible at high SNR.

This paper considers downlink multiantenna communication with base stations that perform cooperative precoding in a distributed fashion. Most previous work in the area has assumed that transmitters have common knowledge of both data symbols of all users and full or partial channel state information (CSI). Herein, we assume that each base station only has local CSI, either instantaneous or statistical. For the case of instantaneous CSI, a parametrization of the beamforming vectors used to achieve the outer boundary of the achievable rate region is obtained for two multi-antenna transmitters and two single-antenna receivers. Distributed generalizations of classical beamforming approaches that satisfy this parametrization are provided, and it is shown how the distributed precoding design can be improved using the so-called virtual SINR framework. Conceptually analog results for both the parametrization and the beamforming design are derived in the case of local statistical CSI. Heuristics on the distributed power allocation are provided in both cases, and the performance is illustrated numerically.

Training-based estimation of channel state information in multi-antenna systems is analyzed herein. Closed-form expressions for the general Bayesian minimum mean square error (MMSE) estimators of the channel matrix and the squared channel norm are derived in a Rayleigh fading environment with known statistics at the receiver side. When the second-order channel statistics are available also at the transmitter, this information can be exploited in the training sequence design to improve the performance. Herein, mean square error (MSE) minimizing training sequences are considered. The structure of the general solution is developed, with explicit expressions at high and low SNRs and in the special case of uncorrelated receive antennas. The optimal length of the training sequence is equal or smaller than the number of transmit antennas.

The symbol error performance of spatially correlated multi-antenna systems is analyzed herein. When the transmitter only has statistical channel information, the use of space-time block codes still permits spatial multiplexing and mitigation of fading. The statistical information can be used for precoding to optimize some quality measure. Herein, we analyze the performance in terms of the symbol error rate (SER). It is shown analytically that spatial correlation at the receiver decreases the performance both without precoding and with an SER minimizing precoder. Without precoding, correlation should also be avoided at the transmitter side, but with an SER minimizing precoder the performance is actually improved by increasing spatial correlation at the transmitter. The structure of the optimized precoder is analyzed and the asymptotic properties at high and low SNRs are characterized and illustrated numerically.

In wireless multiple antenna and multi-user systems, the spatial dimensions may be exploited to increase the performance by means of antenna gain, spatial diversity, and multi-user diversity. A limiting factor in such systems is the channel information required by the transmitter to control the intra-cell interference. Herein, the properties of spatially correlated channels with longterm statistical information at the transmitter and fixed-rate feedback of the quantized Euclidean channel norm are analyzed using a spectral subspace decomposition framework. A spatial division multiple access scheme is proposed with interference suppression at the receiver and joint scheduling and zero-forcing beamforming at the transmitter. Closed-form expressions for first and second order moments of the feedback conditional channel statistics are derived. It is shown that only a few bits of feedback are required to achieve reliable rate estimation and weighted sum-rate maximization.

This paper considers quantization and exact minimum mean square error (MMSE) estimation of the squared Frobenius norm and the squared spectral norm of a Rayleigh fading multiple-input multiple-output (MIMO) channel with one-sided spatial correlation. The Frobenius and spectral norms are of great importance when describing the achievable capacity of many wireless communication systems; in particularly, they correspond to the signal-to-noise ratio (SNR) of space-time block coded and maximum ratio combining transmissions, respectively. Herein, a general quantization framework is presented, where the quantization levels are determined to maximize the feedback entropy. Quantization based on the post-user-selection distribution is discussed, and analyzed for a specific scheduler. Finally, exact results on MMSE estimation of the capacity and the SNR, conditioned on a quantized channel norm, are presented.