We study the impact of imperfect line-of-sight (LoS) phase tracking on the uplink performance of cell-free massive MIMO networks. Unlike prior works that assume perfectly known or completely unknown phases, we consider a realistic regime where LoS phases are estimated with residual uncertainty due to hardware impairments, mobility, and synchronization errors. To this end, we propose a Rician fading model where LoS components are rotated by imperfect phase estimates and attenuated by a deterministic phase-error penalty factor.We derive a linear MMSE channel estimator that accounts for statistical phase errors and unifies prior results, reducing to the Bayesian MMSE estimator when phase is perfectly known and to a zero-mean model when no phase information is available. To address the non-Gaussian setting, we introduce a virtual uplink model that preserves second-order statistics of channel estimation, enabling the derivation of tractable virtual centralized and distributed MMSE beamformers. To ensure fair assessment of network performance, we apply these virtual beamformers to the operational uplink model that reflects the actual physical channel and compute the spectral efficiency bounds available in the literature.Numerical results show that our framework bridges idealized assumptions and practical tracking limitations, providing rigorous performance benchmarks and design insights for 6G cell-free networks.

This paper addresses uplink long-term joint power control, beamformer design, and time-sharing in overloaded cell-free massive MIMO networks, aiming to achieve max-min fairness among users. Resource allocation leverages slowly-varying channel statistics rather than instantaneous channel state information, reducing information-sharing overhead and enabling optimization over longer timescales. We propose a block coordinate ascent algorithm in which each subproblem is optimally solved using a combination of bisection search, fixed point iterations, and linear programming, guaranteeing convergence to a local optimum. Numerical simulations corroborate the gains of the proposed joint approach in terms of spectral efficiency and power savings over more conventional disjoint time-sharing schemes adopting baseline scheduling policies.

In this paper, we perform a comparative study of common wireless communication waveforms, namely the single carrier (SC), orthogonal frequency-division multiplexing (OFDM), and orthogonal time-frequency-space (OTFS) modulation in a millimeter wave (mmWave) downlink multi-connectivity scenario, where multiple access points (APs) jointly serve a given user under imperfect time and frequency synchronization errors. For a fair comparison, all the three waveforms are evaluated using variants of common frequency domain equalization (FDE). To this end, a novel cross domain iterative detection for OTFS is proposed. The performance of the different waveforms is evaluated numerically in terms of pragmatic capacity. The numerical results show that OTFS significantly outperforms SC and OFDM at cost of reasonably increased complexity, because of the low cyclic-prefix (CP) overhead and the effectiveness of the proposed detection.

In this study, we revisit the performance analysis of distributed beamforming architectures in dense user-centric cell-free massive multiple-input multiple-output (mMIMO) systems in line-of-sight (LoS) scenarios. By incorporating a recently developed optimal distributed beamforming technique, called the team minimum mean square error (TMMSE) technique, we depart from previous studies that rely on suboptimal distributed beam-forming approaches for LoS scenarios. Supported by extensive numerical simulations that follow 3GPP guidelines, we show that such suboptimal approaches may often lead to significant underestimation of the capabilities of distributed architectures, particularly in the presence of strong LoS paths. Considering the anticipated ultra-dense nature of cell-free mMIMO networks and the consequential high likelihood of strong LoS paths, our findings reveal that the team MMSE technique may significantly contribute in narrowing the performance gap between centralized and distributed architectures.

This study investigates simpler alternatives to coherent joint transmission for supporting robust connectivity against signal blockage in mmWave/sub-THz access networks. By taking an information-theoretic viewpoint, we demonstrate analytically that with a careful design, full macrodiversity gains and significant SNR gains can be achieved through canonical receivers and minimal coordination and synchronization requirements at the infrastructure side. Our proposed scheme extends non-coherent joint transmission by employing a special form of diversity to counteract artificially induced deep fades that would otherwise make this technique often compare unfavorably against standard transmitter selection schemes. Additionally, the inclusion of an Alamouti-like space-time coding layer is shown to recover a significant fraction of the optimal performance. Our conclusions are based on a statistical single-user multi-point intermittent block fading channel model that, although simplified, enables rigorous ergodic and outage rate analysis, while also considering timing offsets due to imperfect delay compensation. In addition, we validate our theoretical approach by means of deterministic ray-tracing simulations that capture the essential features of next generation mmWave/sub-THz communications.

In this study we derive novel optimal algorithms for joint power control and beamforming design in modern large-scale MIMO systems, such as those based on the cell-free massive MIMO and XL-MIMO concepts. In particular, motivated by the need for scalable system architectures, we formulate and solve nontrivial two-timescale extensions of the classical uplink power minimization and max-min fair resource allocation problems. In our formulations, we let the beamformers befunctionsmapping partial instantaneous channel state information (CSI) to beamforming weights, and we jointly optimize these functions and the power control coefficients based on long-term statistical CSI. This long-term approach mitigates the severe scalability issues of competing short-term iterative algorithms in the literature, where a central controller endowed with global instantaneous CSI must solve a complex optimization problem for every channel realization, hence imposing very demanding requirements in terms of computational complexity and signaling overhead. Moreover, our approach outperforms the available long-term approaches, which do not jointly optimize powers and beamformers. The obtained optimal long-term algorithms are then illustrated and compared against existing short-term and long-term algorithms via numerical simulations in a cell-free massive MIMO setup with different levels of cooperation.

In recent years, sleep-mode or access point (AP) on-off switch techniques have attracted significant attention for reducing the energy consumption of cell-free massive MIMO systems. In this context, this work considers the problem of finding the smallest subset of active access points (APs) needed to satisfy minimum quality-of-service requirements while considering the optimal configuration of uplink transmit powers and (potentially distributed) beamformers. To address this challenging problem, we judiciously combine novel fixed-point methods for jointly optimal power control and distributed beamforming design with a global optimization framework based on surrogate machine-learning models. Numerical results show that our proposed on-off switch technique can achieve a significantly higher reduction in total APs power consumption than a baseline that does not jointly configure the uplink transmit powers and the beamformers.

It is generally believed that downlink cell-free net-works perform best under centralized implementations where the local channel state information (CSI) acquired by the access-points (AP) is forwarded to one or more central processing units (CPU) for the computation of the joint precoders based on global CSI. However, mostly due to limited fronthaul capabilities, this procedure incurs some delay that may lead to partially outdated precoding decisions and hence performance degradation. In some scenarios, this may even lead to worse performance than distributed implementations where the precoders are locally computed by the APs based on partial yet timely local CSI. To address this issue, this study considers the problem of robust precoding design merging the benefits of timely local CSI and delayed global CSI. As main result, we provide a novel distributed precoding design based on the recently proposed team minimum mean-square error method. As a byproduct, we also obtain novel insights related to the AP-CPU functional split problem. Our main conclusion, corroborated by simulations, is that the oppor-tunity of performing some local precoding computations at the APs should not be neglected, even in centralized implementations.

We establish necessary and sufficient conditions for a network configuration to provide utilities that are both fair and efficient in a well-defined sense. To cover as many applications as possible with a unified framework, we consider utilities defined in an axiomatic way, and the constraints imposed on the feasible network configurations are expressed with a single inequality involving a monotone norm. In this setting, we prove that a necessary and sufficient condition to obtain network configurations that are efficient in the weak Pareto sense is to select configurations attaining equality in the monotone norm constraint. Furthermore, for a given configuration satisfying this equality, we characterize a criterion for which the configuration can be considered fair for the active links. We illustrate potential implications of the theoretical findings by presenting, for the first time, a simple parametrization based on power vectors of achievable rate regions in modern cell-less systems subject to practical impairments.

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.

We derive a fast and optimal algorithm for solving practical weighted max-min SINR problems in cell-free massive MIMO networks. For the first time, the optimization problem jointly covers long-term power control and distributed beam-forming design under imperfect cooperation. In particular, we consider user-centric clusters of access points cooperating on the basis of possibly limited channel state information sharing. Our optimal algorithm merges powerful power control tools based on interference calculus with the recently developed team theoretic framework for distributed beamforming design. In addition, we propose a variation that shows faster convergence in practice.

Many common instances of power control problems for cellular and cell-free massive MIMO networks can be interpreted as max-min utility optimization problems involving affine interference mappings and polyhedral constraints. We show that these problems admit a closed-form solution which depends on the spectral radius of known matrices. In contrast, previous solutions in the literature have been indirectly obtained using iterative algorithms based on the bisection method, or on fixed-point iterations. Furthermore, we also show an asymptotically tight bound for the optimal utility, which in turn provides a simple rule of thumb for evaluating whether the network is operating in the noise or interference limited regime. We finally illustrate our results by focusing on classical max-min fair power control for cell-free massive MIMO networks.

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.

This paper studies a memoryless state-dependent multiple access channel (MAC) where two transmitters wish to convey a message to a receiver under the assumption of causal and imperfect channel state information at transmitters (CSIT) and imperfect channel state information at receiver (CSIR). In order to emphasize the limitation of transmitter cooperation between physically distributed nodes, we focus on the so-called distributed CSIT assumption, i.e., where each transmitter has its individual channel knowledge, while the message can be assumed to be partially or entirely shared a priori between transmitters by exploiting some on-board memory. Under this setup, the first part of the paper characterizes the common message capacity of the channel at hand for arbitrary CSIT and CSIR structure. The optimal scheme builds on Shannon strategies, i.e., optimal codes are constructed by letting the channel inputs be a function of current CSIT only. For a special case when CSIT is a deterministic function of CSIR, the considered scheme also achieves the capacity region of a common message and two private messages. The second part addresses an important instance of the previous general result in a context of a cooperative multi-antenna Gaussian channel under i.i.d. fading operating in frequency-division duplex mode, such that CSIT is acquired via an explicit feedback of perfect CSIR. The capacity of the channel at hand is achieved by distributed linear precoding applied to Gaussian codes. Surprisingly, we demonstrate that it is suboptimal to send a number of data streams bounded by the number of transmit antennas as typically considered in a centralized CSIT setup. Finally, numerical examples are provided to evaluate the sum capacity of the binary MAC with binary states as well as the Gaussian MAC with i.i.d. fading.

The problem of optimally precoding over cooperative MIMO channels when the transmitters are endowed with different noisy channel state information is a long standing and challenging open problem. Recently an information theoretic result was obtained which characterized the common message capacity of a channel with two transmitters and a single receiver with such distributed channel state information (DCSIT) generated from different feedback links. While classical MIMO precoding with centralized CSIT implies the transmission of a number of spatial streams bounded by the number of transmit and receiver antennas, the above result suggests that, surprisingly, the transmission of additional streams may be beneficial. In this work, we explore the operational implications of the above intuition to optimally tackle the problem of ergodic rate optimization under distributed feedback. In particular, we propose a method for joint distributed precoding and feedback design under asymmetric feedback rate constraints. In doing so, we also optimize the number of spatial data streams under practical complexity constraints. Finally, we provide numerical simulations and illustrate the performance gains compared to conventional precoder design.

In this paper1, we analyze a Network MIMO channel with 2 Transmitters (TXs) jointly serving 2 users, where each TX has a different multi-user Channel State Information (CSI), potentially with a different accuracy. Recently it was shown the surprising result that this decentralized setting can attain the same Degrees-of-Freedom (DoF) as its genie-aided centralized counterpart in which both TXs share the best-quality CSI. However, the DoF derivation alone does not characterize the actual rate and the question was left open as to how big the rate gap between the centralized and the decentralized settings was going to be. In this paper, we considerably strengthen the previous intriguing DoF result by showing that it is possible to achieve asymptotically the same sum rate as that attained by Zero-Forcing (ZF) precoding in a centralized setting endowed with the best-quality CSI. This result involves a novel precoding scheme which is tailored to the decentralized case. The key intuition behind this scheme lies in the striking of an asymptotically optimal compromise between i) realizing high enough precision ZF precoding while ii) maintaining consistent-enough precoding decisions across the non-communicating cooperating TXs.

The availability of accurate and, most importantly, shared channel state information at the transmitter (CSIT) is one of the key factors that enable transmitters cooperation in decentralized wireless systems. However, in some cases, channel information may not be easily or perfectly shared among the transmitters, thus limiting their coordination capabilities. In this paper we shed some light on the fundamental limits of networks with cooperating transmitters impaired by a general distributed CSIT assumption. To this end, we consider a state-dependent memory-less multiple-access channel with common message, and with noisy causal CSIT and noisy channel state information at the receiver (CSIR). Perhaps surprisingly, and in contrast to the same setting in absence of common message, we show that distributed precoding based on current CSIT only (namely, a Shannon strategy) achieves the sum-rate capacity of this channel, for every degree of CSIT and CSIR. By focusing on the transmission of a common message only, we then illustrate this result in a practically relevant Gaussian setting.

We derive novel bounds for the performance of algorithms that estimate the downlink covariance matrix from the uplink covariance matrix in frequency division duplex (FDD) massive multiple-input multiple-output (MIMO) systems. The focus is on algorithms that use estimates of the angular power spectrum as an intermediate step. Unlike previous results, the proposed bounds follow from simple arguments in possibly infinite dimensional Hilbert spaces, and they do not require strong assumptions on the array geometry or on the propagation model. Furthermore, they are suitable for the analysis of set-theoretic methods that can efficiently incorporate side information about the angular power spectrum. This last feature enables us to derive simple techniques to enhance set-theoretic methods without any heuristic arguments. In particular, we show that the performance of a simple algorithm that requires only a simple matrix-vector multiplication cannot be improved significantly in some practical scenarios, especially if coarse information about the support of the angular power spectrum is available.

Knowledge of second-order statistics of channels (e.g. in the form of covariance matrices) is crucial for the acquisition of downlink channel state information (CSI) in massive MIMO systems operating in the frequency division duplexing (FDD) mode. Current MIMO systems usually obtain downlink covariance information via feedback of the estimated covariance matrix from the user equipment (UE), but in the massive MIMO regime this approach is infeasible because of the unacceptably high training overhead. This paper considers instead the problem of estimating the downlink channel covariance from uplink measurements. We propose two variants of an algorithm based on projection methods in an infinite-dimensional Hilbert space that exploit channel reciprocity properties in the angular domain. The proposed schemes are evaluated via Monte Carlo simulations, and they are shown to outperform current state-of-the art solutions in terms of accuracy and complexity, for typical array geometries and duplex gaps.