We demonstrate that separating beamforming (i.e., downlink precoding and uplink combining) and channel estimation in multi-user MIMO wireless systems incurs no loss of optimality under general conditions that apply to a wide variety of models in the literature, including canonical reciprocity-based cellular and cell-free massive MIMO system models. Specifically, we provide conditions under which optimal processing in terms of ergodic achievable rates can be decomposed into minimum mean-square error (MMSE) channel estimation followed by MMSE beamforming, for both centralized and distributed architectures. Applications of our results are illustrated in terms of concrete examples and numerical simulations.

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.

This paper addresses the problem of estimating the angular power spectrum (APS) from an erroneous estimate of the covariance matrix in massive multiple-input multiple-output (MIMO) systems—a key challenge, for instance, for improving the efficiency of frequency-division duplex (FDD) operation. The APS is modeled as a superposition of Gaussian functions, which implicitly imposes a smoothness prior that alleviates the ill-posedness of the estimation problem and that robustifies our APS estimate against the covariance estimation errors. The weights, scales, and centers of the Gaussian components are iteratively updated within a multikernel adaptive filtering framework, enabling real-time tracking of the temporal variation of the APS. Simulations demonstrate that the proposed method achieves high estimation accuracy and remarkable robustness against the covariance errors simultaneously.

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.

The sixth generation (6G) of wireless networks is envisioned to achieve far beyond the capabilities of fifth generation (5G), necessitating significant innovations at the physical layer (PHY). These include exploration of several fundamental trade-offs between spectral efficiency, reliability, and energy consumption, and enhancing the performance of key enablers for 6G PHY. This paper synthesizes key insights from the 6G-ANNA research initiative on emerging PHY technologies for 6G to provide a holistic exploration of the ongoing trends in the 6G research. The investigations span novel waveform and channel coding techniques for improved energy efficiency, the “Gearbox PHY” concept for adaptive transceiver operations, and optimized radio transceiver designs that balance complexity and power consumption. The study also examines advanced multiple access schemes and cell-free massive multiple-input multiple-output (MIMO) architectures to enhance spectral efficiency and uniform coverage. Integrated artificial intelligence (AI) solutions at the PHY layer and insights to security and trustworthiness challenges in 6G networks are also provided. The findings offer insights into the fundamental trade-offs and provide several key PHY innovations that address sustainability, capacity, and resiliency challenges of future 6G wireless systems.

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 beamforming 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.

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 beamforming 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.

It is envisioned that 6G mobile networks will enhance and majorly empower the Industry 4.0 paradigm, evolving towards smart factories with optimized and customized services. Especially the smart factory scenario with real-time and high-capacity data communication presents us with new challenges, both in communications (mmW/sub-THz) and networking. This article discusses these new challenges and proposes extensions to the current Open Radio Access Network (Open RAN) standards for 6G networks to enable further evolution of Industry 4.0 and beyond. We motivate the need for real-time functionalities in Open RAN and an extended interface to the user equipment (UE) to allow for its fine-grained control.

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.

The collaborative research project 6G-ANNA develops concepts for the 6G radio access network (RAN) architecture and technology components. Previous RAN generations have become inherently more complex and reach their limits in handling foreseen future traffic demands with their diverse characteristics in an efficient manner, e.g., for the use-case of mobile eXtended Reality (XR) on a massive scale. One main objective of 6G is to regain both operational and energy efficiency, i.e., by simplification and automation. To achieve this, in this paper a flexible 6G RAN functional architecture and protocol stack as well as implementation and deployment options are described. We outline how performance is optimized by distributed Multiple Input Multiple Output (MIMO) and distributed Carrier Aggregation (CA), and furthermore, how adaptiveness and scalability is enabled by Cloud RAN and service orchestration. Finally, the proposed zero-trust framework mitigates security risks in the described 6G RAN architecture.

We introduce mathematical tools and fixed point algorithms for optimal statistical max-min power control in cellular and cell-less massive MIMO systems. Unlike previous studies that rely on the use-and-then-forget (UatF) lower bound on Shannon achievable (ergodic) rates, our proposed framework can deal with alternative bounds that explicitly consider perfect or imperfect channel state information (CSI) at the decoder. In doing so, we address limitations of UatF-based algorithms, which inherit the shortcomings of the UatF bound. For example, the UatF bound can be overly conservative: in extreme cases, under fully statistical (nonadaptive) beamforming in zero-mean channels, the UatF bound produces trivial (zero) rate bounds. It also lacks scale invariance: merely scaling the beamformers can change the bound drastically, especially when simple beamforming strategies are employed. In contrast, our framework is compatible with information-theoretic bounds that do not suffer from the above drawbacks. We illustrate the framework by solving a max-min power control problem considering a standard bound that exploits instantaneous CSI at the decoder.

This paper addresses the problem of the angular power spectrum (APS) estimation in massive multiple-input multiple-output (MIMO) systems. Estimating the APS is crucial, e.g., for improving the efficiency of frequency division duplex systems. Since the problem is an ill-posed inverse problem in general, the proposed method models the APS as a sum of Gaussian functions so that the smoothness of APS is implicitly used as prior information. The weights, scales, and centers are iteratively learned by leveraging the multikernel adaptive filtering framework. Simulation results show the efficacy of the proposed method as well as its robustness against covariance estimation errors.

It is generally believed that downlink cell-free networks 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 opportunity of performing some local precoding computations at the APs should not be neglected, even in centralized implementations.

We reconsider the problem of joint power control and beamforming design to maximize the weighted sum rate in large and potentially cell-free massive MIMO networks. In contrast to the available short-term methods, where an iterative algorithm is run for every instantaneous channel realization, we derive an iterative algorithm that can be run only sporadically leveraging known channel statistics, with minor performance loss. In addition, our algorithm also applies to the design of non-trivial cooperative beamforming schemes subject to limited sharing of instantaneous channel state information. Furthermore, our algorithm generalizes and outperforms the competing long-term methods from the massive MIMO literature, which are restricted to long-term power control only or to long-term joint power control and large-scale fading decoding design.

We derive a novel uplink-downlink duality principle for optimal joint precoding design under per-transmitter power and information constraints in fading channels. The information constraints model limited sharing of channel state information and data bearing signals across the transmitters. 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 using limited cooperation capabilities. Our duality principle applies to ergodic achievable rates given by the popular hardening bound, and it can be interpreted as a nontrivial generalization of a previous result by Yu and Lan for deterministic channels. This generalization allows us to study involved information constraints going beyond the simple case of cluster-wise centralized precoding covered by previous techniques. Specifically, we show that the optimal joint precoders are, in general, given by an extension of the recently developed team minimum mean-square error method. As a particular yet practical example, we then solve the problem of optimal local precoding design in user-centric cell-free massive MIMO networks subject to per-AP power constraints.

By trading coverage and hardware complexity for abundance of spectrum, sub-THz mobile access networks are expected to operate under highly directive and relatively spectrally inefficient transmission regimes, while still offering enormous capacity gains over current sub-6GHz alternatives. Building on this assumption, and supported by extensive indoor directional channel measurements at 160 GHz, this study advocates the use of very simple modulation and equalization techniques for sub-THz mobile access. Specifically, we demonstrate that, under the aforementioned transmission regimes, little or no equalization is needed for scoring significant capacity gain targets. In particular, we show that single-carrier or low-number-of-subcarriers modulations are very attractive competitors to the dramatically more complex and energy inefficient traditional multi-carrier designs.

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.

The 6th generation of wireless mobile networks is emerging as a paradigm shifting successor to unifying the experience across the physical, digital, and human worlds, pushing boundaries on performance in capacity, throughput, latency, scalability, flexibility, and reliability, while prominently addressing new major factors, including sustainability, security and privacy, as well as digital inclusion. Many research institutions and initiatives worldwide have started investigations to make 6G a reality by approximately 2030. In Germany, federal funding from the German Ministry of Education and Research (BMBF) supports a large-scale 6G initiative, with its lighthouse project, called 6G-ANNA. The core aim of this project is to develop the key aspects of a holistic, sustainable, secure, and resilient 6G system design that will simplify and improve the interaction between humans, digital assets, and the physical environment. This paper shares the vision of the project’s main technical working areas and advances, spanning topics from radio access, integration of multiple networks, as well as automation and simplification in networking to new applications and testbed scenarios, including real-time digital twins and extended reality. The industrial impact and relevance of standardization makes 6G-ANNA uniquely positioned to lead and realize the vision of next-generation wireless mobile network technologies, systems, and applications.