Emil Björnson

Kecheng Pan, Beixiong Zheng, Yanhua Tan et al.

Rotatable antenna (RA) is a promising technology that can exploit new spatial degrees-of-freedom (DoFs) by flexibly adjusting the three-dimensional (3D) boresight direction of antennas. In this letter, we investigate an RA-enhanced cell-free system for downlink transmission, where multiple RA-equipped access points (APs) cooperatively serve multiple single-antenna users over the same time-frequency resource. Specifically, we aim to maximize the sum rate of all users by jointly optimizing the AP-user associations and the RA boresight directions. Accordingly, we propose a two-stage strategy to solve the AP-user association problem, and then employ fractional programming (FP) and successive convex approximation (SCA) techniques to optimize the RA boresight directions. Numerical results demonstrate that the proposed RA-enhanced cell-free system significantly outperforms various benchmark schemes.

Zhe Wang, Shuaifei Chen, Emil Björnson

Motivated by the vision of making sixth-generation (6G) networks sustainable, we study the sparse antenna/array activation problems in uplink cell-free massive multiple-input multiple-output (CF mMIMO) networks. We first develop an antenna-level optimal bilinear equalizer (OBE) weighting framework, in which each access point-user equipment (AP-UE) pair is assigned a matrix-valued long-term weight to shape the contribution of individual antenna elements, thereby generalizing the conventional large-scale fading decoding (LSFD) strategy from scalar coefficients to antenna-element-aware weighting. Building on this structure, we formulate sparse antenna activation as structured sparsity-inducing mean square error (MSE) minimization problems, and design four activation schemes at two granularities: antenna-level and array-level, each with UE-specific and network-wide (all-UEs) variants. The resulting convex problems are solved efficiently via the proximal method with closed-form group-wise updates, while the network-wide schemes are modeled through hierarchical sparsity and handled by a tree-structured proximal operator. Numerical results under correlated Rician channels and a detailed power consumption model demonstrate that the OBE weighting scheme consistently improves spectral efficiency over the LSFD, with gains increasing with the number of antennas. Meanwhile, the studied sparse activation schemes can achieve substantial energy efficiency improvement and power reduction with controllable spectral efficiency loss.

Hei Victor Cheng, Emil Björnson, Erik G. Larsson

This paper considers the jointly optimal pilot and data power allocation in single-cell uplink massive multiple-input-multiple-output (MIMO) systems. Using the spectral efficiency (SE) as performance metric and setting a total energy budget per coherence interval, the power control is formulated as optimization problems for two different objective functions: the weighted minimum SE among the users and the weighted sum SE. A closed form solution for the optimal length of the pilot sequence is derived. The optimal power control policy for the former problem is found by solving a simple equation with a single variable. Utilizing the special structure arising from imperfect channel estimation, a convex reformulation is found to solve the latter problem to global optimality in polynomial time. The gain of the optimal joint power control is theoretically justified, and is proved to be large in the low SNR regime. Simulation results also show the advantage of optimizing the power control over both pilot and data power, as compared to the cases of using full power and of only optimizing the data powers as done in previous work.

Hei Victor Cheng, Emil Björnson, Erik G. Larsson

This paper considers the jointly optimal pilot and data power allocation in single cell uplink massive MIMO systems. A closed form solution for the optimal length of the training interval is derived. Using the spectral efficiency (SE) as performance metric and setting a total energy budget per co- herence interval the power control is formulated as optimization problems for two different objective functions: the minimum SE among the users and the sum SE. The optimal power control policy is found for the case of maximizing the minimum SE by converting it to a geometric program (GP). Since maximizing the sum SE is an NP-hard problem, an efficient algorithm is developed for finding KKT (local maximum) points. Simulation results show the advantage of optimizing the power control over both pilot and data power, as compared to heuristic power control policies.

Özlem Tugfe Demir, Emil Björnson

This paper considers the impact of general hardware impairments in a multiple-antenna base station and user equipments on the uplink performance. First, the effective channels are analytically derived for distortion-aware receivers when using finite-sized signal constellations. Next, a deep feedforward neural network is designed and trained to estimate the effective channels. Its performance is compared with state-of-the-art distortion-aware and unaware Bayesian linear minimum mean-squared error (LMMSE) estimators. The proposed deep learning approach improves the estimation quality by exploiting impairment characteristics, while LMMSE methods treat distortion as noise.

Hyeon Seok Rou, Giuseppe Thadeu Freitas de Abreu, Emil Björnson et al.

Orthogonal frequency-division multiplexing (OFDM) and its static sinusoidal subcarriers have underpinned the 4G and 5G eras, delivering high spectral efficiency and resilience to multipath fading through an efficient multicarrier architecture. However, as future systems move toward doubly dispersive environments driven by high-mobility applications and migration to mmWave/sub-THz bands, the time-invariance assumption underlying OFDM becomes increasingly difficult to maintain, and Doppler-induced degradation becomes prominent. While enhancements such as MIMO, advanced coding, and scheduling provide incremental remedies, they introduce additional overhead, because the sinusoidal subcarrier itself offers no inherent waveform-level robustness to Doppler impairments. Accordingly, two time-frequency spreading philosophies have emerged to improve Doppler resilience by distributing each symbol's energy across both dimensions of the time-frequency plane: (i) 2D isotropic spreading via the delay-Doppler (DD) domain, exemplified by the orthogonal time frequency space (OTFS) family, and (ii) sheared spreading via parameterizable chirps, exemplified by the affine frequency-division multiplexing (AFDM) family. In this article, we examine key considerations for future waveform design across these paradigms and argue that transitioning from the sinusoidal subcarriers of OFDM to the chirp-based subcarriers offers a viable design direction for improving Doppler robustness while retaining much of the mature OFDM infrastructure. This perspective also highlights the suitability of chirp-based waveforms for integrated sensing and communications (ISAC) and their extensibility to emerging physical-layer techniques. Overall, we argue that the transition from sinusoids to chirps is a technically motivated, compelling evolutionary direction for future wireless physical layer design.

Zhenyu Li, Özlem Tuğfe Demir, Emil Björnson et al.

The increasing densification of small-cell networks substantially expands cable-based backhaul infrastructure, creating heightened vulnerability to cable link failures. This paper proposes a reconfigurable intelligent surface (RIS)-assisted backup framework that exploits a key insight: during backhaul cable failures, base station (BS) radio components remain functional, enabling wireless backhaul traffic redistribution. Our framework maintains network connectivity by redistributing disconnected BS backhaul traffic to neighboring BSs through RIS-assisted wireless links. To maximize survivability across varying traffic conditions, we formulate a joint optimization problem that maximizes total resolvable backhaul traffic by jointly deciding BS selection, RIS phase shifts, and precoding vectors. The inherent non-convexity arising from coupling and quadratic fractional term is addressed through an alternating optimization algorithm that iteratively solves tractable convex subproblems via quadratic transformation. Comprehensive numerical evaluations demonstrate that the proposed RIS-enhanced framework significantly improves survivability from 58% to 72% under challenging high-intensity hotspot traffic conditions. Moreover, RIS provides the greatest gains for antenna-constrained systems by extending coverage to access more spare capacity of the distant BSs as well as enhancing the signal strength. Consequently, high survivability is achieved even with only two antennas per BS under moderate traffic intensity.

Özlem Tuğfe Demir, Emil Björnson

Network-controlled repeaters (NCRs) are a low-cost means to extend coverage and strengthen macro diversity in wireless networks. They operate in real time by amplifying and re-transmitting the incoming signal with only hardware-level delays, without requiring any channel state information (CSI) at the repeater itself. However, their power amplifiers (PAs) generate non-linear distortion that is jointly forwarded with the desired signal and can undermine multiuser performance unless the distortion statistics are exploited. This paper develops a distortion-aware (DA) uplink framework for repeater-assisted massive MIMO (RA-MIMO) under PA non-linearities. We adopt a memoryless third-order polynomial model for the repeater PA and characterize the achievable spectral efficiency (SE) using the Bussgang decomposition. Closed-form expressions are derived for the Bussgang gain matrix and the distortion covariance. We also design a DA combining vector that maximizes the effective signal-to-interference-plus-distortion ratio.

Zhaolin Wang, Chongjun Ouyang, Kuranage Roche Rayan Ranasinghe et al.

Emerging wireless systems are evolving toward larger, denser, higher-frequency, and more reconfigurable apertures, which motivates the study of continuous-aperture arrays (CAPAs). Unlike conventional spatially discrete arrays (SPDAs), CAPAs are more naturally modeled as spatially continuous electromagnetic apertures and therefore call for a fundamental shift in both signal processing and information-theoretic analysis. In particular, the underlying channels, signals, and beamformers are no longer finite-dimensional vectors and matrices, but continuous fields and operators governed by Maxwell's equations. This paper provides a tutorial overview of CAPA systems from the perspective of electromagnetic signal and information theory (ESIT), with an emphasis on the transition from discrete array models to physics-consistent continuous-aperture formulations. We review the electromagnetic foundations of CAPAs, practical hardware implementations, line-of-sight and multipath channel modeling, continuous-space beamforming and channel estimation, and the fundamental degrees of freedom and capacity limits of CAPA systems. We also highlight how tools such as wavenumber-domain methods, functional analysis, and compressive sensing can transform challenging infinite-dimensional problems into tractable finite-dimensional ones while preserving the essential physical structure of the channel. Overall, this tutorial aims to clarify the key principles, analytical tools, and open challenges that shape CAPA-enabled wireless communications.

Zhe Wang, Mahmoud Zaher, Vitaly Petrov et al.

This paper studies flexible non-uniform array design for monostatic integrated sensing and communication (ISAC) systems. An antenna pool is considered at the base station, where each candidate antenna can be dynamically assigned to transmit, receive, or inactive modes, such that a non-uniform effective array is jointly constructed with the ISAC precoding design. We formulate a sum communication rate maximization problem by jointly optimizing the ISAC beamforming schemes and antenna-mode assignment under sensing, power, and antenna mode constraints. We develop an alternating-optimization-based solution framework mainly with the aid of weighted minimum mean square error, continuous relaxation-based penalty, and successive convex approximation. Numerical results show that the proposed non-uniform array achieves higher sum-rates than the uniform-array baselines, with particularly large gains when the number of activated antennas is small. Moreover, the proposed non-uniform array can achieve, and in some cases exceed, the performance of uniform array baselines with substantially fewer activated antennas, highlighting geometry-aware non-uniform array design as a compelling alternative to brute-force antenna scaling-based array design.

Afsaneh Mahmoudi, Mahmoud Zaher, Emil Björnson

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.

Afsaneh Mahmoudi, Emil Björnson

Federated learning (FL) is a distributed learning framework where users train a global model by exchanging local model updates with a server instead of raw datasets, preserving data privacy and reducing communication overhead. However, the latency grows with the number of users and the model size, impeding the successful FL over traditional wireless networks with orthogonal access. Cell-free massive multiple-input multipleoutput (CFmMIMO) is a promising solution to serve numerous users on the same time/frequency resource with similar rates. This architecture greatly reduces uplink latency through spatial multiplexing but does not take application characteristics into account. In this paper, we co-optimize the physical layer with the FL application to mitigate the straggler effect. We introduce a novel adaptive mixed-resolution quantization scheme of the local gradient vector updates, where only the most essential entries are given high resolution. Thereafter, we propose a dynamic uplink power control scheme to manage the varying user rates and mitigate the straggler effect. The numerical results demonstrate that the proposed method achieves test accuracy comparable to classic FL while reducing communication overhead by at least 93% on the CIFAR-10, CIFAR-100, and Fashion-MNIST datasets. We compare our methods against AQUILA, Top-q, and LAQ, using the max-sum rate and Dinkelbach power control schemes. Our approach reduces the communication overhead by 75% and achieves 10% higher test accuracy than these benchmarks within a constrained total latency budget.

Afsaneh Mahmoudi, Ming Xiao, Emil Björnson

Federated Learning (FL) enables clients to share learning parameters instead of local data, reducing communication overhead. Traditional wireless networks face latency challenges with FL. In contrast, Cell-Free Massive MIMO (CFmMIMO) can serve multiple clients on shared resources, boosting spectral efficiency and reducing latency for large-scale FL. However, clients' communication resource limitations can hinder the completion of the FL training. To address this challenge, we propose an energy-efficient, low-latency FL framework featuring optimized uplink power allocation for seamless client-server collaboration. Our framework employs an adaptive quantization scheme, dynamically adjusting bit allocation for local gradient updates to reduce communication costs. We formulate a joint optimization problem covering FL model updates, local iterations, and power allocation, solved using sequential quadratic programming (SQP) to balance energy and latency. Additionally, clients use the AdaDelta method for local FL model updates, enhancing local model convergence compared to standard SGD, and we provide a comprehensive analysis of FL convergence with AdaDelta local updates. Numerical results show that, within the same energy and latency budgets, our power allocation scheme outperforms the Dinkelbach and max-sum rate methods by increasing the test accuracy up to $7$\% and $19$\%, respectively. Moreover, for the three power allocation methods, our proposed quantization scheme outperforms AQUILA and LAQ by increasing test accuracy by up to $36$\% and $35$\%, respectively.

Seyed Jalaleddin Mousavirad, Parisa Ramezani, Mattias O'Nils et al.

This paper introduces a novel class of model-driven evolutionary frameworks for near-field multi-source localization, addressing the major limitations of grid-based subspace methods such as MUSIC and data-dependent deep learning approaches. To this end, we develop two complementary evolutionary localization frameworks that operate directly on the continuous spherical-wave signal model and support arbitrary array geometries without requiring labeled data, discretized angle--range grids, or architectural constraints. The first framework, termed NEar-field MultimOdal DE (NEMO-DE) associates each individual in the evolutionary population to a single source and optimizes a residual least-squares objective in a sequential manner, updating the data residual and enforcing spatial separation to estimate multiple source locations. To overcome the limitation of NEMO-DE under large power imbalances among the sources, we propose the second framework, named NEar-field Eigen-subspace Fitting DE (NEEF-DE), which jointly encodes all source locations and minimizes a subspace-fitting criterion that aligns a model-based array response subspace with the received signal subspace. Although the proposed frameworks are algorithm-agnostic and compatible with various evolutionary optimizers, differential evolution (DE) is adopted in this work as a representative search strategy due to its simplicity, robustness, and strong empirical performance. We provide extensive numerical experiments to evaluate the performance of the proposed frameworks under different system configurations. This work establishes evolutionary computation as a powerful and flexible paradigm for model-based near-field localization, paving the way for future innovations in this domain.

Amin Ghazanfari, Trinh Van Chien, Emil Björnson et al.

We study downlink (DL) channel estimation in a multi-cell Massive multiple-input multiple-output (MIMO) system operating in a time-division duplex. The users must know their effective channel gains to decode their received DL data signals. A common approach is to use the mean value as the estimate, motivated by channel hardening, but this is associated with a substantial performance loss in non-isotropic scattering environments. We propose two novel estimation methods. The first method is model-aided and utilizes asymptotic arguments to identify a connection between the effective channel gain and the average received power during a coherence block. The second one is a deep-learning-based approach that uses a neural network to identify a mapping between the available information and the effective channel gain. We compare the proposed methods against other benchmarks in terms of normalized mean-squared error and spectral efficiency (SE). The proposed methods provide substantial improvements, with the learning-based solution being the best of the considered estimators.

Özgecan Özdogan, Emil Björnson

Intelligent reflecting surfaces (IRSs), consisting of reconfigurable metamaterials, have recently attracted attention as a promising cost-effective technology that can bring new features to wireless communications. These surfaces can be used to partially control the propagation environment and can potentially provide a power gain that is proportional to the square of the number of IRS elements when configured in a proper way. However, the configuration of the local phase matrix at the IRSs can be quite a challenging task since they are purposely designed to not have any active components, therefore, they are not able to process any pilot signal. In addition, a large number of elements at the IRS may create a huge training overhead. In this paper, we present a deep learning (DL) approach for phase reconfiguration at an IRS in order to learn and make use of the local propagation environment. The proposed method uses the received pilot signals reflected through the IRS to train the deep feedforward network. The performance of the proposed approach is evaluated and the numerical results are presented.

Emil Björnson, Pontus Giselsson

Deep learning has proved itself to be a powerful tool to develop data-driven signal processing algorithms for challenging engineering problems. By learning the key features and characteristics of the input signals, instead of requiring a human to first identify and model them, learned algorithms can beat many man-made algorithms. In particular, deep neural networks are capable of learning the complicated features in nature-made signals, such as photos and audio recordings, and use them for classification and decision making. The situation is rather different in communication systems, where the information signals are man-made, the propagation channels are relatively easy to model, and we know how to operate close to the Shannon capacity limits. Does this mean that there is no role for deep learning in the development of future communication systems?