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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., Comment: 14 pages, 6 figures, To appear in IEEE Transactions on Wireless Communications

Massive MIMO (multiple-input multiple-output) is no longer a “wild” or “promising” concept for future cellular networks—in 2018 it became a reality. Base stations (BSs) with 64 fully digital transceiver chains were commercially deployed in several countries, the key ingredients of Massive MIMO have made it into the 5G standard, the signal processing methods required to achieve unprecedented spectral efficiency have been developed, and the limitation due to pilot contamination has been resolved. Even the development of fully digital Massive MIMO arrays for mmWave frequencies—once viewed prohibitively complicated and costly—is well underway. In a few years, Massive MIMO with fully digital transceivers will be a mainstream feature at both sub-6 GHz and mmWave frequencies. In this paper, we explain how the first chapter of the Massive MIMO research saga has come to an end, while the story has just begun. The coming wide-scale deployment of BSs with massive antenna arrays opens the door to a brand new world where spatial processing capabilities are omnipresent. In addition to mobile broadband services, the antennas can be used for other communication applications, such as low-power machine-type or ultra-reliable communications, as well as non-communication applications such as radar, sensing and positioning. We outline five new Massive MIMO related research directions: Extremely large aperture arrays, Holographic Massive MIMO, Six-dimensional positioning, Large-scale MIMO radar, and Intelligent Massive MIMO.

In this paper, we adapt to cell-free Massive MIMO (multiple-input multiple-output) the finite-blocklength framework introduced by \"Ostman et al. (2020) for the characterization of the packet error probability achievable with Massive MIMO, in the ultra-reliable low-latency communications (URLLC) regime. The framework considered in this paper encompasses a cell-free architecture with imperfect channel-state information, and arbitrary linear signal processing performed at a central-processing unit connected to the access points via fronthaul links. By means of numerical simulations, we show that, to achieve the high reliability requirements in URLLC, MMSE signal processing must be used. Comparisons are also made with both small-cell and Massive MIMO cellular networks. Both require a much larger number of antennas to achieve comparable performance to cell-free Massive MIMO., Comment: 5 pages, 2 figures, accepted at SPAWC 2021

The prospects of using a reconfigurable intelligent surface (RIS) to aid wireless communication systems have recently received much attention. Among the different use cases, the most popular one is where each element of the RIS scatters the incoming signal with a controllable phase-shift, without increasing its power. In prior literature, this setup has been analyzed by neglecting the electromagnetic interference, consisting of the inevitable incoming waves from external sources. In this letter, we provide a physically meaningful model for the electromagnetic interference that can be used as a baseline when evaluating RIS-aided communications. The model is used to show that electromagnetic interference has a non-negligible impact on communication performance, especially when the size of the RIS grows large. When the direct link is present (though with a relatively weak gain), the RIS can even reduce the communication performance. Importantly, it turns out that the SNR grows quadratically with the number of RIS elements only when the spatial correlation matrix of the electromagnetic interference is asymptotically orthogonal to that of the effective channel (including RIS phase-shifts) towards the intended receiver. Otherwise, the SNR only increases linearly., 5 pages, 5 figures, IEEE Wireless Communication Letters

Proceedings of: IEEE International Conference on Communications (ICC 2021), 14-23 June 2021, Montreal, Canada. This paper presents a rigorous finite-blocklength framework for the characterization and the numerical evaluation of the packet error probability achievable in the uplink and downlink of Massive MIMO for ultra-reliable low-latency communications (URLLC). The framework encompasses imperfect channel-state information, pilot contamination, spatially correlated channels, and arbitrary linear signal processing. For a practical URLLC network setup involving base stations with M = 100 antennas, we show by means of numerical results that a target error probability of 10 −5 can be achieved with MMSE channel estimation and multicell MMSE signal processing, uniformly over each cell, only if orthogonal pilot sequences are assigned to all the users in the network. For the same setting, an alternative solution with lower computational complexity, based on least-squares channel estimation and regularized zero-forcing signal processing, does not suffice unless M is increased significantly. This work was partly supported by the Swedish Research Council under grant 2016-03293 and by the Wallenberg AI, autonomous systems, and software program.

Cell-free Massive MIMO systems consist of a large number of geographically distributed access points (APs) that serve users by coherent joint transmission. Downlink power allocation is important in these systems, to determine which APs should transmit to which users and with what power. If the system is implemented correctly, it can deliver a more uniform user performance than conventional cellular networks. To this end, previous works have shown how to perform system-wide max-min fairness power allocation when using maximum ratio precoding. In this paper, we first generalize this method to arbitrary precoding, and then train a neural network to perform approximately the same power allocation but with reduced computational complexity. Finally, we train one neural network per AP to mimic system-wide max-min fairness power allocation, but using only local information. By learning the structure of the local propagation environment, this method outperforms the state-of-the-art distributed power allocation method from the Cell-free Massive MIMO literature., Comment: Published at 2019 Asilomar Conference on Signals, Systems, and Computers, 5 pages, 3 figures

Imagine a coverage area where each mobile device is communicating with a preferred set of wireless access points (among many) that are selected based on its needs and cooperate to jointly serve it, instead of creating autonomous cells. This effectively leads to a user-centric post-cellular network architecture, which can resolve many of the interference issues and service-quality variations that appear in cellular networks. This concept is called User-centric Cell-free Massive MIMO (multiple-input multiple-output) and has its roots in the intersection between three technology components: Massive MIMO, coordinated multipoint processing, and ultra-dense networks. 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 enable massively large networks with many mobile devices. This monograph covers the foundations of User-centric Cell-free Massive MIMO, starting from the motivation and mathematical definition. It continues by describing the state-of-the-art signal processing algorithms for channel estimation, uplink data reception, and downlink data transmission with either centralized or distributed implementation. The achievable spectral efficiency is mathematically derived and evaluated numerically using a running example that exposes the impact of various system parameters and algorithmic choices. The fundamental tradeoffs between communication performance, computational complexity, and fronthaul signaling requirements are thoroughly analyzed. Finally, the basic algorithms for pilot assignment, dynamic cooperation cluster formation, and power optimization are provided, while open problems related to these and other resource allocation problems are reviewed. All the numerical examples can be reproduced using the accompanying Matlab code., Comment: This is the authors' version of the manuscript: \"Ozlem Tugfe Demir, Emil Bj\"ornson and Luca Sanguinetti (2021), "Foundations of User-Centric Cell-Free Massive MIMO", Foundations and Trends in Signal Processing: Vol. 14, No. 3-4, pp 162-472

In overloaded Massive MIMO (mMIMO) 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 the sum spectral efficiency. This paper aims at identifying cases where code-domain NOMA can improve the spectral efficiency of mMIMO in the classical regime where $K < M$. Novel spectral efficiency expressions are provided for the uplink and downlink with arbitrary spreading signatures and spatial correlation matrices. Particular attention is devoted to the planar arrays that are currently being deployed in pre-5G and 5G networks (in sub$-6$ GHz bands), which are characterized by limited spatial resolution. Numerical results show that mMIMO with such planar arrays can benefit from NOMA in scenarios where the UEs are spatially close to each other. A two-step UE grouping scheme is proposed for NOMA-aided mMIMO systems that is applicable to the spatial correlation matrices of the UEs that are currently active in each cell. Numerical results are used to investigate the performance of the algorithm under different operating conditions and types of spreading signatures (orthogonal, sparse and random sets). The analysis reveals that orthogonal signatures provide the highest average spectral efficiency., to appear IEEE Trans. Vehicular Technology. Copyright (c) 2015 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE

Holographic MIMO is a spatially-constrained MIMO system with a massive number of antennas, possibly thought of, in its ultimate form, as a spatially-continuous electromagnetic aperture. Accurate and tractable channel modeling is critical to understanding the full potential of this technology. This paper considers arbitrary spatially-stationary scattering and provides a 4D plane-wave representation in Cartesian coordinates, which captures the essence of electromagnetic propagation and allows to evaluate the capacity of Holographic MIMO systems with rectangular volumetric arrays. The developed framework generalizes the virtual channel representation, which was originally developed for uniform linear arrays., Comment: 5 pages, 3 figures, presented at the Asilomar Conference on Signals, Systems, and Computers, 2020

A realistic performance assessment of any wireless technology requires the use of a channel model that reflects its main characteristics. The independent and identically distributed Rayleigh fading channel model has been (and still is) the basis of most theoretical research on multiple antenna technologies in scattering environments. This letter shows that such a model is not physically appearing when using a reconfigurable intelligent surface (RIS) with rectangular geometry and provides an alternative physically feasible Rayleigh fading model that can be used as a baseline when evaluating RIS-aided communications. The model is used to revisit the basic RIS properties, e.g., the rank of spatial correlation matrices and channel hardening., Comment: Published in IEEE Wireless Communications Letters, 6 pages, 4 figures

This paper analyzes how the distortion created by hardware impairments in a multiple-antenna base station affects the uplink spectral efficiency (SE), with focus on Massive 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 i.i.d. 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., Published in IEEE Transactions on Communications, 14 pages, 12 figures. This version corrects a typo in Appendix C. arXiv admin note: text overlap with arXiv:1805.07958

International audience; The spectral efficiency (SE) of Massive MIMO (MaMIMO) systems is affected by low quality channel estimates. Rate-Splitting (RS) has recently gained some interest in multiuser multiple antenna systems as an effective means to mitigate the multiuser interference due to imperfect channel state information. This paper investigates the benefits of RS in the downlink of a single-cell MaMIMO system when all the users use the same pilot sequence for channel estimation. Novel expressions for the SE achieved in the downlink by a single-layer RS strategy (that relies on a single successive interference cancellation at each user side) are derived and used to design precoding schemes and power allocation strategies for common and private messages. Numerical results are used to show that the proposed RS solution achieves higher spectral efficiency that conventional MaMIMO with maximum ratio precoding.

Massive MIMO systems, where base stations are equipped with hundreds of antennas, are an attractive way to handle the rapid growth of data traffic. As the number of user equipments (UEs) increases, the initial access and handover in contemporary networks will be flooded by user collisions. In this paper, a random access protocol is proposed that resolves collisions and performs timing estimation by simply utilizing the large number of antennas envisioned in Massive MIMO networks. UEs entering the network perform spreading in both time and frequency domains, and their timing offsets are estimated at the base station in closed-form using a subspace decomposition approach. This information is used to compute channel estimates that are subsequently employed by the base station to communicate with the detected UEs. The favorable propagation conditions of Massive MIMO suppress interference among UEs whereas the inherent timing misalignments improve the detection capabilities of the protocol. Numerical results are used to validate the performance of the proposed procedure in cellular networks under uncorrelated and correlated fading channels. With $2.5\times10^3$ UEs that may simultaneously become active with probability 1\% and a total of $16$ frequency-time codes (in a given random access block), it turns out that, with $100$ antennas, the proposed procedure successfully detects a given UE with probability 75\% while providing reliable timing estimates., 30 pages, 6 figures, 1 table, submitted to Transactions on Communications

The fast adoption of Massive MIMO for high-throughput communications was enabled by many research contributions mostly relying on infinite-blocklength information-theoretic bounds. This makes it hard to assess the suitability of Massive MIMO for ultra-reliable low-latency communications (URLLC) operating with short blocklength codes. This paper provides a rigorous framework for the characterization and numerical evaluation (using the saddlepoint approximation) of the error probability achievable in the uplink and downlink of Massive MIMO at finite blocklength. The framework encompasses imperfect channel state information, pilot contamination, spatially correlated channels, and arbitrary linear spatial processing. In line with previous results based on infinite-blocklength bounds, we prove that, with minimum mean-square error (MMSE) processing and spatially correlated channels, the error probability at finite blocklength goes to zero as the number $M$ of antennas grows to infinity, even under pilot contamination. On the other hand, numerical results for a practical URLLC network setup involving a base station with $M=100$ antennas, show that a target error probability of $10^{-5}$ can be achieved with MMSE processing, uniformly over each cell, only if orthogonal pilot sequences are assigned to all the users in the network. Maximum ratio processing does not suffice., Comment: 15 pages, 5 figures; to appear in IEEE Transactions on Wireless Communications

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 in 5G and base stations (BSs) with $M=64$ full-digital transceivers have been commercially deployed in sub-6\,GHz 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 $M\to\infty$. 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''., 26 pages, 16 figures, IEEE Transactions on Communications

Imagine an array with a massive (possibly uncountably infinite) number of antennas in a compact space. We refer to a system of this sort as Holographic MIMO. Given the impressive properties of Massive MIMO, one might expect a holographic array to realize extreme spatial resolution, incredible energy efficiency, and unprecedented spectral efficiency. At present, however, its fundamental limits have not been conclusively established. A major challenge for the analysis and understanding of such a paradigm shift is the lack of mathematically tractable and numerically reproducible channel models that retain some semblance to the physical reality. Detailed physical models are, in general, too complex for tractable analysis. This paper aims to take a closer look at this interdisciplinary challenge. Particularly, we consider the small-scale fading in the far-field, and we model it as a zero-mean, spatially-stationary, and correlated Gaussian scalar random field. Physically-meaningful correlation is obtained by requiring that the random field be consistent with the scalar Helmholtz equation. This formulation leads directly to a rather simple and exact description of the three-dimensional small-scale fading as a Fourier plane-wave spectral representation. Suitably discretized, this leads to a discrete representation for the field as a Fourier plane-wave series expansion, from which a computationally efficient way to generate samples of the small-scale fading over spatially-constrained compact spaces is developed. The connections with the conventional tools of linear systems theory and Fourier transform are thoroughly discussed., 31 pages, 9 figures, JSAC Special Issue on Multiple Antenna Technologies for Beyond 5G

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 processing and also performs closely to the best unscalable alternatives., To appear in IEEE Transactions on Communications, 14 pages, 6 figures

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., To appear at the 2019 IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (IEEE PIMRC 2019), 5 pages, 5 figures

Communication by joint signal processing from many distributed access points, called Cell-free Massive MIMO, is a potential beyond-5G network infrastructure. The aim of this paper is to provide the first comprehensive comparison with Cellular Massive MIMO. The uplink spectral efficiencies of four different cell-free implementations are analyzed, with spatially correlated fading and arbitrary processing. It turns out that it is possible to outperform cellular networks by a wide margin, but only using the right signal processing. A centralized implementation with optimal processing maximizes performance and, surprisingly, also reduces the fronthaul signaling.

Since the seminal paper by Marzetta from 2010, the Massive MIMO paradigm in communication systems has changed from being a theoretical scaled-up version of MIMO, with an infinite number of antennas, to a practical technology. Its key concepts have been adopted in the 5G new radio standard and base stations, where $64$ fully-digital transceivers have been commercially deployed. Motivated by these recent developments, this paper considers a co-located MIMO radar with $M_T$ transmitting and $M_R$ receiving antennas and explores the potential benefits of having a large number of virtual spatial antenna channels $N=M_TM_R$. Particularly, we focus on the target detection problem and develop a \textit{robust} Wald-type test that guarantees certain detection performance, regardless of the unknown statistical characterization of the clutter disturbance. Closed-form expressions for the probabilities of false alarm and detection are derived for the asymptotic regime $N\to \infty$. Numerical results are used to validate the asymptotic analysis in the finite system regime with different disturbance models. Our results imply that there always exists a sufficient number of antennas for which the performance requirements are satisfied, without any a-priori knowledge of the clutter statistics. This is referred to as the Massive MIMO regime of the radar system., 12 pages, 6 figures, accepted for publication in IEEE Transactions on Signal Processing. A related work has been presented at ICASSP19, Brighton, UK, and is available at arXiv:1904.04184

International audience; Next-generation networks will be characterized by three key features: heterogeneity, in terms of technologies and services, dynamics, in terms of rapidly varying environments and uncertainty, and size, in terms of the numbers of users, nodes, and services. The emergence of such large-scale and decentralized heterogeneous networks operating under dynamic and uncertain environments imposes new challenges in the design, analysis, and optimization of networks. The past decade has witnessed a confluence among the disciplines of networks, games, and economics, which has necessitated novel mathematical tools and designs that can truly remove the boundaries between these disciplines. In this context, advancing game-theoretic models and tailoring them towards the optimization and operation of future networked systems become pressing needs for our research community. The main goal of this IEEE JSAC Special Issue on “Game Theory for Networks” is to collect cutting-edge contributions that address and show the latest developments in game-theoretic models for emerging networking applications. The response of the community to the call has been overwhelming. We received a total of 120 submissions. We want to thank all the authors who submitted their works to this Special Issue. After a strict and selective review process, we accepted 40 papers and decided to publish two issues. Papers were selected based on their appropriateness for and relevance to the Special Issue as well as their technical merits. Unfortunately, a number of interesting papers did not make the cut because of the criteria set forth above and also due to the constraints on the total page count in a JSAC Special Issue. We hope that such interesting papers will find other venues for publication.

This work focuses on a large-scale multi-cell multi-user MIMO system in which $L$ base stations (BSs) of $N$ antennas each communicate with $K$ single-antenna user equipments. We consider the design of the linear precoder that minimizes the total power consumption while ensuring target user rates. Three configurations with different degrees of cooperation among BSs are considered: the coordinated beamforming scheme (only channel state information is shared among BSs), the coordinated multipoint MIMO processing technology or network MIMO (channel state and data cooperation), and a single cell beamforming scheme (only local channel state information is used for beamforming while channel state cooperation is needed for power allocation). The analysis is conducted assuming that $N$ and $K$ grow large with a non trivial ratio $K/N$ and imperfect channel state information (modeled by the generic Gauss-Markov formulation form) is available at the BSs. Tools of random matrix theory are used to compute, in explicit form, deterministic approximations for: (i) the parameters of the optimal precoder; (ii) the powers needed to ensure target rates; and (iii) the total transmit power. These results are instrumental to get further insight into the structure of the optimal precoders and also to reduce the implementation complexity in large-scale networks. Numerical results are used to validate the asymptotic analysis in the finite system regime and to make comparisons among the different configurations., Comment: 32 pages, 6 figures, to appear IEEE Trans. Wireless Commun. A preliminary version of this paper was presented at the IEEE Global Communication Conference, San Diego, USA, Dec. 2015

In the above-named work, [ibid., xxx], there is a typo in the position of the first conjugate operator. The correct definition of the first conjugate operator BN is provided.

This paper focuses on developing a decentralized framework for coordinated minimum power beamforming wherein $L$ base stations (BSs), each equipped with $N$ antennas, serve $K$ single-antenna users with specific rate constraints. This is realized by considering user specific intercell interference (ICI) strength as the principal coupling parameter among BSs. First, explicit deterministic expressions for transmit powers are derived for spatially correlated channels in the asymptotic regime in which $N$ and $K$ grow large with a non-trivial ratio $K/N$. These asymptotic expressions are then used to compute approximations of the optimal ICI values that depend only on the channel statistics. By relying on the approximate ICI values as coordination parameters, a distributed non-iterative coordination algorithm, suitable for large networks with limited backhaul, is proposed. A heuristic algorithm is also proposed relaxing coordination requirements even further as it only needs pathloss values for non-local channels. The proposed algorithms satisfy the target rates for all users even when $N$ and $K$ are relatively small. Finally, the potential benefits of grouping users with similar statistics are investigated to further reduce the overhead and computational effort of the proposed solutions. Simulation results show that the proposed methods yield near-optimal performance., Comment: IEEE Transactions on Communications

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., To appear at the 2019 IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (IEEE PIMRC 2019), 6 pages, 5 figures

The spectral efficiency of wireless networks can be made nearly infinitely large by deploying many antennas, but the deployment of very many antennas requires new topologies beyond the compact and discrete antenna arrays used by conventional base stations. In this paper, we consider the large intelligent surface scenario where small antennas are deployed on a large and dense two-dimensional grid. Building on the heritage of MIMO, we first analyze the beamwidth and sidelobes when transmitting from large intelligent surfaces. We compare different precoding schemes and determine how to optimize the transmit power with respect to different utility functions., Comment: Figures 3(a) and (b) were in wrong order in the last version. Originally published at Asilomar SSC 2029, 5 pages, 5 figures

This work focuses on target detection in a colocated MIMO radar system. Instead of exploiting the classical temporal domain, we propose to explore the spatial dimension (i.e., number of antennas $M$) to derive asymptotic results for the detector. Specifically, we assume no a priori knowledge of the statistics of the autoregressive data generating process and propose to use a mispecified Wald-type detector, which is shown to have an asymptotic $\chi$-squared distribution as $M\to\infty$. Closed-form expressions for the probabilities of false alarm and detection are derived. Numerical results are used to validate the asymptotic analysis in the finite system regime. It turns out that, for the considered scenario, the asymptotic performance is closely matched already for $M\ge 50$., Comment: 8 pages, 2 figures. This is the extended version (with all the proofs in Appendices) of a paper that will be presented at ICASSP 2019, 12-17 May, 2019, Brighton, UK

This work advocates the use of deep learning to perform max-min and max-prod power allocation in the downlink of Massive MIMO networks. More precisely, a deep neural network is trained to learn the map between the positions of user equipments (UEs) and the optimal power allocation policies, and then used to predict the power allocation profiles for a new set of UEs' positions. The use of deep learning significantly improves the complexity-performance trade-off of power allocation, compared to traditional optimization-oriented methods. Particularly, the proposed approach does not require the computation of any statistical average, which would be instead necessary by using standard methods, and is able to guarantee near-optimal performance., 5 pages, 2 figures; presented at ASILOMAR 2018. The training set is available online at https://data.ieeemlc.org while the Matlab code available at https://github.com/lucasanguinetti/ allows to generate further samples

In this lecture note, we introduce the basic concepts of game theory (GT), a branch of mathematics traditionally studied and applied in the areas of economics, political science, and biology, which has emerged in the last 15 years as an effective framework for communications, networking, and signal processing (SP). The real catalyst has been all of the blooming issues related to distributed networks in which the nodes can be modeled as players in a game competing for system resources. Some relevant notions of GT are introduced by elaborating on a simple application in the context of wireless communications, notably the power control in an interference channel (IC) with two transmitters and two receivers.

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 $M\to \infty$) 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 $M\to \infty$, 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 $M\to \infty$ 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., 6 pages, 2 figures, to be presented at GLOBECOM 2018, Abu Dhabi

This work aims at developing a power control framework to jointly optimize energy efficiency (measured in bit/Joule) and delay in wireless networks. A multi-objective approach is taken to deal with both performance metrics, while ensuring a minimum quality-of-service to each user in the network. Each user in the network is modeled as a rational agent that engages in a generalized non-cooperative game. Feasibility conditions are derived for the existence of each player's best response, and used to show that if these conditions are met, the game best response dynamics will converge to a unique Nash equilibrium. Based on these results, a convergent power control algorithm is derived, which can be implemented in a fully decentralized fashion. Next, a centralized power control algorithm is proposed, which also serves as a benchmark for the proposed decentralized solution. Due to the non-convexity of the centralized problem, the tool of maximum block improvement is used, to trade-off complexity with optimality., Comment: 13 pages, 6 figures, to appear on IEEE Transactions on Communications

This paper analyzes how the distortion created by hardware impairments in a multiple-antenna base station affects the uplink spectral efficiency (SE), with focus on Massive MIMO. The 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 the distortion correlation are first uncovered. Then, we focus on third-order non-linearities and prove analytically and numerically that the correlation can be neglected in the SE analysis when there are many users. In i.i.d. Rayleigh fading with equal signal-to-noise ratios, this occurs when having five users., Comment: 5 pages, 3 figures, IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 2018

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., 7 pages, 3 figures; presented at the Global Communications Conference (GLOBECOM'17), 4-8 December, 2017, Singapore

International audience; The max-min signal-to-interference-plus-noise ratio (SINR) problem is considered in a coordinated network wherein L base stations (BSs) each equipped with N antennas serve in total K single-antenna users that are uniformly distributed in the network. We conduct the analysis in the asymptotic regime in which N and K grow large to compute a deterministic approximation for the max-min SINR. The results are independent from fast-fading and users' locations and thus allow one to determine the optimal max-min SINR given basic system parameters such as cell radius, K, N and pathloss exponent. The provided framework can be utilized for analyzing the problem without the need to run system level simulations and for finding the optimal N, K, resource allocation and BS placement. Numerical results are used to validate the analytical results in a finite system regime and to evaluate the effects of system parameters on the system performance.

This work analyzes a mmWave single-cell network, which comprises a macro base station (BS) and an overlaid tier of small-cell BSs using a wireless backhaul for data traffic. We look for the optimal number of antennas at both BS and small-cell BSs that maximize the energy efficiency (EE) of the system when a hybrid transceiver architecture is employed. Closed-form expressions for the EE-optimal values of the number of antennas are derived that provide valuable insights into the interplay between the optimization variables and hardware characteristics. Numerical and analytical results show that the maximal EE is achieved by a 'close-to' fully-digital system wherein the number of BS antennas is approximately equal to the number of served small cells., Comment: 8 pages, 4 figures, 1 table, presented at 15th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt2017), Paris, France, May 2017

This work considers the downlink of a multicell massive MIMO system in which $L$ base stations (BSs) of $N$ antennas each communicate with $K$ single-antenna user equipments randomly positioned in the coverage area. Within this setting, we are interested in evaluating the sum rate of the system when MRT and RZF are employed under the assumption that each intracell link forms a MIMO Rician fading channel. The analysis is conducted assuming that $N$ and $K$ grow large with a non-trivial ratio $N/K$ under the assumption that the data transmission in each cell is affected by channel estimation errors, pilot contamination, and an arbitrary large scale attenuation. Numerical results are used to validate the asymptotic analysis in the finite system regime and to evaluate the network performance under different settings. The asymptotic results are also instrumental to get insights into the interplay among system parameters., 7 pages, 2 figures, submitted to GLOBECOM16, Washington, DC USA. arXiv admin note: text overlap with arXiv:1601.07024

Linear precoding has been widely studied in the context of Massive multiple-input-multiple-output (MIMO) together with two common power normalization techniques, namely, matrix normalization (MN) and vector normalization (VN). Despite this, their effect on the performance of Massive MIMO systems has not been thoroughly studied yet. The aim of this paper is to fulfill this gap by using large system analysis. Considering a system model that accounts for channel estimation, pilot contamination, arbitrary pathloss, and per-user channel correlation, we compute tight approximations for the signal-to-interference-plus-noise ratio and the rate of each user equipment in the system while employing maximum ratio transmission (MRT), zero forcing (ZF), and regularized ZF precoding under both MN and VN techniques. Such approximations are used to analytically reveal how the choice of power normalization affects the performance of MRT and ZF under uncorrelated fading channels. It turns out that ZF with VN resembles a sum rate maximizer while it provides a notion of fairness under MN. Numerical results are used to validate the accuracy of the asymptotic analysis and to show that in Massive MIMO, non-coherent interference and noise, rather than pilot contamination, are often the major limiting factors of the considered precoding schemes., Comment: 12 pages, 3 figures, Accepted for publication in the IEEE Transactions on Vehicular Technology

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. Funding Agencies|ELLIIT; Swedish Foundation for Strategic Research (SSF); ERC Starting MORE [305123]

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., Comment: To appear in IEEE Transactions on Wireless Communications, 17 pages, 7 figures

The reuse of pilot sequences in a Massive MIMO system leads to pilot contamination, which reduces the channel estimation quality and adds coherent interference in the data transmission. A standard method to reduce pilot contamination, known as regular pilots (RPs), is to increase the pilot overhead and reuse pilots more sparsely in the network. Another approach, denoted as superimposed pilots (SPs), is to send a superposition of pilot and data symbols which allows the system to reuse pilots far more sparsely. This work performs a comparative analysis of RPs and SPs in Massive MIMO considering the joint spectral efficiency (SE) of the uplink (UL) and downlink (DL) communications. A rigorous DL lower bound on the capacity with SPs is derived and multiobjective optimization theory is used to compare the UL and DL SE between RPs and SPs. Numerical results indicate that RPs and SPs give comparable SE when both methods are optimized. Funding agencies: Swedish Foundation for Strategic Research (SSF); ERC Starting MORE [305123]; Swedish Research Council; ELLIIT

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 to use longer pilots which, in turn, reduces pilot contamination. We consider the uplink of a multicell Massive MIMO network using maximum ratio combining detection 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., Comment: 32 pages, 12 figures, 3 tables. Submitted in March 2017 to IEEE Transactions on Wireless Communications

International audience; In this paper, we present a distributed matrix exponential learning (MXL) algorithm for a wide range of distributed optimization problems and games that arise in signal processing and data networks. To analyze it, we introduce a novel stability concept that guarantees the existence of a unique equilibrium solution; under this condition, we show that the algorithm converges even in the presence of highly defective feedback that is subject to measurement noise, errors, etc. For illustration purposes, we apply the proposed method to the problem of energy efficiency (EE) maximization in multi-user, multiple-antenna wireless networks with imperfect channel state information (CSI), showing that users quickly achieve a per capita EE gain between 100% and 400%, even under very high uncertainty.

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., IEEE ICC 2017, 6 pages, 5 figures

International audience; —This work focuses on the downlink of a single-cell large-scale MIMO system in which the base station equipped with M antennas serves K single-antenna users. In particular, we are interested in reducing the implementation complexity of the optimal linear precoder (OLP) that minimizes the total power consumption while ensuring target user rates. As most precoding schemes, a major difficulty towards the implementation of OLP is that it requires fast inversions of large matrices at every new channel realizations. To overcome this issue, we aim at designing a linear precoding scheme providing the same performance of OLP but with lower complexity. This is achieved by applying the truncated polynomial expansion (TPE) concept on a per-user basis. To get a further leap in complexity reduction and allow for closed-form expressions of the per-user weighting coefficients, we resort to the asymptotic regime in which M and K grow large with a bounded ratio. Numerical results are used to show that the proposed TPE precoding scheme achieves the same performance of OLP with a significantly lower implementation complexity.

International audience; 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.

International audience; —This paper presents a cooperative multiple-input multiple-output (MIMO) scheme for a wireless sensor network consisting of inexpensive nodes, organised in clusters and transmitting data towards sinks. The transmission is affected by hardware imperfections, imperfect synchronisation, data correlation among nodes of the same cluster, channel estimation errors and interference among nodes of different clusters. Within this setting, we are interested in determining the number of nodes per cluster that maximises the energy efficiency of the network. The analysis is conducted in the asymptotic regime in which the number N of sensor nodes per cluster grows large without bound. Numerical results are used to validate the asymptotic analysis in the finite system regime and to investigate different configurations. It turns out that the optimum number of sensor nodes per cluster increases with the inter-cluster interference and with the number of sinks.

International audience; We consider a heterogeneous network (HetNet) in which multiple small cell base stations (SBSs) aim to offload a quantity of macro cell user equipments (MUEs) to reduce the energy consumption of the network while guaranteeing the QoS requirements of all UEs. We design an ascending-bid auction mechanism to achieve this goal. Unique and closed form solutions for the demand and supply quantities of offloading MUEs are derived. When the MBS has knowledge about the utilities and strategies of the SBSs, the proposed auction can be formulated as a Stackelberg game where the clinching bid price is obtained in closed form. Numerical results verify the theoretical analysis for different scenarios and show that the proposed auction clinches fast at the unique clinching price, thereby resulting in a win-win solution that improves the energy consumption of the HetNet.

Frame detection and timing acquisition are challenging tasks in orthogonal frequency-division multiplexing systems plagued by narrowband interference (NBI). Most existing solutions operate in the time domain by exploiting the repetitive structure of a training symbol and suffer from considerable performance loss in the presence of NBI. In this work, a novel solution in which frame detection is accomplished in the frequency domain on the basis of a suitable likelihood ratio test is presented. In order to increase the resilience to NBI, the interference power is treated as a nuisance parameter that is averaged out from the corresponding likelihood functions. The resulting test statistic depends on the fractional carrier frequency offset (CFO), which is easily estimated. An alternative scheme that dispenses from CFO estimation is also proposed. After frame detection, the test statistic is employed as a timing metric to accurately locate the position of the training symbol within the received data stream. Computer simulations indicate that the proposed solutions are remarkably robust to NBI and outperform existing alternatives in a severe interference scenario. The price for this advantage is a substantial increase in the computational burden.

In a recent study, solutions have been proposed for completely suppressing the multiple access interference (MAI) arising in the uplink of a quasi-synchronous multicarrier code-division multiple-access network as a consequence of multipath distortions and carrier frequency offsets. This result is achieved by employing exponential orthogonal codes or selecting a particular subset of the Walsh-Hadamard code family without the need for any channel state information at the transmitter side. In the present letter, we revisit this problem and show that MAI suppression can be achieved by following a different line of reasoning which leads to a transmission scheme exhibiting a lower peak-to-average power ratio.