Cell-free massive multiple-input multiple-output (mMIMO) networks enhance coverage and spectral efficiency (SE) by distributing antennas across access points (APs) with phase coherence between APs. However, the use of cost-efficient local oscillators (LOs) introduces phase noise (PN) that compromises phase coherence, even with centralized processing. Sharing an LO across APs can reduce costs in specific configurations but cause correlated PN between APs, leading to correlated interference that affects centralized combining. This can be improved by exploiting the PN correlation in channel estimation. This paper presents an uplink orthogonal frequency division multiplexing (OFDM) signal model for PN-impaired cell-free mMIMO, addressing gaps in single-carrier signal models. We evaluate mismatches from applying single-carrier methods to OFDM systems, showing how they underestimate the impact of PN and produce over-optimistic achievable SE predictions. Based on our OFDM signal model, we propose two PN-aware channel and common phase error estimators: a distributed estimator for uncorrelated PN with separate LOs and a centralized estimator with shared LOs. We introduce a deep learning-based channel estimator to enhance the performance and reduce the number of iterations of the centralized estimator. The simulation results show that the distributed estimator outperforms mismatched estimators with separate LOs, whereas the centralized estimator enhances distributed estimators with shared LOs.

This paper introduces a learning-based approach to the near-field source localization problem adopting a hybrid analog-digital beamformer in an extremely large-scale multipleinput multiple-output (XL-MIMO) system. Hybrid analog-digital architectures gained significant attention in the literature due to the limited number of radio-frequency (RF) chains. However, the investigation of effective techniques tailored to partially connected hybrid beamformers for near-field localization is still missing in the literature. To this end, we leverage a Convolutional Neural Network (CNN)-based model to: (i) perform the analog beamformer design with proper training constraints; and (ii) estimate the single-user near-field position in a single snapshot. In the inference stage, the model is divided into two parts: the first accounts for the beamformer design, and the second acts as a localizing function. Simulation results demonstrate superior performance of the proposed method over existing solutions and robustness in multipath propagation conditions. In addition, our network is scalable and requires fewer RF chains than fullyconnected architectures.

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

This paper proposes a power allocation framework based on the per-user quality-of-experience (QoE) conditions for an aerial relay massive MIMO (mMIMO) network, assuming the direct transmission between the mMIMO base station and ground users (UEs) is unavailable. We first derive closed-form spectral efficiency expressions for the mMIMO-based system, with a UAV acting as the aerial relay. Then, we formulate a joint optimization problem of power allocation and QoE in the downlink, aiming to maximize the sum throughput of the serving ground UEs. The problem is generally hard to solve due to the non-convex constraints and non-concave objective function. To address it, we propose a two-step algorithm based on inner convex approximation (ICA) method. However, the ICA-based algorithm requires an initial feasible point, which is difficult to find by generating a random point as commonly conceived in existing approaches while satisfying the QoE constraints. To tackle this issue, we develop a max-min problem, whose solution leads to an initial feasible point that maximizes the difference between the per-user rate and its corresponding QoE threshold. Numerical results are used to demonstrate the validity of the theoretical analysis and the effectiveness of the proposed algorithms.

Large-scale MIMO systems with a massive number N of individually controlled antennas pose significant challenges for minimum mean square error (MMSE) channel estimation, based on uplink pilots. The major ones arise from the computational complexity, which scales with$N^{3}$, and from the need for accurate knowledge of the channel statistics. This paper aims to address both challenges by introducing reduced-complexity channel estimation methods that achieve the performance of MMSE in terms of estimation accuracy and uplink spectral efficiency while demonstrating improved robustness in practical scenarios where channel statistics must be estimated. This is achieved by exploiting the inherent structure of the spatial correlation matrix induced by the array geometry. Specifically, we use a Kronecker decomposition for uniform planar arrays and a well-suited circulant approximation for uniform linear arrays. By doing so, a significantly lower computational complexity is achieved, scaling as$N\sqrt {N}$and$N \log N$for squared planar arrays and linear arrays, respectively.

Holographic MIMO refers to a (possibly large) array with a large number of individually controlled and densely deployed antennas. The objective of this paper is to provide further insight into the use of closely spaced antennas in the uplink and downlink of a multi-user Holographic MIMO system. To this end, we utilize multiport communication theory, which ensures physically consistent uplink and downlink models. We first consider a simple uplink scenario with two side-by-side half-wavelength dipoles, two users, and single-path line-of-sight propagation, and show both analytically and numerically that the receive array gain and average spectral efficiency strongly depend on the directions from which the signals are received and on the array matching network used. The numerical results are then used to extend the analysis to more practical scenarios involving a larger number of dipoles (arranged in a uniform linear array) and a larger number of users. The case where the antennas are densely packed in a space-constrained factor form is also considered. It is found that the spectral efficiency benefits from decreasing the antenna spacing if arrays of moderate size are considered, e.g. in the order of a few wavelengths. In comparison, larger arrays with closely spaced antennas show only marginal improvements in spectral efficiency compared to half-wavelength arrays.

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

Consider a communication system in which a single-antenna user equipment exchanges information with a multi-antenna base station via a reconfigurable intelligent surface (RIS) in the presence of spatially correlated channels and electromagnetic interference (EMI). To exploit the attractive advantages of RIS technology, accurate configuration of its reflecting elements is crucial. In this paper, we use statistical knowledge of channels and EMI to optimize the RIS elements for 1i) accurate channel estimation and 2) reliable data transmission. In both cases, our goal is to determine the RIS coefficients that minimize the mean square error, resulting in the formulation of two non-convex problems that share the same structure. To solve these two problems, we present an alternating optimization approach that reliably converges to a locally optimal solution. The incorporation of the diagonally scaled steepest descent algorithm, derived from Newton’s method, ensures fast convergence with manageable complexity. Numerical results demonstrate the effectiveness of the proposed method under various propagation conditions. Notably, it shows significant advantages over existing alternatives that depend on a suboptimal configuration of the RIS and are derived on the basis of different criteria.

Cell-Free massive MIMO networks provide huge power gains and resolve inter-cell interference by coherent processing over a massive number of distributed instead of colocated antennas in access points (APs). Cost-efficient hardware is preferred but imperfect local oscillators in both APs and users introduce multiplicative phase noise (PN), which affects the phase coherence between APs and users even with centralized processing. In this paper, we first formulate the system model of a PN- impaired uplink Cell-Free massive MIMO orthogonal frequency division multiplexing network, and then propose a PN-aware linear minimum mean square error channel estimator and derive a PN- impaired uplink spectral efficiency expression. Numerical results are used to quantify the spectral efficiency gain of the proposed channel estimator over alternative schemes for different receiving combiners.

We present a general framework for the characterization of the packet error probability achievable in cell-free Massive multiple-input multiple output (MIMO) architectures deployed to support ultra-reliable low-latency (URLLC) traffic. The framework is general and encompasses both centralized and distributed cell-free architectures, arbitrary fading channels and channel estimation algorithms at both network and user-equipment (UE) sides, as well as arbitrary combining and precoding schemes. The framework is used to perform numerical experiments on specific scenarios, which illustrate the superiority of cell-free architectures compared to cellular architectures in supporting URLLC traffic in uplink and downlink. Also, these numerical experiments provide the following insights into the design of cell-free architectures for URLLC:${i}$) minimum mean square error (MMSE) spatial processing must be used to achieve the URLLC targets; ii) for a given total number of antennas per coverage area, centralized cell-free solutions involving single-antenna access points (APs) offer the best performance in the uplink, thereby highlighting the importance of reducing the average distance between APs and UEs in the URLLC regime; iii) this observation applies also to the downlink, provided that the APs transmit precoded pilots to allow the UEs to estimate accurately the precoded channel.

Massive multiple-input multiple-output (MaMIMO) has become an integral part of the fifth-generation (5G) standard, and is envisioned to be further developed in beyond 5G (B5G) networks. With a massive number of antennas at the base station (BS), MaMIMO is best equipped to cater prominent use cases of B5G networks such as enhanced mobile broadband (eMBB), ultra-reliable low-latency communications (URLLC) and massive machine-type communications (mMTC) or combinations thereof. However, one of the critical challenges to this pursuit is the sporadic access behaviour of a massive number of devices in practical networks that inevitably leads to the conspicuous pilot contamination problem. Conventional linearly precoded physical layer strategies employed for downlink transmission in time division duplex (TDD) MaMIMO would incur a noticeable spectral efficiency (SE) loss in the presence of this pilot contamination. In this paper, we aim to integrate a robust multiple access and interference management strategy named rate-splitting multiple access (RSMA) with TDD MaMIMO for downlink transmission and investigate its SE performance. We propose a novel downlink transmission framework of RSMA in TDD MaMIMO, devise a precoder design strategy and power allocation schemes to maximize different network utility functions. Numerical results reveal that RSMA is significantly more robust to pilot contamination and always achieves a SE performance that is equal to or better than the conventional linearly precoded MaMIMO transmission strategy.

Starting from first principles of wave propagation, we consider a multiple-input multiple-output (MIMO) representation of a communication system between two spatially-continuous volumes. This is the concept of holographic MIMO communications. The analysis takes into account the electromagnetic interference, generated by external sources, and the constraint on the physical radiated power. The electromagnetic MIMO model is particularized for a pair of parallel line segments in line-of-sight conditions. Inspired by orthogonal-frequency division-multiplexing, we assume that the spatially-continuous transmit currents and received fields are represented using the Fourier basis functions. In doing so, a wavenumber-division multiplexing (WDM) scheme is obtained, which is not optimal but can be efficiently implemented. The interplay among the different system parameters (e.g., transmission range, wavelength, and sizes of source and receiver) in terms of number of communication modes and level of interference among them is studied with conventional tools of linear systems theory. Due to the non-finite support (in the spatial domain) of the electromagnetic channel, WDM cannot provide non-interfering communication modes. The interference decreases as the receiver size grows, and goes to zero only asymptotically. Different digital processing architectures, operating in the wavenumber domain, are thus used to deal with the interference. The simplest implementation provides the same spectral efficiency of a singular-value decomposition architecture with water-filling when the receiver size is comparable to the transmission range. The developed framework is also used to represent a communication scheme that performs only an integration over short spatial segments. This is equivalent to a classical MIMO system with uniform linear arrays made of electrically small dipoles. Numerical comparisons show that better performance than WDM can be achieved only when a higher number of radio-frequency chains is used.

Imagine a MIMO communication system that fully exploits the propagation characteristics offered by an electromagnetic channel and ultimately approaches the limits imposed by wireless communications. This is the concept of Holographic MIMO communications. Accurate and tractable channel modeling is critical to understanding its full potential. Classical stochastic models used by communications theorists are derived under the electromagnetic far-field assumption, i.e. planar wave approximation over the array. However, such assumption breaks down when electromagnetically large (compared to the wavelength) antenna arrays are considered. In this paper, we start from the first principles of wave propagation and provide a Fourier plane-wave series expansion of the channel response, which fully captures the essence of electromagnetic propagation in arbitrary scattering and is also valid in the (radiative) near-field. The expansion is based on the Fourier spectral representation and has an intuitive physical interpretation, as it statistically describes the angular coupling between source and receiver. When discretized uniformly, it leads to a low-rank semi-unitarily equivalent approximation of the electromagnetic channel in the angular domain. The developed channel model is used to compute the ergodic capacity of a point-to-point Holographic MIMO system with different degrees of channel state information.

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 10−5can 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.

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. However, numerical results for a practical URLLC network setup involving a base station with$M=100$antennas, show that a target error probability of 10−5can 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.

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. A 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 yields 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.

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

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

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.

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 χ-squared distribution as M → ∞. 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 ≥ 50.

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

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

This paper 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.

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

This paper considers a Massive MIMO network with L cells, each comprising a base stations (BS) with M antennas and K single-antenna user equipments. Within this setting, we are interested in deriving approximations of the achievable rates in the uplink and downlink under the assumption that single-cell linear processing is used at each BS and that each intracell link forms an uncorrelated MIMO Rician fading channel matrix; that is, with a deterministic line-of-sight (LoS) path and a stochastic non-LoS component describing a spatial uncorrelated multipath environment. The analysis is conducted assuming that N and K grow large with a given ratio N/K under the assumption that the data transmission in each cell is affected by channel estimation errors, pilot contamination, an arbitrary large scale attenuation and LoS components. Numerical results are used to prove that the approximations are asymptotically tight, but accurate for systems with finite dimensions. The asymptotic results are also used to evaluate the impact of LoS components. In particular, we exemplify how the number of antennas for achieving a target rate can be substantially reduced with LoS links of only a few dBs of strength.

In this paper, we focus on the downlink ergodic sum rate of a single-cell large-scale multiuser MIMO system in which the base station employs N antennas to communicate with K single-antenna user equipments (TIEs). A regularized zero-forcing (RZF) scheme is used for precoding under the assumption that each TIE uses a specific power and each link forms a spatially correlated MIMO Rician fading channel. The analysis is conducted assuming that N and K grow large with a given ratio and perfect channel state information is available at the base station. New results from random matrix theory and large system analysis are used to compute an asymptotic expression of the signal-to-interference-plus-noise ratio as a function of system parameters, spatial correlation matrix, and Rician factor. Numerical results are used to validate the accuracy of asymptotic approximations in the finite system regime and to evaluate the performance under different operating conditions. It turns out that the asymptotic expressions provide accurate approximations even for relatively small values of N and K.

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

This letter aims at introducing the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not necessarily defined by concave and/or convex functions. An iterative algorithm that is provably convergent and enjoys asymptotic optimality properties is proposed. Numerical results are used to validate its accuracy in the nonasymptotic regime when applied to the energy efficiency maximization in multiuser multiple-input multiple-output communication systems.

Massive multiple-input multiple-output (MIMO) systems, where base stations (BSs) 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 BS in closed form using a subspace decomposition approach. This information is used to compute channel estimates that are subsequently employed by the BS 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 massive MIMO networks, under uncorrelated and correlated fading channels. With$2.5 \times 10^{3}$UEs that may simultaneously become active with probability 1%, a total of 16 frequency–time codes, and 100 antennas, a given UE is detected with probability 75%, and the accuracy of its timing estimate is on the order of few samples.

This paper 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 dealing 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 tradeoff complexity with optimality.

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.

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

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

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.

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 uncorrelated 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.

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.

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.

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, andsize, 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 is the second part of the IEEE JSAC Special Issue on “Game Theory for Networks.” 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, each of 20 papers. The first one was published in February 2017. The papers of this second issue cover a wide selection of topics as follows.

In this paper, we study the physical layer multicasting to multiple co-channel groups in large-scale antenna systems. The users within each group are interested in a common message and different groups have distinct messages. In particular, we aim at designing the precoding vectors solving the so-called quality of service (QoS) and weighted max-min fairness (MMF) problems, assuming that the channel state information is available at the base station (BS). To solve both problems, the baseline approach exploits the semidefinite relaxation (SDR) technique. Considering a BS with $N$ antennas, the SDR complexity is more than $\mathcal {O}(N^{6})$ , which prevents its application in large-scale antenna systems. To overcome this issue, we present two new classes of algorithms that, not only have significantly lower computational complexity than existing solutions, but also largely outperform the SDR-based methods. Moreover, we present a novel duality between transformed versions of the QoS and the weighted MMF problems. The duality explicitly determines the solution to the weighted MMF problem given the solution to the QoS problem, and vice versa. Numerical results are used to validate the effectiveness of the proposed solutions and to make comparisons with existing alternatives under different operating conditions.

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 users increases, the initial access and handover in contemporary networks will be flooded by user collisions. In this work, we propose a random access procedure that resolves collisions and also performs timing, channel, and power estimation by simply utilizing the large number of antennas envisioned in massive MIMO systems and the inherent timing misalignments of uplink signals during network access and handover. Numerical results are used to validate the performance of the proposed solution under different settings. It turns out that the proposed solution can detect the collisions with a probability higher than 90%, while providing reliable timing and channel estimates at the same time. Moreover, numerical results demonstrate that it is robust to overloaded situations.

In this work, we focus on the ergodic sum rate in the downlink of a single-cell large-scale multi-user MIMO system in which the base station employs N antennas to communicate with K single-antenna user equipments. A regularized zero-forcing (RZF) scheme is used for precoding under the assumption that each link forms a spatially correlated MIMO Rician fading channel. The analysis is conducted assuming N and K grow large with a non trivial ratio and perfect channel state information is available at the base station. Recent results from random matrix theory and large system analysis are used to compute an asymptotic expression of the signal-to-interference-plus-noise ratio as a function of the system parameters, the spatial correlation matrix and the Rician factor. Numerical results are used to evaluate the performance gap in the finite system regime under different operating conditions.

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.

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

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.

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.

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

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

This paper 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.

This work focuses on the downlink of a large-scale multi-cell multi-user MIMO system in which L base stations (BSs) of N antennas each communicate with KL single-antenna user equipments. We consider the design of the linear precoder that minimizes the total power consumption while ensuring target user rates. Two configurations with different degrees of cooperation among BSs are considered: the coordinated beamforming scheme (only channel state information is shared between BSs) and the coordinated multipoint MIMO technology (channel state and data cooperation). The analysis is conducted assuming that N and K grow large with a non trivial ratio K/N and imperfect channel state information is available at the BSs. In both configurations, tools of random matrix theory are used to compute, often in closed form, deterministic approximations for: the parameters of the optimal precoder; the powers needed to ensure target rates; and the total transmit power. These results are instrumental to get further insights into the structure of the optimal precoder and also to reduce the complexity of its implementation in large-scale networks. Numerical results are used to validate the asymptotic analysis in the finite system regime and to make comparisons among the two different configurations.

This paper considers the problem of energy efficiency maximization in the uplink of a cluster of multiple-antenna coordinated access points. A framework for energy efficiency optimization is developed in which the signal-to-interference-plus-noise ratio takes a more general expression than existing alternatives so as to encompass most 5G candidate technologies. Two energy efficiency optimization problems are formulated, also considering quality-of-service (QoS) constraints: 1) network global energy efficiency maximization; 2) worst-case energy-efficient design. These fractional, non-convex problems are tackled by means of fractional programming coupled with sequential convex optimization, and two low-complexity resource allocation algorithms are designed, which are guaranteed to converge to local optima of the non-convex problems. Numerical results show that the proposed algorithm can efficiently balance between the goals of maximizing the energy efficiency and meeting the QoS constraints. Moreover, it is shown that a small sum-rate reduction allows large energy savings.

International audience

This work proposes a distributed power allocation scheme for maximizing energy efficiency in the uplink of OFDMA-based HetNets where a macro-tier is augmented with small cell access points. Each user equipment (UE) in the network is modeled as a rational agent that engages in a non-cooperative game and allocates its available transmit power over the set of assigned subcarriers to maximize its individual utility (defined as the user's throughput per Watt of transmit power) subject to a target rate requirement. In this framework, the relevant solution concept is that of Debreu equilibrium, a generalization of the concept of Nash equilibrium. Using techniques from fractional programming, we provide a characterization of equilibrial power allocation profiles. In particular, Debreu equilibria are found to be the fixed points of a water-filling best response operator whose water level is a function of rate constraints and circuit power. Moreover, we also describe a set of sufficient conditions for the existence and uniqueness of Debreu equilibria exploiting the contraction properties of the best response operator. This analysis provides the necessary tools to derive a power allocation scheme that steers the network to equilibrium in an iterative and distributed manner without the need for any centralized processing. Numerical simulations are used to validate the analysis and assess the performance of the proposed algorithm as a function of the system parameters.

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

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

In this work, we consider a network composed of several single-antenna transmitter-receiver pairs in which each pair aims at selfishly minimizing the power required to achieve a given signal-to-interference-plus-noise ratio. This is obtained modeling the transmitter-receiver pairs as rational agents that engage in a non-cooperative game. Capitalizing on the well-known results on the existence and structure of the generalized Nash equilibrium (GNE) point of the underlying game, a low complexity, iterative and distributed algorithm is derived to let each terminal reach the GNE using only a limited feedback in the form of link-layer acknowledgements (ACK) or negative acknowledgements (NACK). Numerical results are used to prove that the proposed solution is able to achieve convergence in a scalable and adaptive manner under different operating conditions.

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

In this work, we derive a distributed power control algorithm for energy-efficientuplink transmissions in interference-limited cellular networks, equipped with either multiple or shared relays. The proposed solution is derived by modeling the mobile terminals as utility-driven rational agents that engage in a noncooperative game, under minimum-rate constraints. The theoretical analysis of the game equilibrium is used to compare the performance of the two different cellular architectures. Extensive simulations show that the shared relay concept outperforms the distributed one in terms of energy efficiency in most network configurations.

In this work, we focus on separable convex optimization problems with linear and box constraints and compute the solution in closed-form as a function of some Lagrange multipliers that can be easily computed in a finite number of iterations. This allows us to bridge the gap between a wide family of power allocation problems of practical interest in signal processing and communications and their efficient implementation in practice.

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

Macroscopic mobility of users is important to determine the performance and energy efficiency of a wireless network, because of the temporal correlations it introduces in the consumed power and throughput. In this work, we introduce a methodology that allows to compute the long time statistics of such metrics in a network. After describing the general approach, we consider a specific example of the uplink channel of a mobile user in the vicinity of a base station equipped with a large number of antennas (the so called “massive MIMO” base station). To guarantee a fixed signal-to-noise ratio and rate, the user inverts the pathloss channel power, while moving around in the cell. To calculate the long time distribution of the corresponding consumed energy, we assume that its movement follows a Brownian motion, and then map the problem to the solution of the minimum eigenvalue of a partial differential equation, which can be solved either analytically, or numerically very fast. The single-user throughput is also treated. We then present some results and discuss how they can be generalized if the mobility model is assumed to be a Levy random walk. A roadmap to use this methodology is eventually given to extend results to a multiple user set-up with multiple base stations.

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

This work proposes a distributed power allocation scheme for maximizing the energy efficiency in the uplink of non-cooperative small-cell networks based on orthogonal frequency-division multiple-access technology. This is achieved by modeling user terminals as rational agents that engage in a non-cooperative game in which every terminal selects the power loading so as to maximize its own utility (the user's throughput per Watt of transmit power) while satisfying minimum rate constraints. In this framework, we prove the existence of a Debreu equilibrium (also known as generalized Nash equilibrium) and we characterize the structure of the corresponding power allocation profile using techniques drawn from fractional programming. To attain the equilibrium in a distributed fashion, we also propose a method based on an iterative water-filling best response process. Numerical simulations are then used to assess the convergence of the proposed algorithm and the performance of its end-state as a function of the system parameters.

This paper presents an energy-efficient power allocation for relay-aided heterogeneous networks subject to coupling convex constraints, that make the problem at hand a generalized Nash equilibrium problem. The solution to the resource allocation problem is derived using a sequential penalty approach based on the advanced theory of quasi variational inequality, which allows the network to converge to its generalized Nash equilibrium in a distributed manner. The main feature of the proposed approach is its decomposability, which leads to a two-layer distributed algorithm with provable convergence.

In wireless sensor and actor networks (WSANs), nodes collaborate to accomplish distributed sensing and computation. One of the most attractive features is that global macro- behaviors in the network emerge from local micro-actions in and interactions between nodes. In this paper, we review a recently proposed approach, which bases on a chemical metaphor and its related theory, to design, analyze, and implement systems with such an emerging property. As an example of distributed, emerging computation in WSNs, we extend an existing gossip-like chemistry-inspired protocol (the “Disperser”) and propose a new chemically driven solution to consensus problems that is applicable in WSNs. We analyze it with a signal processing approach and validate results through simulations. The proposed chemical algorithm is not based on the iterative packet-exchange but rather on a continuous rate-modulation. The algorithm is thought to lie at the physical layer and to directly control the basic transmission hardware of the nodes in a sort of protocol-less operation mode.

In this work, a distributed and iterative algorithm for uplink power control in the initial contention-based synchronization procedure of orthogonal frequency-division multiple access networks is derived. This is achieved by letting the mobile terminals maximize their own energy efficiency in terms of power consumption and average synchronization time exploiting a quantized feedback from the base station. The problem is formulated as a constrained finite noncooperative game in which the transmit powers are chosen from a discrete set. The theoretical solution is investigated and compared to the case of continuous powers. In addition, comparisons with existing alternatives (with or without perfect feedback) are made in terms of power expenditure, average synchronization time, and estimation accuracy.

The remarkable promise of multiple-input multiple-output (MIMO) wireless channels has motivated an intense research activity to characterize the theoretical and practical issues associated with the design of transmit (source) and receive (destination) processing matrices under different operating conditions. This activity was primarily focused on point-to-point (single-hop) communications but more recently there has been an extensive work on two-hop or multi-hop settings in which single or multiple relays are used to deliver the information from the source to the destination. The aim of this tutorial is to provide an up-to-date overview of the fundamental results and practical implementation issues in designing amplify-and-forward MIMO relay systems.

The IEEE 802.16 family of standards for nomadic wireless metropolitan area networks adopts orthogonal frequency-division multiple-access as an air interface. In these systems, timing errors between the uplink signals and the base station time reference give rise to interchannel interference as well as multiple-access interference with an ensuing degradation of the error-rate performance. To mitigate this problem, users that intend to establish a communication link go through a synchronization procedure called Initial Ranging (IR) by which uplink signals can arrive at the base station synchronously and with approximately the same power level. In this work, a novel IR scheme compliant with the IEEE 802.16 specifications is presented. In contrast to existing methods, our solution operates on the basis of a generalized likelihood ratio test (GLRT) and provides improved timing and power estimates by properly taking into account the channel correlation across the signal bandwidth. In order to increase the resilience to multiple access interference, the GLRT approach is also exploited to derive a two-stage interference cancellation scheme. Numerical simulations and theoretical analysis are used to demonstrate the effectiveness of the proposed solutions and to make comparisons with existing alternatives.

Wireless communications over unlicensed frequency bands are expected to suffer from significant co-channel interference, which inevitably limits the error-rate performance. In this letter, an orthogonal frequency-division multiplexing system employing bit-interleaved coded-modulation is considered and the problem of reliable decoding in the presence of unknown narrowband interference (NBI) is addressed. The proposed solution operates in an iterative fashion according to the expectation-maximization algorithm and is derived by modeling the interference power on each subcarrier as a random variable with an inverse gamma distribution. Computer simulations indicate that the resulting scheme is effective against NBI and, compared to existing alternatives, it achieves a better trade-off in terms of error rate performance, computational complexity and system overhead.

Frequency estimation in the uplink of an orthogonal frequency-division multiple-access system is a challenging task due to the presence of multiple carrier frequency offsets. Many existing solutions are too complex for practical implementation, while others are restricted to a specific subcarrier assignment strategy. Motivated by the above consideration, in this letter we propose a novel frequency estimator that allows flexible subcarrier assignment while requiring a low computational burden. Our scheme exploits the repetitive structure of the users' training sequences, which are properly designed so as to minimize the multiple-access interference arising in the presence of frequency errors. Computer simulations are used to assess the effectiveness of the proposed method and to make comparisons with competing alternatives.

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.

Uplink synchronization in orthogonal frequency division multiple-access (OFDMA) systems is a challenging task. In IEEE 802.16-based networks, users that intend to establish a communication link with the base station must go through a synchronization procedure called Initial Ranging (IR). Existing IR schemes aim at estimating the timing offsets and power levels of ranging subscriber stations (RSSs) without considering possible frequency misalignments between the received uplink signals and the base station local reference. In this work, a novel IR scheme is presented for OFDMA systems where carrier frequency offsets, timing errors and power levels are estimated for all RSSs in a decoupled fashion. The proposed frequency estimator is based on a subspace decomposition approach, while timing recovery is accomplished by measuring the phase shift between the usersiquest channel responses over adjacent subcarriers. Computer simulations are employed to assess the effectiveness of the proposed solution and to make comparisons with existing alternatives.

In this letter, an initial ranging scheme for orthogonal frequency-division multiple-access systems is proposed by which users that intend to establish a communication link with the base station (BS) perform spreading in both the time and frequency domains and their synchronization parameters are estimated at the BS in closed-form using the ESPRIT algorithm. Compared to existing alternatives, the resulting scheme exhibits increased robustness against residual frequency offsets without involving computationally demanding peak search procedures.

We consider an orthogonal frequency-division multiplexing (OFDM) system and address the problem of carrier frequency estimation in the presence of narrowband interference (NBI) with unknown power. This scenario is encountered in emerging spectrum sharing systems, where coexistence of different wireless services over the same frequency band may result into a remarkable co-channel interference, and also in digital subscriber line transmissions as a consequence of the cross-talk phenomenon. A possible solution for frequency recovery in OFDM systems plagued by NBI has recently been derived using the maximum-likelihood criterion. Such scheme exhibits good accuracy, but involves a computationally demanding grid-search over the uncertainty frequency range. In the present work, we derive an alternative method that provides frequency estimates in closed-form by resorting to the expectation-maximization algorithm. This makes it possible to achieve some computational saving while maintaining a remarkable robustness against NBI.

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.

An efficient scheme for initial ranging has recently been proposed by X. Fu et al. in the context of orthogonal frequency-division multiple-access (OFDMA) networks based on the IEEE 802.16e-2005 standard. The proposed solution aims at estimating the power levels and timing offsets of the ranging subscriber stations (RSSs) without taking into account the effect of possible carrier frequency offsets (CFOs) between the received signals and the base station local reference. Motivated by the above problem, in the present work we design a novel ranging scheme for OFDMA in which the ranging signals are assumed to be misaligned both in time and frequency. Our goal is to estimate the timing errors and CFOs of each active RSS. Specifically, CFO estimation is accomplished by resorting to subspace-based methods while a least-squares approach is employed for timing recovery. Computer simulations are used to assess the effectiveness of the proposed solution and to make comparisons with existing alternatives.

An efficient scheme for limiting the inherent high out-of-band radiation of the orthogonal frequency-division multiplexing signal has been studied by Brandes et al.. The scheme achieves sidelobe suppression by using few subcarriers, referred to as cancellation carriers (CCs), positioned at the edges of the spectrum and modulated by data-dependent complex-valued symbols that are designed so as to minimize the out-of-band radiation. Unfortunately, its performance has been investigated at the input of the power amplifier (PA) without considering the spectral re-growth induced by PA's non-linear region. Motivated by the above consideration, in this work we return to the aforementioned scheme and investigate its performance at the output of the PA. In addition, since reducing the time-domain signal peaks may alleviate the problem of spectral re-growth, we also adopt two well-known tone reservation (TR)-based peak reduction algorithms. Computer simulations are used to assess the performance of the investigated schemes under different operating conditions. It turns out that the CC-based solution may provide some performance gain at the PA output only for input power backoffs larger than 6 dB. Additional benefits can be achieved when used in conjunction with TR and some linearization of the PA characteristic.

Decentralized slot synchronization protocols inspired from nature have recently gained considerable interest. By adjusting the internal time reference of a node in response to the detected timing of a received synchronization word, and by following simple rules, synchronization emerges from an initially completely uncoordinated situation. However these protocols typically assume that synchronization words are detected error free. In this paper the performance of biologically inspired slot synchronization is investigated when a realistic timing synchronization scheme is employed. We consider an ad hoc network where nodes communicate over an orthogonal frequency-division multiplexing (OFDM) air interface. The transmission is organized in frames, and each frame is preceded by a synchronization preamble with known repetitive parts. Specifically one common synchronization preamble is employed for all transmitting terminals, as, e.g., for the wireless LAN standard 802.11. Computer simulations verify that provided a sufficiently long synchronization word, reliable slot synchronization is maintained using a practical synchronization unit.

We consider a unified framework comprising both multicarrier code-division multiple-access (MC-CDMA) and orthogonal frequency-division multiple-access (OFDMA), and discuss nonlinear prefiltering for downlink transmissions based on Tomlinson-Harashima precoding. The base station (BS) is equipped with multiple transmitting antennas and channel state information is assumed to be available at the transmit side. We design the prefiltering matrices so as to minimize the sum of the mean square errors at all mobile terminals when a conventional single-user data detector is employed at the receiver side. In this way, most of the computational burden is moved to the BS, where power consumption and computational resources are not critical requirements. Computer simulations are used to assess the performance of the proposed scheme under different operating scenarios. It turns out that OFDMA outperforms MC-CDMA when the system resources (subcarriers and/or spreading codes) are optimally assigned to the active users according to the channel quality.

An efficient non-linear pre-filtering technique based on Tomlinson-Harashima pre-coding (THP) has recently been proposed by Liu and Krzymien in the context of multiple-antenna multi-user systems. The algorithm is based on the zero-forcing (ZF) criterion and is derived under the assumption that the number of users is equal to the number of transmit antennas. In contrast to other existing methods, it ensures the same signal-to-noise-ratio (SNR) at each mobile terminal so as to guarantee a fair treatment of all active users. In multimedia applications, however, several types of information with different quality-of-service (QoS) requirements must be sent simultaneously on different subchannels. Motivated by the above problem, in the present work we design a THP-based pre-filtering algorithm for multiple-antenna multi-user systems in which the base station allocates the transmit power according to the QoS requirement of each active user. Compared to existing alternatives, the proposed scheme is simpler to implement and suited for practical situations where the number of active users may be less than the number of transmit antennas

In this paper, we address the problem of channel estimation in the uplink of TDD MC-CDMA with combined-equalization. Channel responses are estimated based on least-squares approach assuming that training blocks are periodically inserted into the uplink data stream. Compared to channel estimation approaches that are designed for conventional uplink MC-CDMA with post-equalization, the proposed scheme provides better performance in terms of mean-square channel estimation error and bit-error rate. Moreover, we investigate the impacts of channel variations and of energy boosting of the training blocks on the system performance

Combined equalization has recently been proposed to enhance the error rate performance of conventional multicarrier code-division multiple-access (MC-CDMA) systems. This technique applies pre-equalization at the transmitter in conjunction with post-equalization at the receiver, thereby splitting the overall equalization process into two separate parts. In this way, efficient power allocation over the available subcarriers is possible at the transmitter, while leaving the interference cancellation task at the receiver. In this paper, we consider the uplink of an MC-CDMA system employing combined equalization. As the users transmit from different locations, the uplink signals arrive at the base station after passing through different multipath channels and the goal is to estimate the pre-equalized channel frequency response of each user. This is pursued following two different approaches. The first operates in the frequency-domain and treats the channel gains over adjacent subcarriers as independent unknown parameters. The second operates in the time-domain and achieves better performance by reducing the number of unknown parameters. Both schemes are based on maximum-likelihood reasoning and require knowledge of the transmitted symbols. Numerical examples are given to highlight the effectiveness of the proposed methods.

We consider the downlink of a multi-carrier code-division multiple-access (MC-CDMA) system operating in a time division duplexing (TDD) mode and propose a non-linear pre-filtering scheme based on Tomlinson-Harashima pre-coding. In designing the pre-filtering matrices we adopt a minimum mean square error (MMSE) approach under a constraint on the overall transmit power since multiple access interference and multipath distortions are pre-compensated at the base station, low-complex receivers can be employed at the mobile units. Compared to other existing solutions, the proposed scheme provides better error rate performance

We discuss channel acquisition and tracking in the uplink of a multi-carrier code-division multiple-access (MC-CDMA) system. Channel acquisition is performed jointly with noise power estimation following two different approaches. The first assumes independently faded subcarriers while the second exploits the fading correlation across the signal bandwidth to improve the system performance. Both schemes are based on maximum likelihood (ML) reasoning and exploit some training blocks carrying known symbols. Channel tracking is pursued through least-mean square (LMS) techniques, using data decisions provided by a partial parallel interference cancellation (PPIC) receiver.

Maximum likelihood sequence estimation for orthogonal frequency division multiplexing (OFDM) transmissions over unknown multipath fading channels is analytically infeasible for lack of efficient methods to maximize the likelihood function. A practical solution to this problem has been recently proposed in the context of space-time block-coded OFDM by resorting to the expectation-maximization (EM) algorithm. The resulting detector operates iteratively, exploiting knowledge of the channel statistics and the operating signal-to-noise ratio (SNR). In this work, we address the problem of estimating the above quantities and propose a recursive solution based on ad hoc reasoning. Simulations indicate that the EM detector employing the estimated SNR and channel statistics has better performance than other schemes operating in a mismatched mode. Also, the performance loss with respect to a system with perfect channel knowledge is negligible at SNR values of practical interest.

We discuss a prefiltering technique for interference mitigation in the downlink of a time division duplex (TDD) multicarrier code-division multiple access (MC-CDMA) system. The base station (BS) is equipped with multiple transmit antennas, and channel state information (CSI) is obtained at the transmitter side by exploiting the channel reciprocity between uplink and downlink transmissions. The prefiltering coefficients are designed so as to minimize a proper cost function that depends on the signal-to-interference-plus-noise ratios (SINRs) at the mobile terminals (MTs). The resulting scheme allows using a simple despreading receiver, thereby eliminating the need for channel estimation and equalization. Numerical results show the advantages of the proposed scheme over some existing solutions.

Maximum likelihood sequence detection for OFDM transmissions over unknown multipath fading channels is a challenging task for lack of efficient methods to maximize the likelihood function. A feasible solution to this problem based on the expectation-maximization (EM) algorithm has been recently proposed in the context of space-time block-coded OFDM. The resulting detector operates iteratively and exploits knowledge of the channel statistics and the operating signal-to-noise ratio (SNR). In this work we address the problem of estimating the above quantities in a recursive fashion. Simulations indicate that the EM detector employing the estimated SNR and channel statistics has better performance than other existing schemes that operate in a mismatched mode. Also, the performance loss with respect to a system with perfect channel knowledge is negligible at SNR values of practical interest.