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Cell-free (CF) massive multiple-input multiple-output (MIMO) is an alternative topology for future wireless networks, where a large number of single-antenna access points (APs) are distributed over the coverage area. There are no cells but all users are jointly served by the APs using network MIMO methods. Prior works have claimed that the CF massive MIMO inherits the basic properties of cellular massive MIMO, namely, channel hardening and favorable propagation. In this paper, we evaluate if one can rely on these properties when having a realistic stochastic AP deployment. Our results show that channel hardening only appears in special cases, for example, when the pathloss exponent is small. However, by using 5–10 antennas per AP, instead of one, we can substantially improve the hardening. Only spatially well-separated users will exhibit favorable propagation, but when adding more antennas and/or reducing the pathloss exponent, it becomes more likely for favorable propagation to occur. The conclusion is that we cannot rely on the channel hardening and the favorable propagation when analyzing and designing the CF massive MIMO networks, but we need to use achievable rate expressions and resource allocation schemes that work well also in the absence of these properties. Some options are reviewed in this paper. [ABSTRACT FROM AUTHOR]

This correspondence paper studies the impact of nonidentically distributed channel estimation error on performance of a scheduled space-time block coding with mean-value power allocation in cognitive-radio multiple-input multiple-output system. Using the derived probability density function, the exact closed-form expressions of the proposed system for outage probability, ergodic capacity, and symbol-error rate (SER) with both $\rm M$ -ary quadrature amplitude modulation and phase shift keying modulation are derived. Using asymptotic analysis, this paper quantifies the diversity order for both outage probability and SER in the presence of nonidentically distributed error. From the analysis results, this paper shows that the diversity order is enhanced by the multiuser diversity as the number of user terminals increases regardless of outage probability and SER, while the spatial diversity is eliminated. [ABSTRACT FROM AUTHOR]

Massive multiple-input–multiple-output (MIMO) systems can suffer from coherent intercell interference due to the phenomenon of pilot contamination. This paper investigates a two-layer decoding method that mitigates both coherent and non-coherent interference in multi-cell Massive MIMO. To this end, each base station (BS) first estimates the channels to intra-cell users using either minimum mean-squared error (MMSE) or element-wise MMSE estimation based on uplink pilots. The estimates are used for local decoding on each BS followed by a second decoding layer where the BSs cooperate to mitigate inter-cell interference. An uplink achievable spectral efficiency (SE) expression is computed for arbitrary two-layer decoding schemes. A closed form expression is then obtained for correlated Rayleigh fading, maximum-ratio combining, and the proposed large-scale fading decoding (LSFD) in the second layer. We also formulate a sum SE maximization problem with both the data power and LSFD vectors as optimization variables. Since this is an NP-hard problem, we develop a low-complexity algorithm based on the weighted MMSE approach to obtain a local optimum. The numerical results show that both data power control and LSFD improve the sum SE performance over single-layer decoding multi-cell Massive MIMO systems. [ABSTRACT FROM AUTHOR]

Hardware calibration is essential to restore the uplink/downlink channel reciprocity for multi-user massive multiple-input multiple-output (MIMO) systems operating in a time division duplexing mode. Unfortunately, due to the associated overhead, calibration cannot be performed frequently; furthermore, any calibration procedure leaves behind a residual mismatch between the uplink and downlink channels. In this paper, we study the effects of these calibration errors on the achievable rates in the downlink of a multi-cell, multi-user, and distributed massive MIMO system. Specifically, we develop accurate, yet simple, lower-bounds on the per-user achievable rate, assuming either zero-forcing (ZF) or matched filtering (MF) are used. We also introduce a performance loss coefficient as a measure of sensitivity of the performance to the calibration errors. Using this measure, we identify the conditions under which ZF precoding is more sensitive to calibration errors than MF. Finally, we consider the robust weighted sum-rate maximization problem to mitigate the degrading effects of non-ideal calibration. Our numerical experiments show that the rate lower-bounds developed in this paper accurately quantify the impacts of non-ideal calibration on performance. Also, the proposed robust beamforming scheme improves the average sum-rate by up to 42% compared with the other available schemes. [ABSTRACT FROM AUTHOR]

This paper concerns the uplink of multicell multiuser multiple-input multiple-output (MIMO) systems. To tackle the effect of pilot contamination that is generally viewed as a bottleneck in previous work, this paper presents a superimposed pilot (SP)-aided uplink channel estimation scheme and mathematically characterizes the impact that an SP has on the performance of such a very large MIMO system. It is shown that there are two types of interference components that do not vanish, even when the number of antennas $M$ grows to infinity. The first type, which is referred to as cross-contamination, is due to the correlation between the SP and data among different cells. The second type, which is referred to as self-contamination, is due to the dependence between channel estimation and estimation error. Cross-contamination is, in principle, similar to pilot contamination in a conventional pilot-based multicell MIMO system, whereas self-contamination is unique for the SP-aided scheme. Both theoretical and simulation results demonstrate that the SP-aided scheme can effectively reduce the estimation contamination by increasing the data frame size and, in turn, achieve a significant improvement over the spectral efficiency, in comparison with conventional pilot-based methods. [ABSTRACT FROM AUTHOR]

This paper focuses on precoding design for sum-rate maximization while considering the effects of residual self-interference for multiuser multiple-input–multiple-output (MU-MIMO) full-duplex (FD) systems. The problem formulation leads to a nonconvex matrix-variable optimization problem, where we develop two efficient sum-rate maximization algorithms using sequential convex programming (SCP), namely, the difference of convex functions (DC)-based and the sequential convex approximations for matrix-variable programming (SCAMP) algorithms. In addition, we derive the achievable sum rate under the effect of residual self-interference. Simulation results show that, even in cases of high self-interference and high estimation error, the SCAMP algorithm provides approximately 20%–30% sum-rate improvements over both conventional optimized half-duplex (HD) transmission and the existing state-of-the-art FD algorithm in a wide range of scenarios. Finally, the convergence results indicate that the DC-based algorithm tends to initially give the best performance; however, at convergence, the SCAMP algorithm tends to significantly outperform the other algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we design receivers for filter bank multicarrier-based (FBMC-based) massive MIMO considering practical aspects such as channel estimation and equalization. In particular, we propose a spectrally efficient pilot structure and a channel estimation technique in the uplink to jointly estimate all the users’ channel impulse responses. We mathematically analyze our proposed channel estimator and find the statistics of the channel estimation errors. These statistics are incorporated into our proposed equalizers to deal with the imperfect channel state information (CSI) effect. We revisit the channel equalization problem for FBMC-based massive MIMO, address the shortcomings of the existing equalizers in the literature, and make them more applicable to practical scenarios. The proposed receiver in this paper consists of two stages. In the first stage, a linear combining of the received signals at the base station (BS) antennas provides a coarse channel equalization and removes any multiuser interference. In the second stage, a per subcarrier fractionally spaced equalizer (FSE) takes care of any residual distortion of the channel for the user of interest. We propose an FSE design based on the equivalent channel at the linear combiner output. This enables the applicability of our proposed technique to small and/or distributed antenna setups such as cell-free massive MIMO. Finally, the efficacy of the proposed techniques is corroborated through numerical analysis. [ABSTRACT FROM AUTHOR]

In multi-user multiple-input–multiple-output (MU-MIMO) systems that employ pilot-symbol aided channel estimation, the pilot-to-data power ratio (PDPR) has a large impact on the system performance. In this paper, we consider the problem of setting the PDPR in multi-cell MU-MIMO systems in the presence of channel estimation errors, intercell interference and pilot contamination. To analyze and address this problem, we first develop a model of the multi-cell MU-MIMO system and derive a closed-form expression for the mean squared error of the uplink received data symbols. Building on this result, we then propose two decentralized PDPR-setting algorithms based on game theoretic approaches that are applicable in multi-cell systems. We find that both algorithms converge to a Nash equilibrium and provide performance improvements over systems that do not properly set the PDPR, while they maintain different levels of fairness. [ABSTRACT FROM AUTHOR]

In this paper, we evaluate the uplink spectral efficiency (SE) of a single-cell massive multiple-input-multiple-output (MIMO) system with distributed jammers. We define four different attack scenarios and compare their impact on the massive MIMO system as well as on a conventional single-input-multiple-output (SIMO) system. More specifically, the jammers attack the base station (BS) during both the uplink training phase and data phase. The BS uses either least squares (LS) or linear minimum mean square error (LMMSE) estimators for channel estimation and utilizes either maximum-ratio-combining (MRC) or zero-forcing (ZF) decoding vectors. We show that ZF gives higher SE than MRC but, interestingly, the performance is unaffected by the choice of the estimators. The simulation results show that the performance loss percentage of massive MIMO is less than that of the SIMO system. Moreover, we consider two types of power control algorithms: jamming-aware and jamming-ignorant. In both cases, we consider the max-min and proportional fairness criteria to increase the uplink SE of massive MIMO systems. We notice numerically that max-min fairness is not a good option because if one user is strongly affected by the jamming, it will degrade the other users’ SE as well. On the other hand, proportional fairness improves the sum SE of the system compared with the full power transmission scenario. [ABSTRACT FROM AUTHOR]

This paper proposes a novel joint channel estimation and beamforming approach for multicell wideband massive multiple input multiple output (MIMO) systems. With the proposed channel estimation and beamforming approach, we determine the number of cells $N_{c}$ that can utilize the same time and frequency resource while mitigating the effect of pilot contamination. The proposed approach exploits the multipath characteristics of wideband channels. Specifically, when the channel has a maximum of $L$ uncorrelated multipath taps (or correlated multipath taps satisfying modest criteria which is valid in most practical scenarios), it is shown that $N_{c}=L$ cells can estimate the channels of their user equipments (UEs) and perform beamforming while mitigating the effect of pilot contamination. The proposed approach can also be applied for general correlated multipath taps, and achieves good performance for this scenario as well. In a typical long term evolution (LTE) channel environment having delay spread $T_{d}=4.69\,\,\mu \text{s}$ and channel bandwidth $B=5$ MHz, we have found that $L=36$ cells can use this band. In practice, $T_{d}$ is constant for a particular environment and carrier frequency, and hence $L$ increases as the bandwidth increases. All the analytical expressions have been validated, and the superiority of the proposed design over the existing ones is demonstrated using extensive numerical simulations both for correlated and uncorrelated channels. The proposed channel estimation and beamforming design is linear and simple to implement. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of the optimal dissemination of channel state information (CSI) among $K$ spatially distributed transmitters (TXs) jointly cooperating to serve $K$ receivers. One of the particularities of this paper lies in the fact that the CSI is distributed in the sense that each TX obtains its own estimate of the global multiuser MIMO channel with no further exchange of information being allowed between the TXs. Although this is well suited to model the cooperation between noncolocated TXs, e.g., in cellular coordinated multipoint schemes, this type of setting has received little attention so far in the information theoretic society. We study in this paper what are the CSI requirements at every TX, as a function of the network geometry, to ensure that the maximal number of degrees-of-freedom (DoF) is achieved, i.e., the same DoF as obtained under perfect CSI at all TXs. We advocate the use of the generalized DoF to take into account the geometry of the network in the analysis. Consistent with the intuition, the derived generalized DoF maximizing CSI allocation policy suggests that TX cooperation should be limited to a specific finite neighborhood around each TX. This is in sharp contrast with the conventional (uniform) CSI dissemination policy, which induces CSI requirements that grow unbounded with the network size. The proposed CSI allocation policy suggests an alternative to clustering, which overcomes fundamental limitations, such as: 1) edge interference and 2) unbounded increase of the CSIT requirements with the cluster size. Finally, we show how finite neighborhood CSIT exchange translates into finite neighborhood message exchange so that finally global interference management is possible at finite SNR with only local cooperation. [ABSTRACT FROM AUTHOR]

Channel reciprocity in time-division duplexing (TDD) massive multiple-input multiple-output (MIMO) systems can be exploited to reduce the overhead required for the acquisition of channel state information (CSI). However, perfect reciprocity is unrealistic in practical systems due to random radio-frequency (RF) circuit mismatches in uplink and downlink channels. This can result in a significant degradation in the performance of linear precoding schemes, which are sensitive to the accuracy of the CSI. In this paper, we model and analyse the impact of RF mismatches on the performance of linear precoding in a TDD multi-user massive MIMO system, by taking the channel estimation error into considerations. We use the truncated Gaussian distribution to model the RF mismatch, and derive closed-form expressions of the output signal-to-interference-plus-noise ratio for maximum ratio transmission and zero forcing precoders. We further investigate the asymptotic performance of the derived expressions, to provide valuable insights into the practical system designs, including useful guidelines for the selection of the effective precoding schemes. Simulation results are presented to demonstrate the validity and accuracy of the proposed analytical results. [ABSTRACT FROM AUTHOR]

In frequency division duplex (FDD) massive multi-input multi-output (MIMO), the two-stage beamforming (TSB) using channel covariance matrices significantly reduces the downlink training length (DTL) and channel feedback. Nevertheless, most of the TSB methods focus on the one-ring channel. In this paper, we consider the multiple scatterer clusters (MSC) channel in massive MIMO systems and propose a TSB method based on cluster group. To reduce the channel state information (CSI) feedback, for each cluster we use a cluster-group-based eigen-prebeamformer to sparsify the effective channel matrix. The DTL is also reduced by a graph-based downlink training design. We further develop a multi-user beamformer to mitigate the inter-user interference. To further reduce the DTL, two other methods are also proposed based on the vertex and edge deletion. Simulation results confirm the efficiency of the proposed schemes in improving the effective spectral efficiency. [ABSTRACT FROM AUTHOR]

In this paper, uplink transmission of a cell-free massive multiple-input multiple-output (CF-mMIMO) system coexisting with device-to-device (D2D) communication links is investigated, under the assumption that access points (APs) are equipped with low resolution analog-to-digital converters (ADCs). Lower bounds of achievable rates for both D2D users (DUEs) and CF-mMIMO users (CFUEs) are derived in closed-form, with perfect and imperfect channel state information. Next, in order to reduce pilot contamination, greedy and graph coloring-based pilot allocation algorithms are proposed and analyzed for the considered scenario. Furthermore, to control interference and improve the performance, two power control strategies are designed and their complexity and convergence are also discussed. The first power control strategy aims at maximizing CFUEs’ sum spectral efficiency (SE) subject to quality of service constraints on DUEs, while the second one maximizes the weighted product of CFUEs’ and DUEs’ signal-to-interference-plus-noise-ratios (SINRs). Numerical results show that the proposed pilot and power allocations bring a considerable improvement to the network SE. Also, it is revealed that the activation of D2D links has a positive effect on the system throughput, i.e. the network offloading ensured by the D2D links overcomes the increased interference brought by D2D communications. [ABSTRACT FROM AUTHOR]

In this paper, we evaluate the performance of a filter-bank multicarrier-quadrature amplitude modulation (FBMC-QAM) system with two prototype filters. We analyze the effective channel and derive the signal-to-interference ratio for additive white Gaussian noise channels and multipath fading channels. Based on the analysis, the characteristics of the effective channel according to various prototype filter sets and channel models are investigated. Utilizing the effective channels, we design two types of per-tone channel equalizers and evaluate the bit error rate performances by Monte Carlo simulations. The simulation results show that the FBMC-QAM system with two prototype filters can achieve almost the same bit error rate performance as orthogonal frequency division multiplexing with cyclic prefix by adopting the signal-level per-tone channel equalizer. Finally, the computational complexity of per-tone channel equalizers is analyzed. [ABSTRACT FROM AUTHOR]

Massive multiple-input multiple-output (MIMO) systems have been drawing considerable interest due to the growing throughput demands on wireless networks. In the uplink, massive MIMO systems are commonly studied assuming that each base station (BS) decodes the signals of its user terminals separately and linearly while treating all interference as noise. Although this approach provides improved spectral efficiency which scales with the number of BS antennas in favorable channel conditions, it is generally sub-optimal from an information-theoretic perspective. In this paper, we characterize the spectral efficiency of massive MIMO when the BSs are allowed to jointly decode the received signals. In particular, we consider four schemes for treating the interference, and derive the achievable average ergodic rates for both finite and asymptotic number of antennas for each scheme. Simulation tests of the proposed methods illustrate their gains in spectral efficiency compared with the standard approach of separate linear decoding, and show that the standard approach fails to capture the actual achievable rates of massive MIMO systems, particularly when the interference is dominant. [ABSTRACT FROM AUTHOR]

Visible light communication (VLC) has emerged as a promising supplement to existing radio frequency-based communication systems. Recently, the use of massive light emitting diodes (LED) and photodetector (PD) arrays have been proposed to increase the capacity of the overall VLC link. At the receiver, the signals received by the PD arrays are combined to enhance the achievable data rates. However, successful combining and subsequent detection depends on accurate channel estimation. In this paper, we consider a typical massive multiple input multiple output VLC scenario with maximal ratio combining, and derive an asymptotic analytical expression for the probability density function (p.d.f) of the residual additive distortion for mobile users. Since the minimum error entropy (MEE)-based learning paradigm outperforms the traditional Bussgang approaches due to the incorporation of order statistics, we derive an MEE-based channel estimator using the analytical expression for the p.d.f of the additive distortion. Simulations are carried out for various LED array-sizes, and under various LED transmit half angles. Furthermore, using the analytically derived p.d.f, the proposed MEE-criterion-based channel estimator achieves lower bit error rate, and faster convergence, as compared to existing minimum mean square error based channel estimator. [ABSTRACT FROM AUTHOR]

In this correspondence paper, we design a massive nonorthogonal multiple access (NOMA) scheme with delay provisioning for cellular internet-of-things. In the context of massive access, the severe interuser interference decreases the quality of the received signal, such that it is a nontrivial task to provide a delay provisioning for heterogeneous wireless services. To solve this challenge, we propose a massive NOMA scheme to meet the delay requirements of a large number of users by exploiting the properties of rateless codes. Especially, we present a power allocation algorithm to minimize the power consumption while achieving delay-constrained massive access. Finally, simulation results validate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Cell-free massive multiple-input multiple-output (MIMO) provides more uniform spectral efficiency (SE) for users (UEs) than cellular technology. The main challenge to achieve the benefits of cell-free massive MIMO is to realize signal processing in a scalable way. In this paper, we consider scalable full-pilot zero-forcing (FZF), partial FZF (PFZF), protective weak PFZF (PWPFZF), and local regularized ZF (LRZF) combining by exploiting channel statistics. We derive closed-form expressions of the uplink SE for FZF, PFZF, and PWPFZF combining with large-scale fading decoding over independent Rayleigh fading channels, taking channel estimation errors and pilot contamination into account. Moreover, we investigate the impact of the number of pilot sequences, antennas per AP, and APs on the performance. Numerical results show that LRZF provides the highest SE. However, PWPFZF is preferable when the number of pilot sequences is large and the number of antennas per AP is small. The reason is that PWPFZF has lower computational complexity and the SE expression can be computed in closed-form. Furthermore, we investigate the performance of PWPFZF combining with fractional power control and the numerical results show that it improves the performance of weak UEs and realizes uniformly good service for all UEs in a scalable fashion. [ABSTRACT FROM AUTHOR]

This paper proposes an amplify-and-forward-based massive multiple-input–multiple-output full-duplex relaying (AF-MM-FDR) protocol, where multiple source–destination pairs communicate simultaneously with a common full-duplex relay. A zero-forcing (ZF)-based relay transceiver design with semiblind gain control is presented, considering the problem of relay oscillation. The asymptotic expression of end-to-end signal-to-interference-plus-noise power (SINR) is derived under the general power scaling scheme. The scaling behaviors of echo interference (EI) and effective channel estimation error are determined. Scaling results show that the deployment of very large antenna arrays at the relay has the potential to eliminate the effect of EI due to the full-duplex operation, if the power scaling scheme is selected properly. Moreover, based on the asymptotic analysis, a low-complexity power control scheme is proposed to optimize the spectral efficiency of AF-MM-FDR. Simulation results show that the proposed power control scheme improves the spectral–energy efficiency tradeoff of AF-MM-FDR significantly. [ABSTRACT FROM AUTHOR]

In this paper, we consider time-domain vector perturbation (TDVP) in a large-system limit when channel state information (CSI) is imperfect due to pilot contamination, and we derive the system's achievable sum rate per cell. We use random matrix methods to avoid time-consuming Monte Carlo simulations. Numerical results show that, in general, linear precoding ensures a higher sum rate than TDVP in the massive multiple-input–multiple-output (MIMO) regime. [ABSTRACT FROM AUTHOR]

Massive multi-input multi-output (MIMO) systems require channel state information (CSI) at base stations. In multicell environments, adjacent cells using the same spectrum cause a pilot contamination problem and degrade CSI quality. Under such practical environments, it is important to assess achievable rate of the system for a proper system design. There exist achievable rate bounds of uplink (UL) systems in the literature, but general closed-form rate bounds for downlink (DL) systems are not available yet. This paper studies a practical massive MIMO DL system with or without pilot-aided coherent detection under the scenario of pilot contamination, and derives closed-form approximate achievable DL rate expressions for both maximum ratio combining (MRC) and zero forcing (ZF) precoders. For the case with DL pilot, a corresponding DL effective channel estimator is also developed. Numerical simulation results corroborate accuracy of the closed-form rate expressions and they also show performance characteristics of pilot-contaminated massive MIMO DL systems with MRC and ZF precoders. [ABSTRACT FROM AUTHOR]

For large-scale antenna array multiple-input multiple-output (MIMO) systems, a typical solution often put forward for uplink detection consists in applying low-complexity linear receivers such as zero-forcing (ZF) and minimum mean-square error (MMSE) combiners. In this paper, the performance of uplink MMSE detection has been analyzed in the context of a multi-cell multiuser MIMO system. An approximate expression for the signal-to-interference-plus-noise ratio (SINR) is proposed, which is in simple form and becomes exact in the low SNR regime. This approximate SINR applies to systems where the base station (BS) has the statistical information of the out-of-cell interfering signals, and systems where the BS ignores the presence of such interfering signals. This approximate SINR is tight for arbitrary user powers, arbitrary number of antennas at the base station, and arbitrary channel correlation matrix associated with any particular user. Approximate expressions for capacity and bit-error rate/symbol-error rate have also been derived. Particularly, it can be proven that, when the MMSE receiver ignores the presence of out-of-cell interfering signals, the performance gap between ZF and MMSE vanishes in the high SNR regime. [ABSTRACT FROM AUTHOR]

This paper proposes a flexible pilot assignment method to jointly optimize the uplink and downlink data transmission in multi-cell Massive multiple input multiple output (MIMO) systems with correlated Rayleigh fading channels. By utilizing a closed-form expression of the ergodic spectral efficiency (SE) achieved with maximum ratio processing, we formulate an optimization problem for maximizing the minimum weighted sum of the uplink and downlink SEs subject to the transmit powers and pilot assignment sets. This combinatiorial optimization problem is solved by two sequential algorithms: a heuristic pilot assignment is first proposed to obtain a good pilot reuse set and the data power control is then implemented. Numerical results manifest that the proposed algorithm converges fast to a better minimum sum SE per user than the algorithms in previous works. [ABSTRACT FROM AUTHOR]

In this paper, we study beam selection for millimeter-wave (mm-wave) multiuser multiple input multiple output (MIMO) systems where a base station (BS) and users are equipped with antenna arrays. Exploiting a certain sparsity of mm-wave channels, a low-complexity beam selection method for beamforming by low-cost analog beamformers is derived. It is shown that beam selection can be carried out without explicit channel estimation using the notion of compressive sensing (CS). Due to various reasons (e.g., the background noise and interference), some users may choose the same BS beam, which results in high inter-user interference. To overcome this problem, we further consider BS beam selection by users. Through simulations, we show that the performance gap between the proposed approach and the optimal beamforming approach, which requires full channel state information (CSI), becomes narrower for a larger number of users at a moderate/low signal-to-noise ratio (SNR). Since the optimal beamforming approach is difficult to be used due to prohibitively high computational complexity for large antenna arrays with a large number of users, the proposed approach becomes attractive for BSs and users in mm-wave systems where large antenna arrays can be employed. [ABSTRACT FROM PUBLISHER]

Linear decoding of space–frequency block codes (SFBCs) based on the Alamouti structure with orthogonal frequency-division multiplexing (OFDM) requires the channel to be constant across two consecutive tones. However, time-dispersive multipath fading channels exhibit frequency-selective behavior wherein the channel across two tones will vary. This paper provides analytical tools for evaluating the performance of SFBCs with OFDM in frequency-selective channels. The analysis uses the average signal-to-interference-plus-noise ratio (SINR) as a sufficient statistic to describe the performance of SFBCs in frequency-selective channels. A unified formula is derived to characterize the channel correlation between two consecutive tones for various frequency-selective channels. A closed-form solution of the average SINR is obtained, which takes into account imperfect channel estimation and frequency selectivity. An interpolation method of the channel estimate is proposed, which is shown to improve the bit-error-rate performance by 3 dB at a high SNR. The accuracy of the theoretical analyses is verified by numerical simulations under multipath channels such as the International Telecommunications Union (ITU) pedestrian and vehicular models. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the sum-rate maximization problem in multiple-input multiple-output interference channels. We design the transmit covariance matrix, associated with each transmitter to maximize the sum-rate of the network when the number of data symbols is unknown. The design problem is nonconvex and then hard to be solved. We devise a semidistributed design methodology according to majorization–minimization technique to deal with the optimization problem. This leads us to a convex quadratically constrained quadratic program at each iteration with a semiclosed form solution. The proposed method is computationally efficient and converges to stationary points of the problem. The fact that the method is based on a distributed processing framework along with relatively low computational burden ( $\mathcal{O}(\max \lbrace M,N\rbrace ^{2.3})$ per iteration with $M$ and $N$ being the number of antennas at the transmitter and receiver, respectively) for the user terminals can make it a potential candidate for practical implementations. Finally, we extend the proposed method for the case with channel estimation errors. Simulation results verify the efficiency of the proposed method, and in a typical scenario we have around 60 times lower run-time when compared to the counterparts of the method. [ABSTRACT FROM AUTHOR]

This paper considers a novel virtual pilot-assisted channel estimation algorithm for multiple input multiple output single carrier frequency domain equalization (MIMO-SCFDE) systems over fast time-varying multipath channels. Given that the fast time-varying channels can no longer support the assumption that the channel frequency-domain response remains invariant for the duration of one SC-FDE symbol, most of the channel estimation methods cannot be directly applied to MIMO-SCFDE systems. We put forward an iterative interfrequency interference cancellation method for the time-varying multipath channels over one SC-FDE symbol. The proposed method utilizes the virtual pilot-assisted channel estimation and partial minimum-mean-square-error equalization to improve the accuracy of the estimation. Simulation results validate the improved performance of the proposed method for MIMO-SCFDE systems over fast time-varying multipath channels. [ABSTRACT FROM AUTHOR]

This paper investigates an outage-constrained secrecy rate maximization (OC-SRM) problem based on the statistical channel uncertainty assumption in an underlay multiple-input multiple-output (MIMO) cognitive radio network, where the secondary transmitter provides simultaneous wireless information and power transfer to receivers. Our objective is to design the transmit covariance matrix and artificial noise aided covariance matrix through maximizing the secrecy rate of the secondary user while satisfying the given outage probability requirements. The designed problem is nonconvex and challenging. We employ the existing theory to reformulate the original problem into two equivalent subproblems by introducing auxiliary variables in order to overcome the difficulty arising from the Shannon capacity expression. The Bernstein-type inequality approach is resorted to conservatively approximate the probabilistic constraints. The merit of the transformation and conversion is that the tractable solutions of the original OC-SRM problem can be easily obtained through solving two convex conic subproblems alternately. Furthermore, we extend the proposed algorithm to solve full uncertainty model design. Numerical results demonstrate the efficacy of the proposed designs. [ABSTRACT FROM AUTHOR]

Combined with N-continuous (NC) precoding, the spatial modulation (SM) orthogonal frequency division multiplexing (OFDM) system offers considerable sidelobe suppression for the downlink transmission, at the cost of additional interference to the transmit signal. Therefore, this paper focuses on investigating the impact of the NC precoder on the bit error rate (BER) performance of the SM-OFDM system. The BER performance is analyzed over the frequency-selective Rayleigh fading channel under two distinct scenarios, i.e., perfect channel estimation and interference suppression based minimum mean square error (MMSE) channel estimation. First, we propose an approximate system model for the NC precoded SM-OFDM system along with an analysis on the introduced interference, and then derive the average BER performance of the system with perfect channel estimation. Based on the above proposed approximate system model, we further analyze the interference based upon MMSE channel estimation, and investigate the characteristics of channel estimation errors. Furthermore, we derive the average BER performance of the NC precoded SM-OFDM system with imperfect channel estimation. The numerical results show that the analytical BER closely matches its simulated counterpart under different system configurations, and demonstrate that the proposed approximate system model is in good agreement with the precise one. [ABSTRACT FROM PUBLISHER]

In this paper, we study feedback optimization problems that maximize the users' signal to interference plus noise ratio (SINR) in a two-cell multiple-input multiple-output broadcast channel. Assuming the users learn their direct and interfering channels perfectly, they can feed back this information to the base stations (BSs) over the uplink channels. The BSs then use the channel information to design their transmission scheme. Two types of feedback are considered: 1) analog and 2) digital. In the analog feedback case, the users send their unquantized and uncoded channel state information (CSI) over the uplink channels. In this context, given a user's fixed transmit power, we investigate how he/she should optimally allocate it to feed back the direct and interfering (or cross) CSI for two types of BS cooperation schemes, namely, multicell processing (MCP) and coordinated beamforming. In the digital feedback case, the direct and cross link channel vectors of each user are quantized separately, each using the random vector quantization scheme, with different size codebooks. The users then send the index of the quantization vector in the corresponding codebook to the BSs. Similar to the feedback optimization problem for the analog feedback, we investigate the optimal bit partitioning for the direct and interfering link for both types of cooperation. We focus on regularized channel inversion precoding structures and perform our analysis in the large system limit in which the number of users per cell $(K)$ and the number of antennas per BS (N)$ tend to infinity with their ratio \beta=({K}/{N}) held fixed. We show that for both types of cooperation, for some values of interfering channel gain, usually at low values, no cooperation between the BSs is preferred. This is because, for these values of cross channel gain, the channel estimates for the cross link are not accurate enough for their knowledge to contribute to improving the SINR and there is no benefit in doing BS cooperation under that condition. We also show that for the MCP scheme, unlike in the perfect CSI case, the SINR improves only when the interfering channel gain is above a certain threshold. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate a coordinated multipoint (CoMP) beamforming and power control problem for base stations (BSs) with a massive number of antenna arrays under coarse quantization at low-resolution analog-to-digital converters (ADCs) and digital-to-analog converter (DACs). Unlike high-resolution ADC and DAC systems, non-negligible quantization noise that needs to be considered in CoMP design makes the problem more challenging. We first formulate total power minimization problems of both uplink (UL) and downlink (DL) systems subject to signal-to-interference-and-noise ratio (SINR) constraints. We then derive strong duality for the UL and DL problems under coarse quantization systems. Leveraging the duality, we propose a framework that is directed toward a twofold aim: to discover the optimal transmit powers in UL by developing iterative algorithm in a distributed manner and to obtain the optimal precoder in DL as a scaled instance of UL combiner. Under homogeneous transmit power and SINR constraints per cell, we further derive a deterministic solution for the UL CoMP problem by analyzing the lower bound of the SINR. Lastly, we extend the derived result to wideband orthogonal frequency-division multiplexing systems to optimize transmit power and beamformer for all subcarriers. Simulation results validate the theoretical results and proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we focus on a multi-user multi-cell scenario with full-duplex (FD) base-stations and half-duplex (HD) downlink (DL) and uplink (UL) users, where all nodes are equipped with multiple antennas. Our goal is to design filters for weighted sum rate (WSR) maximization whilst taking into consideration the effect of transmitter and receiver distortion. Since WSR problems are non-convex, we exploit the relationship between rate and mean squared error in order to propose low complexity alternating optimization algorithms, which are guaranteed to converge. While the initial design assumes perfect channel state information (CSI), we also move beyond this assumption and consider WSR problems under imperfect CSI. This is done using two types of error models; the first is a norm-bounded error model, suitable for cases where the CSI error is dominated by quantization issues, and the second is a stochastic error model, suitable for errors that occur during the channel estimation process itself. Results show that rates achieved in FD mode are higher than those achieved by the baseline HD schemes and demonstrate the robust performance of the proposed imperfect CSI designs. In addition, we also extend our original WSR problem to one which maximizes the total DL rate subject to each UL user achieving a desired target rate. This latter design can be used to overcome potential unfairness issues and ensure that all UL users are equally served in every time slot. [ABSTRACT FROM PUBLISHER]

Large-scale multi-input multi-output (MIMO) technique has drawn considerable research interest recently. However, multiuser transmissions in large-scale MIMO systems would face challenging estimation and compensation for multiple carrier frequency offsets (CFOs) that co-exist at the receiver. In this paper, we design a new frequency synchronization scheme in multiuser orthogonal frequency division multiplexing uplink with the aid of scattered pilot symbols. We specifically consider a base station with a large number of antennas and propose to assign a number of scattered pilot subcarriers to each user. With sufficient spatial dimensions offered by the large number of antennas, the designed scheme could estimate CFO for each user individually and eliminate the necessity of the multidimensional search. Moreover, after the CFO estimation, the receive beamforming matrix is further designed for inter-user interference cancelation, which yields an equivalent single user transmission model. The conventional single user channel estimation and data detection can then be performed. Finally, the numerical results are provided to verify the proposed studies. [ABSTRACT FROM AUTHOR]

Massive multi-input multi-output (MIMO) can support high spectral efficiency with simple linear transceivers, and is expected to provide high energy efficiency (EE). In this paper, we analyze the scaling laws of EE with respect to the number of antennas M at each base station of downlink multi-cell massive MIMO systems under spatially correlated channel, where both transmit and circuit power consumptions, channel estimation errors, and pilot contamination (PC) are taken into account. We obtain the maximal EE for the systems with maximum-ratio transmission and zero-forcing beamforming for given numbers of antennas and users by optimizing the transmit power subject to the minimal data rate requirement and maximal transmit power constraint. The closed-form expressions of approximated EE-maximal transmit power and maximal EE, and their scaling laws with M are derived. Our analysis shows that the maximal EE scales with M in for the system without PC, and in \mathcal {O}({1}/{M}) for the system with PC. The EE-maximal transmit power scales up with M in \mathcal O(\sqrt M/\ln M) until reaching the maximal transmit power for the system without PC, and in \mathcal O(1) for the system with PC. The analytical results are validated by simulations under a more realistic 3D channel model. [ABSTRACT FROM AUTHOR]

This paper investigates pilot design and allocation in multi-cell massive multiple-input multiple-output systems with two-tier receiving. As the length of pilot is limited, the pilots cannot be orthogonal and cause interference. The sum rate as well as the signal-to-interference-plus-noise ratio (SINR) of the system are firstly analyzed. The sum rate upper bound and the asymptotic SINR are derived. The analysis shows that the pilot correlation and the spatial correlation jointly affect the sum rate. Based on this observation, the discrete Fourier transform vectors are employed in designing pilots with various correlation values. Then, with the channel correlation information and the designed pilots, the pilots are allocated to the cells in a greedy way with the object of maximizing the sum rate upper bound. Moreover, the sum rate analysis, the pilot design, and the pilot allocation are extended to the scenario with grouped correlations. Simulation results show that the proposed pilot design and allocation performs better than other pilots and the derived upper bound is effective. [ABSTRACT FROM AUTHOR]

Massive multiple-input multiple-output (MIMO) communication is a promising technology for increasing spectral efficiency in wireless networks. Two of the main challenges massive MIMO systems face are degraded channel estimation accuracy due to pilot contamination and increase in computational load and hardware complexity due to the massive number of antennas. In this paper, we focus on the problem of channel estimation in massive MIMO systems, while addressing these two challenges: We jointly design the pilot sequences to mitigate the effect of pilot contamination and propose an analog combiner which maps the high number of sensors to a low number of RF chains, thus reducing the computational and hardware cost. We consider a statistical model in which the channel covariance obeys a Kronecker structure, and treat two special cases, corresponding to fully- and partially-separable correlations. We prove that under these models, the analog combiner design can be performed independently of the pilot sequences. Given the resulting combiner, we derive a closed-form expression for the optimal pilot sequences in the fully-separable case and suggest a greedy sum of ratio traces maximization (GSRTM) method for designing sub-optimal pilots in the partially-separable scenario. We demonstrate via simulations that our pilot design framework achieves lower mean squared error than the common pilot allocation framework previously considered for pilot contamination mitigation. [ABSTRACT FROM AUTHOR]

In this paper, we consider how the uplink transmission of a spatially correlated massive multiple-input multiple-output (MIMO) system can be protected from a jamming attack. To suppress the jamming, we propose a novel framework including a new optimal linear estimator in the training phase and a bilinear equalizer in the data phase. The proposed estimator is optimal in the sense of maximizing the spectral efficiency of the legitimate system attacked by a jammer, and its implementation needs the statistical knowledge about the jammer’s channel. We derive an efficient algorithm to estimate the jamming information needed for implementation of the proposed framework. Furthermore, we demonstrate that optimized power allocation at the legitimate users can improve the performance of the proposed framework regardless of the jamming power optimization. Our proposed framework can be exploited to combat jamming in scenarios with either ideal or non-ideal hardware at the legitimate users and the jammer. Numerical results reveal that using the proposed framework, the jammer cannot dramatically affect the performance of the legitimate system. [ABSTRACT FROM AUTHOR]

Different from the existing works, in this paper we investigate the pilot allocation in multi-cell massive multiple-input multiple-output (MIMO) systems, aiming to maximize the spectral efficiency (SE) subject to the constraint that the number of user equipments (UEs) satisfying the quality of service (QoS) is maximized. Since the considered bilevel optimization problem that is tough to handle, we resort to the greedy algorithms with low computational complexity. We propose a QoS constrained (QC) pilot allocation scheme, which sequentially allocates the pilot sequence having large interference power to the UE with small signal power so that the number of UEs satisfying QoS can be maximized and then the SE can also be maximized. Simulation results show that the propose QC scheme outperforms the conventional scheme and smart pilot allocation (SPA) scheme. [ABSTRACT FROM AUTHOR]

In this paper, we analyze pilot contamination (PC) attacks on a multi-cell massive multiple-input multiple-output (MIMO) network with correlated pilots. We obtain correlated pilots using a user capacity-achieving pilot sequence design. This design relies on an algorithm which designs correlated pilot sequences based on signal-to-interference-plus-noise ratio (SINR) requirements for all the legitimate users. The pilot design is capable of achieving the SINR requirements for all users even in the presence of PC. However, this design has some intrinsic limitations and vulnerabilities, such as a known pilot sequence and the non-zero cross-correlation among different pilot sequences. We reveal that such vulnerabilities may be exploited by an active attacker to increase PC in the network. Motivated by this, we analyze the correlated pilot design for vulnerabilities that can be exploited by an active attacker. Based on this analysis, we develop an effective active attack strategy in the massive MIMO network with correlated pilot sequences. Our examinations reveal that the user capacity region of the network is significantly reduced in the presence of the active attack. Importantly, the SINR requirements for the worst-affected users may not be satisfied even with an infinite number of antennas at the base station. [ABSTRACT FROM AUTHOR]

This paper studies the energy-efficient power allocation problem for physical-layer security in multi-user (MU) distributed massive multiple-input multiple-output (MIMO) systems. A new metric called global average secrecy energy efficiency (GASEE) is proposed to measure the MU secrecy energy efficiency (SEE) with a single eavesdropper (Eve). We first derive closed-form expressions for the signal to interference-plus-noise ratios (SINRs) of legitimate users and the Eve with pilot contamination. Under a power consumption model that incorporates transmit power, backhaul power, remote antenna unit (RAU) circuit and signal processing power, and with transmit power constraints as well as SINR constraints for both users and the Eve, the GASEE maximization problem is formulated as a joint optimization of power allocation, RAU clustering, RAU selection and artificial noise (AN) selection. The formulated problem is a mixed integer nonlinear program (MINLP), which is solved by a double-loop procedure. In the outer loop, the denominator of objective is approximated as a linear function. In the inner loop, an efficient algorithm is proposed to find a near-optimal solution to the approximated problem by solving a sequence of sub-problems. Simulation results demonstrate that the proposed algorithm converges fast and achieves a higher GASEE than some heuristics. [ABSTRACT FROM AUTHOR]

Massive MIMO uses a large number of antennas to increase the spectral efficiency (SE) through spatial multiplexing of users, which requires accurate channel state information. It is often assumed that regular pilots (RP), where a fraction of the time-frequency resources is reserved for pilots, suffices to provide high SE. However, the SE is limited by the pilot overhead and pilot contamination. An alternative is superimposed pilots (SP) where all resources are used for pilots and data. This removes the pilot overhead and reduces pilot contamination by using longer pilots. However, SP suffers from data interference that reduces the SE gains. This paper proposes the Massive-MIMO Iterative Channel Estimation and Decoding (MICED) algorithm where partially decoded data is used as side-information to improve the channel estimation and increase SE. We show that users with precise data estimates can help users with poor data estimates to decode. Numerical results with QPSK modulation and LDPC codes show that the MICED algorithm increases the SE and reduces the block-error-rate with RP and SP compared to conventional methods. The MICED algorithm with SP delivers the highest SE and it is especially effective in scenarios with short coherence blocks like high mobility or high frequencies. [ABSTRACT FROM AUTHOR]

In this paper, we study a multiple-antenna two-way relaying (TWR) cognitive radio (CR) system. A space alignment (SA) technique is adopted by the secondary users (SUs) to avoid interference with the primary users (PUs). We derive the optimal power allocation that maximizes the TWR achievable SU sum-rate while respecting the total power budget and the relay power constraints. We also analyze the case in which the relay is able to optimize its gain matrix structure to enhance the SU sum-rate. In the numerical results, we quantify the sum-rate gain of using the SA in the TWR CR and we show that the SU sum-rate is very limited when the relay power is low or the PU power and its resulting interference are high. In addition, we optimize the relay gain using an iterative algorithm and compare between different relay matrix structures. [ABSTRACT FROM PUBLISHER]

In this paper, we analyze the spectral efficiency of multicell massive multiple-input–multiple-output (MIMO) systems with downlink training and a new pilot contamination precoding (PCP) scheme. First, we analyze the spectral efficiency of the beamforming training (BT) scheme with maximum-ratio transmission (MRT) precoding. Then, we derive an approximate closed-form expression of the spectral efficiency to find the optimal lengths of uplink and downlink pilots. Simulation results show that the achieved spectral efficiency can be improved due to channel estimation at the user side, but in comparison with a single-cell scenario, the spectral efficiency per cell in multicell scenario degrades because of pilot contamination. We focus on the practical case where the number of base station (BS) antennas is large but still finite and propose the BT and PCP (BT-PCP) transmission scheme to mitigate the pilot contamination with limited cooperation between BSs. We confirm the effectiveness of the proposed BT-PCP scheme with simulation, and we show that the proposed BT-PCP scheme achieves higher spectral efficiency than the conventional PCP method and that the performance gap from the perfect channel state information (CSI) scenario without pilot contamination is small. [ABSTRACT FROM AUTHOR]

We address the problem of noise and interference corrupted channel estimation in massive MIMO systems. Interference, which originates from pilot reuse (or contamination), can in principle be discriminated on the basis of the distributions of path angles and amplitudes. In this paper, we propose novel robust channel estimation algorithms exploiting path diversity in both angle and power domains, relying on a suitable combination of the spatial filtering and amplitude based projection. The proposed approaches are able to cope with a wide range of system and topology scenarios, including those where, unlike in previous works, interference channel may overlap with desired channels in terms of multipath angles of arrival or exceed them in terms of received power. In particular, we establish analytically the conditions under which the proposed channel estimator is fully decontaminated. Simulation results confirm the overall system gains when using the new methods. [ABSTRACT FROM AUTHOR]

Massive multiple-input–multiple-output (MIMO) antenna system implies the use of a large number of base station (BS) antennas to serve a relatively small number of user terminals (UTs) for extraordinary spectral efficiency. However, its performance is limited by pilot contamination due to unavoidable reuse of pilot sequences from UTs in different cells. In this paper, we analyze the performance of massive MIMO zero-forcing (ZF) systems using the time-shifted pilot scheme, which was known to combat pilot contamination effectively using conjugate beamforming if there is a very large number of antennas. We derive expressions for achievable sum rates and the signal-to-interference-plus-noise ratios (SINRs) of forward and reverse links if the number of BS antennas is finite. Then, the impact of system parameters, such as cell radius, transmit power, group number (a parameter related to the time-shifted pilot scheme), BS antenna number, etc., on the system performance are revealed. Our model embraces a series of previous works as special cases. Moreover, we compare the performance of conjugate and ZF precoders, from which a simple but effective large-scale fading-based UT scheduling scheme is proposed to enhance the system throughput. [ABSTRACT FROM PUBLISHER]

Massive multiple-input and multiple-output is widely considered as a key enabler of the next generation 5G networks. With a large number of antennas at the base station, both spectral and energy efficiencies can be enhanced. Unfortunately, the downlink channel estimation overhead scales linearly with the number of antennas. This burden is easily mitigated in time division duplex systems by the use of the channel reciprocity property. However, this is unfeasible for frequency division duplex systems, and the method of two-stage beamforming was therefore developed to reduce the amount of channel state information feedback. The performance of this scheme being highly dependent on the users grouping and scheduling mechanisms, we introduce in this paper a new similarity measure coupled with a novel clustering procedure to achieve the appropriate users grouping. We also proceed to formulate the optimal users scheduling policy in joint spatial division and multiplexing (JSDM) and prove that it is NP-hard. This result is of paramount importance since it suggests that, unless P = NP, there are no polynomial time algorithms that solve the general scheduling problem to global optimality and the use of sub-optimal scheduling strategies is more realistic in practice. We, therefore, use graph theory to develop a sub-optimal users scheduling scheme that runs in polynomial time and outperforms the scheduling schemes previously introduced in the literature for JSDM in both sum-rate and throughput fairness. [ABSTRACT FROM AUTHOR]

Recently, a structure of an optimal linear precoder for multi cell downlink systems has been described, and many other references have used simplified versions of this precoder to obtain promising performance gains. These gains have been hypothesized to stem from the additional degrees of freedom that allow for interference mitigation through interference relegation to orthogonal subspaces. However, no conclusive or rigorous understanding has yet been developed. In this paper, we build on an intuitive interference induction trade-off and the aforementioned preceding structure to propose an interference aware RZF (iaRZF) preceding scheme for multi cell downlink systems, and we analyze its rate performance. Special emphasis is placed on the induced interference mitigation mechanism of iaRZF. For example, we will verify the intuitive expectation that the precoder structure can either completely remove induced inter-cell or intra-cell interference. We state new results from large-scale random matrix theory that make it possible to give more intuitive and insightful explanations of the precoder behavior, also for cases involving imperfect channel state information (CSI). We remark especially that the interference-aware precoder makes use of all available information about interfering channels to improve performance. Even very poor CSI allows for significant sum-rate gains. Our obtained insights are then used to propose heuristic precoder parameters for arbitrary systems, whose effectiveness are shown in more involved system scenarios. Furthermore, calculation and implementation of these parameters does not require explicit inter base station cooperation. [ABSTRACT FROM PUBLISHER]

For massive multiuser multiple input multiple output (MIMO) (MU-MIMO) systems, pilot contamination (PC) and data interference (DI) are two main factors that affect the accuracy of the superimposed pilot (SP) based channel estimation, provided that the channel coherence time is less than the total number of users. In this paper, to tackle the effect of the PC, we propose a block-diagonal Grassmannian line packing (GLP) approach, in which the specific sequences for different cells are first designed based on the GLP, and then are block-diagonally extended to form the SP matrices for the users in different cells. To also alleviate the effect of DI on the channel estimation, with the designed SP matrices, an iterative channel estimation (ICE) method based on Tikhonov regularization is presented. The impact that the proposed ICE method has on the signal-to-interference-plus-noise ratio with matched filtering receiver is theoretically analyzed. Moreover, the optimal power allocation factor to the SP by maximizing the spectral efficiency (SE) of the target cell is also derived. Numerical results show that the proposed ICE method with the designed SP matrices effectively mitigates the effects of the PC and DI, and hence, improves the accuracy of channel estimation and further the SE of the massive MU-MIMO systems. [ABSTRACT FROM AUTHOR]

The use of large-scale antenna arrays can bring substantial improvements in energy and/or spectral efficiency to wireless systems due to the greatly improved spatial resolution and array gain. Recent works in the field of massive multiple-input multiple-output (MIMO) show that the user channels decorrelate when the number of antennas at the base stations (BSs) increases, thus strong signal gains are achievable with little interuser interference. Since these results rely on asymptotics, it is important to investigate whether the conventional system models are reasonable in this asymptotic regime. This paper considers a new system model that incorporates general transceiver hardware impairments at both the BSs (equipped with large antenna arrays) and the single-antenna user equipments (UEs). As opposed to the conventional case of ideal hardware, we show that hardware impairments create finite ceilings on the channel estimation accuracy and on the downlink/uplink capacity of each UE. Surprisingly, the capacity is mainly limited by the hardware at the UE, while the impact of impairments in the large-scale arrays vanishes asymptotically and interuser interference (in particular, pilot contamination) becomes negligible. Furthermore, we prove that the huge degrees of freedom offered by massive MIMO can be used to reduce the transmit power and/or to tolerate larger hardware impairments, which allows for the use of inexpensive and energy-efficient antenna elements. [ABSTRACT FROM PUBLISHER]