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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]

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, a low complexity channel estimation method is proposed for two-dimensional (2-D) massive MIMO systems with uniform rectangular arrays of antennas. Instead of assuming independent fading between different transmit–receive antenna pairs, an array-structure-based physical channel model that characterizes the realistic scattering environments via the angles and gains associated with different propagation paths is studied. A 2-D Fourier-transform (FT) based on elevation and azimuth steering factors is applied to derive the spatial spectrum of received signals in angular domain at base station. Based on the spectrum analysis, the spatial spectrum of the received data is used to estimate the channel parameters, including direction of arrival (incident azimuth and elevation angles) and the path amplitude of each resolvable path. Since the channel coefficients are estimated in spatial domain and the proposed 2-D FT can be realized by fast-Fourier-transform, the computational complexity is reduced significantly. Simulation results are provided to verify the accuracy and the complexity of the proposed scheme. [ABSTRACT FROM AUTHOR]

To be differentiated from the literature, in this paper, we aim to alleviate the impact of pilot contamination (PC) on the massive MIMO systems by cooperatively scheduling users (rather than just assigning) among neighboring cells to share the limited orthogonal pilots. To this end, we develop the multi-cell cooperative scheduling (MCCS) algorithm together with the cooperative scheduling indexes (COSIs) for maximizing the data rate, maximizing the Jain's fairness index and reaching a better tradeoff in-between. For convenience, they are denoted by the COSIs for the CMDR, CMMF and CPF schedulers, respectively. However, its high computational complexity may somehow resists its from practical applications. Thus, a low-complexity cooperative proportional fairness (LC-CPF) algorithm is designed to well approach the MCCS algorithm using the CPF COSI; and at the meantime, the order of computational complexity can be significantly reduced. Moreover, its ability to reach a better tradeoff can still be maintained under the impact of high spectrum-sharing interference. In addition, it is interesting to find that using the proposed cooperative scheduling methods, the open-loop power control mechanism is no longer required for compensating the differences of received signal quality between users. [ABSTRACT FROM AUTHOR]

In multi-cell massive multiple-input multiple-output (MIMO) systems, channel estimation is deteriorated by pilot contamination and the effects of pilot contamination become more severe due to hardware impairments. In this paper, we propose a joint pilot design and channel estimation based on deep residual learning in order to mitigate the effects of pilot contamination under the consideration of hardware impairments. We first investigate a conventional linear minimum mean square error (LMMSE) based channel estimator to suppress the interference caused by pilot contamination. After that, a deep learning based pilot design is proposed to minimize the mean square error (MSE) of LMMSE channel estimation, which is utilized to the joint pilot design and channel estimator for transfer learning approach. For the channel estimator, we use a deep residual learning which extracts the features of interference caused by pilot contamination and eliminates them to estimate the channel information. Simulation results demonstrate that the proposed joint pilot design and channel estimation method can effectively reduce the effect of pilot contamination as well as outperforms the conventional approach in multi-cell massive MIMO scenarios. Moreover, the joint pilot design and channel estimation method using transfer learning further enhances the estimation performance when the prior knowledge of pilot contamination cannot be exploited. [ABSTRACT FROM AUTHOR]

In this paper, the achievable rate of the multi-cell multi-user generalized spatial modulation uplink is analyzed in the presence of realistic pilot contamination. A practical channel model associated with arbitrary transmit and receive correlation matrices is assumed for each user and base station (BS). Imperfect channel estimation is assumed with pilot contamination. The performance of a single-cell based minimum mean squared error (SMMSE) combiner is analyzed and compared to the ubiquitous zero forcing (ZF) combiner as well as matched filtering (MF). The transmit antenna (TA) index detection and the classic amplitude/phase modulation signal detection process are carried out separately for the sake of low complexity. Moreover, an algorithm based on order statistics is proposed for calculating the antenna detection probability conditioned on the actual TA. Finally, an approximation of the achievable rate is derived by exploiting the characteristics of massive multiple-input multiple-outputs (MIMO). Simulation results show that SMMSE has the best performance, followed by ZF, and then MF. Furthermore, the relationships between the system's achievable rate and three systems’ parameters, namely the number of BS antennas, the signal-to-noise-ratio (SNR), and the interference factor of pilot contamination, are presented. The performance of different number of activated antennas is also compared. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of channel estimation in a single cell massive multiple-input multiple-output (mMIMO) system with distributed antenna arrays (DAA) under the availability of limited pilots. Specifically, we propose to use pilots that are not only orthogonal within a cluster but also minimally correlated across clusters. We show that pilot sets that form mutually unbiased orthonormal bases (MUOB) minimize both inter- and intra-cluster pilot contamination. This also allows us to optimally choose the number of pilots needed to serve a given number of user equipments (UEs) within a DAA-mMIMO system. Following this, we develop an access point (AP) centered UE clustering algorithm to optimally cluster UEs for MUOB pilot allocation. Our experiments reveal that in a DAA-mMIMO system, MUOB not only offers better fairness compared to the traditional orthogonal pilot reuse scheme in terms of channel estimation error and per-UE throughput, but also delivers a higher sum system throughput. [ABSTRACT FROM AUTHOR]

This paper introduces a hybrid pilot-aided channel estimation technique for mitigating the effect of pilot contamination for the uplink of multi-cell multiuser massive MIMO systems. The proposed hybrid pilot is designed such that it enjoys the complementary advantages between time-multiplexed (TM) pilot and time-superimposed (TS) pilot and, thereby, allows superior solution to the conventional pilot schemes. We mathematically characterize the impact of hybrid pilot on the massive MIMO uplink by deriving a closed-form approximation for the uplink achievable rate. In the large-number-of-antennas regime, we obtain the asymptotically optimal solution for the hybrid pilot by jointly designing the TM pilot and the TS pilot. It is shown that either TM pilot or TS pilot has the advantages for large frame-size and limited frame-size transmission, respectively, while the hybrid pilot scheme can offer a superior performance to that employing either TM pilot or TS pilot. Numerical results demonstrate the effectiveness of the proposed design. [ABSTRACT FROM AUTHOR]

In this paper, a cocktail approach is proposed to delicately integrate the two conventional countermeasures, i.e., the fractional pilot reuse and time-shifted pilots (TSP) schemes, for the pilot contamination problem in the full-duplex massive multiple-input multiple-output system. Specifically, the TSP scheme is applied to duplicate for the inner and edge regions of a cell such that the number of accommodated users can be doubled. To achieve this, the base station should operate in the full-duplex mode; also, the pilot symbols rather than the pilot sequences are used to attain the user diversity gain. The simulation results verify the accuracy of the numerical analysis and the remarkably boosted sum rate for both the downlink and uplink cases. [ABSTRACT FROM AUTHOR]

This paper investigates the performance of massive multiple-input multiple-output (MIMO) cellular systems with pilot contamination. We derive a closed-form approximation of the area spectral efficiency (ASE) for uplink multicell multiuser massive MIMO systems by using a uniformly distributed user location model. Considering a practical power consumption model, we obtain the area energy efficiency (AEE) in a cell. The theoretical results of ASE and AEE can be used to investigate some system parameters of massive MIMO cellular systems, such as the number of antennas at the base station, the number of users, and the number of symbols over which the channel remains constant. We also study the optimal pilot-to-data power ratio for both ASE maximization and AEE maximization. [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]

Pilot contamination resulting from pilot reuse seriously restricts the communication performance of the cell-free massive multiple-input multiple-output (MIMO) networks. To deal with this problem, an efficient pilot assignment scheme using a weighted graphic framework is proposed in this correspondence paper. Specifically, a novel metric is first introduced for capturing the severity of potential mutual pilot contamination in cell-free topology. On this basis, the weighted pilot contamination graph is constructed to depict the dynamic interference relationship corresponding to the network. Then, the pilot assignment optimization is mapped to the Max k-Cut problem, and a heuristic algorithm is exploited to realize pilot decontamination. Numerical simulation results reveal the superior performance of the proposed scheme, which is capable of achieving a significant improvement in throughput with low complexity. [ABSTRACT FROM AUTHOR]

A multicell massive multiple-input multiple-output (MIMO) system, which utilizes a large number of base-station antennas to simultaneously serve a set of users, suffers from pilot contamination (PC) due to unavoidable reuse of pilots in adjacent cells. In this paper, a weighted-graph-coloring-based pilot decontamination (WGC-PD) scheme is proposed to mitigate PC for multicell massive MIMO systems. Specifically, based on limited cooperation among cells, an edge-weighted interference graph (EWIG) is first constructed to depict the potential PC relationship among users, whereby two users in different cells are connected by a weighted edge, indicating the strength of potential PC when they reuse the same pilot. Then, inspired by classical graph coloring algorithms, we develop the WGC-PD scheme by denoting each color as a pilot and each vertex as a user in the EWIG, which is able to mitigate PC by assigning different pilots to connected users with a large weight in a greedy way with insufficient pilot resource. Compared with exhaustive search among numerous pilot assignment solutions, the proposed WGC-PD scheme is able to mitigate PC with significantly reduced complexity, which is verified by numerical results. [ABSTRACT FROM PUBLISHER]

In this paper, we study the energy efficiency (EE) of a downlink multicell massive distributed antenna system (DAS) in the presence of pilot contamination (PC), where the antennas are clustered on the remote radio heads (RRHs). We employ a practical power consumption model by considering the transmit power, the circuit power, and the backhaul power, in contrast to most of the existing works which focus on colocated antenna systems (CASs), where the backhaul power is negligible. For a given average user rate, we consider the problem of maximizing the EE with respect to the number of antennas of each RRH $n$, the number of RRHs $M$, and the number of users $K$ and study the impact of system parameters on the optimal $n$, $M$, and $K$. Specifically, by applying random matrix theory, we derive the closed-form expressions of the optimal $n$ and find the solution of the optimal $M$ and $K$ under a simplified channel model with maximum ratio transmission. From the results, we find that, to achieve the optimal EE, a large number of antennas is needed for a given user rate and PC. As the number of users increases, EE can be improved further by having more RRHs and antennas. Moreover, if the backhauling power is not large, a massive DAS can be more energy efficient than a massive CAS. These insights provide a useful guide to the practical deployment of massive DASs. [ABSTRACT FROM PUBLISHER]

This paper studies generalized spatial modulation (Gen-SM) schemes in multicell multiuser massive multiple-input multiple-output (MIMO) systems as a promising high-throughput and energy-efficient technique for fifth-generation (5G) wireless networks. A detection algorithm for such systems is proposed based on linear processing techniques. By applying the concept of order statistics, a general framework for approximating the achievable sum rates with linear detection is also given. The probability of detecting antenna combinations is analyzed and is used to approximate the sum-rate performance with practical channel conditions, such as antenna correlation, imperfect channel information, and pilot contamination. The fundamental trade-off between spectral efficiency (SE) and energy efficiency (EE) is also investigated. Despite offering less SE, spatial modulation (SM) with a single active antenna per user is shown to be the most energy-efficient transmission mode among the Gen-SM class. Within the operating range of SM (i.e., in the low-to-moderate SE regime), SM is demonstrated to achieve better EE compared with conventional massive MIMO schemes. The performance in terms of economic efficiency, indicating economic profitability (in monetary unit per second), is also analyzed and is shown to serve as a complementary performance metric, enabling an implicit trade-off between SE and EE. [ABSTRACT FROM PUBLISHER]

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 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]

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]

In this paper, the performance of a massive multiple-antenna system under the pilot contamination effect is studied. A 2-D massive antenna array with a uniform circular array (UCA) topology at base stations (BSs) is considered. A 3-D spatial channel model with Von Mises Fisher (VMF) distribution is applied. It is shown that the interfering channels tend to fall into the null space of the desired user's covariance matrix. The pilot contamination can be mitigated if the angle-of-arrival (AoA) pairs of the interfering users have a nonoverlapping region with the AoA of the desired user. The impact of the AoA distribution on the beam pattern is studied as well. Numerical results confirm the analysis and show that the mitigation of pilot contamination depends on the directional dispersion of the multipath AoA distribution. [ABSTRACT FROM AUTHOR]

Pilot contamination is known to be one of the main bottlenecks for massive multi-input multioutput (MIMO) networks. For moderately large antenna arrays (of importance to recent/emerging deployments) and correlated MIMO, pilot contamination may not be the dominant limiting factor in certain scenarios. To the best of our knowledge, a rigorous characterization of the achievable rates and their explicit dependence on the angular spread (AS) is not available in the existing literature for moderately large antenna array regime. In this paper, considering eigen-beamforming (EBF) precoding, we derive an exact analytical expression for achievable rates in multicell MIMO systems under pilot contamination, and characterize the relation between the AS, array size, and respective user rates. Our analytical and simulation results reveal that the achievable rates for both the EBF and the regularized zero-forcing precoders follow a nonmonotonic behavior for increasing AS when the antenna array size is moderate. We argue that knowledge of this nonmonotonic behavior can be exploited to develop effective user-cell pairing techniques. [ABSTRACT FROM AUTHOR]

In a massive multiple-input multiple-output (MIMO) system, the serious pilot contamination problem severely restricts its ability to boost the spectrum utilization. To tackle this problem, the conventional concept of softly reusing the spectrum resources for the inner regions of the neighboring cells has been extended to reuse the pilot resources so as to accommodate more users. Alternatively, properly selecting the users to reuse the pilots among the neighboring cells can alleviate the pilot contamination problem as well. In this paper, we delicately integrate these two concepts to properly reuse the pilots allocated to the outer regions of the cells. By well designing the hazard- and secure-edge regions to manage the pilot reuse, the increment of interference can be effectively suppressed, and, consequently, the more accommodated users can contribute to the remarkably higher sum data rates. Furthermore, via some adaptive power adjustment for the users within different regions, the user data rates can further be significantly enhanced. [ABSTRACT FROM AUTHOR]

Massive multiple input multiple output (MIMO) is expected to be one of the enabling technologies for fifth-generation cellular networks. One of the major challenges in massive MIMO systems is the accurate joint estimation of the channel and noise variance, which significantly affects the performance of wireless communications in practical scenarios. In this paper, we first derive a novel maximum likelihood estimator for the noise variance at the receiver of massive MIMO systems considering practical impairments such as pilot contamination. Then, this estimate is used to compute the minimum mean square error estimate of the channel. In order to measure the performance of the proposed noise variance estimator, we derive the corresponding Cramér–Rao lower bound (CRLB). Simulation results show that the estimator is efficient in certain scenarios, outperforming existing approaches in the literature. Furthermore, we develop the estimator and the CRLB for equal and different noise variance at the receive antennas. Although the proposed estimator is valid for all antenna array sizes, its use is particularly effective for massive MIMO systems. [ABSTRACT FROM PUBLISHER]

This paper provides a comprehensive scaling law-based performance analysis for multicell multiuser massive multiple-input-multiple-output (MIMO) downlink systems. Imperfect channel state information (CSI), pilot contamination, and channel spatial correlation are all considered. First, a sum-rate lower bound is derived by exploiting the asymptotically deterministic property of the received signal power, while keeping the random nature of other components in the signal-to-interference-plus-noise-ratio (SINR) intact. Via a general scaling model on important network parameters, including the number of users, the channel training energy and the data transmission power, with respect to the number of base station antennas, the asymptotic scaling law of the effective SINR is obtained, which reveals quantitatively the tradeoff of the network parameters. More importantly, pilot contamination and pilot contamination elimination (PCE) are considered in the analytical framework. In addition, the applicability of the derived asymptotic scaling law in practical systems with large but finite antenna numbers are discussed. Finally, sufficient conditions on the parameter scalings for the SINR to be asymptotically deterministic in the sense of mean square convergence are provided, which covers existing results on such analysis as special cases and shows the effect of PCE explicitly. [ABSTRACT FROM PUBLISHER]

This paper considers the uplink dynamic resource allocation in a cloud radio access network (C-RAN) serving users belonging to different service providers (called slices) to form virtualized wireless networks (VWN). In particular, the C-RAN supports a pool of base-station (BS) baseband units (BBUs), which are connected to BS radio remote heads (RRHs) equipped with massive massive multiple input multiple output (MIMO), via fronthaul links with limited capacity. Assuming that each user can be assigned to a single RRH–BBU pair, we formulate a resource allocation problem aiming to maximize the total system rate, constrained on the minimum rates required by the slices and the maximum number of antennas and power allocated to each user. The effects of pilot contamination error on the VWN performance are investigated and pilot duration is considered as a new optimization variable in resource allocation. This problem is inherently nonconvex, NP-hard and, thus, computationally inefficient. By applying the successive convex approximation and complementary geometric programming approach, we propose a two-step iterative algorithm: one to adjust the RRH, BBU, and fronthaul parameters, and the other for power and antenna allocation to users. Simulation results illustrate the performance of the developed algorithm for VWNs in a massive-MIMO-aided and fronthaul-limited C-RAN, and demonstrate the effects of imperfect channel state information estimation due to pilot contamination error, and the optimal pilot duration. [ABSTRACT FROM PUBLISHER]

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

The combination of the large-scale multiple-input–multiple-output (MIMO) and orthogonal frequency-division multiplexing (OFDM) transmissions is a promising candidate for future wireless communication systems. We investigate a quality of service (QoS) guaranteed user-scheduling algorithm for large-scale MIMO-OFDM systems, where pilots are assigned to served users. In general, a wireless channel concentrates its energy on a specific region in the angle and delay domains. We suggest to reuse pilots based on this channel property in a macrocellular environment, thus reducing pilot overhead significantly. In the presence of contamination caused by the pilot reuse, we analyze the asymptotic behavior and design an interference cancelation (IC) precoder. For both the simple matched filter (MF) precoder and the sophisticated IC precoder, we derive achievable rates under pilot contamination, which are metrics for QoS. Further, according to the analysis under a special case, the number of QoS-guaranteed users proves to be maximized when an equispaced property in the angle domain is satisfied. The theoretical result facilitates a low-complexity user-scheduling algorithm. Numerical results confirm our analysis and proposed pilot scheme, and they show that the proposed scheduling algorithm can select out the maximum served users with guaranteed QoS. [ABSTRACT FROM AUTHOR]

We study the robust linear equalizer for the uplink of massive multiple-input–multiple-output (MIMO) systems with multicell pilot reuse. We use the worst-case approach for robust design to combat pilot contamination. When the number of base station (BS) antennas is large, we build a novel model to indicate the relationship between the instantaneous channel matrix and the imperfect channel estimation in the presence of channel model uncertainty. Based on this model, we formulate the robust equalizer design problem into a min–max problem. Furthermore, we transform the min–max problem into an unconstrained one, and the optimality conditions are derived. With the resulting optimality conditions, two iterative algorithms and a simple approximation method are proposed to compute the optimal robust equalizers. Simulations are adopted to evaluate the performance of the proposed algorithms and the approximation method. Compared with the conventional equalizers, the proposed robust equalizers achieve a better bit error rate (BER) performance, particularly in the regime of high signal-to-noise ratio (SNR), where pilot contamination is significant. [ABSTRACT FROM AUTHOR]

We investigate the heterogeneous cellular network (HetNet) where the macrocell base stations (MBSs) are equipped with very large antenna arrays. Since such a combined massive multi-input multi-output (MIMO) and HetNet system operates in the co-channel time-division duplex mode, to mitigate the pilot contamination effect to channel estimation, the number of users that can be served simultaneously is limited by the available pilot resources in the conventional designs. We propose a pilot reuse scheme for massive MIMO–HetNet to increase the user capacity. Specifically, location-aware channel estimation is employed at the MBSs to mitigate the severe pilot contamination introduced by pilot reuse, and we propose a novel pilot assignment algorithm to reduce the interference in HetNets. Simulation results demonstrate that our proposed scheme can support more users and increase both the uplink and the downlink sum-rate capacity, in comparison to the conventional scheme, particularly when the antenna number at the MBSs is sufficiently large. [ABSTRACT FROM AUTHOR]

The users at cell edge of a massive multiple-input–multiple-output (MIMO) system suffer from severe pilot contamination (PC), which leads to poor quality of service (QoS). To enhance the QoS for these edge users, soft pilot reuse (SPR) combined with multicell block diagonalization (MBD) precoding is proposed. Specifically, the users are divided into two groups according to their large-scale fading coefficients, which are referred to as the center users, who only suffer from modest PC, and the edge users, who suffer from severe PC. Based on this distinction, the SPR scheme is proposed for improving the QoS for the edge users, whereby a cell-center pilot group is reused for all cell-center users in all cells, whereas a cell-edge pilot group is applied for the edge users in the adjacent cells. By extending the classical block diagonalization precoding to a multicell scenario, the MBD precoding scheme projects the downlink transmit signal onto the null space of the subspace spanned by the intercell channels of the edge users in adjacent cells. Thus, the intercell interference contaminating the edge users' signals in the adjacent cells can be efficiently mitigated, and hence, the QoS of these edge users can be further enhanced. Our theoretical analysis and simulation results demonstrate that both the uplink and downlink rates of the edge users are significantly improved, albeit at the cost of the slightly decreased rate of center users. [ABSTRACT FROM AUTHOR]

We investigate the cell coverage optimization problem for the massive multiple-input multiple-output (MIMO) uplink. By deploying tilt-adjustable antenna arrays at the base stations (BSs), cell coverage optimization can become a promising technique that is able to strike a compromise between covering cell-edge users and pilot contamination suppression. We formulate a detailed description of this optimization problem by maximizing the cell throughput, which is shown to be mainly determined by the user distribution within several key geometrical regions. Then, the formulated problem is applied to different example scenarios. For a network with hexagonal cells and uniformly distributed users, we derive an analytical lower bound of the ergodic throughput in the objective cell; based on this, it is shown that the optimal choice for the cell coverage should ensure that the coverage of different cells does not overlap. For a more generic network with sector-shaped cells and nonuniformly distributed users, we propose an analytical approximation of the ergodic throughput. After that, a practical coverage optimization algorithm is proposed, where the optimal solution can be easily obtained through a simple 1-D line searching within a confined searching region. Our numerical results show that the proposed coverage optimization method is able to greatly increase the system throughput in macrocells for the massive MIMO uplink transmission, compared with the traditional schemes where the cell coverage is fixed. [ABSTRACT FROM PUBLISHER]

An efficient pilot assignment scheme based on graph coloring is proposed to mitigate the severe pilot contamination effect in cell-free massive multiple-input multiple-output systems. By exploiting the large-scale fading coefficients between the access points (APs) and the user equipments, we first utilize an AP selection algorithm to construct an interference graph. Then, the optimal pilot assignment can be achieved by updating the interference graph. In addition, we consider a fair policy for pilot reuse to improve the system performance. Numerical results verify that, compared with conventional pilot assignment schemes, the proposed graph coloring based pilot assignment scheme can significantly increase the 95 $\%$ -likely per-user throughput and reduce the complexity of assigning pilot sequences. [ABSTRACT FROM AUTHOR]

We propose a location-aware pilot allocation algorithm for a massive multiple-input multiple-output (MIMO) network with high-mobility users, where the wireless channels are subject to Rician fading. Pilot allocation in massive MIMO is a hard combinatorial problem and depends on the locations of users. As such, it is highly complex to achieve the optimal pilot allocation in real-time for a network with high-mobility users. Against this background, we propose a low-complexity pilot allocation algorithm, which exploits the behavior of line-of-sight (LOS) interference among the users and allocate the same pilot sequence to the users with small LOS interference. Our examination demonstrates that our proposed algorithm significantly outperforms the existing algorithms, even with localization errors. Specifically, for the system considered in this work, our proposed algorithm provides up to 37.26% improvement in sum spectral efficiency (SE) and improves the sum SE of the worst interference-affected users by up to 2.57 bits/sec/Hz, as compared to the existing algorithms. [ABSTRACT FROM AUTHOR]

We consider a multicell two-way relay network consisting of single-antenna user nodes and amplify-and-forward relay nodes having very large antenna arrays. We investigate the combined impact of co-channel interference (CCI), imperfect channel state information (CSI), pilot contamination, and the antenna correlation at the massive multiple-input multiple-output (MIMO) node. By using a large number of antennas at the relay, we can completely mitigate the effect of CCI. However, the effects of imperfect CSI and pilot contamination degrade the performance even with a large antenna array. Yet, the use of massive MIMO allows power scaling at the user nodes and relay, and thus, even with channel imperfections, the benefits of employing a massive-MIMO-enabled relay on transmit power savings are significant. Furthermore, we derive closed-form approximations for the sum rate when CCI and pilot contamination are absent and CSI is perfect. This result helps to decide the required number of relay antennas to obtain a certain percentage of the asymptotic sum rate. Also, our analysis of antenna correlation shows that it can be mitigated by using a large antenna array. We also find the optimal pilot sequence length to maximize the sum rate of the system. [ABSTRACT FROM AUTHOR]

Given the critical dependence of broadcast channels by the accuracy of channel state information at the transmitter (CSIT), we develop a general downlink model with zero-forcing precoding, applied in realistic heterogeneous cellular systems with multiple-antenna base stations (BSs). Specifically, we take into consideration imperfect CSIT due to pilot contamination, channel aging due to users relative movement, and unavoidable residual additive transceiver hardware impairments (RATHIs). Assuming that the BSs are Poisson distributed, the main contributions focus on the derivations of the upper bound of the coverage probability and the achievable user rate for this general model. We show that both the coverage probability and the user rate are dependent on the imperfect CSIT and RATHIs. More concretely, we quantify the resultant performance loss of the network due to these effects. We depict that the uplink RATHIs have equal impact, but the downlink transmit BS distortion has a greater impact than the receive hardware impairment of the user. Thus, the transmit BS hardware should be of better quality than user's receive hardware. Furthermore, we characterise both the coverage probability and user rate in terms of the time variation of the channel. It is shown that both of them decrease with increasing user mobility, but after a specific value of the normalized Doppler shift, they increase again. Actually, the time variation, following the Jakes autocorrelation function, mirrors this effect on coverage probability and user rate. Finally, we consider space-division multiple access (SDMA), single-user beamforming (SU-BF), and baseline single-input single-output transmission. A comparison among these schemes reveals that the coverage by means of SU-BF outperforms SDMA in terms of coverage. [ABSTRACT FROM PUBLISHER]

A generic performance analysis framework is developed for multicell amplify-and-forward (AF) multiway massive multiple-input multiple-output (MIMO) relay networks. The detrimental effects of imperfect channel state information (CSI), including channel estimation errors and outdated/delayed CSI for multicell massive MIMO AF multiway relay networks, are investigated. Thereby, for the first time in the open literature in the context of massive MIMO relay networks, the cumulative detrimental effects of pilot contamination and channel aging caused by the reuse of nonorthogonal pilot sequences and relative movements of user nodes, respectively, are quantified. The asymptotic signal-to-interference-plus-noise ratio and the achievable spectral efficiency expressions corresponding to three transmit power scaling laws at the user nodes and relay are derived whenever the number of antennas at the relay is substantially higher than the number of user nodes. The asymptotic performance analysis is generic in the sense that the individual effects of the practical transmission impairments, such as cochannel interference, pilot contamination, and channel aging, can be decomposed. The average symbol error rate (SER) and asymptotic SER are derived in closed form. The optimal pilot sequence length, which maximizes the achievable spectral efficiency, is derived in closed form. Our asymptotic analysis for the perfect CSI case reveals that the detrimental effects of cochannel interference can be asymptotically mitigated. Nevertheless, the performance degradation caused due to the cumulative effects of pilot contamination and channel aging cannot be mitigated, even in the limit of infinitely many relay antennas. [ABSTRACT FROM AUTHOR]