Favorable propagation (FP) and channel hardening (CH) are desired properties in massive multiple-input multiple-output (MIMO) systems. To date, these properties have primarily been analyzed for classical \textit{statistical} channel models, or \textit{ray-based} models with very specific angular parameters and distributions. This paper presents a thorough mathematical analysis of the asymptotic system behavior for ray-based channels with \textit{arbitrary} ray distributions, and considers \textit{two} types of antenna array structures at the cellular base station: a uniform linear array (ULA) and a uniform planar array (UPA). In addition to FP and channel hardening, we analyze the \textit{large system potential} (LSP) which measures the asymptotic ratio of the expected power in the desired channel to the expected total interference power when both the antenna and user numbers grow. LSP is said to hold when this ratio converges to a positive constant. The results demonstrate that while FP is guaranteed in ray-based channels, CH may or may not occur depending on the nature of the model. Furthermore, we demonstrate that LSP will not normally hold as the expected interference power grows logarithmically for both ULAs and UPAs relative to the power in the desired channel as the system size increases. Nevertheless, we identify some fundamental and attractive properties of massive MIMO in this limiting regime.
Massive MIMO (multiple-input multiple-output) is no longer a "wild" or "promising" concept for future cellular networks - in 2018 it became a reality. Base stations (BSs) with 64 fully digital transceiver chains were commercially deployed in several countries, the key ingredients of Massive MIMO have made it into the 5G standard, the signal processing methods required to achieve unprecedented spectral efficiency have been developed, and the limitation due to pilot contamination has been resolved. Even the development of fully digital Massive MIMO arrays for mmWave frequencies - once viewed pro…
We demonstrate a high capacity IF-over-fiber mobile fronthaul solution for multi-user massive MIMO 5G RAN. Using this scheme, a record aggregated radio bandwidth of 25.6 GHz was transmitted on a single optical wavelength over 40 km without fiber chromatic dispersion compensation
Grant-free multiple-input multiple-output (MIMO) usually employs non-orthogonal pilots for joint user detection and channel estimation. However, existing methods are too complex for massive grant-free access in massive MIMO. This letter proposes pilot detection reference signal (PDRS) to greatly reduce the complexity. In PDRS scheme, no iteration is required. Direct weight estimation is also proposed to calculate combining weights without channel estimation. After combining, PDRS recovery errors are used to decide the pilot activity. The simulation results show that the proposed grant-free sch…
In this paper, we adapt to cell-free Massive MIMO (multiple-input multiple-output) the finite-blocklength framework introduced by Östman et al. (2020) for the characterization of the packet error probability achievable with Massive MIMO, in the ultra-reliable low-latency communications (URLLC) regime. The framework considered in this paper encompasses a cell-free architecture with imperfect channel-state information, and arbitrary linear signal processing performed at a central-processing unit connected to the access points via fronthaul links. By means of numerical simulations, we show that, …
In cell-free massive MIMO networks, an efficient distributed detection algorithm is of significant importance. In this paper, we propose a distributed expectation propagation (EP) detector for cell-free massive MIMO. The detector is composed of two modules, a nonlinear module at the central processing unit (CPU) and a linear module at the access point (AP). The turbo principle in iterative decoding is utilized to compute and pass the extrinsic information between modules. An analytical framework is then provided to characterize the asymptotic performance of the proposed EP detector with a larg…
We study support for unmanned aerial vehicle (UAV) communications through a cell-free massive MIMO architecture. Under the general assumption that the propagation channel between the mobile stations, either UAVs or ground users, and the access points follows a Ricean distribution, we derive closed form spectral efficiency lower bounds for uplink and downlink with linear minimum mean square error (LMMSE) channel estimation. We also propose power allocation and user scheduling strategies for such a system. Our numerical results reveal that a cell-free massive MIMO architecture may provide better…
Massive access is one of the main use cases of beyond 5G (B5G) wireless networks and massive MIMO is a key technology for supporting it. Prior works studied massive access in the co-located massive MIMO framework. In this paper, we investigate the activity detection in grant-free random access for massive machine type communications (mMTC) in cell-free massive MIMO network. Each active device transmits a pre-assigned non-orthogonal pilot sequence to the APs and the APs send the received signals to a central processing unit (CPU) for joint activity detection. We formulate the maximum likelihood…
Multiuser massive multiple-input multiple-output (MU-MIMO) systems can be used to meet high throughput requirements of 5G and beyond networks. In an uplink MUMIMO system, a base station is serving a large number of users, leading to a strong multi-user interference (MUI). Designing a high performance detector in the presence of a strong MUI is a challenging problem. This work proposes a novel detector based on the concepts of expectation propagation (EP) and graph neural network, referred to as the GEPNet detector, addressing the limitation of the independent Gaussian approximation in EP. The …
Efficient massive/ultra-massive multiple-input multiple-output (MIMO) detection algorithms with satisfactory performance and low complexity are critical to meet the high throughput and ultra-low latency requirements in 5G and beyond communications, given the extremely large number of antennas. In this paper, we propose a low-complexity graph neural network (GNN) enhanced approximate message passing (AMP) algorithm, AMP-GNN, for massive/ultra-massive MIMO detection. The structure of the neural network is customized by unfolding the AMP algorithm and introducing the GNN module for multiuser inte…
DOA estimation for massive multiple-input multiple-output (MIMO) system can provide ultra-high-resolution angle estimation. However, due to the high computational complexity and cost of all digital MIMO systems, a hybrid analog digital (HAD) structure MIMO was proposed. In this paper, a fast ambiguous phase elimination method is proposed to solve the problem of direction-finding ambiguity caused by the HAD MIMO. Only two-data-blocks are used to realize DOA estimation. Simulation results show that the proposed method can greatly reduce the estimation delay with a slight performance loss.
Grant-free random access (RA) with massive MIMO is a promising RA technique for massive access with low signaling overhead. In the grant-free RA with massive MIMO, preamble length has a critical impact on the performance of the system. In this paper, the optimal preamble length is investigated to maximize spectral efficiency (SE) of the grant-free RA with massive MIMO, where effects of the preamble length on the preamble collision and preamble overhead as well as channel estimation accuracy are taken into account. Simulation results agree well with our analyses and confirm the existence of opt…
Full Duplex (FD) communication can revolutionize wireless communications as it avoids using independent channels for bi-directional communications. This work generalizes the point-to-point FD communication in millimeter wave (mmWave) band consisting of K-pairs of massive MIMO FD nodes operating simultaneously. We present a novel joint hybrid beamforming (HYBF) and combining scheme for weighted sum-rate (WSR) maximization to enable the coexistence of massive MIMO FD links cost-efficiently. The proposed algorithm relies on alternative optimization based on the minorization-maximization method. M…
Efficient channel state information at transmitter (CSIT) for frequency division duplex (FDD) massive MIMO can facilitate its backward compatibility with existing FDD cellular networks. To date, several CSIT estimation schemes have been proposed for FDD single-cell massive MIMO systems, but they fail to consider inter-cell-interference (ICI) and suffer from downlink pilot contamination in multi-cell scenario. To solve this problem, this paper proposes a compressive sensing (CS)-based CSIT estimation scheme to combat ICI in FDD multi-cell massive MIMO systems. Specifically, angle-domain massive…
Optimal data detection in massive multiple-input multiple-output (MIMO) systems requires prohibitive computational complexity. A variety of detection algorithms have been proposed in the literature, offering different trade-offs between complexity and detection performance. In this paper, we build upon variational Bayes (VB) inference to design low-complexity multiuser detection algorithms for massive MIMO systems. We first examine the massive MIMO detection problem with perfect channel state information at the receiver (CSIR) and show that a conventional VB method with known noise variance yi…
We propose sparsity-adaptive beamspace channel estimation algorithms that improve accuracy for 1-bit data converters in all-digital millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) basestations. Our algorithms include a tuning stage based on Stein's unbiased risk estimate (SURE) that automatically selects optimal denoising parameters depending on the instantaneous channel conditions. Simulation results with line-of-sight (LoS) and non-LoS mmWave massive MIMO channel models show that our algorithms improve channel estimation accuracy with 1-bit measurements in a computatio…
Future wireless networks need to support massive machine type communication (mMTC) where a massive number of devices accesses the network and massive MIMO is a promising enabling technology. Massive access schemes have been studied for co-located massive MIMO arrays. In this paper, we investigate the activity detection in grant-free random access for mMTC in cell-free massive MIMO networks using distributed arrays. Each active device transmits a non-orthogonal pilot sequence to the access points (APs) and the APs send the received signals to a central processing unit (CPU) for joint activity d…
Massive MIMO, a key technology for increasing area spectral efficiency in cellular systems, was developed assuming moderately sized apertures. In this paper, we argue that massive MIMO systems behave differently in large-scale regimes due to spatial non-stationarity. In the large-scale regime, with arrays of around fifty wavelengths, the terminals see the whole array but non-stationarities occur because different regions of the array see different propagation paths. At even larger dimensions, which we call the extra-large scale regime, terminals see a portion of the array and inside the first …
In overloaded Massive MIMO systems, wherein the number K of user equipments (UEs) exceeds the number of base station antennas M, it has recently been shown that non-orthogonal multiple access (NOMA) can increase performance. This paper aims at identifying cases of the classical operating regime K < M, where code-domain NOMA can also improve the spectral efficiency of Massive MIMO. Particular attention is given to use cases in which poor favorable propagation conditions are experienced. Numerical results show that Massive MIMO with planar antenna arrays can benefit from NOMA in practical scenar…
Massive multiple-input multiple-output (MIMO) systems have attracted much attention lately due to the many advantages they provide over single-antenna systems. Owing to the many antennas, low-cost implementation and low power consumption per antenna are desired. To that end, massive MIMO structures with low-resolution analog-to-digital converters (ADC) have been investigated in many studies. However, the effect of a strong interferer in the adjacent band on quantized massive MIMO systems have not been examined yet. In this study, we analyze the performance of uplink massive MIMO with low-resol…
Massive multi-user multiple-input multiple-output (MU-MIMO) enables significant gains in spectral efficiency and link reliability compared to conventional small-scale MIMO technology. Furthermore, linear precoders, e.g., using zero forcing or Wiener filter (WF) precoding, are sufficient to achieve excellent error-rate performance in the massive MU-MIMO downlink. However, these methods necessitate centralized processing at the base-station (BS), which causes (i) excessively high interconnect and chip input/output data rates, and (ii) high implementation complexity. We propose two feedforward ar…
To compensate the loss from outdated channel state information in wideband massive multiple-input multipleoutput (MIMO) systems, channel prediction can be performed by leveraging the temporal correlation of wireless channels. Machine learning (ML)-based channel predictors for massive MIMO systems were designed recently; however, the time overhead to collect a large amount of training data directly affects the latency of the system. In this paper, we propose a novel ML-based channel prediction technique, which can reduce the time overhead to collect the training data by transforming the domain …
Massive multiple-input multiple-output (MIMO) and reconfigurable intelligent surface (RIS) are two promising technologies for 5G-and-beyond wireless networks, capable of providing large array gain and multiuser spatial multiplexing. Without requiring additional frequency bands, those technologies offer significant improvements in both spectral and energy efficiency by simultaneously serving many users. The performance analysis of an RIS-assisted Massive MIMO system as a function of the channel statistics relies heavily on fundamental properties including favorable propagation, channel hardenin…
Antenna selection is capable of handling the cost and complexity issues in massive multiple-input multiple-output (MIMO) channels. The sum-rate capacity of a multiuser massive MIMO uplink channel is characterized under the Nakagami fading. A mathematically tractable sum-rate capacity upper bound is derived for the considered system. Moreover, for a sufficiently large base station (BS) antenna number, a deterministic equivalent (DE) of the sum-rate bound is derived. Based on this DE, the sum-rate capacity is shown to grow double logarithmically with the number of BS antennas. The validity of th…
Since the first cellular networks were trialled in the 1970s, we have witnessed an incredible wireless revolution. From 1G to 4G, the massive traffic growth has been managed by a combination of wider bandwidths, refined radio interfaces, and network densification, namely increasing the number of antennas per site. Due its cost-efficiency, the latter has contributed the most. Massive MIMO (multiple-input multiple-output) is a key 5G technology that uses massive antenna arrays to provide a very high beamforming gain and spatially multiplexing of users, and hence, increases the spectral and energ…
Massive multiple-input multiple-output (MIMO) is a key technology for fifth generation (5G) communication system. MIMO symbol detection is one of the most computationally intensive tasks for a massive MIMO baseband receiver. In this paper, we analyze matrix decomposition algorithms for massive MIMO systems, which were traditionally used for small-scale MIMO detection due to their numerical stability and modular design. We present the computational complexity of linear detection mechanisms based on QR, Cholesky and LDL-decomposition algorithms for different massive MIMO configurations. We compa…
A new wave of wireless services, including virtual reality, autonomous driving and internet of things, is driving the design of new generations of wireless systems to deliver ultra-high data rates, massive number of connected devices and ultra low latency. Massive multiple-input multiple-output (MIMO) is one of the critical underlying technologies that allow future wireless networks to meet these service needs. This article discusses the application of deep learning (DL) for massive MIMO channel estimation in wireless networks by integrating the underlying characteristics of channels in future…
Massive multiple-input multiple-out (MIMO) technology is vital in millimeter-wave (mmWave) bands to obtain large array gains. However, there are practical challenges, such as high hardware cost and power consumption in such systems. A promising solution to these problems is to adopt a hybrid beamforming architecture. This architecture has a much lower number of transceiver (TRx) chains than the total antenna number, resulting in cost- and energy-efficient systems. In this paper, we present a real-time mmWave (28 GHz) massive MIMO testbed with hybrid beamforming. This testbed has a 64-antenna/1…
Cell-free massive multiple-input multiple-output (MIMO) employs a large number of distributed access points (APs) to serve a small number of user equipments (UEs) via the same time/frequency resource. Due to the strong macro diversity gain, cell-free massive MIMO can considerably improve the achievable sum-rate compared to conventional cellular massive MIMO. However, the performance of cell-free massive MIMO is upper limited by inter-user interference (IUI) when employing simple maximum ratio combining (MRC) at receivers. To harness IUI, the expanded compute-and-forward (ECF) framework is adop…
This letter presents and analyzes orthogonal frequency-division multiplexing (OFDM)-based multi-carrier transmission for cell-free massive multi-input multi-output (CFmMIMO) over frequency-selective fading channels. Frequency-domain conjugate beamforming, pilot assignment, and user-specific resource allocation are proposed. CFmMIMO-OFDM is scalable to serve a massive number of users and is flexible to offer diverse data rates for heterogeneous applications.
This paper investigates Cell-Free massive MIMO networks, where each access point (AP) is equipped with a hybrid transceiver, reducing the complexity and cost compared to a fully digital transceiver. Asymptotic approximations for the spectral efficiency are derived for uplink and downlink. Capitalizing on these expressions, a max-min problem is formulated to optimize the (i) analog beamformer at the APs and (ii) pilot assignment. Simulations show that the optimization of these variables substantially increases the network performance.
This paper compares the sum rates and rate regions achieved by power-domain NOMA (non-orthogonal multiple access) and standard massive MIMO (multiple-input multiple-output) techniques. We prove analytically that massive MIMO always outperforms NOMA in i.i.d.~Rayleigh fading channels, if a sufficient number of antennas are used at the base stations. The simulation results show that the crossing point occurs already when having 20-30 antennas, which is far less than what is considered for the next generation cellular networks.
We propose a novel uplink communication method, coined random orthogonalization, for federated learning (FL) in a massive multiple-input and multiple-output (MIMO) wireless system. The key novelty of random orthogonalization comes from the tight coupling of FL model aggregation and two unique characteristics of massive MIMO - channel hardening and favorable propagation. As a result, random orthogonalization can achieve natural over-the-air model aggregation without requiring transmitter side channel state information, while significantly reducing the channel estimation overhead at the receiver…
The recently commercialized fifth-generation (5G) wireless communication networks achieved many improvements, including air interface enhancement, spectrum expansion, and network intensification by several key technologies, such as massive multiple-input multiple-output (MIMO), millimeter-wave communications, and ultra-dense networking. Despite the deployment of 5G commercial systems, wireless communications is still facing many challenges to enable connected intelligence and a myriad of applications such as industrial Internet-of-things, autonomous systems, brain-computer interfaces, digital …
A distributed massive MIMO channel sounder for acquiring large CSI datasets, dubbed DICHASUS, is presented. The measured data has potential applications in the study of various machine learning algorithms for user localization, JCAS, channel charting, enabling massive MIMO in FDD operation, and many others. The proposed channel sounder architecture is distinct from similar previous designs in that each individual single-antenna receiver is completely autonomous, enabling arbitrary, spatially distributed antenna deployments, and offering virtually unlimited scalability in the number of antennas…
Cell-free massive MIMO provides ubiquitous connectivity for multiple users, and implementation using radio stripes is very efficient. Compared with collocated massive MIMO, the major cost includes fronthaul overheads and AP hardware. Maximum ratio combination (MRC) achieves a low fronthaul loading and low-cost AP, but the performance is bad. This letter proposes to implement a quasi-LMMSE (Q-LMMSE) processing using MRC fronthaul design. Q-LMMSE is derived from a standard LMMSE, which gains interference information from MRC signal via singular value decomposition. Simulation results show that t…
Channel estimation is of crucial importance in massive multiple-input multiple-output (m-MIMO) visible light communication (VLC) systems. In order to tackle this problem, a fast and flexible denoising convolutional neural network (FFDNet)-based channel estimation scheme for m-MIMO VLC systems was proposed. The channel matrix of the m-MIMO VLC channel is identified as a two-dimensional natural image since the channel has the characteristic of sparsity. A deep learning-enabled image denoising network FFDNet is exploited to learn from a large number of training data and to estimate the m-MIMO VLC…
We study support for unmanned aerial vehicle (UAV) communications through a cell-free massive MIMO architecture, wherein a large number of access points (APs) is deployed in place of large co-located massive MIMO arrays. We consider also a variation of the pure cell-free architecture by applying a user-centric association approach, where each user is served only from a subset of APs in the network. Under the general assumption that the propagation channel between the mobile stations, either UAVs or ground users (GUEs), and the APs follows a Ricean distribution, we derive closed-form spectral e…
Massive multiuser multiple-input multiple-output (MU-MIMO) has been the mainstream technology in fifth-generation wireless systems. To reduce high hardware costs and power consumption in massive MU-MIMO, low-resolution digital-to-analog converters (DAC) for each antenna and radio frequency (RF) chain in downlink transmission is used, which brings challenges for precoding design. To circumvent these obstacles, we develop a model-driven deep learning (DL) network for massive MU-MIMO with finite-alphabet precoding in this article. The architecture of the network is specially designed by unfolding…
Algorithms for Massive MIMO uplink detection typically rely on a centralized approach, by which baseband data from all antennas modules are routed to a central node in order to be processed. In case of Massive MIMO, where hundreds or thousands of antennas are expected in the base-station, this architecture leads to a bottleneck, with critical limitations in terms of interconnection bandwidth requirements. This paper presents a fully decentralized architecture and algorithms for Massive MIMO uplink based on recursive methods, which do not require a central node for the detection process. Throug…
High-speed train (HST) communications with orthogonal frequency division multiplexing (OFDM) techniques have received significant attention in recent years. Besides, cell-free (CF) massive multiple-input multiple-output (MIMO) is considered a promising technology to achieve the ultimate performance limit. In this paper, we focus on the performance of CF massive MIMO-OFDM systems with both matched filter and large-scale fading decoding (LSFD) receivers in HST communications. HST communications with small cell and cellular massive MIMO-OFDM systems are also analyzed for comparison. Considering t…
Ubiquitous cell-free massive MIMO (multiple-input multiple-output) combines massive MIMO technology and user-centric transmission in a distributed architecture. All the access points (APs) in the network cooperate to jointly and coherently serve a smaller number of users in the same time-frequency resource. However, this coordination needs significant amounts of control signalling which introduces additional overhead, while data co-processing increases the back/front-haul requirements. Hence, the notion that the "whole world" could constitute one network, and that all APs would act as a single…
Channel hardening characterises the diminishing influence of small scale fading on large scale antenna systems. The effective massive MIMO time domain channel is introduced and applied to a maximum diversity channel with rectangular power delay profile. This model bounds channel hardening and allows a proper interpretation from a radio design perspective. The reduced variability of the effective channel enables power inversion to obtain a downlink channel that only depends on the large scale fading properties.
Cell-free massive MIMO is a promising technology for beyond-5G networks. Through the deployment of many cooperating access points (AP), the technology can significantly enhance user coverage and spectral efficiency compared to traditional cellular systems. Since the APs are distributed over a large area, the level of favorable propagation in cell-free massive MIMO is less than the one in colocated massive MIMO. As a result, the current linear processing schemes are not close to the optimal ones when the number of AP antennas is not very large. The aim of this paper is to develop nonlinear vari…
This paper investigates the performance of reconfigurable intelligent surface (RIS)-aided massive multiple-input multiple-output (MIMO) systems with direct links, and the phase shifts of the RIS are designed based on the statistical channel state information (CSI). We first derive the closed-form expression of the uplink ergodic data rate. Then, based on the derived expression, we use the genetic algorithm (GA) to solve the sum data rate maximization problem. With low-complexity maximal-ratio combination (MRC) and low-overhead statistical CSI-based scheme, we validate that the RIS can still br…
In this letter, we consider the problem of channel estimation for large intelligent metasurface (LIM) assisted massive multiple-input multiple-output (MIMO) systems. The main challenge of this problem is that the LIM integrated with a large number of low-cost metamaterial antennas can only passively reflect the incident signal by a certain phase shift, and does not have any signal processing capability. To deal with this, we introduce a general framework for the estimation of the transmitter-LIM and LIM-receiver cascaded channel, and propose a two-stage algorithm that includes a sparse matrix …
Since the seminal paper by Marzetta from 2010, Massive MIMO has changed from being a theoretical concept with an infinite number of antennas to a practical technology. The key concepts are adopted in 5G and base stations (BSs) with $M=64$ full-digital transceivers have been commercially deployed in sub-6\,GHz bands. The fast progress was enabled by many solid research contributions of which the vast majority assume spatially uncorrelated channels and signal processing schemes developed for single-cell operation. These assumptions make the performance analysis and optimization of Massive MIMO t…
Precoding is a method of compensating the channel at the transmitter. This work presents a novel method of data detection in turbo coded single user massive multiple input multiple output (MIMO) systems using precoding. We show via computer simulations that, when precoding is used, re-transmitting the data does not result in significant reduction in bit-error-rate (BER), thus increasing the spectral efficiency, compared to the case without precoding. Moreover, increasing the number of transmit and receive antennas results in improved BER.
We consider timing and frequency synchronization for the massive multiuser (MU) multiple-input multiple-output (MIMO) downlink where 1-bit digital-to-analog converters (DACs) are used at the base station (BS). We focus on the practically relevant scenario in which orthogonal-frequency division multiplexing (OFDM) is used to communicate over frequency-selective channels. Our contributions are twofold. First, we use Bussgang's theorem to analyze the impact on performance caused by timing and frequency offsets in the presence of 1-bit DACs at the BS. Second, we demonstrate the efficacy of the wid…
Massive MIMO systems with uniform circular and cylindrical antenna arrays are studied. Favorable propagation property is rigorously shown to hold asymptotically in LOS environment for a fixed antenna spacing and under some mild conditions. The analysis is based on a novel method using a Bessel function expansion, a new bounding technique and a simplified representation of inter-user interference for array geometries obeying Kronecker structure.
The design of highly scalable multiple access schemes is a main challenge in the evolution towards future massive machine-type communications, where reliability and latency constraints must be ensured to a large number of uncoordinated devices. In this scenario, coded random access (CRA) schemes, where successive interference cancellation algorithms allow large improvements with respect to classical random access protocols, have recently attracted an increasing interest. Impressive performance can be potentially obtained by combining CRA with massive multiple input multiple output (MIMO). In t…
This paper considers sparse device activity detection for cellular machine-type communications with non-orthogonal signatures using the approximate message passing algorithm. This paper compares two network architectures, massive multiple-input multiple-output (MIMO) and cooperative MIMO, in terms of their effectiveness in overcoming inter-cell interference. In the massive MIMO architecture, each base station (BS) detects only the users from its own cell while treating inter-cell interference as noise. In the cooperative MIMO architecture, each BS detects the users from neighboring cells as we…
This article presents a tutorial on multiuser multiple-antenna wireless systems with a very large number of antennas, known as massive multi-input multi-output (MIMO) systems. Signal processing challenges and future trends in the area of massive MIMO systems are presented and key application scenarios are detailed. A linear algebra approach is considered for the description of the system and data models of massive MIMO architectures. The operational requirements of massive MIMO systems are discussed along with their operation in time-division duplexing mode, resource allocation and calibration…
Massive MIMO and small cell are both recognized as the key technologies for the future 5G wireless systems. In this paper, we investigate the problem of user association in a heterogeneous network (HetNet) with massive MIMO and small cells, where the macro base station (BS) is equipped with a massive MIMO and the picocell BS's are equipped with regular MIMOs. We first develop centralized user association algorithms with proven optimality, considering various objectives such as rate maximization, proportional fairness, and joint user association and resource allocation. We then model the massiv…
