In this paper, we study the beamforming design problem in frequency-division duplexing (FDD) downlink massive MIMO systems, where instantaneous channel state information (CSI) is assumed to be unavailable at the base station (BS). We propose to extract the information of the angle-of-departures (AoDs) and the corresponding large-scale fading coefficients (a.k.a. spatial information) of the downlink channel from the uplink channel estimation procedure, based on which a novel downlink beamforming design is presented. By separating the subpaths for different users based on the spatial information and the hidden sparsity of the physical channel, we construct near-orthogonal virtual channels in the beamforming design. Furthermore, we derive a sum-rate expression and its approximations for the proposed system. Based on these closed-form rate expressions, we develop two low-complexity beam selection schemes and carry out asymptotic analysis to provide valuable insights on the system design. Numerical results demonstrate a significant performance improvement of our proposed algorithm over the state-of-the-art beamforming approach.
This paper investigates downlink channel estimation in frequency-division duplex (FDD)-based massive multiple-input multiple-output (MIMO) systems. To reduce the overhead of downlink channel estimation and uplink feedback in FDD systems, cascaded precoding has been used in massive MIMO such that only a low-dimensional effective channel needs to be estimated and fed back. On the other hand, traditional channel estimations can hardly achieve the minimum mean-square-error (MMSE) performance due to lack of the a priori knowledge of the channels. In this paper, we design and analyze a strategy for …
One challenge for FDD massive MIMO communication system is how to obtain the downlink channel state information (CSI) at the base station. Except for traditional codebook feedback through uplink pilot transmission, some channel reciprocity properties can be utilized through uplink channel estimation and channel parameter estimation algorithms. In this paper, the uplink and downlink channel reciprocity properties are analyzed. It is theoretically proved that not all multipath parameters for FDD downlink and uplink channels are equivalent. Therefore, the so called full reciprocity property does …
This paper addresses the problem of uplink and downlink channel estimation in FDD Massive MIMO systems. By utilizing sparse recovery and compressive sensing algorithms, we are able to improve the accuracy of the uplink/downlink channel estimation and reduce the number of uplink/downlink pilot symbols. Such successful channel estimation builds upon the assumption that the channel can be sparsely represented under some basis/dictionary. Previous works model the channel using some predefined basis/dictionary, while in this work, we present a dictionary learning based channel model such that a dic…
Massive MIMO is considered as one of the key enablers of the next generation 5G networks.With a high number of antennas at the BS, both spectral and energy efficiencies can be improved. Unfortunately, the downlink channel estimation overhead scales linearly with the number of antenna. This does not create complications in Time Division Duplex (TDD) systems since the channel estimate of the uplink direction can be directly utilized for link adaptation in the downlink direction. However, this channel reciprocity is unfeasible for the Frequency Division Duplex (FDD) systems where different physic…
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…
We consider the problem of downlink training and channel estimation in frequency division duplex (FDD) massive MIMO systems, where the base station (BS) equipped with a large number of antennas serves a number of single-antenna users simultaneously. To obtain the channel state information (CSI) at the BS in FDD systems, the downlink channel has to be estimated by users via downlink training and then fed back to the BS. For FDD large-scale MIMO systems, the overhead for downlink training and CSI uplink feedback could be prohibitively high, which presents a significant challenge. In this paper, …
In this work we extend the concept of uplink-downlink rate balancing to frequency division duplex (FDD) massive MIMO systems. We consider a base station with large number antennas serving many single antenna users. We first show that any unused capacity in the uplink can be traded off for higher throughput in the downlink in a system that uses either dirty paper (DP) coding or linear zero-forcing (ZF) precoding. We then also study the scaling of the system throughput with the number of antennas in cases of linear Beamforming (BF) Precoding, ZF Precoding, and DP coding. We show that the downlin…
In this paper, we propose a new channel estimation scheme for TDD/FDD massive MIMO systems by reconstructing uplink/downlink channel covariance matrices (CCMs) with the aid of array signal processing techniques. Specifically, the angle information and power angular spectrum (PAS) of each multi-path channel is extracted from the instantaneous uplink channel state information (CSI). Then, the uplink CCM is reconstructed and can be used to improve the uplink channel estimation without any additional training cost. In virtue of angle reciprocity as well as PAS reciprocity between uplink and downli…
In this paper, we propose an efficient downlink channel reconstruction scheme for a frequency-division-duplex multi-antenna system by utilizing uplink channel state information combined with limited feedback. Based on the spatial reciprocity in a wireless channel, the downlink channel is reconstructed by using frequency-independent parameters. We first estimate the gains, delays, and angles during uplink sounding. The gains are then refined through downlink training and sent back to the base station (BS). With limited overhead, the refinement can substantially improve the accuracy of the downl…
Transmitter channel state information (CSIT) is indispensable for the spectral efficiency gains offered by massive multiple-input multiple-output (MIMO) systems. In a frequency-division-duplexing (FDD) massive MIMO system, CSIT is typically acquired through downlink channel estimation and user feedback, but as the number of antennas increases, the overhead for CSI training and feedback per user grows, leading to a decrease in spectral efficiency. In this paper, we show that, using uplink pilots in FDD, the downlink sum spectral efficiency gain with perfect downlink CSIT is achievable when the …
Massive multiple-input multiple-output (MIMO) systems deploying a large number of antennas at the base station considerably increase the spectrum efficiency by serving multiple users simultaneously without causing severe interference. However, the advantage relies on the availability of the downlink channel state information (CSI) of multiple users, which is still a challenge in frequency-division-duplex transmission systems. This paper aims to solve this problem by developing a full transceiver framework that includes downlink channel training (or estimation), CSI feedback, and channel recons…
Cell-free system where a group of base stations (BSs) cooperatively serves users has received much attention as a promising technology for the future wireless systems. In order to maximize the cooperation gain in the cell-free systems, acquisition of downlink channel state information (CSI) at the BSs is crucial. While this task is relatively easy for the time division duplexing (TDD) systems due to the channel reciprocity, it is not easy for the frequency division duplexing (FDD) systems due to the CSI feedback overhead. This issue is even more pronounced in the cell-free systems since the us…
In order to unlock the full advantages of massive multiple input multiple output (MIMO) in the downlink, channel state information (CSI) is required at the base station (BS) to optimize the beamforming matrices. In frequency division duplex (FDD) systems, full channel reciprocity does not hold, and CSI acquisition generally requires downlink pilot transmission followed by uplink feedback. Prior work proposed the end-to-end design of pilot transmission, feedback, and CSI estimation via deep learning. In this work, we introduce an enhanced end-to-end design that leverages partial uplink-downlink…
In a frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) system, the acquisition of downlink channel state information (CSI) at base station (BS) is a very challenging task due to the overwhelming overheads required for downlink training and uplink feedback. In this paper, we reveal a deterministic uplink-to-downlink mapping function when the position-to-channel mapping is bijective. Motivated by the universal approximation theorem, we then propose a sparse complex-valued neural network (SCNet) to approximate the uplink-to-downlink mapping function. Different from …
Reconfigurable intelligent surfaces (RISs) are able to provide passive beamforming gain via low-cost reflecting elements and hence improve wireless link quality. This work considers two-way passive beamforming design in RIS-aided frequency division duplexing (FDD) systems where the RIS reflection coefficients are the same for downlink and uplink and should be optimized for both directions simultaneously. We formulate a joint optimization of the transmit/receive beamformers at the base station (BS) and the RIS reflection coefficients. The objective is to maximize the weighted sum of the downlin…
When operating massive multiple-input multiple-output (MIMO) systems with uplink (UL) and downlink (DL) channels at different frequencies (frequency division duplex (FDD) operation), acquisition of channel state information (CSI) for downlink precoding is a major challenge. Since, barring transceiver impairments, both UL and DL CSI are determined by the physical environment surrounding transmitter and receiver, it stands to reason that, for a static environment, a mapping from UL CSI to DL CSI may exist. First, we propose to use various neural network (NN)-based approaches that learn this mapp…
Channel state information (CSI) acquisition is a significant bottleneck in the design of Massive MIMO wireless systems, due to the length of the training sequences required to distinguish the antennas (in the downlink) and the users (for the uplink where a given spectral resource can be shared by a large number of users). In this article, we focus on the downlink CSI estimation case. Considering the presence of spatial correlation at the base transceiver station (BTS) side, and assuming that the per-user channel statistics are known, we seek to exploit this correlation to minimize the length o…
Massive Multiple-Input Multiple-Output (massive MIMO) is a variant of multi-user MIMO in which the number of antennas at each Base Station (BS) is very large and typically much larger than the number of users simultaneously served. Massive MIMO can be implemented with Time Division Duplexing (TDD) or Frequency Division Duplexing (FDD) operation. FDD massive MIMO systems are particularly desirable due to their implementation in current wireless networks and their efficiency in situations with symmetric traffic and delay-sensitive applications. However, implementing FDD massive MIMO systems is k…
University of Toronto（多伦多大学）；Ontario Tech University（安大略理工大学）
It is well accepted that acquiring downlink channel state information in frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems is challenging because of the large overhead in training and feedback. In this paper, we propose a deep generative model (DGM)-based technique to address this challenge. Exploiting the partial reciprocity of uplink and downlink channels, we first estimate the frequency-independent underlying channel parameters, i.e., the magnitudes of path gains, delays, angles-of-arrivals (AoAs) and angles-of-departures (AoDs), via uplink training, s…
We propose an innovative machine learning-based technique to address the problem of channel acquisition at the base station in frequency division duplex systems. In this context, the base station reconstructs the full channel state information in the downlink frequency range based on limited downlink channel state information feedback from the mobile terminal. The channel state information recovery is based on a convolutional neural network which is trained exclusively on collected channel state samples acquired in the uplink frequency domain. No acquisition of training samples in the downlink…
We consider downlink channel training of a frequency division duplex (FDD) massive multiple-input-multiple-output (MIMO) system when a multi-antenna jammer is present in the network. The jammer intends to degrade mean square error (MSE) of the downlink channel training by designing an attack based on second-order statistics of its channel. The channels are assumed to be spatially correlated. First, a closed-form expression for the channel estimation MSE is derived and then the jammer determines the conditions under which the MSE is maximized. Numerical results demonstrate that the proposed jam…
The concept of deploying a large number of antennas at the base station, often called massive multiple-input multiple-output (MIMO), has drawn considerable interest because of its potential ability to revolutionize current wireless communication systems. Most literature on massive MIMO systems assumes time division duplexing (TDD), although frequency division duplexing (FDD) dominates current cellular systems. Due to the large number of transmit antennas at the base station, currently standardized approaches would require a large percentage of the precious downlink and uplink resources in FDD …
In this work, we propose a convolutional neural network (CNN) based low-complexity approach for downlink (DL) channel estimation (CE) in frequency division duplex (FDD) systems. In contrast to existing work, we use training data which solely stems from the uplink (UL) domain. This allows to learn the CNN centralized at the base station (BS). After training, the network parameters are offloaded to mobile terminals (MTs) within the coverage area of the BS. The MTs can then obtain channel state information (CSI) of the MIMO channels with the low-complexity CNN estimator. This circumvents the nece…
The design of message passing (MP) algorithms on factor graphs is an effective manner to implement channel estimation (CE) in wireless communication systems, which performance can be further improved by exploiting prior probability models that accurately match the channel characteristics. In this work, we study the CE problem in a downlink massive multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system. As the prior probability, we propose the Markov chain two-state Gaussian mixture with large variance differences (TSGM-LVD) model to exploit the structure…
In this paper, we consider user selection and downlink precoding for an over-loaded single-cell massive multiple-input multiple-output (MIMO) system in frequency division duplexing (FDD) mode, where the base station is equipped with a dual-polarized uniform planar array (DP-UPA) and serves a large number of single-antenna users. Due to the absence of uplink-downlink channel reciprocity and the high-dimensionality of channel matrices, it is extremely challenging to design downlink precoders using closed-loop channel probing and feedback with limited spectrum resource. To address these issues, a…
This paper proposes a model-driven deep learning-based downlink channel reconstruction scheme for frequency division duplexing (FDD) massive multi-input multi-output (MIMO) systems. The spatial non-stationarity, which is the key feature of the future extremely large aperture massive MIMO system, is considered. Instead of the channel matrix, the channel model parameters are learned by neural networks to save the overhead and improve the accuracy of channel reconstruction. By viewing the channel as an image, we introduce You Only Look Once (YOLO), a powerful neural network for object detection, …
This paper proposes a new transmission strategy for the multiuser massive multiple-input multiple-output (MIMO) systems, including uplink/downlink channel estimation and user scheduling for data transmission. A discrete Fourier transform (DFT) aided spatial basis expansion model (SBEM) is first introduced to represent the uplink/downlink channels with much few parameter dimensions by exploiting angle reciprocity and the physical characteristics of the uniform linear array (ULA). With SBEM, both uplink and downlink channel estimation of multiuser can be carried out with very few amount of train…
When base stations (BSs) are deployed with multiple antennas, they need to have downlink (DL) channel state information (CSI) to optimize downlink transmissions by beamforming. The DL CSI is usually measured at mobile stations (MSs) through DL training and fed back to the BS in frequency division duplexing (FDD). The DL training and uplink (UL) feedback might become infeasible due to insufficient coherence time interval when the channel rapidly changes due to high speed of MSs. Without the feedback from MSs, it may be possible for the BS to directly obtain the DL CSI using the inherent relatio…
Massive multiple-input multiple-output (MIMO) is widely recognized as a promising technology for future 5G wireless communication systems. To achieve the theoretical performance gains in massive MIMO systems, accurate channel state information at the transmitter (CSIT) is crucial. Due to the overwhelming pilot signaling and channel feedback overhead, however, conventional downlink channel estimation and uplink channel feedback schemes might not be suitable for frequency-division duplexing (FDD) massive MIMO systems. In addition, these two topics are usually separately considered in the literat…
Tsinghua University（清华大学）；Beijing National Research Center for Information Science and Technology（北京信息科学与技术国家研究中心）
Channel state information (CSI) feedback is necessary for the frequency division duplexing (FDD) multiple input multiple output (MIMO) systems due to the channel non-reciprocity. With the help of deep learning, many works have succeeded in rebuilding the compressed ideal CSI for massive MIMO. However, simple CSI reconstruction is of limited practicality since the channel estimation and the targeted beamforming design are not considered. In this paper, a jointly optimized network is introduced for channel estimation and feedback so that a spectral-efficient beamformer can be learned. Moreover, …
In this paper, we propose a novel method for efficient implementation of a massive Multiple-Input Multiple-Output (massive MIMO) system with Frequency Division Duplexing (FDD) operation. Our main objective is to reduce the large overhead incurred by Downlink (DL) common training and Uplink (UL) feedback needed to obtain channel state information (CSI) at the base station. Our proposed scheme relies on the fact that the underlying angular distribution of a channel vector, also known as the angular scattering function, is a frequency-invariant entity yielding a UL-DL reciprocity and has a limite…
We investigate the joint uplink-downlink configuration of an intelligent reflecting surface (IRS) for multi-user frequency-division-duplexing (FDD) and time-division-duplexing (TDD) systems. This is motivated in FDD since uplink and downlink transmissions occur simultaneously and hence an IRS must be jointly configured for both transmissions. In TDD, while a joint design is not strictly necessary, it can significantly reduce feedback overhead, power consumption, and configuration periods associated with updating the IRS. To compute the trade-off between uplink and downlink rates achieved by a …
State Key Lab of Intelligent Technologies and Systems（智能技术与系统国家重点实验室）；Beijing National Research Center for Information Science and Technology（北京信息科学与技术国家研究中心）；Department of Automation, Tsinghua University（清华大学自动化系）；State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University（北京交通大学轨道交通控制与安全国家重点实验室）
Artificial intelligence (AI) based downlink channel state information (CSI) prediction for frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems has attracted growing attention recently. However, existing works focus on the downlink CSI prediction for the users under a given environment and is hard to adapt to users in new environment especially when labeled data is limited. To address this issue, we formulate the downlink channel prediction as a deep transfer learning (DTL) problem, where each learning task aims to predict the downlink CSI from the uplink CS…
In this paper we consider optimal multiuser downlink beamforming in the presence of a massive number of arbitrary quadratic shaping constraints. We combine beamforming with full-rate high dimensional real-valued orthogonal space time block coding (OSTBC) to increase the number of beamforming weight vectors and associated degrees of freedom in the beamformer design. The original multi-constraint beamforming problem is converted into a convex optimization problem using semidefinite relaxation (SDR) which can be solved efficiently. In contrast to conventional (rank-one) beamforming approaches in …
A massive multiple-input multiple-output (MIMO) system, operating in Frequency Division Duplexing (FDD) mode of operation, suffers from prohibitively high overhead associated with downlink channel state information (CSI) acquisition and downlink precoding, due to the lack of uplink/downlink channel reciprocity. In this paper, a heuristic edge-weighted vertex-coloring based pattern division (EWVC-PD) scheme is proposed to alleviate the overhead of a two-layer precoding approach, in a practical scenario where the user clusters undergo serious angular-spreading-range (ASR) overlapping. Specifical…
The overheads associated with feedback-based channel acquisition can greatly compromise the achievable rates of FDD based massive MIMO systems. Indeed, downlink (DL) training and uplink (UL) feedback overheads scale linearly with the number of base station (BS) antennas, in sharp contrast to TDD-based massive MIMO, where a single UL pilot trains the whole BS array. In this work, we propose a graph-theoretic approach to reducing DL training and UL feedback overheads in FDD massive MIMO systems. In particular, we consider a single-cell scenario involving a single BS with a massive antenna array …
Physical wireless transceivers suffer from a variety of impairments that distort the transmitted and received signals. Their degrading impact is particularly evident in modern systems with multiuser transmission, high transmit power, and low-cost devices, but their existence is routinely ignored in the optimization literature for multicell transmission. This paper provides a detailed analysis of coordinated beamforming in the multicell downlink. We solve two optimization problems under a transceiver impairment model and derive the structure of the optimal solutions. We show numerically that th…
Opportunistic scheduling and beamforming schemes with reduced feedback are proposed for MIMO-OFDMA downlink systems. Unlike the conventional beamforming schemes in which beamforming is implemented solely by the base station (BS) in a per-subcarrier fashion, the proposed schemes take advantages of a novel channel decomposition technique to perform beamforming jointly by the BS and the mobile terminal (MT). The resulting beamforming schemes allow the BS to employ only {\em one} beamforming matrix (BFM) to form beams for {\em all} subcarriers while each MT completes the beamforming task for each …
This paper considers the beamforming design for a multiuser multiple-input single-output (MISO) downlink with an arbitrary number of (context-specific) shaping constraints. In this setup, the state-of-the-art beamforming schemes cannot attain the well-known performance bound promised by the semidefinite program (SDP) relaxation technique. To close the gap, we propose a redundant-signal embedded linear beamforming (REEL-BF) scheme, where each user is assigned with one information beamformer and several shaping beamformers. It is shown that the proposed REEL-BF scheme can perform general rank-$K…
Opportunistic scheduling and beamforming schemes are proposed for multiuser MIMO-SDMA downlink systems with linear combining in this work. Signals received from all antennas of each mobile terminal (MT) are linearly combined to improve the {\em effective} signal-to-noise-interference ratios (SINRs). By exploiting limited feedback on the effective SINRs, the base station (BS) schedules simultaneous data transmission on multiple beams to the MTs with the largest effective SINRs. Utilizing the extreme value theory, we derive the asymptotic system throughputs and scaling laws for the proposed sche…
The downlink of a multiple-input multiple output (MIMO) broadcast channel (BC) is considered, where each receiver is equipped with a single antenna and the transmitter performs nonlinear Dirty-Paper Coding (DPC). We present an efficient algorithm that finds the optimum transmit filters and power allocation as well as the optimum precoding order(s) possibly affording time-sharing between individual DPC orders. Subsequently necessary and sufficient conditions for the optimality of an arbitrary precoding order are derived. Based on these we propose a suboptimal algorithm showing excellent perform…
The opportunistic beamforming in the downlink of multiple-input single-output (MISO) systems forms $N$ transmit beams, usually, no more than the number of transmit antennas $N_t$. However, the degrees of freedom in this downlink is as large as $N_t^2$. That is, at most $N_t^2$ rather than only $N_t$ users can be simultaneously transmitted and thus the scheduling latency can be significantly reduced. In this paper, we focus on the opportunistic beamforming schemes with $N_t<N\le N_t^2$ transmit beams in the downlink of MISO systems over Rayleigh fading channels. We first show how to design the …
In cellular networks, admission control and beamforming optimization are intertwined problems. While beamforming optimization aims at satisfying users' quality-of-service (QoS) requirements or improving the QoS levels, admission control looks at how a subset of users should be selected so that the beamforming optimization problem can yield a reasonable solution in terms of the QoS levels provided. However, in order to simplify the design, the two problems are usually seen as separate problems. This paper considers joint admission control and beamforming (JACoB) under a coordinated multicell MI…
This paper investigates the optimal transmit beamforming design of simultaneous wireless information and power transfer (SWIPT) in the multiuser multiple-input-single-output (MISO) downlink with specific absorption rate (SAR) constraints. We consider the power splitting technique for SWIPT, where each receiver divides the received signal into two parts: one for information decoding and the other for energy harvesting with a practical non-linear rectification model. The problem of interest is to maximize as much as possible the received signal-to-interference-plus-noise ratio (SINR) and the ene…
Downlink beamforming in Massive MIMO either relies on uplink pilot measurements - exploiting reciprocity and TDD operation, or on the use of a predetermined grid of beams with user equipments reporting their preferred beams, mostly in FDD operation. Massive MIMO in its originally conceived form uses the first strategy, with uplink pilots, whereas there is currently significant commercial interest in the second, grid-of-beams. It has been analytically shown that in isotropic scattering (independent Rayleigh fading) the first approach outperforms the second. Nevertheless there remains controvers…
Beamforming is an effective means to improve the quality of the received signals in multiuser multiple-input-single-output (MISO) systems. Traditionally, finding the optimal beamforming solution relies on iterative algorithms, which introduces high computational delay and is thus not suitable for real-time implementation. In this paper, we propose a deep learning framework for the optimization of downlink beamforming. In particular, the solution is obtained based on convolutional neural networks and exploitation of expert knowledge, such as the uplink-downlink duality and the known structure o…
In millimeter-wave communication systems with large-scale antenna arrays, conventional digital beamforming may not be cost-effective. A promising solution is the implementation of hybrid beamforming techniques, which consist of low-dimensional digital beamforming followed by analog radio frequency (RF) beamforming. This work studies the optimization of hybrid beamforming in the context of a cloud radio access network (C-RAN) architecture. In a C-RAN system, digital baseband signal processing functionalities are migrated from remote radio heads (RRHs) to a baseband processing unit (BBU) in the …
Wireless powered sensor networks (WPSNs) have emerged as a key development towards the future self-sustainable Internet of Things (IoT) networks. To achieve a good balance between self-sustainability and reliability, partially WPSNs with a mixed power solution are desirable for practical applications. Specifically, most of the sensor nodes are wireless powered but the key sensor node adopts traditional wire/battery power for reliability. As a result, this paper mainly investigates optimal design for the partially WPSNs in which simultaneous wireless information and power transfer (SWIPT) is ad…
Massive multiple-input multiple-output (MIMO) systems require downlink channel state information (CSI) at the base station (BS) to better utilize the available spatial diversity and multiplexing gains. However, in a frequency division duplex (FDD) massive MIMO system, CSI feedback overhead degrades the overall spectral efficiency. Convolutional neural network (CNN)-based CSI feedback compression schemes has received a lot of attention recently due to significant improvements in compression efficiency; however, they still require reliable feedback links to convey the compressed CSI information …
In this paper, randomly-directional beamforming (RDB) is considered for millimeter-wave (mmwave) multi-user (MU) multiple-input single-output (MISO) downlink systems. By using asymptotic techniques, the performance of RDB and the MU gain in mm-wave MISO are analyzed based on the uniform random line-of-sight (UR-LoS) channel model suitable for highly directional mm-wave radio propagation channels. It is shown that there exists a transition point on the number of users relative to the number of antenna elements for non-trivial performance of the RDB scheme, and furthermore sum rate scaling arbit…
