This paper studies fast downlink beamforming algorithms using deep learning in multiuser multiple-input-single-output systems where each transmit antenna at the base station has its own power constraint. We focus on the signal-to-interference-plus-noise ratio (SINR) balancing problem which is quasi-convex but there is no efficient solution available. We first design a fast subgradient algorithm that can achieve near-optimal solution with reduced complexity. We then propose a deep neural network structure to learn the optimal beamforming based on convolutional networks and exploitation of the duality of the original problem. Two strategies of learning various dual variables are investigated with different accuracies, and the corresponding recovery of the original solution is facilitated by the subgradient algorithm. We also develop a generalization method of the proposed algorithms so that they can adapt to the varying number of users and antennas without re-training. We carry out intensive numerical simulations and testbed experiments to evaluate the performance of the proposed algorithms. Results show that the proposed algorithms achieve close to optimal solution in simulations with perfect channel information and outperform the alleged theoretically optimal solution in experiments, illustrating a better performance-complexity tradeoff than existing schemes.
Accurate downlink channel information is crucial to the beamforming design, but it is difficult to obtain in practice. This paper investigates a deep learning-based optimization approach of the downlink beamforming to maximize the system sum rate, when only the uplink channel information is available. Our main contribution is to propose a model-driven learning technique that exploits the structure of the optimal downlink beamforming to design an effective hybrid learning strategy with the aim to maximize the sum rate performance. This is achieved by jointly considering the learning performance…
In this paper, a novel optimization model for joint beamforming and power control in the downlink (DL) of a cell-free massive MIMO (CFmMIMO) system is presented. The objective of the proposed optimization model is to minimize the maximum user interference while satisfying quality of service (QoS) constraints and power consumption limits. The proposed min-max optimization model is formulated as a mixed-integer nonlinear program, that is directly tractable. Numerical results show that the proposed joint beamforming and power control scheme is effective and outperforms competing schemes in terms …
In limited feedback multi-user multiple-input multiple-output (MU-MIMO) cellular networks, users send quantized information about the channel conditions to the associated base station (BS) for downlink beamforming. However, channel quantization and beamforming have been treated as two separate tasks conventionally, which makes it difficult to achieve global system optimality. In this paper, we propose an augmented deep unfolding (ADU) approach that jointly optimizes the beamforming scheme at the BSs and the channel quantization scheme at the users. In particular, the classic WMMSE beamformer i…
Downlink beamforming is an essential technology for wireless cellular networks; however, the design of beamforming vectors that maximize the weighted sum rate (WSR) is an NP-hard problem and iterative algorithms are typically applied to solve it. The weighted minimum mean square error (WMMSE) algorithm is the most widely used one, which iteratively minimizes the WSR and converges to a local optimal. Motivated by the recent developments in meta-learning techniques to solve non-convex optimization problems, we propose a meta-learning based iterative algorithm for WSR maximization in a MISO downl…
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 …
Full-dimensional (FD) multi-user massive multiple input multiple output (m-MIMO) systems employ large two-dimensional (2D) rectangular antenna arrays to control both the azimuth and elevation angles of signal transmission. We introduce the sum of two outer products of the azimuth and elevation beamforming vectors having moderate dimensions as a new class of FD beamforming. We show that this low-complexity class is capable of outperforming 2D beamforming relying on the single outer product of the azimuth and elevation beamforming vectors. It is also capable of performing close to its FD counter…
Jeonbuk National University（国立全北大学）；Pukyong National University（釜庆国立大学）
This paper investigates a learning solution for robust beamforming optimization in downlink multi-user systems. A base station (BS) identifies efficient multi-antenna transmission strategies only with imperfect channel state information (CSI) and its stochastic features. To this end, we propose a robust training algorithm where a deep neural network (DNN), which only accepts estimates and statistical knowledge of the perfect CSI, is optimized to fit to real-world propagation environment. Consequently, the trained DNN can provide efficient robust beamforming solutions based only on imperfect ob…
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…
Considering intelligent reflecting surface (IRS), we study a multi-cluster multiple-input-single-output (MISO) non-orthogonal multiple access (NOMA) downlink communication network. In the network, an IRS assists the communication from the base station (BS) to all users by passive beamforming. Our goal is to minimize the total transmit power by jointly optimizing the transmit beamforming vectors at the BS and the reflection coefficient vector at the IRS. Because of the restrictions on the IRS reflection amplitudes and phase shifts, the formulated quadratically constrained quadratic problem is h…
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…
In this paper, we investigate the robust beamforming schemes for a multi-user multiple-input-single-output (MU-MISO) system with per-antenna power constraints and quantized channel direction information (CDI) feedback. Our design objective is to maximize the expectation of the weighted sum-rate performance by means of controlling the interference leakage and properly allocating the power among user equipments (UEs).First, we prove the optimality of the non-robust zero-forcing (ZF) beamforming scheme in the sense of generating the minimum amount of average inter-UE interference under quantized …
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 multiuser communication systems, user scheduling and beamforming (US-BF) design are two fundamental problems that are usually studied separately in the existing literature. In this work, we focus on the joint US-BF design with the goal of maximizing the set cardinality of scheduled users, which is computationally challenging due to the non-convex objective function and the coupled constraints with discrete-continuous variables. To tackle these difficulties, a successive convex approximation based US-BF (SCA-USBF) optimization algorithm is firstly proposed. Then, inspired by wireless intelli…
In this work, we consider a downlink NOMA network with multiple single-antenna users and multi-antenna UAVs. In particular, the users are spatially located in several clusters by following the Poisson Cluster Process and each cluster is served by a hovering UAV with NOMA. For practical considerations, we assume that only imperfect CSI of each user is available at the UAVs. Based on this model, the problem of joint user clustering and robust beamforming design is formulated to minimize the sum transmission power, and meanwhile, guarantee the QoS requirements of users. Due to the integer variabl…
This paper considers the downlink of a single-cell massive MIMO (multiple-input multiple-output) system with dual-polarized antennas at both the base station and users. We consider a channel model that takes into account several practical aspects that arise when utilizing dual polarization, such as channel cross-polar discrimination (XPD) and cross-polar receive and transmit correlations (XPC). We derive the statistical properties of the minimum mean squared error (MMSE) channel estimator for this model. Using these estimates for maximum ratio precoding, a rigorous closed-form downlink spectra…
This paper studies the fast adaptive beamforming for the multiuser multiple-input single-output downlink. Existing deep learning-based approaches assume that training and testing channels follow the same distribution which causes task mismatch, when the testing environment changes. Although meta learning can deal with the task mismatch, it relies on labelled data and incurs high complexity in the pre-training and fine tuning stages. We propose a simple yet effective adaptive framework to solve the mismatch issue, which trains an embedding model as a transferable feature extractor, followed by …
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…
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…
In this paper, we consider a multi-cell network where every base station (BS) serves multiple users with an antenna array. Each user is associated with only one BS and has a single antenna. Assume that only long-term channel state information (CSI) is available in the system. The objective is to minimize the network downlink transmission power needed to meet the users' signal-to-interference-plus-noise ratio (SINR) requirements. For this objective, we propose an asynchronous distributed beamforming and power control algorithm which provides the same optimal solution as given by centralized alg…
With the explosive growth of smart devices and mobile data traffic, limited fronthaul capacity has become a notable bottleneck of green communication access networks, such as cloud radio access networks(C-RANs). In this paper, we proposed a joint user association and downlink beamforming scheme for green C-RANs to minimize the network power consumption with the limited fronthaul links. We first formulate the design problem as a mixed integer nonlinear programming (MINLP), and then transformed the MINLP problem into a mixed integer second-order cone program (MI-SOCP) which is a convex program w…
In most multiple-input multiple-output (MIMO) communication systems, e.g., Massive MIMO, the antenna spacing is generally no less than half a wavelength. It helps to reduce the mutual coupling and therefore facilitate the system design. The maximum array gain is the number of antennas in this settings. However, when the antenna spacing is made very small, the array gain of a compact array can be proportional to the square of the number of antennas - a value much larger than the traditional array. To achieve this so-called "superdirectivity" however, the calculation of the excitation coefficien…
The design of a set of beamformers for the multiuser multiple-input single-output (MISO) downlink that provides the receivers with prespecified levels of quality-of-service (QoS) can be quite challenging when the channel state information is not perfectly known at the base station. The constraint of having the SINR meet or exceed a given threshold with high probability is intractable in general, which results in problems that are fundamentally hard to solve. In this paper, we will develop a high quality approximation of the SINR outage constraint that, along with a semidefinite relaxation, ena…
This paper considers the reconfigurable intelligent surface (RIS)-assisted multi-user communications, where an RIS is used to assist the base station (BS) for serving multiple users. The RIS consisting of passive reflecting elements can manipulate the reflected direction of the incoming electromagnetic waves by adjusting the phase shifts of the reflecting elements. Alternating optimization (AO) based approach is commonly used to determine the phase shifts of the RIS elements. While AO-based approaches have shown significant gain of RIS, the complexity is quite high due to the coupled structure…
In this paper, an optimization framework is proposed for joint transceiver beamforming and admission control in massive MIMO cognitive radio networks. The objective of the optimization problem is to support maximum number of secondary users in downlink transmission with constraints on the total power allocated to users, the rate achieved at secondary users and the interference at the primary nodes. The proposed framework takes into account the imperfect knowledge of the channels between the secondary and the primary nodes and also mitigates the interference caused by the primary users at secon…
Base station (BS) cooperation can turn unwanted interference to useful signal energy for enhancing system performance. In the cooperative downlink, zero-forcing beamforming (ZFBF) with a simple scheduler is well known to obtain nearly the performance of the capacity-achieving dirty-paper coding. However, the centralized ZFBF approach is prohibitively complex as the network size grows. In this paper, we devise message passing algorithms for realizing the regularized ZFBF (RZFBF) in a distributed manner using belief propagation. In the proposed methods, the overall computational cost is decompos…
Hybrid beamforming is known to be a cost-effective and wide-spread solution for a system with large-scale antenna arrays. This work studies the optimization of the analog and digital components of the hybrid beamforming solution for remote radio heads (RRHs) in a downlink cloud radio access network (C-RAN) architecture. Digital processing is carried out at a baseband processing unit (BBU) in the "cloud" and the precoded baseband signals are quantized prior to transmission to the RRHs via finite-capacity fronthaul links. In this system, we consider two different channel state information (CSI) …
We analyze the mean and the variance of the useful signal and interference powers in a multi-cell network using zero-forcing beamforming (ZF-BF) with two beamformer normalization approaches. While the mean has been the main focus in earlier studies on ZF-BF, analysis of the variance has not been tackled. Our analysis provides a complete statistical study, sheds light on the importance of the variance by deriving closed-form expressions for the signals' two moments, and provides a practical use for these expressions; we use the gamma or lognormal distribution for the interference power to analy…
Cell-free Massive MIMO (multiple-input multiple-output) refers to a distributed Massive MIMO system where all the access points (APs) cooperate to coherently serve all the user equipments (UEs), suppress inter-cell interference and mitigate the multiuser interference. Recent works demonstrated that, unlike co-located Massive MIMO, the \textit{channel hardening} is, in general, less pronounced in cell-free Massive MIMO, thus there is much to benefit from estimating the downlink channel. In this study, we investigate the gain introduced by the downlink beamforming training, extending the previou…
With the dense deployment of the remote radio heads (RRHs), the huge network power consumption has become a great challenge for green cloud radio access networks (Cloud-RANs), and multiuser downlink beamforming has been proposed as a promising solution. Moreover, the increasing number of mobile users (MUs) causes that admission control is essential for Cloud-RAN with limited fronthaul capacity and predefined power budget. In this paper, we consider the problem of joint multiuser downlink beamforming and admission control (JBAC) to enhance the admitted MUs in the network and reduce the network …
This paper studies fast adaptive beamforming optimization for the signal-to-interference-plus-noise ratio balancing problem in a multiuser multiple-input single-output downlink system. Existing deep learning based approaches to predict beamforming rely on the assumption that the training and testing channels follow the same distribution which may not hold in practice. As a result, a trained model may lead to performance deterioration when the testing network environment changes. To deal with this task mismatch issue, we propose two offline adaptive algorithms based on deep transfer learning an…
