Multiuser Downlink Beamforming Research Articles

Multi-User Downlink Beamforming Using Uplink Downlink Duality With 1-Bit Converters for Flat Fading Channels

The increased power consumption of high-resolution data converters at higher carrier frequencies and larger bandwidths is becoming a bottleneck for communication systems. In this paper, we consider a fully digital base station equipped with 1-bit analog-to-digital (in uplink) and digital-to-analog (in downlink) converters on each radio frequency chain. The base station communicates with multiple single antenna users with individual SINR constraints. We first establish the uplink downlink duality principle under 1-bit hardware constraints under an uncorrelated quantization noise assumption. We then present a linear solution to the multi-user downlink beamforming problem based on the uplink downlink duality principle. The proposed solution takes into account the hardware constraints and jointly optimizes the downlink beamformers and the power allocated to each user. Optimized dithering obtained by adding dummy users to the true system users ensures that the uncorrelated quantization noise assumption is true under realistic settings. Detailed simulations carried out using 3GPP channel models generated from <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Quadriga</i> show that our proposed solution outperforms state of the art solutions in terms of the ergodic sum and minimum rate especially when the number of users is large. We also demonstrate that the proposed solution significantly reduces the performance gap from non-linear solutions in terms of the uncoded bit error rate at a fraction of the computational complexity.

MISO NOMA downlink beamforming optimization with per-antenna power constraints

Consider a multiuser downlink beamforming optimization problem for the non-orthogonal multiple access (NOMA) transmission in a multiple-input single-output (MISO) system with a general number of users. The total transmission power minimization problem is formulated subject to both quality-of-service (QoS) constraints under the NOMA principal and per-antenna power constraints, which are more realistic since each antenna has its own power amplifier and is limited individually by the linearity of the power amplifier. The problem is a nonconvex quadratically constrained quadratic program, and the conventional semidefinite program (SDP) relaxation is not tight. In order to tackle the non-convex problem, we construct second-order cone program (SOCP) approximation for each signal-to-interference-plus-noise ratio (SINR) constraint and form an iterative algorithm, in which a sequence of SOCPs are solved. The optimal values of SOCPs in the sequence are proved to be non-increasing, and converging to a locally optimal value. In particular, we show that the SDP relaxation is tight for two-user case if one of the SINR constraints is strict (non-binding) at the optimality. Detailed simulation results are presented to demonstrate the performance gains of the NOMA downlink beamforming with per-antenna power constraints through the proposed algorithm, which is compared with some state-of-the-art methods.

Joint beamforming and admission control for cache‐enabled Cloud‐RAN with limited fronthaul capacity

Caching is a promising solution for the cloud radio access network (Cloud-RAN) to mitigate the traffic load problem in the fronthaul links. Multiuser downlink beamforming plays an important role in efficient utilisation of spectrum and transmission power while satisfying the user's quality of service requirements. When the number of users exceeds the serving capacity of the network, certain users will have to be dropped or rescheduled. This is normally achieved by appropriate admission control mechanisms. Introducing local storage or cache at the remote radio heads where some popular contents are cached, the authors propose beamforming and admission control techniques for cache-enabled Cloud-RAN in the downlink. This minimises the total network cost including power and fronthaul cost while admitting as many users as possible. They formulate this multi-objective optimisation problem as a single objective optimisation problem. The original problem, which is a mixed-integer non-linear programme, is first converted to the mixed-integer second-order cone programming form. The branch and bound algorithm is then used to determine the optimal and suboptimal solutions. A simulation study has been conducted to assess the performance of both methods.

Spectral and Energy Efficiency Tradeoff for Massive MIMO

Achieving a good tradeoff between spectral efficiency (SE) and energy efficiency (EE) is important for the emerging wireless communication systems. Motivated by this, we study multiuser downlink beamforming in massive multiple-input multiple-output systems for maximizing a new metric of resource efficiency (RE), which is defined as a weighted combination of EE and SE. The new measure has more flexibility in striking the balance between SE and EE, but brings enormous difficulties in solving the resulting problem. To this end, we first investigate an uplink–downlink duality for the RE maximization. The conventional uplink–downlink duality only applies in the SE or the capacity region, and has yet not been explicitly established for the EE or the RE. In this paper, we prove with rigorous derivation that the duality has a more general form, which can be directly used to tackle the EE or RE beamforming optimization problem. Based on the duality, we then develop an optimization algorithm to realize spectral and energy efficient multiuser beamforming with either instantaneous or statistical channel state information (CSI). Numerical results finally verify that the design based on statistical CSI is able to asymptotically achieve the performance obtained with instantaneous CSI, but with much lower complexity.

Coalitional Games for Downlink Multicell Beamforming

A coalitional game is proposed for multicell multi-user downlink beamforming. Each base station intends to minimize its transmission power while aiming to attain a set of target signal-to-interference-plus-noise-ratio (SINR) for its users. To reduce power consumption, base stations have incentive to cooperate with other base stations to mitigate intercell interference. The coalitional game is introduced where base stations are allowed to forge partial cooperation rather than full cooperation. The partition form coalitional game is formulated with the consideration that beamformer design of a coalition depends on the coalition structure outside the considered coalition. We first formulate the beamformer design for a given coalition structure in which base stations in a coalition greedily minimize the total weighted transmit power without considering interference leakage to users in other coalitions. This can be considered as a non-cooperative game with each player as a distinct coalition. By introducing cost for cooperation, the coalition formation game is considered for the power minimization-based beamforming. A merge-regret-based sequential coalition formation algorithm has been developed that is capable of reaching a unique stable coalition structure. Finally, an ${\alpha }$ -Modification algorithm has been proposed to improve the performance of the coalition formation algorithm.

Non-orthogonal multiple access in a downlink multiuser beamforming system with limited CSI feedback

Non-orthogonal multiple access (NOMA) has been recognized as a promising multiple access technology for fifth generation (5G) mobile communication system. However, the advantage of NOMA is only verified under the ideal condition that the transmitter has the perfect knowledge of channel state information (CSI). In this paper, NOMA downlink multiuser system, in which the transmitter acquires the CSI through limited feedback channel, is studied. Two traditional beamforming technologies, zero-forcing beamforming and random beamforming, are investigated in the NOMA downlink multiuser system. Making use of the imperfect CSI feedback, channel direction information (CDI), and channel quality indicator (CQI), we propose the user selection scheme to reduce the interference between the NOMA users. Furthermore, a power allocation scheme is proposed to improve the sum-rate of NOMA system. Numerical results show that NOMA system with limited feedback channel still gains larger system rate than traditional orthogonal multiple access system. It is also shown that random beamforming is more suitable for the NOMA system with limited CSI feedback.

Tight Probabilistic SINR Constrained Beamforming Under Channel Uncertainties

In downlink multi-user beamforming, a single basestation is serving a number of users simultaneously. However, energy intended for one user may leak to other unintended users, causing interference. With signal-to-interference-plus-noise ratio (SINR) being one of the most crucial quality metrics to users, beamforming design with SINR guarantee has always been an important research topic. However, when the channel state information is not accurate, the SINR requirements become probabilistic constraints, which unfortunately are not tractable analytically for general uncertainty distribution. Therefore, existing probabilistic beamforming methods focus on the relatively simple Gaussian and uniform channel uncertainties, and mainly rely on probability inequality based approximated solutions, resulting in conservative SINR outage realizations. In this paper, based on the local structure of the feasible set in the probabilistic beamforming problem, a systematic method is proposed to realize tight SINR outage control for a large class of channel uncertainty distributions. With channel estimation and quantization errors as examples, simulation results show that the SINR outage can be realized tightly, which results in reduced transmit power compared to the existing inequality based probabilistic beamformers.

Downlink Multiuser Beamforming With Compensation of Channel Reciprocity From RF Impairments

In this paper, we consider the uncertainty of channel reciprocity due to radio frequency (RF) frontend impairments for downlink multiuser beamforming in time division duplexing (TDD) based systems. In particular, we focus on conversion gain error (CGE) in analog RF frontends that results in independent in-phase and quadrature-phase (IQ) imbalances for each RF chain. A parameter of conversion gain factors for each RF chain is considered for the compensation of downlink beamforming as it can be easily estimated by a base station (BS) itself. With the set of these parameters, we study downlink multiuser beamforming for given uplink channel vectors that are available through uplink training phases. Based on performance analysis, we observe that the CGE in receive RF frontend can result in more performance degradation than those in transmit RF frontend.

Interference‐leakage based non‐cooperative beamforming with low‐dimensional approximation

In this study, the authors have studied downlink multiuser non-cooperative beamforming in a time-division duplexing-based multicell system with a non-linear Jacobi-like iterative algorithm, where each base station is to minimise the interference leakage to adjacent cells in forming beams with signal-to-interference-plus-noise ratio constraints for users in its cell. The resulting approach is referred to as altruistic non-cooperative beamforming (ANB). To reduce the computational complexity for ANB per cell, a low-dimensional beamforming approach, which can be easily solved as it has a standard downlink multiuser beamforming formulation, has also been considered at the expense of degraded performance.

Joint Discrete Rate Adaptation and Downlink Beamforming Using Mixed Integer Conic Programming

Multiuser downlink beamforming for sum-rate maximization has been intensively studied in the literature assuming that the achievable data rates of the mobile stations (MSs) are continuous and strictly increasing functions of the received signal-to-interference-plus-noise ratios (SINRs). However, in practical cellular networks that employ adaptive modulation and coding, the data rates of the MSs are determined by the specific modulation and coding schemes and thus attain discrete values. We consider in this paper discrete rate adaptation and downlink beamforming (RAB), where the discrete rate assignment is jointly optimized along with the beamformer design to achieve the maximum sum-rate with minimum total transmitted power of the base station. User admission control is embedded in the discrete rate assignment procedure. We address the RAB problem using a mixed integer second-order cone program (MI-SOCP) approach, proposing a standard big-M MI-SOCP formulation that supports the branch-and-cut (BnC) method. To reduce the complexity of the BnC algorithm, we further develop an improved extended MI-SOCP formulation. We analytically show that the extended formulation generally admits strictly tighter continuous relaxations (and thus less computational complexity) than that of the big-M formulation. Efficient strategies are proposed to customize the standard BnC method for the RAB problem. For applications in large-scale networks, we develop low-complexity SOCP based inflation and deflation procedures to find suboptimal solutions of the RAB problem. Simulations show that the inflation and deflation procedures yield sum-rates that are very close to that of the optimal solutions.

General Rank Multiuser Downlink Beamforming With Shaping Constraints Using Real-Valued OSTBC

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 which an optimal beamforming solution can be obtained only when the SDR solution (after rank reduction) exhibits the rank-one property, in our approach optimality is guaranteed when a rank of eight is not exceeded. We show that our approach can incorporate up to 79 additional shaping constraints for which an optimal beamforming solution is guaranteed as compared to a maximum of two additional constraints that bound the conventional rank-one downlink beamforming designs. Simulation results demonstrate the flexibility of our proposed beamformer design.

Robust Downlink Beamforming With Partial Channel State Information for Conventional and Cognitive Radio Networks

We address the problem of robust multiuser downlink beamforming under the assumption that the transmitter has partial covariance-based channel state information (CSI). In our approach, the uncertainty on the channel covariance matrices is assumed to be confined in an ellipsoid of given size and shape, where prior knowledge about the statistical distribution of the CSI mismatch is taken into account. The goal is to minimize the transmitted power under the worst-case quality-of-service (QoS) constraints. We extend the developed robust problem to downlink beamforming in cognitive radio (CR) networks where QoS constraints apply to the users of the secondary network (SN) and interference leaked to the primary users (PUs) is required to be below a given interference threshold. We avoid the coarse approximations used by previous solutions and obtain exact reformulations for both worst-case problems based on Lagrange duality. The resulting problems can then be approximated using semidefinite relaxation (SDR). Further, we consider a popular alternative robust approach that is based on probabilistic QoS and interference constraints and show that both approaches are generally equivalent. Computer simulations show that the proposed techniques provide substantial performance improvements over earlier robust downlink beamforming techniques for both the conventional and the CR scenarios.

Convex approximation techniques for joint multiuser downlink beamforming and admission control

Multiuser downlink beamforming under quality of service (QoS) constraints has attracted considerable interest in years, because it is particularly appealing from a network operator's perspective (e.g., UMTS, 802.16e). When there are many co-channel users and/or the service constraints are stringent, the problem becomes infeasible and some form of admission control is necessary. We advocate a cross-layer approach to joint multiuser transmit beamforming and admission control, aiming to maximize the number of users that can be served at their desired QoS. It is shown that the core problem is NP-hard, yet amenable to convex approximation tools. Two computationally efficient convex approximation algorithms are proposed: one is based on semidefinite relaxation of an equivalent problem reformulation; the other takes a penalized second-order cone approach. Their performance is assessed in a range of experiments, using both simulated and measured channel data. In all experiments considered, the proposed algorithms work remarkably well in terms of the attained performance-complexity trade-off, consistently exhibiting close to optimal performance at an affordable computational complexity.

Quality of Service and Max-Min Fair Transmit Beamforming to Multiple Cochannel Multicast Groups

The problem of transmit beamforming to multiple cochannel multicast groups is considered, when the channel state is known at the transmitter and from two viewpoints: minimizing total transmission power while guaranteeing a prescribed minimum signal-to-interference-plus-noise ratio (SINR) at each receiver; and a fair approach maximizing the overall minimum SINR under a total power budget. The core problem is a multicast generalization of the multiuser downlink beamforming problem; the difference is that each transmitted stream is directed to multiple receivers, each with its own channel. Such generalization is relevant and timely, e.g., in the context of the emerging WiMAX and UMTS-LTE wireless networks. The joint problem also contains single-group multicast beamforming as a special case. The latter (and therefore also the former) is NP-hard. This motivates the pursuit of computationally efficient quasi-optimal solutions. It is shown that Lagrangian relaxation coupled with suitable randomization/cochannel multicast power control yield computationally efficient high-quality approximate solutions. For a significant fraction of problem instances, the solutions generated this way are exactly optimal. Extensive numerical results using both simulated and measured wireless channels are presented to corroborate our main findings.

A Subspace Multiuser Beamforming Algorithm for the Downlink in Mobile Communications

A new algorithm for downlink multiuser beamforming in mobile communications is described. The optimization problem is reformulated by modifying the constraints so that weight vectors of different mobile stations are optimized in a reduced feasible region which is a subset of that of the multiuser beamforming problem. The downlink beamforming weight vectors of different mobile stations are then jointly optimized in a subspace instead of searching in the entire parameter space. Simulation results show that the modified optimization problem leads to solutions that satisfy the signal-to-noise-plus-interference ratio specification at each mobile station and that the total power transmitted from the base station is very close to the optimal one. The solution of the modified optimization problem requires significantly less computation than the optimal multiuser beamforming algorithms

On downlink beamforming with greedy user selection: performance analysis and a simple new algorithm

This paper considers the problem of simultaneous multiuser downlink beamforming. The idea is to employ a transmit antenna array to create multiple "beams" directed toward the individual users, and the aim is to increase throughput, measured by sum capacity. In particular, we are interested in the practically important case of more users than transmit antennas, which requires user selection. Optimal solutions to this problem can be prohibitively complex for online implementation at the base station and entail so-called Dirty Paper (DP) precoding for known interference. Suboptimal solutions capitalize on multiuser (selection) diversity to achieve a significant fraction of sum capacity at lower complexity cost. We analyze the throughput performance in Rayleigh fading of a suboptimal greedy DP-based scheme proposed by Tu and Blum. We also propose another user-selection method of the same computational complexity based on simple zero-forcing beamforming. Our results indicate that the proposed method attains a significant fraction of sum capacity and throughput of Tu and Blum's scheme and, thus, offers an attractive alternative to DP-based schemes.

Multi-user downlink beamforming with multiple transmit and receive antennas

Downlink multiple-input, multiple-output (MIMO) systems assuming a large number of base station antennas, a small number of mobile station antennas, and rich-scattering, quasi-stationary, and flat-fading channel environments are considered. A MIMO space-division multiple access (SDMA) technique is proposed which enables concurrent transmission of multiple data streams to each multiple mobile station. The proposed method can achieve much higher downlink channel capacity than conventional MIMO techniques.