Duy H. N. Nguyen

Multiuser Downlink Beamforming in Multicell Wireless Systems: A Game Theoretical Approach

This paper is concerned with the game theoretical approach in designing the multiuser downlink beamformers in multicell systems. Sharing the same physical resource, the base-station of each cell wishes to minimize its transmit power subject to a set of target signal-to-interference-plus-noise ratios (SINRs) at the multiple users in the cell. In this context, at first, the paper considers a strategic noncooperative game (SNG) where each base-station greedily determines its optimal downlink beamformer strategy in a distributed manner, without any coordination between the cells. Via the game theory framework, it is shown that this game belongs to the framework of standard functions. The conditions guaranteeing the existence and uniqueness of a Nash Equilibrium (NE) in this competitive design are subsequently examined. The paper then makes a revisit to the fully coordinated design in multicell downlink beamforming, where the optimal beamformers are jointly designed between the base-stations. A comparison between the competitive and coordinated designs shows the benefits of applying the former over the latter in terms of each designs distributed implementation. Finally, in order to improve the efficiency of the NE in the competitive design, the paper considers a more cooperative game through a pricing mechanism. The pricing consideration enables a base-station to steer its beamformers in a more cooperative manner, which ultimately limits the interference induced to other cells. The study on the existence and uniqueness of the new games NE is then given. The paper also presents a condition on the pricing factors that allow the new NE point to approach the performance established by the coordinated design, while retaining the distributed nature of the multicell game.

Joint Power Allocation and Relay Selection in Cooperative Networks

In this paper, we study the joint power allocation and relay selection problem for multi-user amplify-and-forward (AF) cooperative networks. To increase the systems spectral efficiency under the orthogonal transmission assumption, each source-destination pair is constrained to be assisted by a small subset of a set of available relays. The aim of this work is to establish a framework that determines which relays to help which users and with how much power. In particular, we propose the joint schemes under two design criteria: i) maximization of user rates, and ii) minimization of the total transmit power at the relays. As the original problem formulations are shown to be nonconvex integer optimization problems, and thus, are combinatorially hard, we also propose an efficient convex relaxation approach to solve the problems with low complexity. Numerical results demonstrate the effectiveness of the proposed approaches.

Distributed Beamforming in Relay-Assisted Multiuser Communications

This paper considers a communication network with multiple pairs of source and destination, assisted by multiple relays. It is assumed that perfect channel state information (CSI) is available at the relays. In a two-stage AF protocol, all the sources broadcast their signals to all the relays in the first stage. The received signal at each relay is processed by a beamforming weight and then re-broadcasted to all the destinations at the same time with other relays in the second stage. The focus is to find the optimal beamforming weights to meet a given set of target signal-to-interference-and-noise ratio (SINR) at the destinations, while minimizing the total transmitted power at the relays. We show that this problem can be formulated as a nonconvex quadratically constrained quadratic program (QCQP). Through relaxations, the problem can be solved efficiently by convex programming.

Block-Diagonalization Precoding in a Multiuser Multicell MIMO System: Competition and Coordination

This paper studies a multiuser multicell system where block-diagonalization (BD) precoding is utilized on a per-cell basis. We examine and compare the multicell system under two operating modes: competition and coordination. In the competition mode, the paper considers a strategic non-cooperative game (SNG), where each base-station (BS) greedily determines its BD precoding strategy in a distributed manner, based on the knowledge of the inter-cell interference at its connected mobile-stations (MS). Via the game-theory framework, the existence and uniqueness of a Nash equilibrium in this SNG are subsequently studied. In the coordination mode, the BD precoders are jointly designed across the multiple BSs to maximize the network weighted sum-rate (WSR). Since this WSR maximization problem is nonconvex, we consider a distributed algorithm to obtain at least a locally optimal solution. Finally, we extend our analysis of the multicell BD precoding to the case of BD-Dirty Paper Coding (BD-DPC) precoding. We characterize BD-DPC precoding game for the multicell system in the competition mode and propose an algorithm to jointly optimize BD-DPC precoders for the multicell system in the coordination mode. Simulation results show significant network sum-rate improvements by jointly designing the BD or BD-DPC precoders across the multicell system in the coordination mode over the competition mode.

Sum-Rate Maximization in the Multicell MIMO Multiple-Access Channel with Interference Coordination

This paper is concerned with the maximization of the weighted sum-rate (WSR) in the multicell MIMO multiple access channel (MAC). We consider a multicell network operating on the same frequency channel with multiple mobile stations (MS) per cell. Assuming the interference coordination mode in the multicell network, each base-station (BS) only decodes the signals for the MSs within its cell, while the inter-cell transmissions are treated as noise. Nonetheless, the uplink precoders are jointly optimized at MSs through the coordination among the cells in order to maximize the network weighted sum-rate (WSR). Since this WSR maximization problem is shown to be nonconvex, obtaining its globally optimal solution is rather computationally complex. Thus, our focus in this work is on low-complexity algorithms to obtain at least locally optimal solutions. Specifically, we propose two iterative algorithms: one is based on successive convex approximation and the other is based on iterative minimization of weighted mean squared error. Both solution approaches shall then reveal the structure of the optimal uplink precoders. In addition, we also show that the proposed algorithms can be implemented in a distributed manner across the coordinated cells. Simulation results show a significant improvement in the network sum-rate by the proposed algorithms, compared to the case with no interference coordination.

Distributed Beamforming in Multiuser Multi-Relay Networks with Guaranteed QoS

This paper considers optimal distributed beamforming designs in a multi-relay network with multiple sources and multiple destinations. It is assumed that all source-destination pairs operate in orthogonal channels to avoid inter-user interference at the destinations. The distributed beamforming designs are carried out to minimize the sum relay power with guaranteed quality of service (QoS) in terms of signal-to-noise-ratio (SNR) at the destinations. Considered are optimization problems with and without per-relay power constraints. Although the two optimization problems can be readily transformed into convex second-order conic programs (SOCPs), the paper proposes simple and fast iterative algorithms to efficiently solve them.

Sum-Rate Maximization in the Multicell MIMO Broadcast Channel With Interference Coordination

This paper studies the precoding designs to maximize the weighted sum-rate (WSR) in a multicell multiple-input multiple-output (MIMO) broadcast channel (BC). We consider a multicell network under universal frequency reuse with multiple mobile stations (MS) per cell. With interference coordination (IC) between the multiple cells, the base-station (BS) at each cell only transmits information signals to the MSs within its cell using the dirty paper coding (DPC) technique, while coordinating the inter-cell interference (ICI) induced to other cells. The main focus of this work is to jointly optimize the encoding covariance matrices across the BSs in order to maximize the network-wide WSR. Since this optimization problem is shown to be nonconvex, obtaining its globally optimal solution is highly complicated. To address this problem, we consider two low-complexity solution approaches with distributed implementation to obtain at least locally optimal solutions. In the first approach, by applying a successive convex approximation technique, the original nonconvex problem is decomposed into a sequence of simpler problems, which can be solved optimally and separately at each BS. In the second approach, the WSR problem is solved via an equivalent problem of weighted sum mean squared error minimization. Both solution approaches will unfold the control signaling among the coordinated BSs to allow their distributed implementation. Simulation results confirm the convergence of the proposed algorithms, as well as their superior performances over schemes with linear precoding or no interference coordination among the BSs.

Joint beamforming design and base-station assignment in a coordinated multicell system

This study is concerned with the downlink beamforming designs in a coordinated multicell system with dynamic base-station (BS) assignment. At each cell, a multiple-antenna BS employs linear beamforming to send multiple data streams to its assigned mobile-stations (MSs). Exploiting multicell coordination, the multiple BSs jointly optimise the beamformers and the BS-MS assignments to enhance the overall system performance. With per-BS power constraints, considered are the coordinated beamforming problems under the following two design criteria: (i) minimising the transmit power margin at the BS with a set of target signal-to-interference-plus-noise ratios (SINR) at the MSs and (ii) jointly maximising the minimum SINR margin at the MSs. As the original problem formulations are shown to be non-convex integer programs, which are combinatorially hard, the authors propose an efficient convex relaxation approach to solve the problems with low complexity. Simulations show that the convex relaxation-based assignment schemes significantly outperform heuristic fixed assignment schemes.

Power allocation in wireless multiuser multi-relay networks with distributed beamforming

This article studies optimal power allocation schemes in a multi-relay cooperating network employing amplify-and-forward (AF) protocol with multiple source–destination pairs. It is assumed that full channel state information is available at the relays. As such, distributed beamforming is employed in forwarding signals to the destinations. In this context, the authors extend recent works on distributed beamforming for a single source–destination pair to the scenario where multiple source–destination pairs are competing for the power resource at the relays. Under orthogonal transmissions of each source–destination pair, considered are the two following power allocation problems: (i) minimise the sum relay power with guaranteed quality of service (QoS) in terms of signal-to-noise ratio (SNR) at the destinations, and (ii) jointly maximise the SNR margin at the destinations subject to individual power constraints at the relays. Although these optimisation problems can be formulated as second-order conic programs (SOCP), the main contribution of this work are proposals of simple and fast converging numerical algorithms, based on the fixed point iteration framework, to efficiently solve these two problems.

SNR Maximization and Distributed Beamforming in Multiuser Multi-Relay Networks

This paper studies optimal distributed beamforming designs to jointly maximize the signal-to-noise (SNR) margin in a multiuser multi-relay network. Considered are optimization problems with two different types of power constraints: sum relay power constraint and per-relay power constraints. Although these two problems can be readily solved by the bisection method via a sequence of second-order conic feasibility programs, we propose simple and fast converging iterative algorithms to directly solve the two optimization problems under consideration.