Joint Beamforming Research Articles

Erratum to: Joint Beamforming and Power Allocation for Cognitive MIMO Systems Under Imperfect CSI Based on Game Theory

Erratum to: Joint Beamforming and Power Allocation for Cognitive MIMO Systems Under Imperfect CSI Based on Game Theory

Energy Efficient Transmissions in MIMO Cognitive Radio Networks

In this paper, we study energy-efficient transmissions for multiple-input multiple-output (MIMO) cognitive radio (CR) networks in which the secondary unlicensed users coexist with the primary licensed users. We want to optimize the time allocations and beamforming vectors for the secondary users (SUs), in order to minimize the energy consumption of the SUs while satisfying the SUs' rate requirements and the primary receivers' interference constraints. Compared with the tradition MIMO networks, the challenge here is that the SUs may not always be able to obtain the channel state information (CSI) to the primary receivers. We are interested in two different scenarios. The first is when the SUs have the luxury of knowing the CSI to the primary receivers, and the second is when the SUs do not have such an luxury. The corresponding optimization formulations involve joint time scheduling and beamforming, which are non-convex and are complicated to solve. Fortunately, we show that when the SUs are not able to obtain the CSI, the optimal time allocation and the optimal beamforming vectors can be found very efficiently in polynomial-time through a proper decomposition. When the SUs have perfect knowledge about the CSI, we show that the optimal solutions can still be obtained in polynomial time when the secondary system is under-utilized. If the traffic load to the secondary system is heavy, we propose a polynomial-time heuristic to generate a near-optimal solution. The simulation results show that our proposed energy-optimal-transmission algorithms can achieve an energy-saving of 30% to 91%, compared with the simplistic maximum-rate transmission policy, depending on the secondary system's traffic load.

Max-Min Energy Efficient Beamforming for Multicell Multiuser Joint Transmission Systems

Energy efficient communication technology has attracted much attention due to the explosive growth of energy consumption in current wireless communication systems. In this letter we focus on fairness-based energy efficiency and aim to maximize the minimum user energy efficiency in the multicell multiuser joint beamforming system, taking both dynamic and static power consumptions into account. This optimization problem is a non-convex fractional programming problem and hard to tackle. In order to find its solution, the original problem is transformed into a parameterized polynomial subtractive form by exploiting the relationship between the user rate and the minimum mean square error, and using the fractional programming theorem. An iterative algorithm with proved convergence is then developed to achieve a near-optimal performance. Numerical results validate the effectiveness of the proposed solution and show that our algorithm significantly outperforms the max-min rate optimization algorithm in terms of maximizing the minimum energy efficiency.

Dynamic Coalition Formation for Network MIMO in Small Cell Networks

In this paper, we apply the concepts of network multiple-input-multiple-output (MIMO) to small cell networks. To do so, the issue of imperfect channel state information (CSI) at the transmitter is considered when frequency-division duplexing is used, for which the feedback channel is limited. We first introduce a regret based learning approach to optimize the transmit beamforming parameters for the cases when the feedback channel is temporarily unavailable during deep fades. We then propose a coalition formation game model to cluster the small cell base stations so that they can perform cluster-wise joint beamforming. We take the \tit{recursive core} as the solution concept of the coalition formation game. To obtain the recursive core, we first consider a typical merge-split algorithm. However, we show that this algorithm can be unstable. Alternatively, we adopt the merge-only algorithm which guarantees the formation stability and show that its outcome belongs to the recursive core. Finally, we analyze the average number and the average size of coalitions that can form during such a coalition formation process. Numerical simulations are given to illustrate the behavior of the coalition formation among small cell base stations.

Joint Beamforming and Power Allocation for Cognitive MIMO Systems Under Imperfect CSI Based on Game Theory

The problem of joint beamforming and power allocation for cognitive multi-input multi-output systems is studied via game theory. The objective is to maximize the sum utility of secondary users (SUs...

QoS-Based Source and Relay Secure Optimization Design with Presence of Channel Uncertainty

In this letter, we study relay-aided networks with presence of single eavesdropper. We provide joint beamforming design of the source and relay that can minimize the overall power consumption while satisfying our predefined quality-of-service (QoS) requirements. Additionally, we investigate the case that the channel between relay and eavesdropper suffers from channel uncertainty. Finally, simulation results are provided to verify the effectiveness of our algorithm.

An Optimal Iterative Algorithm for Codebook-Based Downlink Beamforming

This letter considers joint beamformer assignment and power allocation (BAPA) for codebook-based downlink beamforming. The BAPA problem represents a mixed integer combinatorial program since beamformer assignments involve binary decisions and beamformer assignments of multiple users are coupled in the downlink SINR constraints. We develop a mixed integer linear program formulation of the BAPA problem, which can be solved using, e.g., the branch-and-cut method. To derive low-complexity solutions, we introduce a virtual uplink problem, in which beamformer assignments of different users are decoupled. We establish the uplink-downlink duality of the two problems and develop a customized iterative algorithm to solve the BAPA problem. Analytic studies show that the customized algorithm yields either optimal (within the desired numerical accuracy) solutions of the BAPA problem (when it is feasible), or infeasibility certificates (when infeasible). The performance of the algorithm is demonstrated with numerical examples.

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.

Joint Beamforming and Power Allocation for Multiple Primary Users and Secondary Users in Cognitive MIMO Systems via Game Theory

We consider a system where a licensed radio spectrum is shared by multiple primary users(PUs) and secondary users(SUs). As the spectrum of interest is licensed to primary network, power and channel allocation must be carried out within the cognitive radio network so that no excessive interference is caused to PUs. For this system, we study the joint beamforming and power allocation problem via game theory in this paper. The problem is formulated as a non-cooperative beamforming and power allocation game, subject to the interference constraints of PUs as well as the peak transmission power constraints of SUs. We design a joint beamforming and power allocation algorithm for maximizing the total throughput of SUs, which is implemented by alternating iteration of minimum mean square error based decision feedback beamforming and a best response based iterative power allocation algorithm. Simulation results show that the algorithm has better performance than an existing algorithm and can converge to a locally optimal sum utility.

Joint Beamforming and Power Control in Coordinated Multicell: Max-Min Duality, Effective Network and Large System Transition

This paper studies joint beamforming and power control in a coordinated multicell downlink system that serves multiple users per cell to maximize the minimum weighted signal-to-interference-plus-noise ratio. The optimal solution and distributed algorithm with geometrically fast convergence rate are derived by employing the nonlinear Perron-Frobenius theory and the multicell network duality. The iterative algorithm, though operating in a distributed manner, still requires instantaneous power update within the coordinated cluster through the backhaul. The backhaul information exchange and message passing may become prohibitive with increasing number of transmit antennas and increasing number of users. In order to derive asymptotically optimal solution, random matrix theory is leveraged to design a distributed algorithm that only requires statistical information. The advantage of our approach is that there is no instantaneous power update through backhaul. Moreover, by using nonlinear Perron-Frobenius theory and random matrix theory, an effective primal network and an effective dual network are proposed to characterize and interpret the asymptotic solution.

Joint Beamforming and Antenna Subarray Formation for MIMO Cognitive Radios

The antenna subarray formation (ASF) is a promising technique for multiple-input multiple-output (MIMO) receiver. For MIMO cognitive radio systems, we propose a joint beamforming and ASF scheme in this letter which maximizes the cognitive achievable capacity subject to the peak transmit power constraint at the secondary transmitter, peak interference power constraint at the primary receiver, and the limited number of nonzero elements in the ASF matrix. To solve the joint optimization problem, we propose a relax-and-recover scheme. Simulation results have shown that the proposed scheme outperforms the conventional antenna selection scheme.

MIMO radar clutter mitigation based on joint beamforming and joint domain localized processing

In this article, we propose a space–time adaptive processing scheme via a generalized sidelobe canceler (GSC) architecture for airborne multiple-input multiple-output (MIMO) radar. This scheme employs the waveforms extracted by the matched filter bank that is cascaded at the receive end and utilizes digital beamforming technique to synthesize a certain number of transmit–receive beams, therefore, the operation of target detection in clutter environment can be conducted in all the directions of the formed beams in parallel. The GSC architecture is derived to implement adaptive reduced-rank (RR) clutter mitigation in a localized angle-Doppler space based on a novel RR multistage Wiener filter algorithm. The number of iterative stages in this algorithm is automatically selected in terms of a rank decision methodology. Meanwhile, beamforming and beam selecting methods are provided for this scheme, aiming at adaptively suppressing the clutter in localized domain. This scheme reverses the unavailability of the PA-efficient joint domain localized algorithm for MIMO radar. Moreover, it adapts to MIMO radar with arbitrary transmit–receive array space ratio. Even better, the proposed scheme has lower computation complexity than the traditional sample matrix inversion algorithm. The simulation results show that the proposed algorithm provide a signal-to-interference-plus-noise ratio improvement than traditional algorithms.

Joint beamforming and power control in downlink multiuser multiple-input multiple-output systems

In this paper, we study joint beamforming and power control for downlink multiple-input multiple-output systems with multiple users and target values for signal-to-interference plus noise ratios SINRs. We formulate this as a constrained optimization problem of minimizing total interference subject to constraints on the beamforming vector norms, target SINRs, and total transmit power. Necessary and sufficient conditions satisfied by the optimal beamformer and power allocation are presented, and a new algorithm for joint beamforming and power control is proposed. This adapts the beamforming vectors and transmit powers incrementally, and it stops when the specified SINR targets are achieved with minimum powers. The proposed algorithm is illustrated with numerical results obtained from simulations, which study its convergence and compare it with other similar algorithms. Copyright © 2013 John Wiley & Sons, Ltd.

Multiantenna Relay Beamforming Design for QoS Discrimination in Two-Way Relay Networks

This paper investigates the relay beamforming design for quality of service (QoS) discrimination in two-way relay networks. The purpose is to keep legitimate two-way relay users exchange their information via a helping multiantenna relay with QoS guarantee while avoiding the exchanged information overhearing by unauthorized receiver. To this end, we propose a physical layer method, where the relay beamforming is jointly designed with artificial noise (AN) which is used to interfere in the unauthorized user's reception. We formulate the joint beamforming and AN (BFA) design into an optimization problem such that the received signal-to-interference-ratio (SINR) at the two legitimate users is over a predefined QoS threshold while limiting the received SINR at the unauthorized user which is under a certain secure threshold. The objective of the optimization problem is to seek the optimal AN and beamforming vectors to minimize the total power consumed by the relay node. Since the optimization problem is nonconvex, we solve it by using semidefinite program (SDP) relaxation. For comparison, we also study the optimal relay beamforming without using AN (BFO) under the same QoS discrimination constraints. Simulation results show that both the proposed BFA and BFO can achieve the QoS discrimination of the two-way transmission. However, the proposed BFA yields significant power savings and lower infeasible rates compared with the BFO method.

Price-Based Joint Beamforming and Spectrum Management in Multi-Antenna Cognitive Radio Networks

We consider the problem of maximizing the throughput of a multi-antenna cognitive radio (CR) network. With spatial multiplexing over each frequency band, a multi-antenna CR node controls its antenna radiation directions and allocates power for each data stream by appropriately adjusting its precoding matrix. Our objective is to design a set of precoding matrices (one per band) at each CR node so that power and spectrum are optimally allocated for the node and its interference is steered away from unintended receivers. The problem is non-convex, with the number of variables growing quadratically with the number of antenna elements. To tackle it, we translate it into a noncooperative game. We derive an optimal pricing policy for each node, which adapts to the node's neighboring conditions and drives the game to a Nash-Equilibrium (NE). The network throughput under this NE equals to that of a locally optimal solution of the non-convex centralized problem. To find the set of precoding matrices at each node (best response), we develop a low-complexity distributed algorithm by exploiting the strong duality of the convex per-user optimization problem. The number of variables in the distributed algorithm is independent of the number of antenna elements. A centralized (cooperative) algorithm is also developed. Simulations show that the network throughput under the distributed algorithm rapidly converges to that of the centralized one. Finally, we develop a MAC protocol that implements our resource allocation and beamforming scheme. Extensive simulations show that the proposed protocol dramatically improves the network throughput and reduces power consumption.

Performance Tradeoffs in Amplify-and-Forward Bidirectional Network Beamforming

We study and compare the performance of two bidirectional network beamforming schemes, namely the multiple access broadcast channel (MABC) strategy and the time division broadcast channel (TDBC) protocol, using joint optimal power control and beamforming design. To do so, we first design two TDBC-based bidirectional network beamformers, through minimization of the total power consumed in the whole network subject to quality of service (QoS) constraints, for the two cases with and without a direct link between the two transceivers. The corresponding power minimization problems are carried out over the transceiver transmit powers as well as relay beamforming weights, thus resulting in a jointly optimal power allocation and beamforming criterion. We devise optimal second-order cone programming based solutions as well as fast gradient-based solutions to these problems. We then use these solutions to compare the performance of the underlying TDBC-based approach to that of the MABC-based technique. This comparison is important because the TDBC approach appears to have certain advantages which can be exploited towards improving the performance of two-way network beamforming. These advantages include the additional degrees of freedom as well as the possibility of benefitting from the availability of a direct link between the two transceivers. Interestingly, in the absence of a direct link between the two transceivers, we show that when the QoS constraints are imposed to meet certain given probabilities of uncoded error [or, equivalently, to meet certain signal-to-noise ratio (SNR) constraints], these two schemes perform closely in terms of the minimum total transmit power. However, when the QoS constraints are used to guarantee certain given rates, the MABC-based scheme outperforms the TDBC counterpart. In the case when a direct link exists between the two transceivers, the TDBC-based approach can outperform the MABC-based method, even for rate satisfying QoS constraints, provided that the direct link is strong enough.

Coordinated Multi-Cell Transmission for Distributed Antenna Systems with Partial CSIT

In this letter, a multi-cell distributed antenna system (DAS) with multiple users served via linear beamforming in each cell is considered. We focus on joint beamformer optimization (JBO) with the target of system weighted sum capacity maximization based on only partial channel state information at the transmitter (CSIT), which includes instantaneous intra-cell and large-scale inter-cell CSIT. After the formulation of a non-convex JBO problem, an algorithm is proposed to find the globally optimal beamformers based on monotonic optimization and the bisection method. Simulation results are provided to show the superiority of the proposed algorithm and the noticeable performance gain of the JBO based on partial CSIT. The proposed algorithm can be used as a benchmark for low-complexity JBO scheme design for practical applications.

Feedback‐based multi‐layered STBC system for MIMO multi‐cellular networks with cochannel interference

AbstractA feedback‐based multi‐layered STBC (MLSTBC) system, which is adapted to cochannel interference, is proposed. This system can adjust its transmitter configuration so that the largest throughput for the given SINR is obtained, also, it can use joint beamforming and power control to minimize cochannel interference so that the throughput requirement is satisfied. We propose an iterative algorithm to realize joint beamforming and power control for the feedback‐based MLSTBC system, and in this algorithm, we derive the required SINR and the corresponding transmitter configuration for attaining the throughput requirement. Some properties and simulation results are presented, they show that the proposed algorithm helps the feedback‐based MLSTBC system increase the probability of the success in meeting the throughput requirement, also they show that the feedback‐based MLSTBC system results in larger throughput than MLSTBC (with fixed transmitter configuration), STBC, and V‐BLAST. Copyright © 2010 John Wiley & Sons, Ltd.

Efficient Wireless Broadcasting through Joint Network Coding and Beamforming

We develop a framework that exploits network coding (NC) and multiple-input/multiple-output (MIMO) techniques, jointly together, to improve throughput of downlink broadcast channels. Specifically, we consider a base station (BS) equipped with multiple transmit antennas that serves multiple mobile stations (MSs) simultaneously by generating multiple signal beams. Given the large number of MSs and the small number of transmit antennas, the BS must decide, at any transmission opportunity, which group of MSs it should transmit packets to, in order to maximize the overall throughput. We propose two algorithms for grouping MSs that take advantage of NC and the orthogonality of user channels to improve the overall throughput. Our results indicate that the proposed techniques increase the achievable throughput significantly, especially in highly lossy environments.

Distributed Multicell Beamforming Design Approaching Pareto Boundary with Max-Min Fairness

This paper addresses coordinated downlink beamforming optimization in multicell time-division duplex (TDD) systems where a small number of parameters are exchanged between cells but with no data sharing. With the goal to reach the point on the Pareto boundary with max-min rate fairness, we first develop a two-step centralized optimization algorithm to design the joint beamforming vectors. This algorithm can achieve a further sum-rate improvement over the max-min optimal performance, and is shown to guarantee max-min Pareto optimality for scenarios with two base stations (BSs) each serving a single user. To realize a distributed solution with limited intercell communication, we then propose an iterative algorithm by exploiting an approximate uplink-downlink duality, in which only a small number of positive scalars are shared between cells in each iteration. Simulation results show that the proposed distributed solution achieves a fairness rate performance close to the centralized algorithm while it has a better sum-rate performance, and demonstrates a better tradeoff between sum-rate and fairness than the Nash Bargaining solution especially at high signal-to-noise ratio.