Beamforming For Two-way Relay Networks Research Articles

Distributed Beamforming in Two-Way Relay Networks With Interference and Imperfect CSI

This paper studies the problem of optimal beamforming and power allocation for an amplify-and-forward (AF)-based two-way relaying network in the presence of interference and channel state information (CSI) uncertainty. In particular, we obtain the beamforming vector as well as the users’ transmit powers under two assumptions on the availability of the CSI of the interfering links, namely norm-bounded uncertainty model and the second-order statistics scenario. To do so, we develop two design approaches. The first approach is based on the total transmit power minimization technique. We start with the norm-bounded uncertainty model and derive the optimal solution to the corresponding problem. To reduce the computational complexity, we also develop a low-complexity algorithm which offers performance that is very close to the optimal one. In the second approach, we apply a signal-to-interference-plus-noise ratio (SINR) balancing technique. We propose another low-complexity algorithm based on the SINR balancing criteria. Next, we consider the scenario where the second-order statistics of the CSIs are available. Again we start with the total power minimization method and derive both optimal and suboptimal algorithms. Finally, we apply the SINR balancing technique to this scenario and develop another low-complexity algorithm, which is suitable for practice.

Efficient Solutions to Distributed Beamforming for Two-Way Relay Networks Under Individual Relay Power Constraints

This paper investigates distributed beamforming (DBF) designs for two-way relay networks (TWRNs), where two terminal nodes exchange information through a set of amplify-and-forward (AF) relays. We assume individual relay power constraints and study two important design problems, namely, the max–min fairness (MMF) problem and the weighted sum-rate maximization (WSRM) problem. For the MMF problem, unlike the existing works that usually solve the problem by a bisection method, we propose an efficient optimal solution by solving one convex second-order cone program (SOCP) only. For the WSRM problem, we develop an efficient iterative algorithm based on SOCP reformulation and the successive convex approximation (SCA) technique. For both the MMF and WSRM designs, we further propose a distributed implementation framework where each of the relays can independently compute its beamforming weight using its local channel state information (CSI) and some common parameters broadcasted by a control center. Simulation results are presented to demonstrate the performance advantages of the proposed solutions.

Max-Min Optimal Joint Power Control and Distributed Beamforming for Two-Way Relay Networks Under Per-Node Power Constraints

This paper deals with optimal joint user power control and relay distributed beamforming for two-way relay networks, where two end-users exchange information through multiple relays, each of which is assumed to have its own power constraint. The problem includes the design of the distributed beamformer at the relays and the power control scheme for the two end-users to optimize the network performance. Considering the overall two-way network performance, we maximize the lower signal-to-noise ratio (SNR) of the two communication links. For single-relay networks, this maximization problem is solved analytically. For multi-relay networks, we propose an iterative numerical algorithm to find the optimal solution. While the complexity of the optimal algorithm is too high for large networks, two sub-optimal algorithms with low complexity are also proposed, which are numerically shown to perform close to the optimal technique. It is also shown via simulation that for two-way networks with both single relay and multiple relays, proper user power control and relay distributed beamforming can significantly improve the network performance, especially when the power constraints of the two end-users in the networks are unbalanced. Our approach also improves the power efficiency of the network largely.

Robust Relay Beamforming for Two-Way Relay Networks

We study the design of robust relay beamforming for two-way relay networks by considering channel feedback errors. Our objective is to maximize the minimum worst-case signal-to-noise ratios (SNRs) of two sources subject to a total relay power budget. We first decompose this non-convex problem into a series of relay power minimization problems under minimum SNR constraints by using bisection search. Then the relay power minimization problem is recast to a semidefinite programming relaxation (SDR) problem. A suboptimal but efficient solution is finally obtained for the original design. A necessary condition for the power minimization problem to be feasible is also given. For the special case with perfect channel state information, an alternative algorithm is introduced to find the optimal beamformer, which has lower complexity than the existing method.

Filter-and-Forward Distributed Beamforming for Two-Way Relay Networks With Frequency Selective Channels

In filter-and-forward (FF) based two-way relay networks, each transmission for data exchange between two transceivers consists of only two time slots (or phases). In the first time slot, both transceivers transmit their data simultaneously to the relays. The received signal of each relay is filtered using a finite impulse response (FIR) filter to compensate for the frequency selectivity of the channels, and then, the output of the filter is forwarded to both transceivers in the second time-slot. In this paper, new approaches to distributed cooperative beamforming for such two-way relay networks with frequency selective channels are proposed. The first two distributed beamforming approaches assume that the transmitted powers of the transceivers are given and fixed. The first beamformer is based on minimizing the total transmitted power of the relays subject to two constraints on the signal-to-inter-symbol-interference-plus-noise ratio (SINR) at both transceivers. The second beamformer is designed through maximization of the lowest SINR of the two transceivers while keeping the relay transmitted power under certain levels. We show that these two problems can be cast as second-order convex cone programming problems. The other two distributed beamforming methods aim to calculate the transmitted powers of the transceivers as well as the coefficients of the relay filters using two different beamforming techniques. The first technique is based on the minimization of the total transmitted power of the transceivers and the relays subject to the SINR requirements for both transceivers, and the second method maximizes the lowest SINR of the two transceivers subject to a constraint on the total transmitted power. Simulation results demonstrate that using an FF relaying strategy can significantly improve the underlying performance measure as compared to the traditional amplify-and-forward relaying approach.

A Semi-Closed-Form Solution to Optimal Distributed Beamforming for Two-Way Relay Networks

In this correspondence, we present a computationally simple semi-closed-form solution to the problem of designing distributed beamformer for two-way (bi-directional) multi-relay networks. In such a network, the relay nodes use amplify-and-forward relaying protocol to help two transceivers exchange information in a bidirectional manner. We consider a total power minimization approach to optimally find the relay beamforming weights and the transceiver transmit powers. This approach is based on the minimization of the total transmit power, consumed in the whole network, subject to SNR constraints at the two transceivers. We show that as far as the relay beamforming weight vector is concerned, this minimization problem is equivalent to the minimization of the total transmit power for a one-way relay network where the target SNR of the receiving transceiver is equal to the sum of the target SNRs of the two transceivers in the original two-way relay network. Based on this observation, we show that the relay beamforming weight vector can be obtained in a closed from given that an intermediate parameter, namely the transmit power of the transmitter in the equivalent one-way relay network, is available. This intermediate parameter is shown to be the solution to a one-dimensional optimization problem, and thus, it can be obtained using a simple bisection method. Our semi-closed-form solution not only reveals the structure of the optimal beamforming weight vector, but also leads to a one-dimensional search regardless of the number of relays. This provides the computational advantage over the gradient based numerical method of Havary-Nassab , where the gradient dimension reflects the number of relays.

On Design of Collaborative Beamforming for Two-Way Relay Networks

We consider a two-way relay network, where two source nodes, S1 and S2, exchange information through a cluster of relay nodes. The relay nodes receive the sum signal from S1 and S2 in the first time slot. In the second time slot, each relay node multiplies its received signal by a complex coefficient and retransmits the signal to the two source nodes, which leads to a collaborative two-way beamforming system. By applying the principle of analog network coding, each receiver at S1 and S2 cancels the "self-interference" in the received signal from the relay cluster and decodes the message. This paper studies the 2-dimensional achievable rate region for such a two-way relay network with collaborative beamforming. With different assumptions of channel reciprocity between the source-relay and relay-source channels, the achievable rate region is characterized under two setups. First, with reciprocal channels, we investigate the achievable rate regions when the relay cluster is subject to a sum-power constraint or individual-power constraints. We show that the optimal beamforming vectors obtained from solving the weighted sum inverse-SNR minimization (WSISMin) problems are sufficient to characterize the corresponding achievable rate region. Furthermore, we derive the closed form solutions for those optimal beamforming vectors and consequently propose the partially distributed algorithms to implement the optimal beamforming, where each relay node only needs the local channel information and one global parameter. Second, with the non-reciprocal channels, the achievable rate regions are also characterized for both the sum-power constraint case and the individual-power constraint case. Although no closed-form solutions are available under this setup, we present efficient numerical algorithms.

Optimal Beamforming in Two-Way Relay Networks with Cognitive Radio Capabilities

In this paper, we present a cognitive relay network with two primary transceivers that communicate via several distributed relay terminals. Spectrum sensing is deployed at the relays to sense the absence/presence of the primary transceivers based on energy detection. The primary network utilizes a two-step two-way amplify-and-forward (AF) scheme by using the cognitive radio (CR) terminals as its relay nodes when the primary network is not in operation, in contrast, the CRs communicate with their own base station (BS). In the first relaying step, the primary transceivers send their signal to the CRs/relays. Distributed beamforming is then performed in the second relaying step. Our aim is to set the beamforming weights so as to minimize the total power dissipated in the relay network while satisfying a target signal-to-noise ratio (SNR) at the primary transceivers and at the cognitive BS. This is achieved by solving an optimization problem that we formulate as a nonconvex quadratically constrained quadratic program (QCQP). This problem is solved efficiently by semidefinite relaxation (SDR) and Lagrangian duality. Simulation results are provided to demonstrate the superiority of our proposed technique, compared to classical beamforming techniques, in terms of power reduction.

Optimal Distributed Beamforming for Two-Way Relay Networks

In this paper, we consider a relay network which consists of two single-antenna transceivers and n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> single-antenna relay nodes. Considering a two time slot two-way relaying scheme, each relay adjusts the phase and the amplitude of the mixture signal it receives from the two transceivers during the first time slot, by multiplying it with a complex beamforming coefficient. Then each relay transmits the so-obtained signal in the second time slot. Aiming at optimally calculating the beamforming coefficients as well as the transceiver transmit powers, we study two different approaches. In the first approach, we minimize the total transmit power (dissipated in the whole network) subject to two constraints on the transceivers' received signal-to-noise ratios (SNRs). We prove that such a power minimization technique has a unique solution. We also show that the optimal weight vector can be obtained through a simple iterative algorithm which enjoys a linear computational complexity per iteration. We also prove that for symmetric relaying schemes (where the two constraints on the transceiver SNRs are the same), half of the minimum total transmit power will be allocated to the two transceivers and the remaining half will be shared among the relaying nodes. In the second approach, we will study an SNR balancing technique. In this technique, the smaller of the two transceiver SNRs is maximized while the total transmit power is kept below a certain power budget. We show that this problem has also a unique solution which can be obtained through an iterative procedure with a linear computational complexity per iteration. We also prove that this approach leads to a power allocation scheme, where half of the maximum power budget is allocated to the two transceivers and the remaining half will be shared among all the relay nodes. For both approaches, we devise distributed schemes which require a minimal cooperation among the two transceivers and the relays. In fact, we show that both techniques can be implemented such that the bandwidth, required to obtain the beamforming weights in a distributed manner, remains constant as the size of the network grows.