Robust Joint Source-Relay-Destination Design Under Per-Antenna Power Constraints

Abstract

This paper deals with joint source-relay-destination beamforming (BF) design for an amplify-and-forward (AF) relay network. Considering the channel state information (CSI) from the relay to the destination is imperfect, we first aim to maximize the worst case received SNR under per-antenna power constraints. The associated optimization problem is then solved in two steps. In the first step, by revealing the rank-one property of the optimal relay BF matrix, we establish the semi-closed form solution of the joint optimal BF design that only depends on a vector variable. Based on this result, in the second step, we propose a low-complexity iterative algorithm to obtain the remaining unknown variable. We also study the problem for minimizing the maximum per-antenna power at the relay while ensuring a received signal-to-noise ratio (SNR) target, and show that it reduces to the SNR maximization problem. Thus the same methods can be applied to solve it. The differences between our result and the existing related work are also discussed in details. In particular, we show that in the perfect CSI case, our algorithm has the same performance but with much lower cost of computational complexity than the existing method. Finally, in the simulation part, we investigate the impact of imperfect CSI on the system performance to verify our analysis.Index Terms-Amplify-and-forward, multi-antenna relay system, per-antenna power, beamforming I. INTRODUCTIONRelay communications have been studied extensively over the past decades as a means of extending the coverage of wireless network and improving the spatial diversity of the system. Transmission schemes at the relay can be categorized into several groups, i.e., the Amplify-and-Forward (AF) scheme, the Decode-and-Forward scheme [1] etc. Among them, the AF scheme is the most simple scheme, as the relay only performs linear processing on the received signal and re-transmits it to the destination. AF scheme has been efficiently used to exploit the benefit of relaying in the multiple access relay channels [2], the broadcast relay channels [3], and the two-hop relay channels [4]-[6], [11].Performing joint source-relay linear beamforming (BF) can achieve higher data rate [2], [3]. For the relay BF design, many previous works concentrate on the sum power constraints. It

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“…Moreover, the deterministic CSI uncertainty model has been widely used in the worst-case system [5][6][7][8]. In [5], the design of robust relay beamforming for two-way relay networks with channel feedback errors was studied, where each node is equipped with a single antenna.…”

“…In [6], the authors investigated a robust beamforming scheme for the multiantenna non-regenerative cognitive relay network with the bounded channel uncertainties which are modeled by the worst-case model. In [7], the authors investigated the multi-antenna non-regenerative relay network and addressed the joint source-relay-destination beamforming design problem under deterministic imperfect CSI model. In [8], based on the linear beamformer at the relay and QR successive interference cancelation (SIC) at the destination, the authors proposed a robust minimum MSE-regularized zero-forcing (MMSE-RZF) beamformer optimized in terms of rate.…”

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“…Such a constraint is also suitable for distributed multiple inputs system, in which the transmitters are placed at different locations, and the power cannot be shared among antennas [17]. The per-antenna constraint is, therefore, more realistic in many practical systems [18][19][20][21]. While informationtheoretic aspects of multi-antenna systems under per-antenna constraints are less well understood due to the complexity of related optimization problems, several interesting results have been obtained recently, but only for coherent channels [22][23][24].…”