Semidefinite Relaxation and Approximation Analysis of a Beamformed Alamouti Scheme for Relay Beamforming Networks

In this paper, we study amplify-and-forward (AF) schemes in two-hop one-way relay networks. In particular, we consider multigroup multicast transmission between long-distance users. Assuming that perfect channel state information is perceived, our goal is to design the AF process so that the max-min-fair signal-to-interference-plus-noise ratio (SINR) is optimized while generalized power constraints are satisfied. We propose a beamformed Alamouti (BFA) AF scheme and formulate the corresponding AF design problem as a two-block fractional quadratically constrained quadratic program (QCQP). We then tackle the two-block fractional QCQP using the semidefinite relaxation (SDR) technique and analyze the approximation accuracy of the proposed SDR. From a theoretical perspective, our results are fundamentally new and reveal that the proposed BFA AF scheme can outperform the traditional BF AF scheme, especially when there are many users in the system or many generalized power constraints in the problem formulation. From a practical perspective, our proposed BFA AF scheme improves the receivers' SINR by offering two degrees of freedom (DoFs) in beamformer design, as opposed to only one DoF offered by the BF AF scheme. In the latter part of this paper, we demonstrate how this extra DoF leads to provable performance gain by considering two special relay scenarios, in which the AF process is shown to possess a special structure. Numerical simulations further confirm that the proposed BFA AF scheme outperforms the BF AF scheme and works well for large-scale relay systems.