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In this paper, we develop a unified framework for beamforming designs in non-regenerative multiuser two-way relaying (TWR). The core of our framework is the solution to the max-min signal-to-interference-plus-noise-ratio (SINR) problem for multiuser TWR. We solve this problem using a Dinkelbach-type algorithm with near-optimal performance and superlinear convergence. We show that, using the max-min SINR solution as a corner stone, the beamforming designs under various important criteria, such as weighted sum-rate maximization, weighted sum mean-square-error (MSE) minimization, and average bit-error-rate (BER) or symbol-error-rate (SER) minimization, etc, can be reformulated into a monotonic program. A polyblock outer approximation algorithm is then used to find the desired solutions with guaranteed convergence and optimal performance (provided that the core max-min SINR solver is optimal). Furthermore, the proposed unified approach can provide important insights for tackling the optimal beamforming designs in other emerging network models and settings. For instances, we extend the proposed framework to address the beamforming design in collaborative TWR and multi-pair MIMO TWR. Extensive numerical results are presented to demonstrate the merits of the proposed beamforming solutions.

Beamforming Design for Multiuser Two-Way Relaying: A Unified Approach via Max-Min SINR