Joint power allocation and mapping strategy design for MIMO two-way relay channels with finite-alphabet inputs

In this paper, the joint design of power allocation and mapping strategy is developed to maximize the achievable uplink rate for MIMO two-way relay channels (TWRCs) with finite-alphabet inputs. In contrast with the traditional water-filing scheme based on Gaussian inputs, the optimal power allocation for constellation constrained MIMO TWRCs does not only depend on the channel gain, but also on the mapping strategy. The proposed scheme creates multiple non-interference parallel channels in the uplink phase, and multiple independent physical-layer network coding (PNC) streams are implemented over those channels. We then derive the achievable uplink rate in terms of power allocation and mapping strategy. To maximize the achievable rate, the optimal power allocation is obtained for a given mapping strategy, which reduces the joint design problem to one-dimension search of the mapping strategy. Numerical results demonstrate that for the finite-alphabet inputs, the proposed scheme significantly outperforms the traditional water-filling scheme, e.g., 3 dB gain over 8-PSK 4 × 4 MIMO TWRCs.