This paper deals with the superposition coding (SPC) scheme in multiple-input multiple-output two-way relay channels subject to imperfect channel estimation. We determine the achievable rate region and the related channel estimation error degradation and we show how the available power is split between the two bi-directional data flows in order to maximize the system performance and to support fairness. Two main SPC techniques are investigated: (a) SPC without channel state information (CSI) at the users, (b) SPC with CSI at the users where a waterfilling power allocation is employed. We demonstrate that CSI significantly improves the achievable rate at low signal-to-noise ratios (SNRs) while it becomes less critical at high SNRs. Furthermore, a SPC power allocation that incorporates the average channel statistics and is independent on the instantaneous channel conditions as well as on the CSI is also proposed.Index Terms-Two-way relay channel, waterfilling power allocation, channel estimation error, achievable rate region.
I. INTRODUCTIONThe two-way relay channel is an important information theoretic network structure [1]. It consists of two users that establish communication via a shared relay node and characterizes networks with central controllers as well as ad-hoc networks with limited relaying resources. Recently there is a lot of interest in the design of efficient cooperative protocols for two-way relay channels. The proposed schemes can be divided into two main categories based on the number of the required time phases: (a) In the two phase protocol, called Multiple Access Broadcast (MABC) protocol [2], both users simultaneously transmit their data during the first phase and the relay alone transmits during the second phase, while (b) in the three phase protocol the two users sequentially transmit followed by a transmission from the relay [3]. Furthermore, each protocol category can be combined with any relaying strategy resulting in numerous two-way protocols with different complexities and performance. In [4] the authors highlight the most significant two-way relaying protocols and characterize their achievable rate region from an information theoretic point of view. An interesting MABC two-way scheme that employs superposition coding (SPC) at the relay node has been proposed in [5], where the authors analyze its capacity performance for a general Multiple-input multipleoutput (MIMO) two-way relay channel with different channelside information (CSI) requirements.