To Code or Not to Code: Maximizing the Achievable Rate Region of Two-Way Decode-and-Forward Multiantenna Relay Channel

Network coding (NC) can effectively improve the energy and spectral efficiency of two-way relay channels. In this letter, we consider the downlink of the decode-and-forward MISO bidirectional relay channels with a multiantenna relay and two single-antenna users, where channel vectors from the relay to two users are denoted by h₁ and h₂, respectively. Intuitively, NC can enjoy the maximum signal-to-noise ratio (SNR) gain, when h₁ and h₂ are linearly dependent. When h₁ and h₂ are orthogonal, however, NC suffers from the maximum SNR loss. In this case, zero-forcing beamforming (ZFBF) is naturally optimal in terms of the achievable rate region. As a result, we compare the achievable rate regions of NC and ZFBF. Based on the comparison, the optimal ZFBF-NC switching method is proposed.