Capacity region bounds and resource allocation for two-way OFDM relay channels

Most of the existing works on two-way frequency division multiplexing (OFDM) relay channels was centered on per-subcarrier decode-and-forward (DF) relaying, where each subcarrier is treated as a separate channel, and channel coding is performed separately over each subcarrier. In this paper, we show that this per-subcarrier DF relay strategy is suboptimal. More specifically, we present a multi-subcarrier DF relay strategy which achieves a larger rate region by adopting cross-subcarrier channel coding. Then we develop an optimal resource allocation algorithm to characterize the achievable rate region of the proposed multi-subcarrier DF relay strategy. Compared to standard Lagrangian duality optimization algorithms, our algorithm has a much smaller computational complexity due to the use of the structure property of the optimal resource allocation solution. We further prove that our multi-subcarrier DF relay strategy tends to achieve the capacity region of the two-way OFDM relay channels in the low signal-to-noise ratio (SNR) regime, and the amplify-and-forward (AF) relay strategy tends to achieve the multiplexing gain region of the two-way OFDM relay channels in the high SNR regime. Our theoretical analysis and numerical results demonstrate that DF relaying has better performance in the low to moderate SNR regime, while AF relaying is more appropriate in the high SNR regime.