Asynchronous Physical-layer Network Coding Scheme for Broadband Two-Way Relay Channels

Abstract

In OFDM based two-way relay channels, carrier frequency offsets (CFOs) between relay and terminal nodes introduce severe inter-carrier interference which degrades the performance of traditional physical-layer network coding. In this paper, we present a two-step asynchronous physical-layer network coding scheme, which consists of an interference cancelation step and a network coding mapping step, to deal with the frequency asynchrony in two-way OFDM relay system. We show through the average signal-to-interference-plus-noise ratio (SINR) and bit error rate (BER) that the proposed scheme can efficiently map the received superimposed signal, which is corrupted by the CFOs, into the exclusive OR of two terminals’ transmitted symbols. Moreover, a simple upper bound of the average SINR for the proposed scheme is derived. Through the simulation results, it is shown that the exact average SINR curve of the proposed scheme is very close to the upper bound even when the normalized CFO is as large as 0.15. Finally, we show that the average SINR and BER performances of the proposed scheme outperform the reference schemes considerably.

Appendix

After combing the received samples $\varvec{Y}_R(k)$ and $\varvec{Y}_R^*(N-1-k)$, the decision variable of SDC based scheme can be written as [13]

$$\begin{aligned} \varvec{Y}\left( k \right)&= \frac{1}{\sqrt{2}} \sum \limits _{ i = 1 }^2 \left( {{\alpha _i} + \alpha _i^*} \right) {\varvec{H}_i}\left( k \right) {\varvec{X}_i}\left( k,k \right) \\&\quad {} + \frac{1}{\sqrt{2}} \sum \limits _{i = 1}^2 {\sum \limits _{l = 1,l \ne k}^{{N/2} - 1} {\big ( {{\varvec{\varPi } _i}\left( {k,l} \right) + \varvec{\varPi } _i^*\left( {l,k} \right) } \big ){\varvec{H}_i}\left( l \right) {\varvec{X}_i}\left( l,l \right) } } \\ &\quad {} + \frac{1}{\sqrt{2}}\sum \limits _{i = 1}^2 \sum \limits _{l = 1}^{{N /2} - 1} \big ( {{\varvec{\varPi } _i}\left( {k,N - l} \right) + \varvec{\varPi } _i^*\left( {N - k,l} \right) }\big ) \\&\quad {} \times \varvec{H}_i\left( l \right) \varvec{X}_i^*\left( l,l \right) + \varvec{W}\left( k \right) + \varvec{W}^*\left( {N - k} \right) . \end{aligned}$$

(24)

The reason of the $1 / {\sqrt{2}}$ is that the scheme takes two subcarriers to transmit one symbol at terminals. The average SINR on the kth subcarrier can be expressed approximately as

$$\begin{aligned} \begin{aligned} \overline{\textit{SINR}}_{RS.3}\left( k \right) \approx \frac{{\sum \limits _{ i = 1 }^2{{\left| {{\alpha _i} + \alpha _i^*} \right| }^2}\mathcal{E}{{\left| {{\varvec{H}_i}\left( k \right) {\varvec{X}_i}\left( k,k \right) } \right| }^2}}}{\sum \limits _{i=1}^2{\sum \limits _{l = 1,l \ne k}^{{N/2} - 1} {{\beta _i}\left( {k,l} \right) \mathcal{E}{{\left| {{\varvec{H}_i}\left( l \right) {\varvec{X}_i}\left( l,l \right) } \right| }^2} } } }. \end{aligned} \end{aligned}$$

(25)

Using the condition $\varvec{X}_i(k,k) = \varvec{X}_i^*(k,k)$, ${\beta _i}\left( {k,l} \right)$ can be written as

$$\begin{aligned} \begin{aligned} {{\beta _i}\left( {k,l} \right) }&= \bigg | {\varvec{\varPi } _i}\left( {k,l} \right) + \varvec{\varPi } _i^*\left( {l,k} \right) \bigg . \bigg . + {\varvec{\varPi } _i}\left( {k,N - l} \right) + \varvec{\varPi } _i^*\left( {N - k,l} \right) \bigg |^2. \end{aligned} \end{aligned}$$

(26)