Asynchronous Physical-layer Network Coding

A key issue in physical-layer network coding (PNC) is how to deal with the asynchrony between signals transmitted by multiple transmitters. That is, symbols transmitted by different transmitters could arrive at the receiver with symbol misalignment as well as relative carrier-phase offset. A second important issue is how to integrate channel coding with PNC to achieve reliable communication. This paper investigates these two issues and makes the following contributions: 1) We propose and investigate a general framework for decoding at the receiver based on belief propagation (BP). The framework can effectively deal with symbol and phase asynchronies while incorporating channel coding at the same time. 2) For unchannel-coded PNC, we show that for BPSK and QPSK modulations, our BP method can significantly reduce the asynchrony penalties compared with prior methods. 3) For unchannel-coded PNC, with half symbol offset between the transmitters, our BP method can drastically reduce the performance penalty due to phase asynchrony, from more than 6 dB to no more than 1 dB. 4) For channel-coded PNC, with our BP method, both symbol and phase asynchronies actually improve the system performance compared with the perfectly synchronous case. Furthermore, the performance spread due to different combinations of symbol and phase offsets between the transmitters in channel-coded PNC is only around 1 dB. The implication of 3) is that if we could control the symbol arrival times at the receiver, it would be advantageous to deliberately introduce a half symbol offset in unchannel-coded PNC. The implication of 4) is that when channel coding is used, symbol and phase asynchronies are not major performance concerns in PNC.Comment: Full length version of APN

Channel Estimation for Two-Way Relay Networks in the Presence of Synchronization Errors

This paper investigates pilot-aided channel estimation for two-way relay networks (TWRNs) in the presence of synchronization errors between the two sources. The unpredictable synchronization error leads to time domain offset and signal arriving order (SAO) ambiguity when two signals sent from two sources are superimposed at the relay. A two-step channel estimation algorithm is first proposed, in which the linear minimum mean-square-error (LMMSE) estimator is used to obtain initial channel estimates based on pilot symbols and a linear minimum error probability (LMEP) estimator is then developed to update these estimates. Optimal training sequences and power allocation at the relay are designed to further improve the performance for LMMSE based initial channel estimation. To tackle the SAO ambiguity problem, the generalized likelihood ratio testing (GLRT) method is applied and an upper bound on the SAO detection error probability is derived. By using the SAO information, a scaled LMEP estimation algorithm is proposed to compensate the performance degradation caused by SAO detection error. Simulation results show that the proposed estimation algorithms can effectively mitigate the negative effects caused by asynchronous transmissions in TWRNs, thus significantly outperforming the existing channel estimation algorithms.Comment: 14 pages, 9 figure