Full Diversity Achieving Analog Network Coding for Asynchronous Two-Way Relay Networks with Linear Receivers
Time asynchronism is a practical issue needs to be addressed for a general distributed two-way relay network, where two terminal nodes exchange information through multiple spatial-separated relay nodes. In this paper, the authors propose an Analog Network Coding (ANC) scheme for a time asynchronous two-way relay network. In the proposed scheme, each relay node linearly transforms the received mixed asynchronous signals in the first time-slot by a Toeplitz matrix, and then broadcasts them back to the terminals in the second time-slot. A sufficient condition is derived for the proposed ANC to achieve full cooperative diversity using only linear receivers at the terminal nodes, such as Zero-Forcing (ZF), or Minimum Mean Square Error (MMSE) receivers, with any delay profiles of the timing errors.