Channel capacity of analog network coding in a wireless channel

Radio channel is characterized by a multipath propagation that is suitable for application of network coding (NC) to improve the network capacity. In particular, physical layer network coding (PNC) scheme is known to double the network capacity of bi-directional communication between pairs of end users assisted by a relay terminal in a Gaussian channel. Recently, analog network coding (ANC) has been proposed with a simpler implementation complexity in comparison with PNC scheme, but the same achievable network capacity. On the other hand, an important question is how much the channel capacity is improved over a conventional point-to-point communication in a frequency-selective fading channel. In this paper, we present the ergodic channel capacity analysis of bi-directional transmission with analog network coding in a frequency-selective fading channel. The channel capacity expression for transmission with frequency domain equalization (FDE) is derived based on the Gaussian approximation of the inter-symbol interference (ISI) after FDE.