Source fidelity over a two-hop fading channel

This paper studies the transmission of a continuous source over a two-hop fading channel. The source data traverses at least one intermediate node in order to reach the destination node. We assume a Gaussian source with Rayleigh fading links, and model the effect of each link through its outage capacity. We start with a single link, and optimize the transmission rate to minimize the received distortion. This minimum distortion is characterized as a function of transmission time, average channel gain, and transmitted power. We then consider a two-hop channel and optimize the transmission rates and transmission times over the two links. Two cases are compared: (i) The relay is allowed to optimize the transmission rate over the second link; and (ii) The relay retransmits the received bits over the second link at the same rate. Numerical examples show that both types of relays perform similarly over a wide parameter range of interest. We characterize the minimum achievable distortion in each case when the ratio between channel gains becomes large, and show that the former (smart) relay gives a performance gain of at most three dB.