Joint Power Allocation in Wireless Relay Networks: the Case of Hybrid Digital-Analog Transmission

In conventional digital communication systems, the quality of the received signal does not improve beyond a certain level as the channel quality increases. Such kind of quality saturation effect is caused by the unrecoverable quantization errors produced by source coding. The Hybrid Digital-Analog (HDA) transmission, where the quantization errors are transmitted in an analog mode along with the quantized data in a digital mode, has been recognized as an effective technique to combat the quality saturation effect. In this paper, we introduce HDA transmission in Wireless Relay Networks (WRNs) over Rayleigh slow-fading channels to eliminate the quality saturation effect and achieve graceful improvement for the better channel quality. Our goal is to minimize the end-to-end distortion by optimal power allocation. We note that digital-analog power allocation involved in HDA transmission is coupled with source-relay power allocation in WRNs. Therefore, the joint power allocation problem should be considered. We investigate this problem for two kinds of relays in WRNs, i.e., Amplify-and-Forward (AF) relays and Decode-and-Forward (DF) relays. In the case of AF relays, we find that the joint power problem is concave and thus derive the explicit expressions of the optimal solution. In the case of DF relays, we formulate the joint power allocation problem as a nonlinear fractional programming problem and then propose an efficient algorithm to search the optimal solution. Simulation results show that the proposed joint power allocation schemes outperform existing schemes in terms of end-to-end distortion in both WRNs with AF relays and that with DF relays under various channel conditions.