Achievable rates and training optimization for fading relay channels with memory

In this paper, transmission over time-selective, flat fading relay channels is studied. It is assumed that channel fading coefficients are not known a priori. Transmission takes place in two phases: network training phase and data transmission phase. In the training phase, pilot symbols are sent and the receivers employ single-pilot MMSE estimation or noncausal Wiener filter to learn the channel. Amplify-and-Forward (AF) and Decode-and-Forward (DF) techniques are considered in the data transmission phase and achievable rate expressions are obtained. The training period, and data and training power allocations are jointly optimized by using the achievable rate expressions. Numerical results are obtained considering Gauss-Markov and lowpass fading models. Achievable rates are computed and energy-per-bit requirements are investigated. The optimal power distributions among pilot and data symbols are provided.