Optimal energy allocation between pilot and data symbols for minimizing frame error probability under imperfect fading channel information

In this paper, we study the issue of optimally allocating the transmission energy between a pilot symbol and data symbols for a point-to-point communication system over the slow fading channel. In the system studied, our performance criterion for the optimal energy allocation is the frame error probability (FEP). A pilot symbol-assisted modulation (PSAM) scheme is used along with a channel estimation scheme based on the minimum mean square error (MMSE) criterion. We derive an approximate expression for the FEP in the presence of channel estimation error and use this expression for minimizing the FEP in allocating the transmission energy. Numerical simulation results are presented to show that the derived approximate FEP expression is close to the actual FEP.