Pilot symbol transmission for time-varying fading channels: An information-theoretic optimization

Abstract—We consider the optimal design of pilot-symbol-assisted modulation (PSAM) in time-varying flat-fading channels (FFC). The FFC is modeled as an autoregressive Gauss-Markov random process, whose realization is unknown at the transmitter or at the receiver. Our measure of optimality for channel estimation is the rate of information transfer through the channel. The parameters that are available for this optimization are the power ratio and the fraction of time that are allocated to pilot transmission. Our approach is different from (and builds upon) a recent study of PSAM for the Gauss-Markov FFC, where the aim was to minimize the maximum steady-state minimum mean square error (MMSE) of channel estimation for equal power allocated to pilot and data symbols and for a fixed pilot insertion ratio. To this end, we examine a lower bound on the capacity and find the optimal pilot transmission parameters that maximize this bound. Our analysis shows that this capacity lower bound is more sensitive to the pilot power allocation ratio in relatively slow fading channels (with the normalized fading rate fDTs ' 0.01). We observe that for such slow fading rates, optimal power allocation and optimal pilot spacing are more sensitive to the operating SNR. Another finding is that equal power allocation strategy is suboptimal by at most 1 dB for the slow fading rate of fDTs ' 0.01