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Enabling linear minimum-mean square error (LMMSE)-based estimation of random time-selective channels, pilot-symbol-assisted modulation (PSAM) has well-documented merits as a fading counter-measure boosting bit-error rate performance. We design average-rate optimal PSAM transmissions by maximizing a tight lower bound of the average channel capacity. Relying on a simple closed-form expression of this bound in terms of the LMMSE channel estimator variance, we obtain PSAM transmissions with optimal spacing of pilot symbols and optimal allocation of the transmit-power budget between pilot and information symbols. Equi-powered transmitted symbols, channels with special Doppler spectra, and analytical and simulation based comparisons of possible alternatives shed more light on information-theoretic aspects of PSAM-based transmissions.