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The author presents pilot-symbol-assisted modulation (PSAM) on a solid analytical basis, a feature missing from previous work. Closed-form expressions are presented for the bit error rate (BER) in binary-phase-shift-keying (BPSK) and in quadrature-phase-shift-keying (QPSK), for a tight upper bound on the symbol error rate in 16 quadrature-amplitude-modulation (16-QAM), and for the optimized receiver coefficients. The error rates obtained are lower than for differential detection for any combination of signal-to-noise ratio (SNR) and Doppler spread, and the performance is within 1 dB of a perfect reference system under slow-fading conditions and within 3 dB when the Doppler spread is 5% of the symbol rate.>
J.K. Cavers (Tue,) studied this question.