Coherent reception of signals with digital modulation requires information about the channel state, in particular, about the phase offset introduced by the channel. Actually, receiving side estimates channel state using special pilot elements incorporated into the signal structure. Transmission of these pilot signals requires extra power and time-frequency resource, that reduces spectral and energy efficiency of the communication system, so the number of pilots should be minimized. The paper describes two views on the reception of short data packets transmitted by phase shift keying. On the one hand, coherent reception with semi-blind channel estimation is considered, namely, phase shift estimation is performed by a blind algorithm using all symbols of the packet, and pilot symbols are only used to resolve ambiguity inherent for blind estimates. The method of approximate theoretical calculation of the bit error probability for this reception method is described. The results of these calculations demonstrate good agreement with computer simulations. On the other hand, the whole packet is treated as a signal from a signal set suitable for noncoherent reception. Union bound and maximum-correlation approximation for bit error probability are evaluated and compared with results obtained for coherent reception with channel estimation. Computer simulation showed that even for very short BPSK and QPSK packets bit error probability for semi-blind channel estimation coincides with achievable limits for noncoherent reception of the packet as a whole.
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