  The low-snr capacity of M-ary PSK transmission over both the additive white
Gaussian noise (AWGN) and fading channels is analyzed when hard-decision
detection is employed at the receiver. Closed-form expressions for the first
and second derivatives of the capacity at zero snr are obtained. The
spectral-efficiency/bit-energy tradeoff in the low-snr regime is analyzed by
finding the wideband slope and the bit energy required at zero spectral
efficiency. Practical design guidelines are drawn from the
information-theoretic analysis. The fading channel analysis is conducted for
both coherent and noncoherent cases, and the performance penalty in the
low-power regime for not knowing the channel is identified.
