On the capacity of the blockwise incoherent MPSK channel

The capacity of M-ary phase-shift keying (MPSK) over an additive white Gaussian noise (AWGN) channel with carrier phase unknown but constant over L symbols is investigated. It is shown that capacity-achieving channel inputs are uniformly distributed and independent MPSK symbols. Capacity over a range of signal-to-noise ratio (SNR) and L is presented for binary phase-shift keying (BPSK) and quaternary phase-shift keying (QPSK). Upper and lower easy-to-compute bounds on capacity are derived. It is proven that for large L the coherent capacity is approached. An analytic asymptotic expression for low L/spl middot/SNR is derived exhibiting the expected quadratic dependence on the SNR.