Bounds on the Capacity of the Blockwise Noncoherent APSK-AWGN Channels
  Capacity of M-ary Amplitude and Phase-Shift Keying(M-APSK) over an Additive White Gaussian Noise(AWGN) channel that also introduces an unknown carrier phase rotation is considered. The phase remains constant over a block of L symbols and it is independent from block to block. Aiming to design codes with equally probable symbols, uniformly distributed channel inputs are assumed. Based on results of Peleg and Shamai for M-ary Phase Shift Keying(M-PSK) modulation, easily computable upper and lower bounds on the effective M-APSK capacity are derived. For moderate M and L and a broad range of Signal-to-Noise Ratios(SNR's), the bounds come close together. As in the case of M-PSK modulation, for large L the coherent capacity is approached. 
Daniel C. Cunha and Jaime Portugheis