Bounds on the Capacity of the Blockwise Noncoherent APSK-AWGN Channels

TL;DR

This paper derives bounds on the capacity of blockwise noncoherent M-APSK channels over AWGN, showing that for moderate M and L, the bounds are tight and capacity approaches the coherent case as L increases.

Contribution

It provides the first easily computable upper and lower bounds on M-APSK channel capacity under blockwise unknown phase rotation, extending previous PSK results.

Findings

Bounds are tight for moderate M and L across SNR range.

Capacity approaches coherent capacity as block length L increases.

Results facilitate code design for noncoherent M-APSK channels.

Abstract

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.