On Rotated-QAM Based Probabilistic Shaping Transmission Scheme for Rayleigh Fading Channels

Abstract

Probabilistic shaping (PS) combined with amplitude shift keying modulation is a spectrally efficient transmission scheme. To exploit the shaping gain in fading channels, we design a rotated quadrature amplitude modulation (QAM) based PS strategy. With discrete inputs, we first derive the ergodic constellation constrained (CC) capacity, which is found to be mutually influenced by both the probability mass function (PMF) and the rotation angle (RA) of input signals. Correspondingly, the optimal PMF and RA for maximizing the ergodic CC capacity are attained by the alternative optimization method. Furthermore, based on this non-equiprobable transmission scheme, the closed- form pairwise error probability is obtained for the first time. Finally, compared with the uniform scheme with elaborate rotation, the proposed PS strategy shows more than 1 dB gain in terms of both the efficiency and the error performance.