How Good Is PSK for Peak-Limited Fading Channels in the Low-SNR Regime?

This paper investigates the achievable information rate of phase-shift keying (PSK) over frequency nonselective Rayleigh and Rician fading channels without channel state information (CSI). The fading process exhibits general temporal correlation characterized by its spectral density function. We consider both discrete-time and continuous-time channels, and find their asymptotics at low signal-to-noise ratio (SNR). Compared to known capacity upper bounds under peak constraints, these asymptotics lead to negligible rate loss in the low-SNR regime for slowly time-varying fading channels. We further specialize to case studies of Gauss-Markov and Clarke's fading models