On The Performance of Phase-Shift-Keying Systems

Abstract

Coherent phase-shift keying (CPSK) and differential phase-shift keying (DPSK) are widely used modulation methods in digital communications. Bandwidth efficiency, good noise immunity, constant envelope, and simplicity of implementation make these schemes particularly attractive for use over the satellite, terrestrial radio and voiceband telephone channels. While system analyses abound in the literature, treatment is usually restricted to the additive Gaussian channel. Important issues determining ultimate performance, such as the joint effect of intersymbol interference and the acquisition of carrier phase have not been adequately addressed. The main purpose of this paper is to develop analytical tools that can be used to assess system performance under practical operating conditions. Pure coherent demodulation schemes such as CPSK are ideals which are rarely achieved in practice, and carrier phase must be estimated prior to and/or during data transmission. This requires start-up time, as well as added equipment, and the fidelity of the phase estimate ultimately determines performance. In contrast, DPSK is independent of carrier phase, since decisions are made on phase differences. However, this comes at a price, and it is known that ideal multiphase DPSK suffers an asymptotic performance penalty of 3 dB in signal-to-noise ratio (s/n) over ideal CPSK. We develop a new rigorous method for calculating the error rates of both CPSK and DPSK, under a variety of operating conditions. In particular, we find that the intersymbol interference penalty for quaternary DPSK is about 1 dB worse in s/n than for CPSK. We demonstrate that the detection efficiency of CPSK approaches the ideal, provided that the s/n of the phase-recovery circuit is about 10 dB more than that at the receiver input. Alternatively, for the same s/n, a 10-baud phase-locked loop integration time is required to achieve near-ideal performance.