Influence of imperfect cophasing on performance of EGC receiver of BPSK and QPSK signals transmitted over Weibull fading channel

Abstract

This paper presents an analysis of maximum ratio combining (MRC) receiver of quaternary phase-shift keying (QPSK) signals transmitted over a Weibull fading channel. We determine the influence of imperfect cophasing and branches unbalance on bit error rate dependence on average signal-to-noise ratio. The performance dependence on diversity order and fading severity is also observed. Keywords — Cophasing, Diversity systems, Error probability, Fading. I. INTRODUCTION N order to reduce the influence of multipath fading on signal detection, it is possible to use spatially separated receiver antennas at the reception and to combine the signals from different branches of the receiver in a certain manner. The optimal combining technique is maximum ratio combining (MRC). This combining technique involves cophasing of the useful signal in all branches, multiplication of the received signal in each branch by the estimated envelope of that particular signal and summing of the received signals from all antennas (1). By cophasing, all the random phase fluctuations of the signal that emerged during the transmission are eliminated. For this process it is necessary to estimate the phase of the received signal. This phase estimation can be performed from the modulated or unmodulated received signal carrier. In previous papers concerning this matter the assumptions of the ideal phase estimation of the incoming signal were mainly used (2), (3). Only in (4) and (5) the influence of the imperfect phase estimation was examined and that was in the case of the equal gain combining (EGC) in the receiver. In paper (4), the influence of the phase error on the error probability in the case of digital binary (BPSK) and quaternary phase-shift keying (QPSK) signal detection was observed. This error probability was calculated applying the Gram-Charlier expansion. The analysis is performed under the assumption of the uncorrelated Rayleigh fading at receiving antennas. In paper (5) closed-form expressions for outage probability and error probability during the BPSK and QPSK signal detection over the Nakagami-m fading channel were obtained. Dual branch EGC technique was applied. In both papers the analysis of the system was done under the assumption that the branches of the receiver are balanced. However, as it is well-known (6), it is very rare to meet in practice the identical propagation paths in each branch. Also, the electrical components in different branches of the receiver are not ideal. Thus, it is also of interest to consider the influence of the branch unbalance in the receiver on system performances. In this paper an analysis of QPSK signal reception is presented. The signal is transmitted over the Weibull fading channel and MRC technique is applied in the receiver, while the receiving branches are assumed unbalanced. The phase estimation is performed from the unmodulated carrier and is not ideal. The difference between the phase of the incoming signal and the estimated phase for that signal is a statistical process and it follows the Tikhonov distribution (4), (5), (7). It is shown in which measure the imperfect phase estimation affects the bit-error rate (BER).