Influence of phase error on M-QAM demodulation in a non-Gaussian environment

Abstract

This paper considers the influence of a deterministic phase error for coherent M-QAM demodulators in a non-Gaussian environment; the latter is modeled as a combination of a white Gaussian process and a filtered Poisson process whose enveloped amplitude obeys the Rayleigh distribution. General results show that when approaching the critical limit, the symbol error rate quickly reaches a plateau having a relatively large width. I. INTRODUCTIONDigital communications systems are becoming more and more popular in every day use to the point of being considered just another consumer good. Among digital modulation schemes, M-QAM is the most employed because of its bandwidth efficiency [1]. To receive QAM signals, we have to use coherent detection which requires a perfect phase synchronization. In practice, the phase error can never be cancelled. In many research works that analyze the performance of QAM, this phase error is rarely taken into account [2,3]. Furthermore, in the modern operating environment of digital communication systems, non-Gaussian noise is observed as a dominating factor [4,5]. It is then quite natural to look at the influence of these two factors on the behavior of QAM demodulators.In this paper, the non-Gaussian perturbation is considered as the sum of a white Gaussian noise with spectral density N 0 / 2 and an impulsive noise modeled as a filtered Poisson process with Rayleigh distribution for the envelope amplitude. This model has been used by several authors, among them Kosmopoulos et al. [2]; however, in their work, they just use a first order approximation and apply the Fourier-Bessel technique to perform numerical computations. In practice, the number of impulses occurring in the detection interval is not small enough to justify the first order approximation [4]. It then becomes important to find a way for a general analysis.The phase error statistics in the presence of non-Gaussian noise are still not well studied. Some preliminary results have been reported for a first order phase locked loop [6]. In such a situation, it is preferable to analyze the receiver behavior for fixed phase errors and to study the symbol error rate for a practical range of these phase error values, up to the critical phase error for each constellation size.In a recent work [7], using the characteristic function method, we had obtained an exact analytical expression of the joint probability density function f XY (x,y) of the in-phase and quadrature outputs of a correlator-receiver, which is optimum for additive white Gaussian noise, using the maximum likelihood criteria. The detection thresholds remain unchanged while the phase error θ makes the received signal move. These changes can be computed analytically in such a way that the symbol error rate computations can be formulated in terms of f XY (x,y). We can easily compute the symbol error rate for any situation and the numerical values can be obtained as precisely as desired.The paper is structured as follows. In Section 2, we briefly present the receive...

Optimal detection of QAM in a man-made noise environment

“…Using the analytical expression of the pdf, the symbol error rate of the matched filter receiver has been shown to be (1) (5) where P k is given by (6) E a is the mean energy of each signal constellation.…”

“…Experimentally, the observed man-made noise appears as large impulses occurring during the detection interval (3), (4). In a series of papers by the authors, it was shown that this type of non-Gaussian noise has a dramatic effect on the performance of QAM modems when linear (matched fitter) detection is used (5), (6), (7). The performance is shown to be strongly dependent on two parameters: the impulsive index (A) and the power ratio of the impulsive noise component and the Gaussian noise component ( ).…”