The Gaussian distribution is typically used to model the additive noise affecting communication systems. However, in many cases the noise cannot be modeled by a Gaussian distribution. In this thesis, we investigate the performance of different communication systems perturbed by nonGaussian noise. Three families of noise are considered in this work, namely the generalized Gaussian noise, the Laplace noise/interference, and the impulsive noise that is modeled by an αstable distribution. More specifically, in the first part of this thesis, the impact of an additive generalized Gaussian noise is studied by computing the average symbol error rate (SER) of one dimensional and two dimensional constellations in fading environment. We begin by the simple case of two symbols, i.e. binary phase shift keying (BPSK) constellation. From the results of this constellation, we extended the work to the average SER of an M pulse amplitude modulation (PAM). The first
2 − D constellation is the M quadrature amplitude modulation (QAM) (studied for two geometric shapes, namely square and rectangular), which is the combination of two orthogonal PAM signals (inphase and quadrature phase PAM). In the second part, the system performance of a circular constellation, namely M phase shift keying (MPSK) is studied in conjunction with a Laplace noise with independent noise components. A closed form and an asymptotic expansion of the SER are
derived for two detectors, maximum likelihood and minimum distance detectors. Next, we look at the intra cell interference of a full duplex cellular network which is shown to follow a Laplacian distribution with dependent, but uncorrelated, complex components. The densities of that interference are expressed in a closed form in order to obtain the SER of several communication systems (BPSK, PAM, QAM, and MPSK). Finally, we study the statistics of the αstable distribution. Those statistics are expressed in closed form in terms of the Fox H function and used to get the SER of BPSK, PAM, and QAM constellations. An approximation and an asymptotic expansion for high signal to noise ratio are presented also and their efficiency is proved using Monte Carlo simulations. It is worth mentioning that all the error rates presented in this work are averaged over a generalized flat fading, namely the extended generalized K, which has the ability to capture most of the known fading distribution. Many special cases are treated and simpler closed form expressions of the probability of error are derived and compared to some previous reported results.
Date of Award  Jun 29 2016 

Original language  English (US) 

Awarding Institution   Computer, Electrical and Mathematical Sciences and Engineering


Supervisor  MohamedSlim Alouini (Supervisor) 

 non gaussian noise
 probability of error
 wireless communication
 fading
 lapace distribution
 stable distribution