SIMPLIFIED SEP APPROXIMATION OF HQAM IN COMBINED TIME SHARED NAKAGAMI-LOGNORMAL AND RICIAN FADING CHANNEL

Abstract

Due to di erent atmospheric conditions, signals transmitted through wireless medium experience several distortions. As a result, the received signal randomly gets attenu- ated in amplitude and distortion in phase. Therefore, irregularity is observed in received signal strength. The performance of the wireless communication system gets degraded in fading environment, relative to the additive white Gaussian noise (AWGN) environ- ment. The mobile user experiences di erent fading scenarios, which can be characterized as multi-path fading, shadow fading and mixture of both (composite fading). There are some known fading models such as Rayleigh, Rician, Nakagami-m, Weibull and composite fading channel (Rayleigh/Log-Normal (R/L), Rician/Log-Normal (Rice/L),Weibull/Log- Normal (W/L)or Nakagami/Log Normal (N/L)). In this dissertation, di erent fading scenarios are discussed and analyzed, and the corresponding probability distribution function (PDF) has been analysed. The Gaussian Q function has been approximated using the trapezoidal rule. The computational complexity involved in the calculation of the double integral in the expression of SEP for composite N/L channel is very high. Therefore, two closed form approximations for the PDF of the composite N/L channel are obtained using the approx- imations proposed by Holtzman and Gauss Hermite. Further, these two approximations are incorporated in the expression of SEP to reduce the computational complexity. In order to evaluate the performance of these two approximations, they are compared with the exact SEP expression. It is found that SEP result from the approximations proposed by Holtzman and Gauss Hermite are very close to the exact SEP obtained for low and high SNR, respectively. Further, the performance of the two approximations are evaluated in a combined (time shared) N/L and Rician fading channel. Afterwards, the sensitivity analysis is carried out to study the e ect of Rician k factor, Nakagami-m factor and time shared factor in the combined channel.