Performance analysis of DS/CDMA systems with shadowing and flat fading

A new method is developed for evaluating the error probability (Pe) for direct sequence, code division multiple access (DS/CDMA) wireless systems that includes the effects of shadowing and fading. The method is based on saddle point integration (SPI) of the test statistic's moment generating function (MGF) in the complex plane. The SPI method is applicable to both ideal and wireless channels. For wireless channels, a Padé approximation (PA) of the MGF, which is derived from the moments of the channel's shadowing and fading distributions, allows efficient evaluation of the Pe. The SPI method can be used to model independent channels using separate shadowing and fading moments for each individual channel. The relative error between the probability density function (PDF) of the composite variate representing log-normal shadowing and Rayleigh fading and the PDF found from the inverse Laplace transform of the PA is negligible. Results show that log-normal shadowing increases the Pe by 100–1000% compared to channels exhibiting fading only.