Average error probability for quadriphase modulated DS-SSMA communications through Nakagami fading channel

An asynchronous direct sequence spread spectrum multiple access system using quadrature phase shift keying modulation through Nakagami'sm-distributed fading channel is considered for nondiversity reception. Approximation to the average error probability is evaluated in two steps. Using the Gauss quadrature rule, the moments of the multiple interferences are used to evaluate the conditional probability conditioned on a fixed fading amplitude of the desired signal. The probability density function of the desired signal is Nakagami distributed. The average error probability which is the expected value of the conditional probability is evaluated by the trapezoidal integration method. This method provides a good approximation to the average error probability for a small to a fairly large number of users. Numerical results are presented for a set of Gold code of code length 127.