Selection diversity for DS-SSMA communications on Nakagami fading channels

Average error probability and outage probability for asynchronous binary direct sequence spread-spectrum multiple access communications through slow nonselective Nakagami fading channels are evaluated for nondiversity and diversity receptions. Using a Gauss quadrature rule, the moments of the multipath interference and multiple access interferences are used to evaluate the conditional probability conditioned on a fixed fading amplitude of the desired signal. Average error probability which is the expected value of the conditional probability is evaluated by trapezoidal integration. The PDF of the desired signal is Nakagami m-distributed for nondiversity reception. For diversity reception, the PDF of the desired signal is evaluated for selection diversity. Combining the diversity technique and Reed-Solomon codes, comparisons between the uncoded nondiversity DS-SSMA system and that of the coded diversity system are shown for a Gold code of codelength 127. Using fourth-order diversity and Reed-Solomon coding, the maximum achievable number of users is 12% of the codelength for Rayleigh fading, when the average error probability is 10^-3. The corresponding outage probability is less than 5%