Large Deviations for Code Division Multiple Access Systems

We derive approximations for the probability of a bit error for a code division multiple access (CDMA) system with one-stage soft decision parallel interference cancellation. More precisely, we derive the exponential rates, Jk with cancellation and Ik without cancellation, of a CDMA system with k users and processing gain equal to n as n → ∞. Whereas the rates Ik follow explicitly from Cramér’s theorem, the rates Jk are given in terms of an optimization problem that can be evaluated numerically. We prove that Jk > Ik for k ≥ 3, which shows that interference cancellation is effective. For the case without interference cancellation, we investigate the second order (Bahadur–Rao) asymptotics. For the case with interference cancellation, we can obtain second order asymptotics only for k = 3. Together the limits provide excellent approximations for the probability of a bit error in a wide range of interest.