Large Deviations for Code Division Multiple Access Systems
Gerard Hooghiemstra, Marten J. Klok, Remco van der Hofstad · SIAM Journal on Applied Mathematics · 2002
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, J k with cancellation and I k without cancellation, of a CDMA system with k users and processing gain equal to n as $n\to\infty$. Whereas the rates I k follow explicitly from Cramér's theorem, the rates J k are given in terms of an optimization problem that can be evaluated numerically. We prove that J k >I k for $k\ge3$, 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.