Large deviations for code division multiple access systems (Q2783746)

Let us consider a problem from telecommunications. Suppose that a system has \(k\) users and that all users transmit data simultaneously. In oder to do so, each user multiplies his data signal by an individual coding sequence. At the receiver, the signal of the \(m\)th \((1\leq m\leq k)\) user can be retrieved by taking the inner product of the transformed total signal and the \(m\)th coding sequence. In the case in which the coding sequences are orthogonal, all data that do not originate from the \(m\)th user will be annihilated. This technique is known as code division multiple access (CDMA); cf. \textit{R. K. Morrow} and \textit{J. S. Lehnert} [IEEE Trans. Commun. 37, 1052-1061 (1989).NEWLINENEWLINENEWLINEIn the paper, approximations for the probability of a bit error for a CDMA system with one-stage soft decision parallel interference cancellation are derived. More precisely, 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 \(n\to\infty\) are derived. 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. For \(k\geq 3\) the inequality \(J_k>I_k\) is proved. This shows that interference cancellation is effective. In special cases the second order (Bahadur-Rao) asymptotics is investigated. The references contain 9 bibliographical hints.