An Analysis of Nonlinear Direct-Sequence Correlators

The performance of nonlinear correlation reception of direct-sequence signals is analyzed in single and multiuser channels. The communications channel is modeled as containing non-Gaussian background noise and, in some cases, multiple-access interference as well. The error-probability behavior is studied asymptotically as the lengths of the spreading codes increase without bound, and conditions on the spreading sequences are obtained that assure asymptotic achievement of single-user performance in a multiuser system. A long-spreading sequence approximation to the average error probability is also derived, and this result is applied to the analysis of smooth-limiting correlation receivers in impulsive channels. Simulation results are also provided to verify the analysis. Average bit-error probabilities are computed via Monte Carlo simulations for linear, hard-limiting, and smooth-limiting correlation receivers in both single and two-user impulsive channels. The simulation results are compared to the error rates obtained in this paper via asymptotic approximations for the smooth-limiter and also to those from previous studies on linear and hard-limiting correlators.