Convergence of linear interference cancellation multiuser receivers

We consider the convergence in norm of several iterative implementations of linear multiuser receivers, under the assumption of long random spreading sequences. We find that asymptotically, linear parallel interference cancellation diverges for systems loads of greater than about 17%. Using known results from the theory of iterative solutions for linear systems we derive optimal or near-optimal relaxation parameters for parallel (first- and second-order stationary, Chebyshev) and serial cancellation (successive relaxation) methods. An analytic comparison of the asymptotic convergence factor for the various methods is given. Simulations are used to verify results for finite size systems.