Convergence analysis of multi-stage PIC detectors

This paper analyses the convergence behaviour of the parallel interference cancellation (PIC) detector in code division multiple access (CDMA) systems. Using the results from previous stability analysis of an iterated-map neural network, the paper derives a general condition from which the sufficient condition for convergence of the PIC detector with tentative decision functions that are monotonically increasing at a sublinear rate can be calculated. As examples, the paper derives the sufficient conditions for convergence of the PIC detector with the clip decision and the hyperbolic tangent decision functions. The paper also examines the convergence behaviour of the PIC detector with hyperbolic tangent decision function via computer simulation and compares it with the analytical results.