LENGTH-DEPENDENT AND COST-DEPENDENT LOCAL MINIMA OF UNCONSTRAINED BLIND CHANNEL EQUALIZERS

Baud-rate linear blind equalizers may converge to undesirable stable e quilibria due to different mechanisms. One such mechanism is the use o f linear FIR filters as equalizers. In this paper, it is shown that th is type of local minima exist for all unconstrained blind equalizers w hose cost functions satisfy two general conditions. The local minima g enerated by this mechanism are thus called length-dependent local mini ma. Another mechanism is generated by the cost function adopted by the blind algorithm itself. This type of local minima are called cost dep endent local minima. It shall be shown that several well-designed algo rithms do not have cost-dependent local minimum, whereas other algorit hms, such as the decision-directed equalizer and the stop-and-go algor ithm (SGA), do. Unlike many existing convergence analysis, the converg ence of the Godard algorithms (GA's) and standard cumulant algorithms (SCA's) under Gaussian noise is also presented here. Computer simulati ons are used to verify the analytical results.