Analysis of a first-order adaptive recursive predictor

Adaptive all-pole predictors have recently found renewed interest in the area of digital data transmission due to their ability to perform blind magnitude equalization of the communication channel. The pseudolinear regression (PLR) algorithm constitutes an appealing candidate for the predictor update, since it is computationally simpler than its forerunners. We analyze the behavior of a first-order complex-valued PLR-updated predictor to show that the stationary point is unique even in general undermodelled settings, and that the predictor pole will not escape the unit circle for sufficiently slow adaptation. With no undermodelling, global convergence is also established. Additional properties of PLR solutions in undermodelled scenarios are also given, such as expressions for their prediction gain.