On the Stochastic Modeling of the NLMS Algorithm Operating with Bilinear forms

This paper deals with the stochastic modeling of the normalized least-mean-square algorithm for bilinear forms (NLMS-BF), which is defined from the temporal and spatial impulse responses of a multiple-input single-output (MISO) spatiotemporal system. Specifically, considering a system identification problem with stationary plant and Gaussian input data, model expressions are derived describing the mean weight behavior of the temporal, spatial, and spatiotemporal adaptive filters, the learning curve, as well as some correlation-like matrices required. Simulation results are shown confirming that the model predicts satisfactorily the algorithm behavior for both transient and steady-state phases.