Adaptation with constant gains: Analysis for fast variations

Adaptation laws with constant gains, that adjust parameters of linear regression models, are investigated. The class of algorithms includes LMS as its simplest member, while other algorithms such as Wiener LMS may improve performance by including linear filters. Expressions in closed form for the tracking MSE are obtained for rapidly varying parameters of FIR systems with white inputs. This situation may occur in e.g. the tracking of fading communication channels. Stability and convergence in MSE are ascertained by the stability of a transfer function, without assuming independent regressor vectors. A key technique for obtaining these results is a transformation of these adaptation algorithms into linear time-invariant filters, called learning filters, that operate in open loop for slow parameter variations.