On Convergence of Proportionate-Type Nlms Adaptive Algorithms

We specify the general form of proportionate-type NLMS adaptive algorithms and show that for sufficiently small adaptation stepsize parameter, the algorithms can be exponentially stable, globally convergent and robust to unmodeled dynamics and measurement noise. Also, we show that for small adaptation stepsize parameter and stationary inputs, behavior of proportionate-type NLMS algorithms can be modeled by proportionate-type steepest descent algorithms. This motivates designing of proportionate-type NLMS adaptive algorithms by looking at the adjoint proportionate-type steepest descent algorithms.