Convergence analysis of the sign algorithm with badly behaved noise (Q1853406)

The paper analyzes the convergence of the sign algorithm when the noise distribution has a dead zone that includes the origin. The analysis is done in the context of the identification of a plant with a stationary Gaussian input. Upper bounds of the time-averaged mean absolute excess estimation error and the time-averaged mean norm of the weight misalignment vector are derived. The former bound does not depend on the data correlation while the latter one does. The bounds hold for all values of the algorithm step size \(\mu\). Both bounds tend to zero as \(\mu\) tends to zero. The bounds are significantly dependent on the width of the dead zone while they are weakly dependent on \(\mu\) when \(\mu\) is less than some threshold. The threshold is proportional to the width of the dead zone. The speed-accuracy trade-off of the algorithm is found to be poor in comparison with that in the case of a Gaussian noise. The wider the dead zone is, the worse the trade-off. The theoretical results of the paper are supported by simulations.