Analysis of an echo canceller with an adaptive FIR filter using the Sign algorithm for Gaussian transmit and receive signals

The paper proposes a new method of analyzing an echo canceller equipped with a stochastic gradient adaptive FIR filter using the Sign algorithm for Gaussian transmit and receive signals. Under the assumption that the “errors at the taps” are jointly Gaussian distributed, recurrence formulae for their mean and covariance are derived which give theoretical convergence curves in an excellent agreement with empirical results. Also derived are simpler approximate recurrence formulae and a closed-form solution together with a theoretical expression for the mean squared residual echo after convergence