Step-size Control in Blind Source Separation

The behavior of the classic algorithm for blind source separation (BSS) is detailed for a fixed step size. To improve the algorithm in speed and exactness, essential in tracking a time-varying mixing environment, a variable step size must be employed. The ideal step size should decrease or increase as the overall system error decreases or increases. It is shown analytically that the coefficients of the estimating function provide a "measure of error" that is available to automatically control the algorithm step size. This paper proposes a self-adjusting, time-varying step size that is built from the square of the running average of the coefficients of the estimating function. Error free convergence is achieved for a time-invariant environment. The ability of the algorithm to improve the convergence in a time-invariant mixing environment and to track a changing mixing environment is demonstrated by extensive simulation results.