Stochastic gradient algorithm for system identification using adaptive FIR-filters with too low number of coefficients

The stochastic gradient algorithm for the adaptive finite-impulse response (FIR)-identification of a linear quasi-time-invariant system is impaired if the number of impulse response samples of the system to be identified, which are different from zero, is greater than the number of coefficients of the adaptive FIR-filter. The degree of impairment is dependent on the kind of signal used for adjustment. Adjustment performed with stationary white noise causes only a stationary error, but when signals of instationary power (for instance, speech) are used, the convergence behavior of the algorithm is strongly deteriorated. To avoid this effect, the stochastic gradient algorithm is modified by lengthening the adjustment signal vector for the calculation of the step-size factor. The results are illustrated by the example of adaptive echo cancellation on telephone lines