Dynamics of adaptive signal corrector

An adaptive signal corrector in the form of transversal filter used as a delay line with adjustable weight factors at the taps is considered for use in transmission of digital data over frequency-limited channels. A data signal proceeds from such a channel through a synchronous detector and a readout switch to the corrector. The stability of this device and the convergence rate, in the mean-square sense, of its algorithm of pseudosteepest descent are evaluated on the basis of a general analysis applicable to any kind of modulation. The calculations yield the mean-square error at the corrector output and its convergence to a fixed value for a constant adaptation factor within the OMu1 range as well as the steady-state error as a function of the number of taps. The results reveal that the convergence rate is not always a monotonically increasing function of the adaptation factor and, when the number of taps is large, reaches its maximum at the optimum value of the adaptation factor. There is also an upper bound for the adaptation factor which corresponds to the stability limit.