Convergence Criteria for Transversal Equalizers
Dean W. Lytle · Bell System Technical Journal · 1968
Two basic problems in the equalization of data channels using pulse-amplitude modulation are considered. The first of these is to determine just what pulses can be equalized and what the general equalization solution is when using a transversal filter. The second problem is to determine if a simple iterative search routine will converge to a solution if its exists. The unequalized channel impulse response is represented by a polynomial whose coefficients are the sample values of the impulse response. If no roots of this polynomial lie on the unit circle, the channel can be equalized. The transversal filter which equalizes the pulse has tapweight values given by weighted sums of powers of the polynomial roots. Various necessary and sufficient conditions for iterative convergence are developed. Iterative convergence can be guaranteed if the proper linear weighting of the output sample errors is used in adjusting the tap-weights.