An Efficient Exact-Least-Squares Fractionally Spaced Equalizer Using Intersymbol Interpolation

An efficient exact-least-squares procedure is presented specifically for the adaptive adjustment of a fractionally spaced equalizer (FSE). The intersymbol interpolation of the desired training sequence is used by this new procedure to reduce computational requirements and to improve convergence. For a FSE ( being the data symbol rate and the number of taps that span one symbol period), a factor of improvement in "start-up" time is attained by this new procedure in comparison to the multichannel FSE versions of the "fast-Kalman" leastsquares algorithms of Falconer and Ljung [7] and in comparison to the Ling-Proakis [10] simplification for multichannel versions of the "fastlattice" least-squares algorithms of Satorius and Pack [8 ]Substantial reductions in computational and storage requirements are also achieved by the new procedure through the elimination of the inversion of matrices in these multichannel versions. Additional reductions in computational requirements are achieved by a special exact-least-squares modification for the passband "Nyquist" FSE structure of Mueller and Werner [6]. The procedure is shown to be most efficiently implemented using a transversal-filter realization of the fast exact-least-squares algorithmns. The per-iteration and per-unit-time computational requirements of the new procedure ( FSE) are found to be approximately the same as those of the more conventional, but much slower converging, ( ) tap-leakage stochastic-gradient algorithms of Gitlin, Meadors, and Weinstein [15]. Finally, simulations are conducted to verify the operation of the new procedure for both the training and decision-directed modes of operation.