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 T/p FSE ( 1/T being the data symbol rate and p the number of taps that span one symbol period), a factor of p 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 p \times p 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 ( T/4 FSE) are found to be approximately the same as those of the more conventional, but much slower converging, ( T/2 ) 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.
['John M. Cioffi', 'Thomas Kailath']
An Efficient Exact-Least-Squares Fractionally Spaced Equalizer Using Intersymbol Interpolation