Improved Methods of Accelerating the Convergence of Adaptive Equalizers for Partial-Response Signals

In order to accelerate the convergence of adaptive equalizers for partial-response signals it is necessary to transform the input signal, and use the transformed values in one of two ways-to calculate both the equalizer output and the tap updates, or to calculate only the tap updates. These methods are called double-sided and single-sided orthogonalizalion, respectively; this paper confirms previous suggestions that the latter is preferable. In an early implementation of the double-sided orthogonalization (DSO) the number of multiplications was proportional to the square of the number of taps (N
²
); this was later reduced to
2N
multiplications; the only implementation of single-sided orthogonalization (SSO) that has been described used of the order of N
²
multiplications. This paper describes an implementation of SSO that needs only
2N
multiplications,and gives explicit formulas for the two partial-response systems of most interest-I and IV. Two examples of the improved convergence are given, and the application of this method to complex equalizers is discussed.