On the Rapid Initial Convergence of Least-Squares Equalizer Adjustment Algorithms

Adaptive equalizers are important building blocks in modems for digital data transmission over linear dispersive channels. They adaptively mitigate the adverse effects of intersymbol interference. A critical parameter in the start-up performance of modems is the speed of convergence of the equalizer adjustment algorithm. The overall data throughput depends on it and, consequently, a high convergence speed is desirable. Various different equalizer structures are known at this time. In the following, we concentrate on the frequently used transversal filter 2345 structure.1 Many equalizer update algorithms are based on the steepest descent, or gradient technique, which minimizes the mean-squared error (mse) between the equalizer output and the transmitted data symbols.2 In particular, the stochastic approximation of the gradient algorithm with an mse criterion is used frequently. The convergence speed of this algorithm was analyzed in Refs. 3 and 4. It was found to be dependent on the number of coefficients used and, to a lesser degree, on the eigenvalue spread of the channel autocorrelation matrix. Several methods to improve the convergence speed of the gradient algorithm were published in Refs. 5 to 8. In Ref. 5, prior knowledge of the transmission channel is assumed and a transformation of the received signal is proposed which reduces the effect of a large eigenvalue spread on the convergence speed, whereas in Ref. 6 a transformation of the correction vectors, yielding the same performance, is proposed.