Effects of input data correlation on the convergence of blind adaptive equalizers

A variety of blind equalization algorithms exist. These algorithms, which draw on some theoretical justification for the demonstration or analysis of their purportedly ideal convergence properties, almost invariably rely on the input data being independent and identically distributed (i.i.d.). In contrast, in this paper we show that input correlation can have a marked effect on the character of algorithm convergence. We demonstrate that under suitable input data correlation and channels: (i) undesirable local minima present in the i.i.d. case are absent for certain correlated sources implying ideal global convergence for some situations and, (ii) the most commonly employed practical algorithm can exhibit ill-convergence to closed-eye minima even under the popular single spike initialization when an eye-opening equalizer parameterization is possible.