Convergence of Decision-Directed Adaptive Equalizer

摘要

An adaptive equalizer is used to recover a sequence of digital symbols transmitted over a noisy, dispersive and unknown linear communication channel. In this report, an adaptive decision-directed equalizer, in which the estimates of the transmitted data are used for the adaptation of the equalizer parameters, is analyzed. The stability of the limit equation associated with the stochastic adaptation algorithm is proven. The weak convergence theory is applied for the convergence of the adaptive equalizer algorithm and an ordinary differential equation (ODE) associated with the decision-directed equalizer algorithm is derived. The local stability of the ODE for the infinite dimensional equalizer case is studied. It is shown that the stable point of the ODE for the case when noise is present differs from that of the noise-free case. Also, the stable point is different from the one obtained for the linear mean square algorithm. Some bounds for the stability of the domain of the ODE are provided and stability results are obtained for the finite dimensional equalizer case.