Exact analysis of the tracking capability of time-varying channels: the finite alphabet inputs case

The tracking performances of adaptive filters are, analyzed in a real context of digital transmission where the time variations of the channel's "impulse response" are modeled by a general L-order Markovian process and where the input data to be transmitted belongs to a finite alphabet. In this paper two approaches are developed to analyse the Least Mean Square algorithm (LMS), for large step size and correlated inputs. However, it is the tailored approach for the finite alphabet inputs that leads to the exact analysis of tracking performances. In this case, the analysis is made without any constraints or unrealistic hypothesis.