Analysis of modified "Bussgang" algorithms (MBAs) for channel equalization

In previous papers, we introduced two modified "Bussgang" algorithms (MBAs) for blind-channel equalization based on Bayesian iterative estimation of the source sequence. They were developed in order to reduce the computational complexity of the original "Bussgang" algorithm as well as to make it more flexible by introducing a kind of source adaptivity. However, the previous work relied on some heuristic findings, validated by a series of computer-based experiments. The aim of this paper is to present a theoretical investigation of some particular aspects of the adapting equations, namely, the steady-state conditions, in order to ameliorate the performances of the MBAs and to better explain their numerical behavior.