Multiple-Input Multiple-Output (MIMO) digital communications standards usually acquire Channel State Information (CSI) by means of supervised algorithms, which implies loss of performance since pilot symbols do not convey information. We propose obtaining this CSI by using semi-blind techniques, which combine both supervised and unsupervised (blind) methods. The key idea consists in introducing a decision criterion to determine when the channel suffered a significant change. In such a case, transmission of pilot symbols is required. The use of this criterion also allows us to determine the time instants in which CSI has to be sent to the transmitter from the receiver through a low-cost feedback channel.
In this article a method is presented to find systematically the domain of attraction (DOA) of hybrid non-linear systems. It has already been shown that there exists a sequence of special kind of Lyapunov functions Vn in a rational functional form approximating a maximal Lyapunov function VM that can be used to find an estimation for the DOA. Based on this idea, an improved method has been developed and implemented in a \textit{Mathematica}-package to find such Lyapunov functions Vn for a class of hybrid (piecewise non-linear) systems, where the dynamics is continuous on the boundary of the different regimes in the state space. In addition, a computationally feasible method is proposed to estimate the DOA using a maximal fitting hypersphere.