Analysis of communication systems using iterative methods based on Banach’s contraction principle

In this paper, the application of a well known mathematical theorem, Banach´s fixed point theorem (Banach, 1922), is investigated in iterative signal processing in communications. In most practical communication systems some sort of a contraction mapping is used to enhance the operation of the system. Thus, using a suitable iterative approach, one can set the system in its fixed point and hence, the distortion produced in the transmitter, channel and the receiver can be compensated. In other words, a loosely designed transceiver can be enhanced by an iterative method. In order to verify the truth of the proposed iterative method, the distortion of A/D and D/A converters is compensated at the receiver. Although analyses are performed on a linear system, they could be generalized to non linear ones.