A new mathematical analysis of the cyclic prefix effect on removing ISI and ICI in DMT systems

In this paper, a new mathematical analysis is presented that shows the effects of cyclic prefix insertion on removing inter symbol interference (ISI) and inter carrier interference (ICI) in the discrete multi-tone (DMT) systems. In the DMT, for subcarriers modulating, the input data stream is divided into lower rate sub-streams. The ISI is eliminated almost entirely by adding a guard interval (GI) at the beginning of each DMT symbol. However, rather than using an empty GI, this interval is filled with the end part of the DMT symbol. Through this method ISI and ICI are avoided. In all the previous works, the authors have shown the above results by only matrix analysis, without any information insight in different steps, but in this work we analyze it by a new method via signal processing analysis for the first time. Therefore, one knows what will be happen for every symbol in each step.