Study of the Effect of Interleavers on the Power Spectral Density Application to the Matrix Interleaver

Abstract

Interleavers used to be considered with a temporal approach. Hence, no work has ever proposed a theoretical study of the frequency effect of an interleaver and we propose here to address this issue. This work is chiefly motivated by the recent use of interleavers as a Spread Spectrum tool. For that purpose, we first point out the equivalence between Periodic Clock Changes (PCC) and interleavers. Furthermore, because of its Linear Periodic Time Varying (LPTV) nature, a PCC turns any Wide Sense Stationary (WSS) process into a Wide Sense Cyclostationary process (WSC). Then, we propose to stationarize the output of a PCC in order to derive a theoretical expression of the output Power Spectral Density (PSD). Thanks to the previous equivalence, this result can be applied to any interleaver and we propose to investigate the frequency effect of the matrix interleaver.