Properties of faster-than-Nyquist channel matrices and folded-spectrum, and their applications

Faster-than-Nyquist (FTN) signaling has recently emerged as a potential technology for the next generation mobile, long-haul optical, and satellite broadcasting. The fundamental features of the FTN signaling including the number of signaling dimensions, the theoretical capacity limits, and the optimal power allocation can be inferred from the structure of the discrete-time FTN channel matrices. In particular, their eigenvalues are closely related to a function of frequency known as folded-spectrum. This work studies key properties of the FTN channel matrices and the folded-spectrum, and elucidate precise relationships between the two. We then apply the presented properties to provide key insights in to FTN signaling including how many signaling dimensions FTN has access to, qualities of those dimensions, and how fast should the symbol rate be for the FTN signaling.