Precoding based on matrix decomposition for faster-than-Nyquist signaling
We extend the concept of faster-than-Nyquist (FTN) signaling to linear digital modulation using arbitrary modulation pulses, called generalized faster-than-Nyquist signaling (GFTN). A universal definition of nominal bandwidth is given so that “how fast” can be measured for GFTN like FTN using T-orthogonal pulses. The capacities and their asymptotic behaviors are compared between GFTN and Nyquist signaling. We show that the gain of GFTN increases unboundedly with SNR. In high SNR regime the power gain is considerable. Our extension from FTN to GFTN gives more freedom on the design of pulses to achieve good performance and acceptable detection complexity.