A review of faster than Nyquist signaling with an extension to four-level modulation

Faster than Nyquist signals transmit data with non-orthogonal pulses. They carry up to twice the bits of orthogonal methods per Hz and second, have a more favorable Shannon capacity, and can achieve bandwidth-efficiencies above 5 bits/Hzs. They can be coded or not. When coded they usually require iterative decoding, but perform relatively near capacity for schemes with their complexity. This paper is a tutorial on the present art, and it presents new work that extends FTN to 4-level modulation. Certain components of the method must change, including intrinsic information subtraction, code design and the BCJR algorithm.