Faster-Than-Nyquist Signaling

The use of Nyquist pulses g(t) sin (irt/T) (Tt/T) to send binary (or multilevel) data without intersymbol interference over a channel of bandwidth W = (l/2T)Hz is classic. If we assume t h a t one receives the pulse train u(t) = Aj T £ ang{t -- nT), an = ± 1, independently, (1) n=N in additive white gaussian noise of two-sided spectral density Nq/2, then the optimum detector has a bit-error rate P e given by 1451 where Q(x) = ~^ J" e~vil2dy = >er f c ^ (3)