Signal design for PAM data transmission to minimize excess bandwidth

In a conventional PAM data transmission system, the transmitted signal is x(t) = Σ α
n
g(t - nT), where {α
n
} is a 2
^L
-level data sequence, and g(t) is a Nyquist pulse (g(0) ≠ 0, g(mT) = 0, m ≠ 0). Ideally, the bandwidth of the pulse g(t) and, therefore, the bandwidth of x(t) can be made equal to 1/2T = ρ/2L, where ρ is the data rate. In practice, however, an “excess bandwidth” of at least 10 to 20 percent is required. Using a class of real sequences called “discrete prolate spheroidal sequences,” we show how to construct a modulated signal with bandwidth just slightly in excess of the optimal ρ/2L (say, by 2 to 4 percent). The new signal is similar in many ways to a conventional PAM signal, and in particular an ad-hoc receiver structure is suggested for which the resulting error performance is about the same as for a conventional PAM system operating in the same environment.