Bandwidth-Efficient Digital Modulation with Application to Deep-Space Communications

Chapter 5

Strictly Bandlimited Modulations with Large Envelope Fluctuation (Nyquist Signaling)

Nyquist signaling schemes, which by the very nature of their construction are strictly bandlimited, clearly result in the most bandwidth-efficient modulations of all the ones considered previously in this monograph; however, they also result in modulations with the largest envelope fluctuation. Since the theory of Nyquist signaling is well documented in many textbooks on digital communications, e.g., [1–3], we shall present here only a brief summary of the basic principles simply as a matter of completeness. Although most of the discussion will be focussed on single-channel binary signaling, the extension to multilevel and quadrature signaling schemes such as QAM will be immediately obvious and will receive a brief treatment.

5.1 Binary Nyquist Signaling

The Nyquist criterion is a condition imposed on a waveform that results in zero ISI when a sequence of such waveforms amplitude-modulated by the data is sequentially transmitted at a fixed data rate. Specifically, a binary Nyquist signal is one whose underlying pulse shape, p(t), has uniform samples taken at the bit rate, 1/T_b (i.e., herein referred to as the Nyquist rate), that satisfy

Since the Nyquist criterion is derived based on the sampling theorem, the signals to which it is applied are inherently strictly bandlimited. To see this, ...