The basics of digital modulation over additive white Gaussian noise (AWGN) channels are studied. To facilitate a formal study, the concepts of signal space and signal constellations are introduced. The Gram–Schmidt orthonormalization procedure, a systematic method to obtain an orthogonal and normalized basis for a given set of signals, is described. Binary antipodal signaling is studied in detail; the MAP and ML receivers are derived, and the average probability of error is computed. The concepts are then generalized to the case of M-ary signaling, and the union bound is introduced as a performance analysis tool. Correlation-type and matched filter-type receivers are described. The properties of the matched filter are summarized. Different signal constellations are compared in terms of their error rate performance through a simplified (asymptotic) analysis. As specific examples, the details of two important digital modulation schemes, pulse amplitude modulation and orthogonal signaling, are given. Finally, timing recovery techniques are briefly studied.