In order to move data through a communications channel a modulator at the transmitter applies a succession of transformations to a binary data stream. The demodulator at the receiver must invert these transformations to form estimates of the data stream originally presented to the modulator. A typical set of transformations are the mapping of binary data to symbol amplitudes, mapping the symbol amplitudes to baseband symbol waveforms, and spectral translation of the baseband waveforms to a carrier centered version for ease of insertion into the channel. The ideal channel delivers a noisy timedelayed version of the signal to the receiver. The receiver then applies the inverse transformations consisting of a spectral translation to baseband, matched filtering to minimize noise while mapping the symbol waveforms back to symbol amplitudes, and a detector to map the symbol amplitudes back to binary data.

We assume of course that the receiver has knowledge of the frequency and phase of the carrier required for the down conversion process, and has knowledge of the frequency and phase of the waveform symbol boundaries required for the matched filter processing. In fact, the receiver does not have this knowledge and must extract it from the received signal as a background task while performing the primary signal processing tasks. The task of recovering the carrier and timing information from the signal is performed by a set of phase locked loops (PLL). The PLLs may be assisted in their tasks by the presence of pilot signals and training waveforms delivered with the waveform modulated signal. In early point-to-point communication tasks, the handshake that initiated the communication link provided the necessary training signals to the PLLs.

Many modern communication systems do not include pilot and training signals. The demodulator must extract the carrier and timing information from the received signals based on secondary signal properties related to excess bandwidth and state transition activity. This tutorial reviews the process of extracting carrier information from received signals. As an aside, when very bad channels are encountered, these secondary clues are too unreliable and pilot and training signals must accompany the data signal. Timing recovery is the topic of another tutorial.