Unit content
Signal constellations and decision regions
A coherent digital modulation can represent each possible symbol by a point in a signal space. For I/Q modulation, that point has coordinates
$$(I,Q).$$
The set of allowed points is the constellation.
The receiver observes a point that may differ from the transmitted one because the communication path and measurement are imperfect. It therefore divides the signal plane into decision regions and chooses the symbol associated with the region containing the observation.
A common decision rule chooses the constellation point with the smallest Euclidean distance to the received point. Whether that rule is statistically optimal depends on the disturbance model and prior symbol probabilities.
Constellation geometry makes trade-offs visible. Points farther apart are easier to distinguish, while packing more points into a fixed signal range allows more bits per symbol but reduces the distance between alternatives.
A constellation describes symbol geometry, not pulse timing. Pulse shaping determines how successive constellation symbols are turned into a continuous waveform.