Digital communication systems transmit multiple bits, encoded as magnitude and phase at a specific time point or at a specific sub-carrier frequency, depending on the type of modulation used. Filtering is used to limit the bandwidth and to minimise receiver noise. This chapter outlines the formation of the constellation diagram and the use of ‘error vectors’, deviation from the ideal constellation points, containing contributions from both the transmitter and the receiver. Error vectors can be used to characterise impairments or reported as a single-parameter ‘error vector magnitude’ (EVM), which can be used directly as a measurement tool to assess parameters and systems. The IEEE 1765 standard uses known data, but in general the data is not known in advance, and the nearest constellation point is selected, leading to a saturation of the EVM value. We describe statistical methods to recover the true constellation point of a repeated data sequence.