Editing Phase-shift keying (section)

==Introduction==
There are three major classes of [[digital modulation]] techniques used for transmission of [[Digital data|digital]]ly represented data:

* [[Amplitude-shift keying]] (ASK)
* [[Frequency-shift keying]] (FSK)
* Phase-shift keying (PSK)

All convey data by changing some aspect of a base signal, the [[carrier wave]] (usually a [[sinusoid]]), in response to a data signal. In the case of PSK, the phase is changed to represent the data signal. There are two fundamental ways of utilizing the phase of a signal in this way:

* By viewing the [[Phase (waves)|phase]] itself as conveying the information, in which case the [[demodulator]] must have a reference signal to compare the received signal's phase against; or
* By viewing the ''change'' in the phase as conveying information{{snd}} [[#Differential encoding|''differential'']] schemes, [[#Differential phase-shift keying .28DPSK.29|some]] of which do not need a reference carrier (to a certain extent).

A convenient method to represent PSK schemes is on a [[constellation diagram]]. This shows the points in the [[complex plane]] where, in this context, the [[real number|real]] and [[imaginary number|imaginary]] axes are termed the in-phase and quadrature axes respectively due to their 90° separation. Such a representation on perpendicular axes lends itself to straightforward implementation. The amplitude of each point along the in-phase axis is used to modulate a cosine (or sine) wave and the amplitude along the quadrature axis to modulate a sine (or cosine) wave.  By convention, in-phase modulates cosine and quadrature modulates sine.

In PSK, the [[constellation diagram|constellation points]] chosen are usually positioned with uniform [[angle|angular]] spacing around a [[circle]]. This gives maximum phase-separation between adjacent points and thus the best immunity to corruption. They are positioned on a circle so that they can all be transmitted with the same energy. In this way, the moduli of the [[complex number]]s they represent will be the same and thus so will the amplitudes needed for the cosine and sine waves. Two common examples are "binary phase-shift keying" ([[#Binary phase-shift keying (BPSK)|BPSK]]) which uses two phases, and "quadrature phase-shift keying" ([[#Quadrature phase-shift keying (QPSK)|QPSK]]) which uses four phases, although any number of phases may be used. Since the data to be conveyed are usually binary, the PSK scheme is usually designed with the number of constellation points being a [[power (mathematics)|power]] of two.