A constellation diagram is a representation of a digital modulation scheme in the complex plane. A digital system is one that uses discrete values rather than a continuous spectrum of values: compare analog. ... Modulation is the process of varying a carrier signal, typically a sinusoidal signal, in order to use that signal to convey information. ... The complex numbers are an extension of the real numbers, in which all non-constant polynomials have roots. ...

8-PSK constellation diagram.

The real and imaginary axes are often called the in-phase, or I-axis and the quadrature, or Q-axis. By choosing a set of complex numbers to represent the modulation symbols in this way, they may be physically transmitted by varying the amplitude of a cos wave and a sin wave since these are naturally 90° out-amplitude of the sine wave to the absolute value of the real part. The example shown here is for 8-PSK, which has also been given a Gray coded bit assignment. Constellation diagram for Gray-coded 8-PSK. File links The following pages link to this file: Phase-shift keying Constellation diagram Categories: GFDL images | User-created public domain images ... Constellation diagram for Gray-coded 8-PSK. File links The following pages link to this file: Phase-shift keying Constellation diagram Categories: GFDL images | User-created public domain images ... PSK can relate to: phase-shift keying a telecommuncations term, or; Pre-Shared Key as a method to set encryption keys in Wi-Fi Protected Access, a wireless security scheme. ... In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line. ... In mathematics, an imaginary number (or purely imaginary number) is a complex number whose square is a negative real number or zero. ... The word axis has several meanings: In geometry, it may refer to: An axis of rotation A coordinate axis An axis of symmetry In anatomy, the axis is the second cervical vertebra. ... In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ... In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ... PSK can relate to: phase-shift keying a telecommuncations term, or; Pre-Shared Key as a method to set encryption keys in Wi-Fi Protected Access, a wireless security scheme. ... A Gray code is a binary numeral system where two successive values differ in only one digit, originally designed to prevent spurious output from electromechanical switches. ...

These two carrier-wave components are both at the same frequency but may be separated at the receiver owing to their phase-difference. They are often referred to as quadrature carriers.

The diagram so-formed is called a constellation diagram and the points on it constellation points. They are a set of modulation symbols which comprise the modulation alphabet. Upon reception of the signal, the demodulator examines the received symbol, which may have been corrupted by e.g. additive white Gaussian noise and selects as its estimate of what was actually transmitted that point on the constellation diagram which is closest (in a Euclidean distance sense) to that of the received signal. Thus it will demodulate incorrectly if the corruption has meant that the received signal finishes up closer to another contellation point than the one transmitted. This process is called maximum likelihood detection. The constellation diagram allows a straightforward visualization of this process — imagine the received symbol as an arbitrary point in the I-Q plane and then decide that the transmitted symbol is whichever constellation point is closest to it. A demodulator is an electronic circuit used to recover the information content from the carrier wave of a signal. ... In communications, the additive white Gaussian noise (AWGN) channel is one in which the only impairment is the linear addition of wideband Gaussian noise with a constant spectral density (expressed as watts per hertz of bandwidth). ... The Euclidean distance of two points x = (x1,...,xn) and y = (y1,...,yn) in Euclidean n-space is computed as It is the ordinary distance between the two points that one would measure with a ruler, which can be proven by repeated application of the Pythagorean theorem. ... Maximum likelihood estimation (MLE) is a popular statistical method used to make inferences about parameters of the underlying probability distribution of a given data set. ...