Constellation diagram

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A constellation diagram is a representation of a digital modulation scheme in the complex plane.

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 cosine wave and a sine wave since these are naturally 90° out-of-phase with one another and are a convenient representation of the two axes. The amplitude of the cos wave (or sin wave) is set to the absolute value of the imaginary part of the symbol to be transmitted and the amplitude of the sin wave (or cos 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.

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 constellation 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.