Error vector magnitude

The error vector magnitude or EVM is a measure used to quantify the performance of a digital radio transmitter or receiver. A signal sent by an ideal transmitter or received by a receiver would have all constellation points precisely at the ideal locations, however various imperfections in the implementation (such as carrier leakage, low image rejection ratio, phase noise etc.) cause the actual constellation points to deviate from the ideal locations. Informally, EVM is a measure of how far the points are from the ideal locations.

Transmitter EVM can be measured by specialised equipment, which demodulates the received signal in a similar way to how a real radio demodulator does it. One of the stages in a typical phase-shift keying demodulation process produces a stream of I-Q points which can be used as a reasonably reliable estimate for the ideal transmitted signal in EVM calculation.

Definition

An error vector is a vector in the I-Q plane between the ideal constellation point and the point received by the receiver. Its average length (or magnitude), defined as the Euclidean distance between the two points, is the EVM.

The error vector magnitude is equal to the ratio of the power of the error vector to the root mean square (RMS) power of the reference. It is defined in dB as:

:$mathrm\{EVM\; (dB)\}\; =\; 10\; log\_\{10\}\; left\; (\; \{P\_mathrm\{error\}\; over\; P\_mathrm\{reference\; ight\; )$

where P_error is the RMS power of the error vector, and P_reference is the RMS power of ideal transmitted signal.

EVM is defined as a percentage in a compatible way:

:$mathrm\{EVM\; (\%)\}\; =\; sqrt\{\; \{P\_mathrm\{error\}\; over\; P\_mathrm\{reference\; \}\; *\; 100\%$

with the same definitions.

EVM has been used also for modulation formats that use more complex constellation diagrams. It is closely related to the modulation error ratio (MER), but for EVM the power of the constellation point with the highest power is used as the reference power.

ee also

*Modulation error ratio
*Carrier to Noise Ratio
*Signal-to-noise ratio