Error vector magnitude
The error vector magnitude or EVM (sometimes also called receive constellation error or RCE) 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. In other words, it is the difference between actual received symbols and ideal symbols. The average power of the error vector, normalized to signal power, is the EVM. For the percentage format, root mean square (RMS) average is used.
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:
where Perror is the RMS power of the error vector. For single carrier modulations, Preference is, by convention, the power of the outermost (highest power) point in the reference signal constellation. More recently, for multi-carrier modulations, Preference is defined as the reference constellation average power.[1]
EVM is defined as a percentage in a compatible way:
with the same definitions.
EVM, as conventionally defined for single carrier modulations, is a ratio of a mean power to a peak power. Because the relationship between the peak and mean signal power is dependent on constellation geometry, different constellation types (e.g. 16-QAM and 64-QAM), subject to the same mean level of interference, will report different EVM values.
EVM, as defined for multi carrier modulations, is arguably the more satisfactory measurement because it is a ratio of two mean powers and is insensitive to the constellation geometry. In this form, EVM is closely related to Modulation error ratio, the ratio of mean signal power to mean error power.