error vector maginitude (EVM)

Error vector magnitude (EVM) is a measurement of demodulator performance in the presence of impairments. The measured symbol location obtained after decimating the recovered waveform at the demodulator output are compared against the ideal symbol locations. The root-mean-square (RMS) EVM and phase error are then used in determining the EVM measurement over a window of N demodulated symbols.

As shown in Figure 1 below, the measured symbol location by the demodulator is given by w. However, the ideal symbol location (using the symbol map) is given by v. Therefore, the resulting error vector is the difference between the actual measured and ideal symbol vectors, that is, e=w–v. The error vector e for a received symbol is graphically represented as follows:

Figure 1. Graphical Representation of Error Vector

In Figure 1,
v is the ideal symbol vector,
w is the measured symbol vector,
w–v is the magnitude error,
θ is the phase error,
e=w–v) is the error vector, and
e/v is the EVM.

This quantifies, but does not necessarily reveal, the nature of the impairment. To remove the dependence on system gain distribution, EVM is normalized by |v|, which is expressed as a percentage. Analytically, RMS EVM over a measurement window of N symbols is defined as

where
 is the I component of the j-th symbol received,
 is the Q component of the j-th symbol received,
 is the ideal I component of the j-th symbol received,
 is the ideal Q component of the j-th symbol received.

EVM is related to the MER and ρ, where ρ measures the correlation between the two signals. EVM and MER are proportional.

Refer to the RF & Communications Resources page for additional information about RF terminology, fundamentals, and National Instruments RF products.

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