Modulation Error Ratio (MER) and Error Vector Magnitude (EVM)

This tutorial is part of the National Instruments Measurement Fundamentals series. Each tutorial in this series, will teach you a specific topic of common measurement applications, by explaining the theory and giving practical examples. This tutorial covers an introduction to RF, wireless and high-frequency signals and systems.

For the complete list of tutorials, return to the NI Measurement Fundamentals Main page or for more RF tutorials refer to the NI RF Fundamentals main subpage. For more information on National Instruments RF products, visit www.ni.com/rf.

Modulation Error Ratio (MER)

The modulation error ratio (MER) is a measure of the signal-to-noise ratio (SNR) in a digitally modulated signal. Like SNR, MER is usually expressed in dB. MER over N number of symbols is defined as:

In this equation,
Ij is the I component of the j-th symbol received,
Qj is the Q component of the j-th symbol received,
~Ij is the ideal I component of the j-th symbol received, and
~Qj is the ideal Q component of the j-th symbol received.

Error Vector Magnitude (EVM)

Error vector magnitude (EVM) is a measurement of demodulator performance in the presence of impairments. The soft symbol decisions obtained after decimating the recovered waveform at the demodulator output are compared against the ideal symbol locations. The root mean square (rms) error vector magnitude and phase error are then used in determining the EVM measurement over a window of N demodulated symbols.
As shown in the figure below, the symbol decision output 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, ie, e=w–v. The error vector e for a received symbol is graphically represented as follows:


where:
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:
Ij is the I component of the j-th symbol received,
Qj is the Q component of the j-th symbol received,
~Ij is the ideal I component of the j-th symbol received,
~Qj is the ideal Q component of the j-th symbol received.

EVM is related to the modulation error ratio, or MER and ρ. There is a one-to-one relationship between EVM and MER. And while EVM measures the vector difference between the measured and ideal signals, ρ measures the correlation between the two signals.

Related Products

NI PXI-5660 2.7 GHz RF Vector Signal Analyzer
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NI PXI-5671 2.7 GHz RF Vector Signal Generator
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Conclusion

For the complete list of tutorials, return to the NI Measurement Fundamentals Main page or for more RF tutorials refer to the NI RF Fundamentals main subpage. For more information on National Instruments RF products, visit www.ni.com/rf.

Reader Comments | Submit a comment »

Thank you for your explanation of the MER and EVM. I do not understand the statement in which MER and EVM have a one-to-one relationship. If they did wouldn't their ratio be one? Since EVM uses the max ideal vector as a reference while MER uses the square sum of all ideal vectors the relationship cannot be one to one unless the max vector and the square sum are equal. Perhaps this is the case for QPSK, but not for higher modulation modes like 16QAM, 64QAM etc.. We have been discussing this at work for a while. Perhaps you can shed some light. Thank you
- Feb 28, 2008