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

Publish Date: Apr 02, 2012 | 24 Ratings | 2.58 out of 5 |  PDF

## Overview

This tutorial is part of the National Instruments Measurement Fundamentals series. Each tutorial in this series teaches 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 about National Instruments RF products, visit www.ni.com/rf.

## Table of Contents

### 1. 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 decibels (dB). MER over number of symbols, N 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 and
is the ideal Q component of the j-th symbol received.

### 2. Error Vector Magnitude (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, ie, e=wv. 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,
wv is the magnitude error,
θ is the phase error,
e=(wv) 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.

### 3. Related Products

NI PXIe-5663 6.6 GHz RF Vector Signal Analyzer
The National Instruments PXIe-5663 is a modular 6.6 GHz RF vector signal analyzer with 50 MHz of instantaneous bandwidth optimized for automated test.

NI PXIe-5673 6.6 GHz RF Vector Signal Generator
The National Instruments PXIe-5673 is a 4-slot 6.6 GHz RF vector signal generator that delivers signal generation from 85 MHz to 6.6 GHz, 100 MHz of instantaneous bandwidth, and up to 512 MB of memory.

NI PXI-5660 2.7 GHz RF Vector Signal Analyzer
The National Instruments PXI-5660 is a modular 2.7 GHz RF vector signal analyzer with 20 MHz of instantaneous bandwidth optimized for automated test.

NI PXI-5671 2.7 GHz RF Vector Signal Generator
The National Instruments PXI-5671 module is a 3-slot RF vector signal generator that delivers signal generation from 250 kHz to 2.7 GHz, 20 MHz of instantaneous bandwidth, and up to 512 MB of memory.

NI PXI-5652 6.6 GHz RF and Microwave Signal Generator
The National Instruments PXI-5652 6.6 GHz RF and microwave signal generator is continuous-wave with modulation capability. It is excellent for setting up stimulus response applications with RF signal analyzers.

NI RF Switches
The National Instruments RF switch modules are ideal for expanding the channel count or increasing the flexibility of systems with signal bandwidths greater than 10 MHz to bandwidths as high as 26.5 GHz.

NI LabVIEW
National Instruments LabVIEW is an industry-leading graphical software tool for designing test, measurement, and automation systems.

NI Modulation Toolkit
The National Instruments Modulation Toolkit extends the built-in analysis capability of LabVIEW with functions and tools for signal generation, analysis, visualization, and processing of standard and custom digital and analog modulation formats.

### 4. 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 about National Instruments RF products, visit  www.ni.com/rf.

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