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# EVM Measurement

Calculate vector magnitude difference between ideal reference signal and measured signal

Utility Blocks

## Description

Error Vector Magnitude (EVM) is a measurement of modulator or demodulator performance in an impaired signal.

While certain mask selections can change EVM block behavior, the block always has two input signals: a reference signal (at the reference port, Ref) and a corrupted signal (at the input port, In). You must select which normalization method the block uses when performing EVM calculations and which calculations you want as outputs.

The block either normalizes to the average reference signal power, average constellation power, or peak constellation power. For RMS EVM, Max EVM, and X-percentile EVM, the output computations reflect the normalization method.

The default EVM output is RMS EVM in percent, with an option of Output maximum EVM or Output X-percentile EVM values. The maximum EVM represents the worst-case EVM value per burst. For the X-percentile option, you can select to output the number of symbols processed in the percentile computations.

The following table shows the output type, the activation (what selects the output computation), computation units, and the corresponding computation duration.

OutputActivationUnitsComputation Duration
RMS EVMDefaultPercentagePer burst
Max EVMParameter settingPercentagePer burst
Percentile EVMParameter settingPercentageContinuous
Number of symbolsParameter setting if you select Output X-percentile EVMNoneContinuous

The computation duration in per burst mode spans the symbols in the present burst. The computation duration in continuous mode spans all the symbols across multiple bursts.

### Dimension

The block computes measurements for bursts of data. The data must be of length N, where N is the size of the burst. When computing RMS EVM or Max EVM, the block computes a unique output for each incoming burst; therefore, the computation duration is per burst.

The block computes the X-percentile for all incoming symbols across multiple bursts. This computation duration is the continuous mode (in contrast to the per burst duration for RMS EVM or Max EVM).

#### Input Signals

This block accepts scalar-valued or column vector input signals. The input and reference signals must have identical dimensions.

#### Output Signals

The output is always a scalar value.

### Data Type

The block accepts double, single, and fixed-point data types. The output of the block is always double type.

### Algorithms

The EVM block provides three different normalization methods. You can normalize measurements according to the average power of the reference signal, average constellation power, or peak constellation power. Different industry standards follow one of these normalization methods.

The following table lists how the block calculates the RMS EVM value for different normalization methods.

EVM Normalization MethodAlgorithm
Reference Signal

$EV{M}_{RMS}=\sqrt{\frac{\frac{1}{N}\sum _{k=1}^{N}\left({e}_{k}\right)}{\frac{1}{N}\sum _{k=1}^{N}\left({I}_{k}^{2}+{Q}_{k}^{2}\right)}}*100$

Average Power

$EV{M}_{RMS}=\sqrt{\frac{\frac{1}{N}\sum _{k=1}^{N}\left({e}_{k}\right)}{{P}_{avg}}}*100$

Peak Power

$EV{M}_{RMS}=\sqrt{\frac{\frac{1}{N}\sum _{k=1}^{N}\left({e}_{k}\right)}{{P}_{\mathrm{max}}}}*\text{​}100$

where,

ek = ${\left({I}_{k}-\stackrel{~}{{I}_{k}}\right)}^{2}+{\left({Q}_{k}-{\stackrel{~}{Q}}_{k}\right)}^{2}$

Ik = In-phase measurement of the kth symbol in the burst

Qk = Quadrature phase measurement of the kth symbol in the burst

N = Input vector length

Pavg = The value for Average constellation power

Pmax = The value for Peak constellation power

Ik and Qk represent ideal (reference) values. ${\stackrel{~}{I}}_{k}$ and ${\stackrel{~}{Q}}_{k}$ represent measured (received) symbols.

The max EVM is the maximum EVM value in a frame or $EV{M}_{\mathrm{max}}=\underset{k\in \left[1,...,N\right]}{\mathrm{max}}\left\{EV{M}_{k}\right\}$

where k is the kth symbol in a burst of length N.

The definition for EVMk varies depending upon which normalization method you select for computing measurements. The block supports the algorithms in the following table.

EVM NormalizationAlgorithm
Reference Signal

$EV{M}_{k}=\sqrt{\frac{{e}_{k}}{\frac{1}{N}\sum _{k=1}^{N}\left({I}_{k}^{2}+{Q}_{k}^{2}\right)}}*\text{​}100$

Average Power

$EV{M}_{k}=\sqrt{\frac{{e}_{k}}{{P}_{avg}}}*100$

Peak Power

$EV{M}_{k}=\sqrt{\frac{{e}_{k}}{{P}_{\mathrm{max}}}}*\text{​}100$

The block computes X-percentile EVM by creating a histogram of all the incoming EVMk values. The output provides the EVM value below which X% of the EVM values lay.

## Dialog Box

Normalize RMS error vector by:

Selects the method by which the block normalizes measurements:

• Average reference signal power

• Average constellation power

• Peak constellation power

This parameter defaults to Average reference signal power.

Average constellation power:

Normalizes EVM measurement by the average constellation power. This parameter only appears if you set Normalize RMS error vector to Average constellation power.

Peak constellation power:

Normalizes EVM measurement by the peak constellation power. This parameter only appears if you set Normalize RMS error vector to Peak constellation power.

Output maximum EVM

Outputs the maximum EVM of an input vector or frame.

Output X-percentile EVM

Enables an output X-percentile EVM measurement. When you select this option, specify X-percentile value (%).

X-percentile value (%)

This parameter only appears when you select Output X-percentile EVM. The Xth percentile is the EVM value below which X% of all the computed EVM values lie. The parameter defaults to the 95th percentile. Therefore, 95% of all EVM values are below this output.

Output the number of symbols processed

Outputs the number of symbols that the block uses to compute the Output X-percentile EVM. This parameter only appears when you select Output X-percentile EVM.

## Examples

To see an example using the EVM block, refer to Measuring Modulator Accuracy in the Communications System Toolbox™ User's Guide.

## References

[1] IEEE Standard 802.16-2004: "Part 16: Air interface for fixed broadband wireless access systems," October 2004. http://ieee802.org/16/published.html

[2] 3 GPP TS 45.005 V8.1.0 (2008-05): "Radio Access Network: Radio transmission and reception"

[3] IEEE Standard 802.11a-1999: "Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) specifications: High-speed Physical Layer in the 5 GHz Band," 1999.