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# MER Measurement

Measure signal-to-noise ratio (SNR) in digital modulation applications

Utility Blocks

## Description

The Modulation Error Ratio (MER) is a measure of the signal-to-noise ratio (SNR) in digital modulation applications. You can use these types of measurements to determine system performance in communications applications. For example, determining if an EDGE system conforms to 3GPP radio transmission standards requires accurate MER, Minimum MER, and 95th percentile for the MER measurements. The block measures all outputs in decibels (dB).

The MER block receives an ideal input signal (at reference port, Ref) and an AWGN corrupted signal (at input port, In). The MER block then outputs a measure of the modulation accuracy by comparing these inputs. The Modulation Error Ratio is the ratio of the average reference signal power to the mean square error. This ratio corresponds to the SNR of the AWGN channel.

The block output defaults to MER in decibels (dB), with an option of Output minimum MER or Output X-percentile MER values. The minimum MER represents the best-case MER 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
MERDefaultDecibelsPer burst
Min MERParameter settingDecibelsPer burst
Percentile MERParameter settingDecibelsContinuous
Number of symbolsParameter setting if you select Output X-percentile MERNoneContinuous

### Dimension

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

#### Input Signals

The input signals must be 1-D or 2-D sample-based column vectors or 2-D frame-based column vectors. 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

MER is a measure of the SNR in a modulated signal calculated in dB. MER over N symbols is

$MER=10*\text{​}{\mathrm{log}}_{10}\left(\frac{\sum _{n=1}^{N}\left({I}_{k}^{2}+{Q}_{k}^{2}\right)}{\sum _{n=1}^{N}\left({e}_{k}\right)}\right)dB$

The MER for the kth symbol is

$ME{R}_{k}=10*\text{​}{\mathrm{log}}_{10}\left(\frac{\frac{1}{N}\sum _{n=1}^{N}\left({I}_{k}^{2}+{Q}_{k}^{2}\right)}{{e}_{k}}\right)db$

The minimum MER represents the minimum MER value in a burst or

$ME{R}_{\mathrm{min}}=\underset{k\in \left[1,...,N\right]}{\mathrm{min}}\left\{ME{R}_{k}\right\}$

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

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

The block computes X-percentile MER by creating a histogram of all the incoming MERk values. The output provides the MER value above which X% of the MER values lay.

## Dialog Box

Output Minimum MER

Outputs the minimum MER of an input vector or frame.

Output X-percentile MER

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

X-Percentile value (%)

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

Output the number of symbols processed

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