# Modulation Error Ratio

The Modulation Error Ratio describes the quality of an modulated digital signal, and gives a hint how fuzzy symbols in a constellation are.

It is defined as the average power of symbols to the average power of the vector between ideal symbol position and real symbol position in constellation diagram:

```MER = Psym/Perr
```

or, in logarithmic scale

```MER(dB) = 10 * log10(Psym/Perr) [dB]
```

with

```Psym : average symbol power = sum(I.j^2  + Q.j^2)  w. j = 1..N
Perr : average error power  = sum(dI.j^2 + dQ.j^2) w. j = 1..N
```

The higher MER is, the better transmitted symbols can be recognized. If MER is too low, bit errors will happen.

On the other hand, high MER values doesn't guarantee for good SNR values, if bursts or intermittent interference occur.

TODO: formula as image.

TODO: add image for symbol error vector in I/Q plane.
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