# MER & CNR
###### tags: `signal` `MER` `CNR`

$\mathrm{MER(dB)={10}\log_{10} \left(\dfrac{{P}_{signal}}{P_{error}}\right)}$

$\mathrm{MER(\%)=\sqrt{\dfrac{P_{error}}{P_{signal}}}\ \times 100\%}$

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$\mathrm{CNR=\dfrac{C}{N}= \left(\dfrac{{V}_{C}}{{V}_{N}}\right)^2}$

$\mathrm{\begin{split}CNR(dB) &=
{10}\log_{10} \left(\dfrac{C}{N}\right)\\
&=C_{dBm}-N_{dBm}\\
&={10}\log_{10} \left(\dfrac{{V}_{C}}{{V}_{N}}\right)^2\\
&={20}\log_{10} \left(\dfrac{{V}_{C}}{{V}_{N}}\right)\end{split}}$