A theoretical question in echo cancellation performance evaluation: $\mathrm{ERLE}$ = $\mathrm{E}$cho $\mathrm{R}$eturn $\mathrm{L}$oss $\mathrm{E}$nhancement, is defined as $$ \mathrm{ERLE} = 10 \log_{10}\left(\frac{\mbox{power before EC}}{\mbox{power after EC}}\right) $$ Modeling the echo canceller as $x = d + e$ where $x$ is the signal received by the mic, $d$ is the desired audio and $e$ is the echo. The estimate echo by the EC is $\hat{e}$. The signal after EC is $y = x - \hat{e} = d + e - \hat{e}$.

When I want to evaluate the EC performance using $\mathrm{ERLE}$, do I need to assume or measure only when $d = 0$? That is: there is no other sound / audio signal except for the echo we wish to eliminate.


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The answer is yes. It might be misleading sometimes, when there is a concern of distorting the desired signal. But, usually, as the desired signal is uncorrelated with the reference signal, this issue may be overlooked as negligible.
So best it to compute ERLE with $d=0$.


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