ITU E-model

The E-model [68] was originally designed to evaluate the quality of the public switched telephony network (PSTN) by taking into account the encoding distortion, delay and delay variation, echo etc. However, people use this metric to evaluate the quality of Voice over IP (VoIP) applications [36]. The advantage of this metric over all the other mentioned ones is that it does not require the access to the original speech signal. Thus, it is computationally simple and can be used in real-time applications. However, as we will show in Section 5.5, this metric is not reliable as the correlation coefficient is very bad with subjective quality tests. This is not surprising because the metric output is calculated from this very simple equation:

$$R=R_0-I_s-I_d-I_e+A,$$

where, $R$ is the metric output, $R_0$ corresponds to the quality with no distortion at all, $I_s$ corresponds to the impairment of the speech signal itself, $I_d$ corresponds to the impairment level caused by the delay and jitter, $I_e$ corresponds to the impairments caused by the encoding artifacts and $A$ is the expectation factor, which expresses the decrease in the rating R that a user is willing to tolerate because of the access advantage that certain systems have over traditional wire-bound telephony. As we can see, this metric evaluates the quality by linear transformation, however the quality is nonlinear with respect to all the affecting parameters.