Time Domain Metrics

The most straightforward approach for model performance assessment is to evaluate its prediction error that corresponds to the discrepancy between the desired and estimated output signals in the time domain. In fact, the model equation as well as the input and output signals are naturally described in a time domain. Two time domain metrics have been regularly utilized for the performance assessment of behavioral models: the normalized mean square error (NMSE) and the memory effects modeling ratio (MEMR). These metrics, which are computed using the signal ydesired(n) and yestimated(n) shown in Figure 3.4, are defined next.

Normalized Mean Square Error

The NMSE is commonly used for the performance assessment of behavioral models. It is often expressed in decibels, and is defined according to:

where L refers to the length of each of the time domain waveforms ydesired(n) and yestimated(n). The accuracy of a model is inversely proportional to the NMSE since a lower NMSE value indicates a superior model accuracy. Given that the power in the adjacent channels is usually much lower than that in the in-band and that the NMSE is calculated in the time domain where the contribution of these different bands is blended, this metric mainly reflects the performance of the model and its accuracy in the in-band region of the DUT output spectra [1,2]. Thus, it is less sensitive for detecting discrepancies between the desired and estimated signals in the adjacent channels than in the in-band frequency range. Moreover, since memory effect contributions to the behavior of the DUT are much less significant than that of the static distortions, the NMSE metric applied in accordance with the setting of Figure 3.4 does not precisely expose the ability of the model to mimic the memory effects of the DUT. Thus, in behavioral modeling applications, the NMSE calculated from the signals at the output of the DUT and its model is not a reliable approach to estimating the memory depth of the system being modeled.

 
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