In various applications, multiscale entropy (MSE) is often used as a feature to characterize the complexity of the signals in order to classify them. It consists of estimating the sample entropies (SEs) of the signal under study and its coarse-grained (CG) versions, where the CG process amounts to (1) filtering the signal with an average filter whose order is the scale and (2) decimating the filter output by a factor equal to the scale. In this paper, we propose to derive a new variant of the MSE. Its novelty stands in the way to get the sequences at different scales by avoiding distortions during the decimation step. To this end, a linear-phase or null-phase low-pass filter whose cutoff frequency is well suited to the scale is used. Interpretations on how the MSE behaves and illustrations with a sum of sinusoids, as well as white and pink noises, are given. Then, an application to detect attentional tunneling is presented. It shows the benefit of the new approach in terms of p value when one aims at differentiating the set of MSEs obtained in the attentional tunneling state from the set of MSEs obtained in the nominal state. It should be noted that CG versions can be replaced not only for the MSE but also for other variants.

For a battery driven terminal, the power amplifier (PA) efficiency must be optimized. Consequently, non-linearities may appear at the PA output in the transmission chain. To compensate these distortions, one solution consists of using a digital detector based on a Volterra model of both the PA and the channel and a Kalman filter (KF) based algorithm to jointly estimate the Volterra kernels and the transmitted symbols. Here, we suggest addressing this issue when dealing with cognitive radio (CR). In this case, additional constraints must be taken into account. Since the CR terminal may switch from one sub-band to another, the PA non-linearities may vary over time. Therefore, we propose to design a digital detector based on an interacting multiple model combining various KF based estimators using different model parameter dynamics. This makes it possible to track the time variations of the Volterra kernels while keeping accurate estimates when those parameters are static. Furthermore, the single and multicarrier cases are addressed and validated by simulation results. Our solution corresponds to a compromise between computational cost and bit-error-rate performance.