*5.1. Experimental Setup*

In our experiments we consider a data set composed by nineteen subjects who repeated each activity for three times, for a total of 168 different acquisitions. Three different activities were examined:


Note that we do not consider a data set built ad hoc: each subject was simply asked to walk in a "slow" or in a "fast" way, without specifying the number of steps or the time required to complete the activity, in order to generate data as realistic as possible. In addition acquisitions belonging to subjects of different height and weight were collected to provide a set comprehensive of a large variety of characteristics. Walking speed difference is subtle and depends on the person examined, who interpreted it subjectively. In general, the average speed measured for the fast walk is around 2 m/s, while for the slow walk, with both free hands or hands in pockets is about 1.2 m/s. Differences in subjects' speed, including the "holding the arm" case (which is similar to our "hands in pockets"), have been considered in References [45,46], although their datasets were composed by 8 and 3 subjects, respectively.

The radar configuration parameters are chosen according to the measurement area selected and to the kind of activity required to the subjects. Some parameters are chosen according to the following range *R* equation

$$R = \frac{f\_{\text{heat}} \cdot c}{2 \cdot S},\tag{4}$$

where *fbeat* is the beat frequency and *c* is the speed of light. We can evaluate the maximum speed of the target as

$$
\omega\_{\text{targe}} = \frac{\lambda}{4 \cdot t\_{\text{chirp}}},\tag{5}
$$

where *λ* represents the wavelength of the transmitted signal and *tchirp* is the time duration of the chirp. The measurement area is an hallway, about 12 meters long, and is free of furniture. During each activity the subject goes from the starting point in front of the RADAR to a distance of about 9 meters, and then comes back. Due the fact that the measurement time is of 16 seconds, it is possible that the acquisition ends before the subject returns to the initial position. The parameters used for the measurements are reported in Table 1.

A first analysis has been made on the background without any subject, which is depicted in Figure 7. Only one measurement has been performed, since the test area is the same for all the subjects. From this analysis is possible to see that the background does not affect the measurements, thus we can neglect its effect in the movements classification.

**Figure 7.** Analysis on the background in absence of subjects using (**a**) Range-Doppler map and (**b**) Doppler-Time map.

In Figure 8 we show an example a subject walking in different ways, displaying both Range-Doppler maps (on the left) and Doppler-time maps (on the right). It is possible to observe that slow and fast walk are easily recognizable in the maps. As expected, maps related to slow walk with hands in pockets present a slightly less evident Doppler with respect to free hands, but this effect is scarcely noticeable.

**Figure 8.** Example of a person walking slowly (**<sup>a</sup>**,**b**), slowly with hands in pockets (**<sup>c</sup>**,**d**) and fast (**<sup>e</sup>**,**f**).


### **Table 1.** RADAR parameters.
