#### 3.2.1. Radar Module

Radar systems can be categorized based on their radio-wave bandwidth into: narrowband (NB) and UWB. The UWB is a radio technology using either pulse (IR) or CW of very short duration, and operating on frequency range wider than 500 MHz or 25% of the center frequency. More specifically, the UWB-IR, operating over a larger bandwidth and wider range of frequencies [

20], provides additional features over UWB-CW, particularly useful in AAL (Ambient Assisted Living) contexts. The sub-millimeter range resolution and high penetration power enable the detection of very small target event through obstacles (e.g., through-wall sensing of vital signs). The shorter pulse duration, lower than the total travel time of the wave even in case of multiple reflections, is helpful to deal with multipath effects particularly insidious in indoor environments. The very low power spectral density prevents interferences with other radio systems operating in the same frequency range, and guarantees a low probability of interception; enabling secure high-data-rate communication in short range (e.g., up to 500 Mbps at 3 m).

The Time Domain PulsON P410 [

73], reported in

Figure 2a, is a state-of-the-art UWB-IR radar module, enabling precise measurements in high multipath and high clutter environments. The P410 is characterized by low cost, small size (7.6 × 8.0 × 1.6 cm board dimensions), as well as low power operation (from −33 dBm to −13 dBm) conforming to FCC requirements; all made possible by a dedicated UWB chipset, which includes various software-configurable parameters useful for application customization. The pulse waveform is a bandpass signal with frequency spectrum 3.1–5.3 GHz centred at 4.3 GHz, as exemplified in

Figure 2b, generated at a pulse repetition rate of 10 MHz, and received at sampling rate of 61 ps.

The Monostatic Radar Module (MRM) receiver architecture of P410 is represented in

Figure 3. As seen from this figure, the radar scan data are converted into 32 bins (i.e., the green-colored cells in

Figure 3), having time duration of 1.907 ps (i.e., the fast-time sampling is 31 × 1.907 ps ≈ 61 ps), and then they are stacked into a stack segment of 96 bins covering a total time of 5859.36 ps (i.e., the orange-colored cells in

Figure 3).

The distance range covered by the radar is associated with a time-axis, known as fast-time (i.e., the red colored arrow in

Figure 3), expressed in the order of nanoseconds. Conversely, the time-axis along to the sampling interval is called slow-time (i.e., the green colored arrow in

Figure 3) and expressed in microseconds. As well known, the relation between distance R and total travel time T is the following:

$\mathrm{R}=c\text{}\ast \text{}\mathrm{T}/2$, where

$c$ is the speed of the light in vacuum. However, T cannot be chosen at will, but must be quantized according to timing constraints imposed by the MRM architecture. More accurately, given a desired distance range interval

$[\tilde{\mathrm{R}1},\text{}\tilde{\mathrm{R}2}]\text{}$(with

$\tilde{\mathrm{R}1}<\tilde{\mathrm{R}2}$, in meters), the actual range interval representable within the RMR will be

$\left[\mathrm{R}1,\text{}\mathrm{R}2\right]$ that can be estimated as follows. Firstly, given

$\tilde{\mathrm{R}1}$ and

$\tilde{\mathrm{R}2}$ the total number of scan bins

N (i.e., blue colored cells in

Figure 3) can be obtained by considering that each stack bin has a time duration of 5.8594 ns and is further subdivided into 96 bins, thus:

where the angled brackets

$\lceil \xb7\rceil $ indicate the ceiling operator, and

$c\text{}=\text{}0.29979$ m/ns. Secondly, the fast-time instant T1 corresponding to R1 can be empirically estimated as follows:

where T1 is expressed in ns, the angled brackets

$\lfloor \xb7\rfloor $ indicate the flooring operator, 1.9073 ps is the time duration of a radar scan bin, and 10 ns is the minimum fast-time instant accepted by the RMR. Similarly, the instant T2 (in ns), corresponding to R2, can be empirically estimated as follows:

Finally, the actual range interval

$\left[\mathrm{R}1,\text{}\mathrm{R}2\right]$ can be estimated as follows:

Since the receiver architecture is based on several parallel samplers (i.e., rake receiver), it allows the integration of multiple scans

${S}_{k}$ in order to improve the SNR (Signal-to-Noise Ratio) of radar returns. The minimum number of integrated scans is 64 (i.e., 2

^{6}) corresponding to a SNR increase of 18 dB which further increases of 3 dB at each doubling of integrated scans, up to a maximum of 32,768 (i.e., 2

^{15}) scans, i.e., 45 dB. The time duration

${t}_{s}$ of a full scan depends on two factors: (1) the number of integrations given by

${2}^{\mathrm{PII}}$, where PII (Pulse Integration Index) spans from 6 to 15; and (2) the distance range, i.e., the size of the scan window, given by

$\mathrm{T}2-\mathrm{T}1$. Hence,

${t}_{s}$ (expressed in μs) can be estimated as follows:

where T1 and T2 are in ns, 5.8594 ns is the time duration of each stack segment, and 0.792 μs is the time duration of a scan in slow-time (see

Figure 3, green arrow direction).

In addition, between one scan and another, there is a further time interval

${t}_{i}$, so that the (slow-time) sampling frequency is given by

${F}_{s}={t}_{s}+{t}_{i}$. In the present study, the MRM parameters were selected in order to cover a distance range varying from 0.5 m to 5.77 m, at sampling frequency of

${F}_{s}=50$ Hz and with 36 dB of increase in the SNR (i.e.,

$\mathrm{PII}$ = 12). For this purpose,

$\tilde{\mathrm{R}1}$ was kept fixed at 0.5 m and

$\tilde{\mathrm{R}2}$ was increased from 1.5 to 5.5 at steps of 1 m. The corresponding RMR parameters, estimated as said above, are reported in

Table 1.

#### 3.2.2. Bandpass Filtering

Interference and noise due to various types of sources may cause undesirable signal degradation. In presence of wideband sources, the related noise has the form of short random pulses which can be significantly attenuated by integrating (and averaging) multiple received signals, thanks to the, previously described, rake receiver architecture. Instead, in the case of narrowband sources, which mainly are nearby systems generating electromagnetic interference with sinusoidal waveform and random amplitudes, usually a bandpass filtering is used to attenuate this type of noise. To this end, in the present study, the received radar signal was filtered by a 16th-order Butterworth with bandpass in the radar operating frequency range, i.e., from 3.1 to 5.3 GHz.

The filter order was obtained by considering a max. passband ripple of 3 dB and attenuation in stopband of 30 dB. Then, the stopband width was gradually decreased starting from 1.5 GHz (i.e., 3rd-order Butterworth), while measuring the time delay (execution time) due to the filtering processing. The processing workload was evaluated by filtering a radar scan at the maximum range (i.e.,

N = 576 bins) on the reference computing platform reported in

Section 3.5. A good compromise was found with 16 ns delay and 230 MHz stopband width, corresponding to a 16th-order Butterworth [

74].

#### 3.2.3. Clutter Removal

Beside noise and interference, the clutter is another problem which may reduce the SNR of radar returns. The clutter returns are unwanted signal components induced by reflection from static structures included in the environment (i.e., walls, furniture), and whose energy can be several orders magnitude larger than the useful signals reflected from the person’s body (e.g., torso, limbs, chest cavity, etc.).

In the past years, many clutter removal techniques have been investigated, which can be roughly classified as background subtraction [

75], filtering [

76], wall-parameter modeling [

77], statistical approaches [

78], and nonlinear approaches [

79]. Among these techniques, background subtraction, filtering and wall-parameter modeling are not particularly versatile, since they require underlying assumptions, such as, on either background scene (free of moving objects) or spectrum bandwidths (wall and target reflections) [

80]. Nonlinear approaches are the most general, but they are also quite computationally expensive owing to the iterative nature [

79]. Conversely, statistical approaches are the most interesting ones, since they have low computational complexity and often exhibit feature extraction capabilities.

Verma et al. compared some of the most promising statistical approaches, namely principal component analysis (PCA), independent component analysis (ICA), factor analysis (FA) and singular value decomposition (SVD) [

78]. The ICA approach gave the better result, in particular for through-wall imaging of low-dielectric targets. Instead, PCA, SVD and FA performed in a quite similar way. In this study, the SVD-based clutter-removal was chosen for its low computational cost and simplicity over the other approaches. Following this approach [

81], the signal matrix was SVD decomposed obtaining a diagonal matrix whose first “few” descending-ordered singular values conveyed the largest amount of clutter energy. By setting these singular values to zero and reconstructing the signal matrix, the clutter energy was removed and the SNR improved.

#### 3.2.4. Micro-Doppler Spectrogram Processing

In radar sensing, the velocity of the moving target can be obtained by exploiting the Doppler effect, based on which the frequency of the received signal is shifted from the frequency of the transmitted signal [

82]. The Doppler frequency shift is proportional to the radial (i.e., in the direction of the line of sight) velocity of the target: it is positive if the target approaches the radar, and negative if the target moves away. Thus, when the target is not a rigid body but has several parts characterized by an oscillatory motion (e.g., a walking human), such oscillation produces an additional Doppler frequency modulation called micro-Doppler effect [

82]. Such micro-Doppler modulation can be regarded as a distinctive signature able to account for unique properties of a target. More specifically in this study, the micro-Doppler signature is exploited to detect, localize and track a monitored person, as well as to discriminate normal activities from abnormal ones, such as falls.

The Doppler spectrogram was used first for estimating the distance of the person’s body from the radar, and then for extracting the micro-motion signature useful for both person localization and activity recognition. The body position was estimated by projecting the spectrogram on the distance range. After that, the micro-motion signature was obtained by projecting the Doppler spectrum on frequencies, but restricted to the only region of the distance range including the estimated body position. Both procedures are exemplified in

Figure 4. The Doppler spectrogram was computed by applying the discrete-time Fourier transform (DTFT) to the analytic version of the clutter-free signal, i.e., the output signal provided by the clutter removal module. As well known the analytic signal is a complex signal obtained by setting the imaginary part to be equal to the Hilbert transform of the original real signal [

83]. The DTFT length was fixed to

$N=16$, for computational efficiency reasons, to which corresponded a time duration of

${\mathrm{T}}_{\mathrm{DTFT}}=\frac{N}{\mathrm{Fr}}=$ 320 ms by considering a short-time sampling frequency of Fr = 50 Hz. As an example, the Doppler spectrum related to a walking action is depicted in

Figure 4 (top-left image).