*2.2. Transmitted Signals*

Signals are transmitted using Frequency Modulated Continuous Wave (FMCW) modulation, this requires that the transmission frequency varies linearly from a minimum value to a maximum value in a time interval, called *chirp* time. The transmitted chirps are grouped into frames. Inside each frame, which has a time duration called *periodicity*, the radar transmits a certain number of chirps, as schematized in Figure 1.

**Figure 1.** RADAR frame periodicity.

Each chirp is built as shown in Figure 2. We have an *Idle Time*, needed because the ramp generator requires some time to restart the ramp and generate a new chirp. Then a guard time, or analog-to-digital converter (ADC) Valid Start Time, is considered in the first part of the ramp, which is not linear and may lead to a performance reduction, as described in Reference [39].

**Figure 2.** Chirps timing.

Then we have the effective ADC Sampling Time, which represents the time duration of the ramp acquired by the radar. Within this interval analog-to-digital converters (ADCs) samples of the IF signals are collected. As easily observable in Figure 2, a time shorter than the total ramp time *tramp* is used, so the used radar bandwidth *B* is smaller than the maximum possible *TB*, and is calculated as

$$B = AD \mathbb{C}\_{\text{SamplingTime}} \cdot S \le TB = t\_{ramp} \cdot S\_\star \tag{1}$$

where *S* represents the slope of the ramp and *ADCSamplingTime* is given by the product between the the number of samples *nsamples* acquired for each chirp and the sampling period *tsampling*. The devices configuration must take in account these parameters in order to avoid as much as possible the non linear effects of the sensor.

The importance of avoiding the first part of the ramp is evident from the analysis of the intermediate frequency (IF) signal during time and on the complex plane. As briefly described in Reference [40], it is possible to see this effect on the IQ plot. Using different calibrations, the first with analog-to-digital converter (ADC) Valid Start Time equal to zero, and the second with time equal to 6 μ*s* it is possible to observe how this imperfection can be avoided without the need of using an algorithm. Figure 3a shows 500 samples of IF signal across two different chirps. If the guard time is not used, there is a spike at the beginning of the first chirp. In Figure 3b the case of the same segmen<sup>t</sup> of IF signal, with an analog-to-digital converter (ADC) Valid Start Time of 6 μ*s* is depicted, not showing the same effect. The spike disappears with a minimum value of 3 μ*s*.

**Figure 3.** IF signal (**a**) without guard interval, highlighting the presence of a spike, and (**b**) with guard interval.
