# Persistent Homology Approach for Human Presence Detection from 60 GHz OTFS Transmissions
## 5 Results
### Performance of CFAR and Persistent Homology Detectors on Measured Data  
Firstly, we have been interested in the behavior of the conventional CFAR detector on the real data, with the non-integer ratio between the real delay and Doppler shift of the reflected components and their OTFS grid counterparts. Example results are shown in Figure 10. Through these results, we point out that the conventional CFAR detector may lead to the emergence of a number of falsely detected targets. For frames 7 and 9, all the points in the grid above the threshold are neighboring, and the detector identifies a single target. This is not the case for the three remaining example frames (23,32,52) for which the two (frames 32 and 52) or even three (frame 23) isolated objects are identified. Note that for frame number 32, the persistent homology-based detector also identifies two distinct targets.  
Figure 9: Max-hold plots of delay-Doppler profiles for example person activities—static person (**top left**), randomly walking person (**top right**), sprinting person (**bottom left**), and dancing person (**bottom right**).  
A numerical comparison of the overall performance of three used target detectors is provided in Figure 11, which shows the probability of the number of detected targets (isolated peaks in delay-Doppler images). These results have been obtained by averaging over 12 distinct realizations of single-person movement in the monitored area. Each realization contains about 300 OTFS slots on average. The results confirm a large number of falsely detected targets in the case of the basic CFAR algorithm for both configurations of guard and training cells. The use of the two remaining detectors employing the persistent homology leads to a much lower number of false targets, with the persistent homology method on the SNR map providing only a slightly higher probability of the detection of a single target (one human presence).  
To provide better insight into the performance of the three investigated detectors, Figure 12 compares the peak detection probability for three different kinds of activities--a slow walk, jumping, and a fast sprint of a person--that correspond to three distinct delay-Doppler variations--the slow changes in both delay and Doppler domains, the fast changes in the Doppler domain only, and fast changes in both delay and Doppler domains. The detectors based on the persistent homology principle achieve the best performance in the case of changes in the Doppler domain only (jumping of the person at a constant distance from the receiver). On the contrary, the worst performance is achieved for very fast changes in both delay and Doppler domains (printing person).  
Figure 11: _Cont._  
Figure 10: Conventional CFAR in the presence of delay-Doppler grid mismatch for selected OTFS frames.  
Figure 11: Comparison of various target detection techniques for two sets of training and guard cell settings of CFAR detector. Results were obtained by averaging 12 realizations of OTFS transmission, with \(\approx\)300 delay-Doppler images for each realization. During all experiments, a single person was present in the monitored environment, i.e., the expected number of detected peaks is equal to 1. In less than 10% of images, the reflection from a static object is present (distance of approx. 4.5 m, see Figure 9).  
Figure 12: _Cont._