# Persistent Homology Approach for Human Presence Detection from 60 GHz OTFS Transmissions
## 1 Introduction  
In the past ten years, there has been continuous research on replacing camera-based technology with their counterparts employing radio signal transmissions [1]. For example, Ultra Wide Band (UWB) [2] or Frequency-Modulated Continuous-Wave (FMCW) [3] signals were widely investigated to detect the presence and location of individuals or groups of persons. The sixth generation (6G) wireless communication systems are expected to closely integrate sensing together with wireless communication. One of the key enablers for high-precision sensing is the envisaged exploitation of higher-frequency bands, either in millimeter-wave (mm-wave), sub-THz or even THz frequencies [4]. Integrated Communication and Sensing (ICaS) systems [5] have the potential to provide an alternative to dedicated environment sensing and person monitoring technologies used, e.g., for home control, elderly people fall detection, gaming, or person vital function monitoring applications. This has already been reflected in standardization activities. Recently, an IEEE 802.11 bf task group has been established to create a new amendment to the IEEE 802.11 Wireless Local Area Networks (WLAN) standards family, to provide advanced sensing requirements while minimizing the effect on communications [6]. Orthogonal Frequency Division Multiplex (OFDM) is widely used in contemporary communication systems and is extensively researched in radar and target detection applications. The OFDM-based radars have been investigated, fabricated, and tested in various frequency bands and use cases, including a C-band automotive radar [7] with the results presented in the form of max-hold plots in the delay-Doppler domain. An OFDM radar with 200 MHz bandwidth and 500 MHz sampling frequency operating in the 77 GHz mm-wave band tested in the task of static and moving target detection was presented in [8]. Recently, a new communication waveform, named Orthogonal Time Frequency Space (OTFS), has been proposed [9], and has been declared to have superior performance overOFDM in doubly dispersive channels [10]. There have not been many OTFS transmission experiments so far, but some exceptions can be mentioned, such as the Software Defined Radio (SDR) based experiment [11] highlighting the problem of RF front-end impairments' influence. These were further studied by simulation in [12]. The OTFS transmission performance in mm-waves was simulated for 28 GHz [13] or 60 GHz [14] bands. The use of OTFS scheme has also been investigated in potential radar applications, but rather through simulations, often under simplified assumptions. A comparison of OTFS and OFDM for object range and velocity estimation was presented in [15]. In [16], the OTFS-based automotive radar was analyzed, but with an assumption of delays and Doppler shifts induced by the targets are integer multiples of designed delay and Doppler grid resolution. The same assumption was set in a thorough investigation of a 28 GHz radar in [17]. Constant False Alarm Rate (CFAR) detectors [18] represent one common, robust, and practical option to detect the targets in two-dimensional (2D) data, with the noise power estimated from the cells neighboring the expected targets. Although several advanced variants of CFAR detectors with adaptive threshold settings [19] have been proposed, the CFAR detectors suffer from performance degradation in non-homogenous environments [20], and the use of CFAR may be suboptimal if the detected target spans over several bins in the delay-Doppler grid. In general, conventional CFAR detectors fail if applied to complex scenarios, especially with multiple targets, as a result of target masking [21]. In such a case, a persistent homology method [22] from the family of topological approaches [23] may be more suitable, as it does not require background noise estimation and is thus more immune to the additional targets in the vicinity of the cell under test. Moreover, it naturally assigns significance (persistence) to each of the detected targets.