## 3 Numerical Analysis
### STPA Performances in JCAS Scenarios and Benchmarking
#### 3.2.2 Sensing Performance in Scenario 1: Non-Overlapping Communication and Sensing Beams
By observing the EBP of SPA and STPA in Figure 9e,f, the SLLs in the neighborhood of the main beam at \((\bar{u},\bar{v})=(0,0)\) in STPA are higher than that of SPA, which causes more errors in the accurate detection and association of targets, therefore \(\mu_{RMSE}^{\text{STPA}}>\mu_{RMSE}^{\text{SPA}}\). 2.3 Communication Performance in Scenario 2: Overlapping Communication and Sensing Beams When UE Blocks the Sensing Target  
As the same waveform is used for both beams, when overlapping occurs either in the scanning mode or in the tracking mode with the range of the tracking target being larger than the range of the UE, which is the case in Figure 4b, the signal power at the UE is increased, therefore spectral efficiency is supposed to increase. Let us consider that if the user is at the angle \((\theta_{UE},\phi_{UE})=(20^{\circ},50^{\circ})\), the sensing is in the scanning mode and the sensing beam first scans over azimuth at the elevation \(\theta=20^{\circ}\) and then over elevation at azimuth \(\phi=50^{\circ}\) angles. The average spectral efficiencies at an SNR of 10 dB are presented in Figure 16a,b. The deviation from the spectral efficiency without overlapping is noticeable for the STPA only when the difference between the communication angle and scanning  
Figure 14: The DLR when (**a**) \(N_{\text{targets}}=4\), (**b**) \(N_{\text{targets}}=8\) and (**c**) \(N_{\text{targets}}=12\). angle is \(10^{\circ}\), whereas this number for the CUPA is \(24^{\circ}\). STPA and SPA perform similarly in this case. Figure 16a,b and the discussion above on the communication link are also valid for the tracking mode of a target with a larger range than the UE, e.g., \(r_{UE}=70\) m and \(r_{t}=140\) m, since the tracking and communication beams are overlapping and the power in the resultant aggregated beam is captured by the UE. Regarding sensing performance in these cases, the received signal at the BS from the scanning or tracking beam when it reaches the angle of the UE is negligible due to weak reflection from UE, which is the assumption in this paper. In the overlapping when the tracked target is behind the UE, the received reflected signal at the BS is zero again and the target is also lost. The spectral efficiency of the communication link increased since the sensing and communication beam have the same waveform, if one intends to use separate waveforms in separate beams, then beam overlapping is detrimental for the SNR at the user. 2.4 Communication Performance in Scenario 3: Overlapping Communication and Sensing Beams When the Sensing Target Blocks the UE  
The range for UE is considered to be \(r_{UE}=70\) m, the target body moves at the constant azimuth of \(\phi_{t}=50^{\circ}\), perpendicular to the LoS path, crossing it at \(r_{m}=35\) m, as in Figure 4c. The parameters for the body in (13) are assumed as \(\epsilon_{b}=0.1-j2.33\), \(\sigma_{b}=0.45\) dB [38] and the incident angle on the body \(\delta=\theta_{t}\). The variation of spectral efficiency at an SNR of 10 dB for the STPA, CUPA, and SPA are shown in Figure 17. There is an increased oscillation in the spectral efficiency just before and after blockage occurrence, which is due to the constructive and destructive addition of \(\mathbf{H}_{target,1}\) and \(\mathbf{H}_{LoS}\)[43]. The most noticeable difference between the STPA and CUPA is the time of blockage where the STPA, due to its narrower beamwidth, has a shorter blockage time. In these scenarios, the blockage time is proportional to the overlapping angles of communication and sensing beam, hence it is observed in Figure 17 that the STPA has a 40% shorter blockage time than CUPA in the scanning of the elevation angle. The blockage time and oscillation of STPA and SPA are not noticeably different. Figure 16: The effect of the scanning beam on the spectral efficiency for the STPA compared with CUPA and SPA while scanning in (**a**) azimuth, and (**b**) elevation.