## 4 Conclusions  
Analog beamforming arrays can increase the gain of radiation and overcome propagation attenuation in millimeter wave communication and sensing links. Therefore, in alliance with the fully-connected analog beamforming arrays, a sparse tiled planar array (STPA) is proposed for joint communication and sensing (JCAS) applications. The benchmarks are a conventional uniform planar array (CUPA) and a sparse planar array (SPA).  
* _The array configuration_ of STPA is based on a modular design, narrow beamwidth, and decreased number of phase shifters. The design is based on maximum entropy in the phase centers of the tiles in the array and sparse subarrays. The results show that an STPA with 125 domino tiles has stable radiation up to 1.625 times the center frequency of operation, whereas this number is 1.125 for CUPA. A realistic radiation pattern of an STPA, including antenna imperfections, is shown by full-wave simulation.
* The results show improvement in _sensing performance_, namely, when the sensing and communication beams are not overlapping, CUPA, SPA, and STPA guarantee the same spectral efficiency in the communication link, whereas a better angular resolution is achieved by SPA and STPA in sensing, e.g., the simulations show that the detection loss rate for STPA and SPA are less than for CUPA. The side lobes in SPA and STPA also result in the same average error in detection as CUPA. The percentages of improvement in detection loss and accuracy depend on the number of targets and false-alarm probability, which were the parameters of study.
* _JCAS performance_ is analyzed through blockage time when the sensing beam is tracking a target and overlapping with the communication beam. As SPA and STPA have a  
Figure 17: The spectral efficiency when the target blocks the LOS path at the angle \(\theta_{t}=20^{\circ}\).  
narrower beamwidth than the CUPA, the blockage time is 40% shorter while the target moves towards the boresight of the apertures. Finally, we conclude that STPA can be utilized when a smaller beamwith with a modular design is desired, otherwise SPA still outperforms STPA in sensing performance.  
In future works, there is space to further improve the aperture efficiency of the designed STPA. This can be tackled by assigning tiles with different sizes to the outer subarrays. Regarding communication, the effect of SLLs of SPA and STPA on the NLoS and multi-users communication case is still an open question. Regarding sensing, the tracking of extended or multiple targets demands a dynamic pattern configuration in which narrow beamwidth or high SLL may not be optimum. Therefore, beam squinting or antenna selections can also be applied then.  
Conceptualization, H.A., A.K. and Y.M.; Methodology, H.A. and Y.M.; Software, H.A.; Validation, H.A., A.K. and Y.M.; Formal analysis, H.A. and Y.M.; Investigation, H.A.; Writing--original draft, H.A. and Y.M.; Writing--review & editing, A.K.; Supervision, A.K. and Y.M.; Project administration, Y.M.; Funding acquisition, Y.M. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Dutch Sector Plan.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.