## 1 Introduction
### The Contributions of This Paper  
As a solution for BSs, we propose a shared aperture for JCAS, as well as an auxiliary aperture for radar full-duplex operation with a shared waveform. The proposed BS aperture performs in time-division duplexing (TDD) downlink communication and monostatic sensing at the duration of TDD-downlink, and uplink communication and monostatic sensing at the duration of TDD-uplink. The proposed shared aperture for JCAS is a sparse tiled planar array (STPA). Firstly, a large aperture with uniformly distributed antennas is tiled by dominoes based on the maximum entropy of tile centers in the aperture. The sunflower array is then exploited to locate the center of subarrays and lower the number of tiles. When the tiles in subarrays are chosen, the positions of the subarrays are optimized to lower SLL. A comparison of the designed STPA to a conventional uniform planar array (CUPA) and a sunflower sparse planar array (SPA) with the same number of antennas is provided. The employed SPA for comparison has the same aperture size and the same beamwidth as the STPA, but, due to higher freedom in the location of its elements, it has less average SLL and a less modular design. The main contributions of this paper are three-fold.  
* **Array configuration:** In the literature, a JCAS array is communication-centric, as a CUPA is employed in the TDD-downlink [23] or TDD-uplink [25] JCAS. Knowing that a CUPA has a larger beamwidth and is not optimal for sensing, in this paper, an STPA is proposed for JCAS at the BS since a narrow beamwidth of the transmit beam (in TDD-downlink) or receive beam (in TDD-uplink) is required for proper AoA estimation in sensing. This narrow beamwidth is profitable for increasing the number of beams for multi-user communication as well. The numerical results are provided for the duration of TDD-downlink, however, STPA can be adopted for TDD-uplink and monostatic sensing at the BS by the method in Ref. [26]. Considering the large bandwidth in JCAS at, e.g., 5G NR FR2, the irregularity introduced by tiling and sparse subarray geometries, compared to the conventional uniform arrays, results in a low SLL in the radiation pattern over a larger frequency band [27]. The numerical results show that STPA has a proper SLL when the frequency is scaled up to 1.625 times the desired frequency of operation, which results in a 42% increase in the operational frequency of the array compared to the CUPA. A comparison of STPA to SPA shows that SPA is applicable for a wider band, although with slightly higher SLL and more irregularity in the aperture. However, the STPA is uniform array at the subarray level, making it easier to manufacture compared to SPA.
* **Sensing performance:** The angular resolution of the JCAS aperture is improved by suitable adjustment of tiling and sparse design. As stated in Ref. [11], the tiled array has the benefits of modular design and lower SLL in wider scanning angles compared to a solely sparse design. The narrow beamwidth of the proposed STPA compared to CUPA ensures illuminating and receiving from only the desired angle during TDD-downlink and TDD-uplink monostatic sensing at the BS, respectively.  
The narrow beamwidth is achieved at the cost of a higher SLL compared to a CUPA, and the effect of this drawback is observed in the resulting error in the detection accuracy of targets.
* **JCAS performance:** The narrow beamwidth of STPA is beneficial for decreasing the blockage time in a JCAS scenario, since the spectral efficiency is dropped when the blocker reaches the narrower communication beam, i.e., we show in a JCAS scenario that if a tracked target moves towards the boresight of aperture and blocks the communication link, the designed STPA can have a 40% shorter blockage time than a CUPA.  
The following notations are used in this paper: \((.)^{T}\) and \((.)^{*}\) denote the transpose and conjugate transpose operator, respectively. \(\left\|.\right\|_{F}\) is the Frobenius norm.