## 1 Introduction  
In the migration to 6G and connected smart networks, communication and sensing devices have to be integrated to maintain the reliability of high data-rate connectivity and to have accurate information on the surrounding operating environment [1]. There are many open challenges for joint communication and sensing (JCAS), especially for the co-design of communication and radar sensing functionality within a single physical array aperture. For example, what (shared) waveform to use, what shared array aperture configuration, and how to optimize the resource allocation, are all open to be resolved with effectiveness and efficiency [1, 2, 3, 4]. In this paper, our interest lies in the base station (BS) array configuration design--a shared aperture--to optimize the JCAS performance.  
Conventionally, the free-space radiation parameters, i.e., directivity, half-power beamwidth, and side lobe level (SLL) were the figure-of-merits for designing antenna arrays. These free-space radiation parameters are valid for the radio propagation channels with a dominant line-of-sight (LoS) path. However, in case of channels with considerable non-line-of-sight (NLoS) paths, for multi-user multiple-input-multiple-output (MU-MIMO) communications and in a dense mmWave networks [5], the spectral efficiencies of communication links are the reliable performance metrics [6; 7]. Therefore, for an optimal end-to-end communication performance, the beamforming vector applied on the antennas at the BS, and consequently the radiation pattern, shall be determined by the channel dynamics and be configured for maximizing the spectral efficiency of communication links. The optimized BS radiation pattern could be with a narrow or wide beamwidth and single or multi beams. Additionally, the favorable channel of a phased array radar, particularly in millimeter-waves (mmWave)s, is with a dominant reflected (backscattered) path, thus a single beam with low SLL and narrow beamwidth focusing towards the scatterer is always beneficial for improving the signal-to-noise ratio (SNR) and cross-range resolution [8].  
To enable JCAS, a dynamic radiation pattern at the BS is desired, as either communication or sensing might dictate to react to the dynamic channel conditions. To enable a dynamic radiation pattern, antenna selection, which involves synthetic changes in aperture size and geometry [9], may be necessary.  
In the presence of a LoS communication link and the direct illumination of the sensing target, which is the case of study in this paper, instead of antenna selection and synthetic aperture change, the use of all antenna elements in the BS is beneficial for increasing the SNR and hence the performance of JCAS. It is stated in Ref. [10] that increasing the size of the aperture while preserving the same antenna numbers did not improve the directivity, but decreased the beamwidth. Therefore, we focus on designing a shared array aperture for JCAS with a low SLL and narrow beamwidth, given a fixed aperture size. We also focus on maintaining an appropriate number of radiating elements to reduce the system cost and space requirements. In order to manage the number of array elements and at the same time enhancing the performance of communication and sensing, we explore solutions incorporating array tiling [6; 7; 11; 12; 13; 14], sparse arrays [15], and modular design [10]. These goals are studied in Ref. [16], where a reconfigurable mmWave antenna array platform based on antenna tiles was studied and implemented for the communication applications. Therefore, this paper extends those modular tiling solutions to the JCAS scenarios by a sparse subarray design.