Recently, reconfigurable intelligent surfaces (RISs) have drawn intensive attention to enhance the coverage of millimeter wave (mmWave) communication systems. However, existing works mainly consider the RIS as a whole uniform plane, which may be unrealistic to be installed on the facade of buildings when the RIS is extreme large. To address this problem, in this paper, we propose a sparse array of sub-surface (SAoS) architecture for RIS, which contains several rectangle shaped sub-surfaces termed as RIS tiles that can be sparsely deployed. An approximated ergodic spectral efficiency of the SAoS aided system is derived and the performance impact of the SAoS design is evaluated. Based on the approximated ergodic spectral efficiency, we obtain an optimal reflection coefficient design for each RIS tile. Analytical results show that the received signal-to-noise ratios can grow quadratically and linearly to the number of RIS elements under strong and weak LoS scenarios, respectively. Furthermore, we consider the visible region (VR) phenomenon in the SAoS aided mmWave system and find that the optimal distance between RIS tiles is supposed to yield a total SAoS VR nearly covering the whole blind coverage area. The numerical results verify the tightness of the approximated ergodic spectral efficiency and demonstrate the great system performance.
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