Reconfigurable Intelligent Surfaces-Assisted Communications With Discrete Phase Shifts: How Many Quantization Levels Are Required to Achieve Full Diversity?

• Published in: IEEE wireless communications letters Vol. 10; no. 2; pp. 358 - 362
• Main Authors: Xu, Peng, Chen, Gaojie, Yang, Zheng, Renzo, Marco Di
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.02.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); IEEE comsoc
• Subjects: Codes; discrete phase shifts; diversity order; Engineering Sciences; Hardware; Impact analysis; Lower bounds; Measurement; outage probability; phase errors; Power system reliability; Probability; Quantization (signal); Reconfigurable intelligent surface; Reconfigurable intelligent surfaces; Signal and Image processing; Signal to noise ratio; Upper bound; Upper bounds; Wireless communication; Wireless communication systems; Wireless communications; discrete phase shifts; diversity order; Reconfigurable intelligent surface; outage probability; phase errors
• ISSN: 2162-2337; 2162-2345
• DOI: 10.1109/LWC.2020.3031084

Due to hardware limitations, the phase shifts of the reflecting elements of reconfigurable intelligent surfaces (RISs) need to be quantized into discrete values. This letter aims to unveil the minimum required number of phase quantization levels <inline-formula> <tex-math notation="LaTeX">{L} </tex-math></inline-formula> in order to achieve the full diversity order in RIS-assisted wireless communication systems. With the aid of an upper bound of the outage probability, we first prove that the full diversity order is achievable provided that <inline-formula> <tex-math notation="LaTeX">{L} </tex-math></inline-formula> is not less than three. If <inline-formula> <tex-math notation="LaTeX">{L}\,\,= </tex-math></inline-formula> 2, on the other hand, we prove that the achievable diversity order cannot exceed (<inline-formula> <tex-math notation="LaTeX">{N}\,\,+ </tex-math></inline-formula> 1)/2, where <inline-formula> <tex-math notation="LaTeX">{N} </tex-math></inline-formula> is the number of reflecting elements. This is obtained with the aid of a lower bound of the outage probability. Therefore, we prove that the minimum required value of <inline-formula> <tex-math notation="LaTeX">{L} </tex-math></inline-formula> for achieving the full diversity order is <inline-formula> <tex-math notation="LaTeX">{L}\,\,= </tex-math></inline-formula> 3. Simulation results verify the theoretical analysis and the impact of phase quantization levels on RIS-assisted communication systems.