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Due to hardware limitations, the phase shifts of the reflecting elements ofreconfigurable intelligent surfaces (RISs) need to be quantized into discretevalues. This letter aims to unveil the minimum required number of phasequantization levels $L$ in order to achieve the full diversity order inRIS-assisted wireless communication systems. With the aid of an upper bound ofthe outage probability, we first prove that the full diversity order isachievable provided that $L$ is not less than three. If $L=2$, on the otherhand, we prove that the achievable diversity order cannot exceed $(N+1)/2$,where $N$ is the number of reflecting elements. This is obtained with the aidof a lower bound of the outage probability. Therefore, we prove that theminimum required value of $L$ to achieve the full diversity order is $L=3$.Simulation results verify the theoretical analysis and the impact of phasequantization levels on RIS-assisted communication systems.

Reconfigurable Intelligent Surfaces Assisted Communications with  Discrete Phase Shifts: How Many Quantization Levels are Required to Achieve  Full Diversity?