  In this paper, we focus our attention on the mitigation of beam squint for
reconfigurable intelligent surface (RIS) aided wideband millimeter wave
(mmWave) communications. Due to the intrinsic passive property, the phase
shifts of all elements in RIS should be the same for all frequencies. However,
in the wideband scenario, beam squint induced distinct path phases require
designing different phase shifts for different frequencies. The above
irreconcilable contradiction will dramatically affect the system performance,
considering the RIS usually consists of enormous elements and the bandwidth of
wideband mmWave communications may be up to several GHz. Therefore, we propose
some novel phase shift design schemes for mitigating the effect of beam squint
for both line-of-sight (LoS) and non-Los (NLoS) scenarios. Specifically, for
the LoS scenario, we firstly derive the optimal phase shift for each frequency
and obtain the common phase shift by maximizing the upper bound of achievable
rate. Then, for the NLoS scenario, a mean channel covariance matrix (MCCM)
based scheme is proposed by fully exploiting the correlations between both the
paths and the subcarriers. Our extensive numerical experiments confirm the
effectiveness of the proposed phase shift design schemes.
