  We study the performance of a phase-noise impaired double reconfigurable
intelligent surface (RIS)-aided multiuser (MU) multiple-input single-output
(MISO) system under spatial correlation at both RISs and base-station (BS). The
downlink achievable rate is derived in closed-form under maximum ratio
transmission (MRT) precoding. In addition, we obtain the optimal phase-shift
design at both RISs in closed-form for the considered channel and phase-noise
models. Numerical results validate the analytical expressions, and highlight
the effects of different system parameters on the achievable rate. Our analysis
shows that phase-noise can severely degrade the performance when users do not
have direct links to both RISs, and can only be served via the
double-reflection link. Also, we show that high spatial correlation at RISs is
essential for high achievable rates.
