  This paper investigates the impact of spatial channel correlation on the
outage probability of intelligent reflecting surface (IRS)-assisted
single-input single-output (SISO) communication systems. In particular, we
derive a novel closed-form expression of the outage probability for arbitrary
phase shifts and correlation matrices of the indirect channels. To shed light
on the impact of the spatial correlation, we further attain the closed-form
expressions for two common scenarios met in the literature when the large-scale
fading coefficients are expressed by the loss over a propagation distance.
Numerical results validate the tightness and effectiveness of the closed-form
expressions. Furthermore, the spatial correlation offers significant decreases
in the outage probability as the direct channel is blocked.
