On the Position of Intelligent Reflecting Surfaces

We study the positional impact of an intelligent reflecting surface (IRS) on the achievable rate for single and multiple antenna systems. We show that in IRS-aided single antenna systems, it is always best to place the IRS as close as possible to the transmitter or receiver since the large-scale fading for IRS-reflected links is the main factor that characterizes the performance gain. However, for IRS-aided multiple antenna systems, the propagation environment has an important role in characterizing the efficient regions of IRS placement. In the case of a line-of-sight environment, the channel matrix turns out to be rank-deficient. Thus, both far and near IRS placements result in significant achievable rate improvements where the former provides a substantial additional degree-of-freedom, while the latter results in a power gain. Furthermore, as the wireless channel becomes richer with multipath, the rank of the channel matrix increases. Thus, the efficient far placement regions gradually shrink until they disappear in the case of a Rayleigh fading channel where IRS near placements become more efficient than far placements as they result in higher power gains.