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Unlike active array antennas, intelligent reflecting surfaces (IRSs) areefficiently implemented at large dimensions. This allows for traceablerealizations of large-scale IRS-aided MIMO systems in which not necessarily thearray antennas, but the passive IRSs are large. It is widely believed thatlarge IRS-aided MIMO settings maintain the fundamental features of massive MIMOsystems, and hence they are the implementationally feasible technology forestablishing the performance of large-scale MIMO settings. This work gives arigorous proof to this belief. We show that using a large passive IRS, theend-to-end MIMO channel between the transmitter and the receiver alwayshardens, even if the IRS elements are strongly correlated.  For the fading direct and reflection links between the transmitter and thereceiver, our derivations demonstrate that as the number of IRS elements growslarge, the capacity of end-to-end channel converges in distribution to areal-valued Gaussian random variable whose variance goes to zero. The order ofthis drop depends on how the physical dimensions of the IRS grow. We derivethis order explicitly. Numerical experiments depict that the analyticalasymptotic distribution almost perfectly matches the histogram of the capacity,even in practical scenarios.  As a sample application of the results, we use the asymptoticcharacterization to study the dimensional trade-off between the transmitter andthe IRS. The result is intuitive: For a given target performance, the largerthe IRS is, the less transmit antennas are required to achieve the target. Foran arbitrary ergodic and outage performance, we characterize this trade-offanalytically. Our investigations demonstrate that using a practical IRS size,the target performance can be achieved with significantly small end-to-end MIMOdimensions.

Channel Hardening of IRS-Aided Multi-Antenna Systems: How Should IRSs Scale?