Fundamental Limits of Intelligent Reflecting Surface Aided Multiuser Broadcast Channel

Intelligent reflecting surface (IRS) has recently received significant attention in wireless networks owing to its ability to smartly control the wireless propagation through passive reflection. Although prior works have employed the IRS to enhance the system performance under various setups, the fundamental capacity limits of an IRS aided multi-antenna multi-user system have not yet been characterized. Motivated by this, we investigate an IRS aided multiple-input single-output (MISO) broadcast channel by considering the capacity-achieving dirty paper coding (DPC) scheme and dynamic beamforming configurations. We first propose a bisection based framework to characterize its capacity region by optimally solving the sum-rate maximization problem under a set of rate constraints, which is also applicable to characterize the achievable rate region with the zero-forcing (ZF) scheme. Interestingly, it is rigorously proved that dynamic beamforming is able to enlarge the achievable rate region of ZF if the IRS phase-shifts cannot achieve fully orthogonal channels, whereas the attained gains become marginal due to the reduction of the channel correlations induced by smartly adjusting the IRS phase-shifts. The result implies that employing the IRS is able to reduce the demand for implementing dynamic beamforming. Finally, we analytically prove that the sum-rate achieved by the IRS aided ZF is capable of approaching that of the IRS aided DPC with a sufficiently large IRS in practice. Simulation results shed light on the impact of the IRS on transceiver designs and validate our theoretical findings, which provide useful guidelines to practical systems by indicating that replacing sophisticated schemes with easy-implementation schemes would only result in slight performance loss.