  Intelligent reflecting surfaces (IRSs) constitute a disruptive wireless
communication technique capable of creating a controllable propagation
environment. In this paper, we propose to invoke an IRS at the cell boundary of
multiple cells to assist the downlink transmission to cell-edge users, whilst
mitigating the inter-cell interference, which is a crucial issue in multicell
communication systems. We aim for maximizing the weighted sum rate (WSR) of all
users through jointly optimizing the active precoding matrices at the base
stations (BSs) and the phase shifts at the IRS subject to each BS's power
constraint and unit modulus constraint. Both the BSs and the users are equipped
with multiple antennas, which enhances the spectral efficiency by exploiting
the spatial multiplexing gain. Due to the non-convexity of the problem, we
first reformulate it into an equivalent one, which is solved by using the block
coordinate descent (BCD) algorithm, where the precoding matrices and phase
shifts are alternately optimized. The optimal precoding matrices can be
obtained in closed form, when fixing the phase shifts. A pair of efficient
algorithms are proposed for solving the phase shift optimization problem,
namely the Majorization-Minimization (MM) Algorithm and the Complex Circle
Manifold (CCM) Method. Both algorithms are guaranteed to converge to at least
locally optimal solutions. We also extend the proposed algorithms to the more
general multiple-IRS and network MIMO scenarios. Finally, our simulation
results confirm the advantages of introducing IRSs in enhancing the cell-edge
user performance.
