  In this paper, we study the problem of joint active and passive beamforming
for intelligent reflecting surface (IRS)-assisted massive MIMO systems, where
multiple IRSs equipped with a large number of passive elements are deployed to
assist a base station (BS) to simultaneously serve a small number of
single-antenna users in the same time-frequency resource. Our objective is to
maximize the minimum signal to interference plus noise (SINR) at users by
jointly optimizing the transmit precoding vector at the BS and phase shift
parameters at IRSs. We show that an interesting automatic interference
cancelation (AIC) property holds asymptotically as the number of passive
elements approaches infinity, i.e., when an IRS is optimally tuned to serve a
certain user, this IRS will become interference-free to other users. By
utilizing this property, the max-min problem can be converted into an IRS-user
association problem, where the objective is to determine which IRSs are
assigned for each user. An exhaustive search scheme and a greedy search scheme
are proposed to solve the IRS-user association problem. Our theoretical
analysis reveals that our proposed solution attains an SINR that scales
quadratically with the number of reflecting elements. Also, our theoretical
result suggests that even with a moderate number of active antennas at the BS,
a massive MIMO like gain can be achieved by increasing the number of passive
reflecting elements, thus significantly reducing the energy consumption at the
BS. Simulation results are provided to corroborate our theoretical results and
to illustrate the effectiveness of our proposed solution.
