  Millimeter wave (MmWave) communications is capable of supporting
multi-gigabit wireless access thanks to its abundant spectrum resource.
However, the severe path loss and high directivity make it vulnerable to
blockage events, which can be frequent in indoor and dense urban environments.
To address this issue, in this paper, we introduce intelligent reflecting
surface (IRS) as a new technology to provide effective reflected paths to
enhance coverage of mmWave signals. In this framework, we study joint active
and passive precoding design for IRS-assisted mmWave systems, where multiple
IRSs are deployed to assist the data transmission from a base station (BS) to a
single-antenna receiver. Our objective is to maximize the received signal power
by jointly optimizing the transmit precoding vector at the BS and the phase
shift parameters used by IRSs for passive beamforming. Although such an
optimization problem is generally non-convex, we show that, by exploiting some
important characteristics of mmWave channels, an optimal closed-form solution
can be derived for the single IRS case and a near-optimal analytical solution
can be obtained for the multi-IRS case. Our analysis reveals that the received
signal power increases quadratically with the number of reflecting elements for
both the single IRS and multi-IRS cases. Simulation results are included to
verify the optimality and near-optimality of our proposed solutions. Results
also show that IRSs can help create effective virtual LOS paths and thus
substantially improve robustness against blockages in mmWave communications.
