  Intelligent reflecting surface (IRS) has emerged as an enabling technology to
achieve smart and reconfigurable wireless communication environment
cost-effectively. Prior works on IRS mainly consider its passive beamforming
design and performance optimization without the inter-IRS signal reflection,
which thus do not unveil the full potential of multi-IRS assisted wireless
networks. In this paper, we study a double-IRS assisted multi-user
communication system with the \emph{cooperative} passive beamforming design
that captures the multiplicative beamforming gain from the inter-IRS channel.
Under the general channel setup with the co-existence of both double- and
single-reflection links, we jointly optimize the (active) receive beamforming
at the base station (BS) and the cooperative (passive) reflect beamforming at
the two distributed IRSs (deployed near the BS and users, respectively) to
maximize the minimum signal-to-interference-plus-noise ratio (SINR) of all
users. Moreover, for the single-user and multi-user setups, we analytically
show the superior performance of the double-IRS cooperative system over the
conventional single-IRS system in terms of the maximum signal-to-noise ratio
(SNR) and multi-user effective channel rank, respectively. Simulation results
validate our analytical results and show the practical advantages of the
proposed double-IRS system with cooperative passive beamforming designs.
