  Intelligent reflecting surface (IRS) is a promising technology to extend the
wireless signal coverage and support the high performance communication. By
intelligently adjusting the reflection coefficients of a large number of
passive reflecting elements, the IRS can modify the wireless propagation
environment in favour of signal transmission. Different from most of the prior
works which did not consider any cooperation between IRSs, in this work we
propose and study a cooperative double-IRS aided multiple-input multiple-output
(MIMO) communication system under the line-of-sight (LoS) propagation channels.
We investigate the capacity maximization problem by jointly optimizing the
transmit covariance matrix and the passive beamforming matrices of the two
cooperative IRSs. Although the above problem is non-convex and difficult to
solve, we transform and simplify the original problem by exploiting a tractable
characterization of the LoS channels. Then we develop a novel low-complexity
algorithm whose complexity is independent of the number of IRS elements.
Moreover, we analyze the capacity scaling orders of the double-IRS aided MIMO
system with respect to an asymptotically large number of IRS elements or
transmit power, which significantly outperform those of the conventional
single-IRS aided MIMO system, thanks to the cooperative passive beamforming
gain brought by the double-reflection link and the spatial multiplexing gain
harvested from the two single-reflection links. Extensive numerical results are
provided to show that by exploiting the LoS channel properties, our proposed
algorithm can achieve a desirable performance with low computational time.
Also, our capacity scaling analysis is validated, and the double-IRS system is
shown to achieve a much higher rate than its single-IRS counterpart as long as
the number of IRS elements or the transmit power is not small.
