  Intelligent reflecting surface (IRS) is deemed as a promising and
revolutionizing technology for future wireless communication systems owing to
its capability to intelligently change the propagation environment and
introduce a new dimension into wireless communication optimization. Most
existing studies on IRS are based on an ideal reflection model. However, it is
difficult to implement an IRS which can simultaneously realize any adjustable
phase shift for the signals with different frequencies. Therefore, the
practical phase shift model, which can describe the difference of IRS phase
shift responses for the signals with different frequencies, should be utilized
in the IRS optimization for wideband and multi-band systems. In this paper, we
consider an IRS-assisted multi-cell multi-band system, in which different base
stations (BSs) operate at different frequency bands. We aim to jointly design
the transmit beamforming of BSs and the reflection beamforming of the IRS to
minimize the total transmit power subject to signal to interference-plus-noise
ratio (SINR) constraints of individual user and the practical IRS reflection
model. With the aid of the practical phase shift model, the influence between
the signals with different frequencies is taken into account during the design
of IRS. Simulation results illustrate the importance of considering the
practical communication scenario on the IRS designs and validate the
effectiveness of our proposed algorithm.
