  Intelligent reflecting surface (IRS) has been regarded as a promising and
revolutionary technology for future wireless communication systems owing to its
capability of tailoring signal propagation environment in an
energy/spectrum/hardware-efficient manner. However, most existing studies on
IRS optimizations are based on a simple and ideal reflection model that is
impractical in hardware implementation, which thus leads to severe performance
loss in realistic wideband/multi-band systems. To deal with this problem, in
this paper we first propose a more practical and more tractable IRS reflection
model that describes the difference of reflection responses for signals at
different frequencies. Then, we investigate the joint transmit beamforming and
IRS reflection beamforming design for an IRS-assisted multi-cell multi-band
system. Both power minimization and sum-rate maximization problems are solved
by exploiting popular second-order cone programming (SOCP), Riemannian
manifold, minimization-majorization (MM), weighted minimum mean square error
(WMMSE), and block coordinate descent (BCD) methods. Simulation results
illustrate the significant performance improvement of our proposed joint
transmit beamforming and reflection design algorithms based on the practical
reflection model in terms of power saving and rate enhancement.
