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.
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