In this paper, we consider intelligent omni-surfaces (IOSs), which are capable of simultaneously reflecting and refracting electromagnetic waves. We focus our attention on the multiple-input multiple-output (MIMO) broadcast channel, and we introduce an algorithm for jointly optimizing the covariance matrix at the base station, the matrix of reflection and transmission coefficients at the IOS, and the amount of power that is reflected and refracted from the IOS. The distinguishable feature of this work lies in taking into account that the reflection and transmission coefficients of an IOS are tightly coupled. Simulation results are illustrated to show the convergence of the proposed algorithm and the benefits of using surfaces with simultaneous reflection and refraction capabilities.

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