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MSE Balancing in the MIMO BC: Unequal Targets and Probabilistic Interference Constraints

Second order cone (SOC) restrictions have been widely employed in the design of wireless communication systems to recast precoding optimizations in convex form. This paper highlights the flexibility of this framework to handle various transmit power and interference limitations also in the multistream multiple-input multiple-output broadcast channel with imperfect channel state information at the transmitter. In particular, we propose an iterative solution for mean square error (MSE) balancing with such constraints via the Lagrangian dual formulation. The MSE balancing criteria, contrary to signal-to-interference plus-noise ratio and rate criteria, exhibit an interesting property when considering different targets for the receivers. Users with low target values are strictly prioritized in comparison to users with large MSE targets that can even be switched off. Therefore, only a subset of the receivers is served at the solution with stringent limitations for the precoders. An example of such stringent limitations are small power constraints and probabilistic interference temperature constraints that set a measurable threshold on the generated interference in a cognitive radio system. We provide four different approaches to approximate these probabilistic constraints with deterministic SOC constraints, and compare their accuracy.