  This paper studies the problem of robust downlink beamforming design in a
multiuser Multi-Input Single-Output (MISO) Cognitive Radio Network (CR-Net) in
which multiple Primary Users (PUs) coexist with multiple Secondary Users (SUs).
Unlike conventional designs in CR-Nets, in this paper it is assumed that the
Channel State Information (CSI) for all relevant channels is imperfectly known,
and the imperfectness of the CSI is modeled using an Euclidean ball-shaped
uncertainty set. Our design objective is to minimize the transmit power of the
SU-Transmitter (SU-Tx) while simultaneously targeting a lower bound on the
received Signal-to-Interference-plus-Noise-Ratio (SINR) for the SU's, and
imposing an upper limit on the Interference-Power (IP) at the PUs. The design
parameters at the SU-Tx are the beamforming weights, i.e. the precoder matrix.
The proposed methodology is based on a worst case design scenario through which
the performance metrics of the design are immune to variations in the channels.
We propose three approaches based on convex programming for which efficient
numerical solutions exist. Finally, simulation results are provided to validate
the robustness of the proposed methods.
