  Through spatial multiplexing and diversity, multi-input multi-output (MIMO)
cognitive radio (CR) networks can markedly increase transmission rates and
reliability, while controlling the interference inflicted to peer nodes and
primary users (PUs) via beamforming. The present paper optimizes the design of
transmit- and receive-beamformers for ad hoc CR networks when CR-to-CR channels
are known, but CR-to-PU channels cannot be estimated accurately. Capitalizing
on a norm-bounded channel uncertainty model, the optimal beamforming design is
formulated to minimize the overall mean-square error (MSE) from all data
streams, while enforcing protection of the PU system when the CR-to-PU channels
are uncertain. Even though the resultant optimization problem is non-convex,
algorithms with provable convergence to stationary points are developed by
resorting to block coordinate ascent iterations, along with suitable convex
approximation techniques. Enticingly, the novel schemes also lend themselves
naturally to distributed implementations. Numerical tests are reported to
corroborate the analytical findings.
