region, $\delta$, is set to $0.7$. Note that for the small values of $\delta$ and/or large values of $\epsilon$, the problem may turn infeasible. In general, the feasibility of the problem depends on the value of the tightness bound $\delta$ relative to the size of the existing uncertainty in the system, i.e., the volume of the uncertainty set $\epsilon$, and the number of grid points $N_S$ and $N_T$ used to control the beampattern at the area of interest. When $\delta$ is too small, the desired power level across $\Omega_T$ is close to uniform and there may not exist enough degrees of freedom for the design problem to have a solution.

For reference, the optimal covariance matrix when no uncertainty is taken into account, $\mathbf{R}_{nr}$, is obtained by solving problem using only nominal steering vectors $\ahat(\r)$, i.e., $\atil(\r) \equiv {\mathbf{0}}$. The optimal robust covariance matrix, denoted $\R^\star$, is obtained by solving where $\atil(\r) \in \mathcal{E}_{\r}$. For performance evaluation, we consider the power deposition in the tissue under the worst-case perturbations of the steering vectors. This scenario provides a lower bound to the achievable performances of all steering vector perturbations $\atil(\r)$ which belong to the deterministic uncertainty set $\mathcal{E}_{\r}$. In other words, 