Robust downlink beamforming in multi-group multicasting using trace bounds on the covariance mismatches

Transmission strategies under imperfect instantaneous CSIT

“…where the power vector p [P 1 · · · P K ] T and 1 K denotes a K-dimensional column vector with all elements equal to 1 and the auxiliary matrices D 2 and G 2 are given as Since D 2 · G 2 is a non-negative matrix, and by virtue of [28], the optimum power solution to (20) is given as (16) is sufficient to calculate the optimized normalized beamforming vectors {u k } K k=1 . Equations (23) and (16) imply that the amplitude and direction of optimum transmit beamformers can be solved separately, albeit coupled by the inter-dependence between the coefficients in inequality (20) and equation (15).…”

“…Equations (23) and (16) imply that the amplitude and direction of optimum transmit beamformers can be solved separately, albeit coupled by the inter-dependence between the coefficients in inequality (20) and equation (15). A simple iterative algorithm for such dependence can be given as in Algorithm 2.…”

“…Robust formulations circumventing the need of perfect channel state information at the transmitter (CSIT) by defining QoS requirement based on only channel covariance matrix and handling covariance estimation errors by means of conservative spherical bounds was proposed in [17], [18]. Recently, by employing a tighter spherical bounds on the covariance error norm [19] and on the trace such error [20], yielding less conservative solutions were proposed.…”

Worst case robust downlink beamforming on the Riemannian manifold

“…Moreover, due to the approximations used in [15], the techniques presented there are weaker competitors to our method, as we further show through simulations. With respect to the recently proposed approach in [19] where the uncertainty region is limited using trace bounds, our approach is more general in that it can be employed to a larger number of error models on the CSI.…”

“…Simulation results show that our new design significantly outperforms the existing methods in terms of constraint satisfaction and transmitted power. While in this paper our robust beamforming design is applied to a multiple-input single output downlink scenario, the ideas presented can be easily extended to more complicated scenarios including, e.g., cognitive radio [12], [18] or multigroup multicasting [19].…”