  In this paper we consider optimal multiuser downlink beamforming in the
presence of a massive number of arbitrary quadratic shaping constraints. We
combine beamforming with full-rate high dimensional real-valued orthogonal
space time block coding (OSTBC) to increase the number of beamforming weight
vectors and associated degrees of freedom in the beamformer design. The
original multi-constraint beamforming problem is converted into a convex
optimization problem using semidefinite relaxation (SDR) which can be solved
efficiently. In contrast to conventional (rank-one) beamforming approaches in
which an optimal beamforming solution can be obtained only when the SDR
solution (after rank reduction) exhibits the rank-one property, in our approach
optimality is guaranteed when a rank of eight is not exceeded. We show that our
approach can incorporate up to 79 additional shaping constraints for which an
optimal beamforming solution is guaranteed as compared to a maximum of two
additional constraints that bound the conventional rank-one downlink
beamforming designs. Simulation results demonstrate the flexibility of our
proposed beamformer design.
