Abstract-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.Index Terms-Downlink beamforming, shaping constraints, semidefinite relaxation (SDR), orthogonal space time block coding (OSTBC).
I. INTRODUCTIONWith the massive growth of the number of wireless communication users and the increasing demands for high-rate services, the spectral resource is becoming more and more scarce. Research on spectrally efficient transmission schemes for current and next generation cellular networks that are capable of mitigating effects of multiuser and co-channel interference is attracting considerable interest [1]. As a spectrally efficient multi-antenna technique [2], downlink beamforming has been extensively studied in the past few years [3]- [8]. With the aid of channel state information (CSI) at the transmitter, downlink beamforming is employed at the base station of cellular networks to serve multiple co-channel users simultaneously using spatially selective transmission.As a pioneering work in downlink beamforming, the authors in [3] consider the problem of minimizing the total transmitted power subject to quality of service (QoS) constraints in the form of minimum signal to interference plus noise ratio (SINR) requirements at each user. A particular form of uplink-downlink duality theory is established in [3] and under this framework the downlink beamforming problem is solved