Low complexity LMMSE beamforming design for uplink virtual MIMO systems

In this paper, the beamforming designs for uplink virtual MIMO systems are investigated. In such systems, the most challenging difficulty in beamforming designs comes from the fact that the nodes consisting the virtual MIMO are subjected to individual power constraints or named per-antenna power constraints instead of sum power constraints. The instinct individual power constraints for virtual MIMO prohibit the derivation for closed-form solutions. Although in existing works, it has been revealed that under per-antenna power constraints the design problems are still convex and can be efficiently solved using some famous convex optimization tools such as semidefinite programming (SDP). Unfortunately, it is far from desired for practical implementations. In our work, linear minimum mean square error (LMMSE) beamforming is designed under per-antenna power constraints. Exploiting the hidden convexity, an iterative solution is proposed, which has clear structure and well-suited for virtual MIMO communications e.g, the uplink of Machine-to-Machine (M2M)communications in cellular networks. Finally, simulation results demonstrate the advantages of the proposed design.