Joint beamforming, scheduling, and power allocation for hierarchical cellular systems

The idea of cognitive radio (CR) has embodied concretely in hierarchical cellular systems by deploying an underlying microcellular system to reuse the underutilized spectrum licensed by an macrocellular system. The fundamental challenges for successfully realizing such hierarchical systems are to manage the intercell interference between the macrocell and microcell and to pursue the goal of maximizing the spectrum recycling efficiency. In this paper, we jointly consider antenna beamforming, power allocation, and multiuser scheduling for the microcellular system to opportunistically utilize the uplink spectrum of the macrocell and to concurrently serve multiple secondary users in the downlink. With the objective of maximizing the sum rate, the three-dimensional joint design problem is often formulated as a mixed integer nonlinear programming (MINLP) which is an NP-hard problem and very complicated to solve. We resort to semidefinite relaxation (SDR) techniques to convert to the cumbersome optimization problem into a convex problem by introducing an interference-related auxiliary variable. An iterative algorithm based on semidefinite programming is proposed to achieve the optimal solution. The zero-forcing (ZF) beamforming and the singular value decomposition (SVD)-based beamforming with the best scheduling are simulated for performance comparisons, and our simulation shows that the proposed scheme is much superior to the ZF scheme and quite close to the SVD scheme with a slight performance gap of 1 bps/Hz.