Computationally efficient robust design in MIMO broadcast channels with norm bounded error models

Abstract

Using multiple antennas at the transmitter or receiver sides of the communications systems is a trend with no seeming end in forthcoming standards beyond 5G. In such networks, implementing a reasonably realistic beamformer means to challenge with uncertain Channel State Information (CSI). In many published works, the original design problem is a Second Order Cone Programming (SOCP) problem, and the robust counterpart, aiming to solve the design problem with data uncertainty, is a Semidefinite Programming (SDP) problem. In this paper, we study the robust beamforming design of a Broadcast Channel (BC) in a Multiple-user Multiple-Input Multiple-Output (MU-MIMO) scenario by formulating the Sum Mean Square Error (S-MSE) minimization design problem into a single SOCP robust counterpart problem. Each semi-infinite SOCP constraint is replaced with another SOCP constraint while introducing a new slack variable as well. The arithmetic computational complexity of our method is compared with the well-known and well-studied SDP design in closed form, and it is shown that the proposed method is exponentially faster in real-world design scenarios. To better verify our proposal, extensive numerical simulations are carried out, and the results show similar performances.