Online MIMO Wireless Network Virtualization over Time-Varying Channels with Periodic Updates

We consider online downlink precoding design for multiple-input multiple-output (MIMO) wireless network virtualization (WNV) over time-varying channels. In our WNV framework, each service provider (SP) locally designs virtual precoding to serve its own users, while the infrastructure provider (InP) designs the actual global precoding to meet the service demands from the SPs. We consider a periodic update model where partial channel state information (CSI) feedbacks may be received out of order due to delay and the precoding is updated per period. Our goal is to minimize the accumulated deviation of the actual precoding designed by the InP from the virtualization demands made by the SPs, subject to both long-term and short-term transmit power constraints. We propose an online MIMO WNV algorithm, which achieves O(√T) growth of regret on the precoding deviation from the virtualization demand over time horizon T, and maintains O(1) violation of the long-term transmit power constraint. Our proposed online precoding solution is in closed-form. Furthermore, it does not require the knowledge of the channel distribution and only depends on the past CSI. Finally, its effectiveness is shown in simulation and comparison with existing alternatives.