Age of Channel State Information for Collaborative Beamforming
Michael V. Lipski, Clement Kam, Sastry Kompella, Tony Ephremides · 2024
We examine a simplified distributed collaborative beamforming (DCB) system with two transmitters sending data over independent channels with significant time-varying phase distortion. The transmitters sample the state of their respective channels using a periodic sounding waveform sent by the receiver and use the last sensed state along with the sample age to correct for the channel phase distortion. As the age of the last sampled channel state increases, the transmitters are correctly estimating the current state with decreasing likelihood, leading to reduced beamforming gain. However, because sensing and transmitting must occur on the same channel, the transmitters cannot both send data and sample the channel at the same time. As a result, the cost associated with channel sensing is the transmitters not sending data for some duration; this compromise is embodied by the frame-averaged expected beamforming gain. Expressions for instantaneous and averaged expected gain are developed, and an example is presented to demonstrate finding the optimal sensing period and how the optimal sensing period can change depending on the last sensed states of the channels.