  We consider a robust beamforming problem where large amount of downlink (DL)
channel state information (CSI) data available at a multiple antenna access
point (AP) is used to improve the link quality to a user equipment (UE) for
beyond-5G and 6G applications such as environment-specific initial access (IA)
or wireless power transfer (WPT). As the DL CSI available at the current
instant may be imperfect or outdated, we propose a novel scheme which utilizes
the (unknown) correlation between the antenna domain and physical domain to
localize the possible future UE positions from the historical CSI database.
Then, we develop a codebook design procedure to maximize the minimum sum
beamforming gain to that localized CSI neighborhood. We also incorporate a UE
specific parameter to enlarge the neighborhood to robustify the link further.
We adopt an indoor channel model to demonstrate the performance of our
solution, and benchmark against a usually optimal (but now sub-optimal due to
outdated CSI) maximum ratio transmission (MRT) and a subspace based method.We
numerically show that our algorithm outperforms the other methods by a large
margin. This shows that customized environment-specific solutions are important
to solve many future wireless applications, and we have paved the way to
develop further data-driven approaches.
