The point of the data center is to compute, on the fly, unique phase solutions for moving devices being served by multiple antennas, and to compute new solutions as the devices move. It's a huge workload, perfect for a modern, high-speed multiprocessor system to tell the cell-tower antennas which phase delay to apply to (a) each antenna, (b) each data packet, and (c) each device in a separate, changing location.
You don't need a "datacenter" per se, but you need a private control plane shared by the devices so that they can pass relevant information to each other. As long as the sites are interconnected and have some sort of addressing that is tied to their geographic location (i.e. devices know very quickly who their neighbor devices are by address), a central datacenter is not necessary.
TL;DR You need a shared bus for passing geospatial data between geographically local devices.
Perhaps, I'm just using the language from the linked article:
"To work properly, a company backing the pCell technology would need to build out a large data center in addition to deploying the transmitters. It’s in the data center where servers constantly crunch away on the algorithms that form the unique wireless stream aimed at each device."
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