First, let's discuss how to check for some fixed radius ~r~ if all antennas can communicate. Two antennas can communicate directly if their distance is at most ~2r~. We can build a graph over antennas, and add edges for all pairs of antennas that are closer than ~2r~. Then, we need to check if the graph is connected, which can be done for example with DFS.

The optimal ~r~, that is the minimal ~r~ for which the constructed graph is connected, can be found using binary search. For the upper bound, we can put for example ~10^9~. The complexity is ~\mathcal O(n^2 \log_2 10^9)~.