Assuming that the Philadelphia experiment actually took place, a possible connection with Tesla's work could be traced back to his 1883 rotating magnetic field concept and a later proposal for the electronic detection of U-boats found in an article entitled "Tesla's Views on Electricity and the War" [Solutions to Tesla's Secrets].  It is possible that these concepts could have been incorporated into experiments designed to investigate the reduction of radar visibility of naval vessels.

Now, regarding the fabled "set for interplanetary communications," this gadget is spoken of in an unusual book titled Return of the Dove, pp. 195, 205-208. It is said to be reproducible using design clues to be "found in the lectures which Tesla gave between the years of 1890 to 1896..."