The mast with the pyramid at the base is operated by the Royal Signals, to the best of my knowledge. I presume it is/was involved in communications with BAOR in Germany. All of the microwave dishes have been taken down in recent years.
The other remaining mast is used by broadcasters for VHF FM transmissions, and by mobile phone operators.
The fourth mast was knocked down years ago. I think it was used by the Coastguard and became surplus to their requirements when they built their own mast by the Coastguard station.
http://tx.mb21.co.uk/gallery/swingate.php
The masts originally supported the transmitting aerials for the Chain Home radar system. These were wire aerials strung between massive platforms at the top and half way down. The idea of having four masts was to have four independent aerial systems with the wire aerials cut to the correct dimensions for different wavelengths.
In the event of jamming by the Germans, it would then be easy to shift frequency and transfer immediately to the matched aerial system on one of the other masts. In the event, jamming was not a problem and improved aerial arrays were strung between the masts.
An example of one of the radar masts in its original form has been preserved. It was originally at Canewdon and was reconstructed at Great Baddow near the Marconi factory in Chelmsford.
http://www.chelmsford.gov.uk/media/pdf/7/m/Great_Baddow_Mast_A4.pdf
When the remaining two masts are surplus to requirements, it would be gratifying to see one preserved in similar fashion, with the platforms and aerial arrays similarly reconstructed. Swingate was the closest Chain Home station to France and was of pivotal importance in the Battle of Britain and subsequently. The CH stations were very early technology and became less important later in the war but enjoyed a late flowering when their characteristics made them ideal for tracking the ballistic trajectories of the V2 missiles in the closing stages of WW2.
Any preservation is wishful thinking of course as there is already so much history in Dover that is ignored and covered up. The last of the transmitter masts at Bawdsey Manor, where all the research was conducted, was torn down ten years ago so the chances of one being preserved at Dover are remote to say the least.
http://www.independent.co.uk/news/uk/this-britain/fight-lost-to-save-battle-of-britain-radar-mast-698653.html