ZMA Center Controller reported radio frequency problems in an area of one of their sectors. The Controller stated they could not talk to an aircraft that was experiencing icing and had to have another aircraft relay instructions for them.

Narrative

Aircraft X was handed off to us from SJU Center at FL220. After a few minutes I noticed that they were losing altitude so I had the D side call San Juan to find out. They advised us that he had icing and was descending to FL200. A few moments later; they were descending through FL200 and not in contact with SJU Center any longer. I called out for the pilot with no response. I then proceeded to go through a relay with an airline pilot to make sure they did not need any further assistance. Once the pilot was about 20 miles northwest SAPPO intersection I was able to hear them and they reported moderate to extreme rime icing from FL180-FL220.We need to have equipment that will allow us to provide QUALITY air traffic services throughout the entire sector; not just the high altitude air carriers. This aircraft was having an emergency like event and I was unable to provide any service to assist them due to the limitations of our frequency coverage. It is totally inefficient to have to go through a pilot relay when there is a situation like this; and it also can be dangerous if that information is also not being relayed correctly. We either need a new frequency site that provides radio coverage to ALL of the sector; regardless of altitude; or we need to redesign the airspace to account for our limited equipment.