This is very similar to a project I had in mind, also using an SDR for radio spectrum mapping.
Unfortunately there is no ready-made solution to your exact problem, butand specifically there are no entirely Pi-based drones that I know of. But we can get pretty close to itby releasing the constraints a bit.
The simplest build would be an autopilot-equipped copter with an offboard SBC (e.g. the Pi) and an SDR dongle. The SBC would be linked to the flight controller via MAVLink or similar over UART, which would allow it to receive real-time position data and optionally send commands to the FC. The autopilot will then perform a waypoint mission defineduploaded either through the autopilot's ground station software or directly from the onboard Pi, sweeping around the antenna in a tight pattern, and the Pi will record and location-stamp the data. When the drone returns you could use some script of your own design to interpolate that log into a continuous radiationspatial intensity map.
This kind of solution is great in that you could use any waypoint-capable drone, as it only serves as a carrier for the mapping package, and the only integration you need is receiving GPS. You could probably even use a second GPS receiver in order to fully decouple the drone from the SDR package. Or you could go the other way and fully control the drone's behavior from the Pi via the link, the FC only providing the basics of flight and leaving the flightpath up to the Pi.
For the hardware, use any copter capable of carrying a Pi, dongle and antenna. Fully equipped ardupilot-ready kits capable of carrying a camera can be had for around $200, for which you only need to supply your own battery (and, if you wish, a 2.4G RC control link, which I'd recommend, but you can make do with just the 433MHz groundstation link if you're so inclined).
If you want the Pi to be integrated more closely into the drone, there are several Pi-specific solutions that I know of, but they all involve an external microcontroller-based flight controller board. For instance, there's the Navio by Emlid, which is an Ardupilot-equipped flight controller made in the form factor of a Pi HAT. Then there used to be the Outcast Droneworks MicroHawk, a micro-drone that uses a Pi Zero as part of its body. The page for it is now unavailable, however, so I don't know the current status of the project. In any case, this is in essence the same as sticking a regular FC board and a Pi on the same frame and connecting them together, the only difference is the form factor.
For the autopilot package, Ardupilot, PX4 and INAV are the most popular, and there are others as well.
Some parting notes:
I think it would be very beneficial to browse the forums for all of those autopilot packages describing how to perform mapping missions. The relevant threads will likely be mostly about photographic mapping, and thus use way sparser patterns and bigger altitudes, but the principles are exactly the same.
You should probably look into DGPS and RTK, and set up a reference station at the antenna to improve the positional accuracy of the map.
Also you should mind the polarization of your receiving antenna, otherwise your resulting radiation map may be altered significantly by cross-polarization attenuation. Maybe you could use a circular-polarized antenna, set up several linear antennae on the same drone, or make several passes with the receiving antenna in different orientations relative to the transmitting antenna under test.
