I am a PhD student. And my research topic is cellular localisation by using fingerprinting method (database correlation method ). I implement some methods and I want to prove the results by using real RSS (radiomap).
I don't know of a publicly available database, although apps like OpenSIgnal will implicitly have such a database. In terms of actual use of a database, there is a US company, Polaris Wireless, that will integrate its (RSS, path loss -based) location based services solution with operators. These solutions typically work better in radio cluttered areas (urban, indoor) than the TDOA solutions do. You may be able to collaborate with them. Note that such a national map for an operator will change as the network evolves.