To meet the capacity needs of the next generation wireless communications, U.S. Federal Communications Commission has recently introduced Spectrum Access System. Spectrum is shared between three tiers - Incumbents, Priority Access Licensees (PAL) and General Authorised Access (GAA) Licensees. When the incumbents are absent, PAL and GAA share the spectrum under the constraint that GAA ensure the aggregate interference to PAL is no more than −80 dBm within the PAL protection area. Currently GAA users are required to report their geolocations. However, geolocation is private information that GAA may not be willing to share. We propose a distributed GAA power allocation algorithm that does not require centralised coordination on sharing locations with other GAA users via SAS. We analytically proved the critical point of the interference along the PAL protection area to avoid calculating the interference on every points of the area. We proposed exclusion zone, transitional zone and open zone for GAA users to calculate the self-determined transmit power. Simulation results show that our method meets the interference requirement and achieve more than 90% of capacity approximation to the optimal centralised method, while completely masking the GAA locations.