The only way I've figured out how to do that involves a complete mobile network reengineering - anonymous bearer tokens (so not bitcoin) to pay for network access tower-by-tower, and then something like TOR hidden services for the presence registry.
You could approximate it with a rotating prepaid data plan (can you actually obtain these without putting down an ID?) and actual TOR with heavily compensated VOIP (or forgo voice). You'd need to change the IMEI and any other identifying information of the network access device every time you refreshed the plan as well, or you could start a club of periodically exchanging them with likeminded people.
You could approximate it with a rotating prepaid data plan (can you actually obtain these without putting down an ID?) and actual TOR with heavily compensated VOIP (or forgo voice). You'd need to change the IMEI and any other identifying information of the network access device every time you refreshed the plan as well, or you could start a club of periodically exchanging them with likeminded people.