how does a cell phone transmitter work?
no operator nowadays designs 20Km cell radius, Link budgets like that aint workable with modulation schemes and mobile phone class mark power nowadays. 

The example you got was a 1st Generation link budget with a 25 watt handset on narrowband FM analog. 

Most probably you got hold of an NMT link budget calculations used in the mid 80s. NMT or Nordic Mobile Telephone is a standard embraced by nordic countries and other countries outside the baltic.

They are vehicle installed phones, and has powers up to 50Watts and comes in 450MHz and 900MHz band.

NMT was later scrapped as ITU allocated the 900MHz bands for GSM and the North American Equivalent.

Saw NMT until the late 90s for countries with large logging concessional areas, last users of this system were logging and mining companies.