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The mobile phone that is far from the Base station antenna drains more power to sent higher power to over come the path loss and more noise than the one that is close to the Base station.
Depends upon the power and consumption efficiency of the battery, matter of usage also.
It is a function of distance , as much as going far away ; battery life decreases as it should increase the output power over Uplink to reach BTS antennas.... if it is the same as answered by someones then no need for the cost to build GSM sites & phones can use satellites.
In RF , all transmission systems affected by distances which means changes in out power & consequently pwr consumption from battery itself & that's why signaling msg submitted to report Tx/Rx levels using timing advance TA instructions
no matter how far or near you are from Base station , it dependes on how much power consumption by your battery.
The one that is fare the Station
Actually it does not matter if the cell phone is near or far from the base station. The Battery usage depends on the COVERAGE AREA of the base station. When the cell phone is on the edge of the coverage area or to be more specific,if hand offs occur often with poor signal received by the cell phone ,the battery drains faster.
There has to be no difference in Battery drainage.
The power management will work for both the clients and it does not matter if it is near by or far to the base station.