It is told that mobile Base Stations consume approximately 1 kW of power non-stop. Meantime I read that watching a movie every week at your mobile phone consumes as much energy by the network as powering a refrigerator for year or two. Does it mean that power, used by base stations is proportional to the data transfer amount and is about 1 kWh per GB and average can be much lower than 1kW? BTW, why is power consumption so high if mobile does not consume so much communicating with the same station?
I look at this reductively. A base station is a giant radio receiver and transmitter serving a geographic area (cell). Connected to the base station and maybe considered part of it is the access networking piece, some software on some server-style unit that converts to IP and gets the traffic into/out of the carriers network.
There is a fixed basic cost of transmitting even if no one is there: think of a radio tower in a rural location at night, say. When the first phone attaches, the base station has work to do to get them hooked up to the network. And then (depending on where you put the boundary) work to convert radio signaling from the phone to IP. The more phones, the more work. The more work, the more energy used.
Now, given that the amount of work induced by one phone is very much smaller than the work required to power the tower, you might say that effectively the energy requirements are independent of the number of phones attached, but a very accurate accounting would definitely show a difference.