Let me expound a bit on Ironraven's msg. In any digital system, your phone is transmitting all the time, talking to the cells it can hear, and helping determine which is the best cell to talk to.

This information is also used by the network to figure out where calls to your phone need to be routed. Otherwise, calls to you from an external number would never be delivered to you. In your network, there's a server called an HLR, or home location register. This is a database that holds all of your network and account information. When you leave your home network and move to another network, your local information is stored in a VLR, or visitor location register. The interaction between the HLR and VLR are used to figure out how to get a call to you.

This stuff is updated all the time, but ordinarily nobody would be looking at it. The carrier would have to have the engineering staff draw logs from the VLR database (probably manually), figure out what sector on what cell on what switch that was, then go get the radio propagation maps to figure out what that cell and sector was covering. Then they'd know where to look.

An external antenna is absolutely a help. Antenna gain is the same whether you are transmitting or receiving, and every 6dB of gain gives you a doubling in range.