It's an interesting question, to be sure. The process for call setup, maintenance and breakdown is a fairly complex...
one that occurs during the process of making a cellular phone call.
There are many flavors of 3G —Universal Mobile Telecommunications System (UMTS), High Speed Packet Access (HSPA), EV-DO and more—but I will assume for the purposes of this discussion that we are talking about a 3GPP standard and a relatively recent flavor. Right now, that means HSPA, and rather than boiling the ocean on all of the possible parameters that might apply to the process of supporting an HSPA cellular connection, it will be instructive to simply talk in terms of call setup.
To set up a mobile session, the user equipment (UE)—in this case, the cell phone—issues a setup request to the UMTS Terrestrial Radio Access Network—e.g., the cellular network—where it is directed to the closest mobile switching center (MSC), which performs a call routing determination. Assuming the resources are available, the MSC responds to the UE with a call proceeding message.
The call routing determination allows the MSC to select a media gateway (MGW) to handle the call. It then issues an add request to the MGW to establish a new context and places a termination in that context. Once the new context, which is network-facing, is established by the MGW, the MSC server requests the radio area network to establish a radio access bearer (RAB) to handle the call.
When the RAB has been assigned, the MSC server establishes a media connection between the radio network controller (RNC) and the MGW. This process patches up a second termination context facing the RNC. Because the new termination is in the same context as the network-facing termination, a path is created from one side of the MGW to the other.
The MSC then sends an ISDN user port (ISUP) initial address message (IAM) to the PSTN. On receipt of an address completion message, from the far end, the MSC sends an alerting message to the UE. When the called party answers the call, an ISUP answer message is sent to the MSC. Finally, the MSC sends a connect message to the UE and the UE responds with a connect acknowledgement.
Of course, all this happens within milliseconds, so the complexity of the call set up is not usually experienced by the user. This is essentially what happens in all GSM-based networks, with some variations. CDMA procedures are not exactly the same, but are similar. Newer pre-4G networks are substantially different.
For more depth and a lot more detail, I would recommend "3G Wireless Networks" (Clint Smith and Daniel Collins, 2007, McGraw Hill).
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