If you have purchased a new LTE phone(UE) from an AT&T showroom. You walk out of the store all excited. You power on the phone. The map to go from no connection at all to your UE selecting AT&T connection to a cell works in 3 simple steps
What is Cell Selection ?
Cell selection is a procedure which allows UE to camp on to a cell. So that UE can make an actual RF connection to the network, after camping on to the cell. During cell selection off course UE , will look for a cell with better RF coverage. However , the better RF coverage is computed mathematically as shown in Selection criteria at the end below.
Conditions for camping on a Cell
UE will always prefer to camp onto a suitable cell. Therefore , it will always keep on looking for a suitable cell. If it cannot find one, then it will go and camp on an acceptable cell. The question which comes to mind is. What the heck is a suitable cell ?
Suitable Cell:
A suitable cell is defined as a cell which
Types of Cell Selection
There are 3 types of cell selection

If the UE was already connected, and for example went out of coverage. On the return back into good coverage Stored Information cell selection will take place

If the UE is leaving from RRC Connected Mode to RRC Idle Mode, then cell selection will take place like this
Criteria for Cell Selection
In general Cell Selection criteria is based on finding a better RF coverage cell for the UE. The coverage strength and quality of a cell in LTE is measured generally on :
S-Criteria based on RSRP (Cell Selection Criteria)
Cell Selection Criteria(also know as the S-criteria) is defined as
The above criteria is based on RSRP
Parameters for Cell Selection
Qrxlevmeas = RSRP measured by the UE in dBm
Qrxlevmin = minimum required RSRP signaled within System Information Block 1 (SIB 1)
Qrxlevminoffset = measurement offset which is only applied when a cell is evaluated for cell selection as a result of periodic search for higher priority PLMN while camped on a Visited PLMN. Qrxlevminoffset is optionally included within SIB 1 . A value of 0 dB is applied if Qrxlevminoffset is excluded from SIB 1.
Pcompensation = Defined as MAX(P emax – P umax, 0 ) where P emax is the maximum allowed uplink transmit power within the cell, and P umax is the maximum transmit power capability of the UE. If the UE transmit power capability is less than the maximum allowed transmit power , Pcompensation makes cell selection criteria more difficult to achieve . This avoids UE camping on cells for which they have insufficient transmit power to access i.e., towards cell edge
S-Criteria based on RSRQ (Cell Selection Criteria)
The newer version of cell selection criteria(S criteria ) according to release 9 of 3GPP specifications add a quality check to the cell selection criteria given as:
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