Inter-Frequency Handover means mobility in connected mode between two different cells and different LTE frequencies, This topic will be assigned to Event A4 which is used for LTE Inter-Frequency handover.
It is recommended to have a look HO Events in LTE before reading this topic.

Details:

LTE Event A2 is triggered when the serving cell becomes worse than a threshold.
Event A2 triggering (start measurement for inter-frequency):

Mserv + Hyst < Threshold 

LTE Event A1 is triggered when the serving cell becomes better than a threshold.
Event A1 triggering (stop measurement for inter-frequency):

Mserv – Hyst > Threshold 

LTE Event A4 is triggered when a neighboring cell becomes better than a threshold.
Event A4 triggering (start inter-frequency handover):

Mneigh + Oneigh,freq + Oneigh, cell – Hyst > Threshold

Mserv: signal level or quality of the serving cell (RSRP or RSRQ).
Mneigh: signal level or quality of the neighbor cell (RSRP or RSRQ).
Threshold: defined signal threshold and it is different for A1, A2, A4. It is defined in eNodeB.
Hyst: hysteresis, it is defined in eNodeB and used to avoid ping-pong handover.
Oneigh, cell: Indicates the cell individual offset for the inter-frequency neighboring cell.
Oneigh, freq: indicates the frequency-specific offset for the inter-frequency neighboring cell.
Time to Trigger: this timer helps to avoid irregular measurement and handover.

* Note: all types of triggers is evaluated during Time to Trigger period and occur if the condition stays stable during the period, otherwise the event will be cancelled without triggering.

Conclusion:

Signal of serving cell is poor and UE starts to make measurement with A2 to find better neighbour cell, if the serving cell signal is getting better and stays stable during Time to Trigger then the UE stops measurement with A1. If it is not getting better during the Time to Trigger then it will make handover with A4 if neighbour cell condition is sufficient.

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