In LTE all cells have the “same frequence”, so coverage ovelarpping must be reduced for just allow handover continuity. So, please check if main server area is well defined and if coverage overalap is not too much. You can verify it by DT or even better verifying the Time advance (TA) distribution. A possible way to solve it is by optimizing electrical tilt and also verifying antenna vertical and horizontal beam. For urban areas, for example horizontal beam should be kept up to 60 or 65degress. Verify also PCI conflict and antennas VSWR alarms.
Another possible issue is the external interference, mainlym but not exclusive, with TDD networks. For case like that the spectrum analyzer can be used for interence hunting in order to identify external sources at the frequence range of LTE.
Regarding Spectrum Analyzer:
With a directional antenna pointing to the sector antenna, for example. So using this antenna in the area reported as interfered one it is possible by swepping the area to get the external interference source.
Here for example you can see Indication of seven repeatedly transmitted beams plus control data in the time domain: