I saw on Wiki that KM can be used in a technological way or in an organizational way. So, the first thing to do is determine if your interests are aligned with info technology or organizational management.
Are you an IT scholar or a management scholar?! :-)
I suggest these:
Qualitative work, maybe interviews, to determine the effectiveness of a particular KM strategy.
Quantitative work to compare the outcomes of various KM strategies.
A multiple case study approach used to compare various KM software programs.