Does UE also report RI in RRC-connected mode but no data transmitted?

CRS is signal, not data. RI measurement can not be based on crs measurement.

Any measurement cannot be done on data , it can only be done on reference signals. Why, because reference signals are known in amplitude,phase,pattern,position by UE before receiving them. On receiving , UE tries to recover these reference signals. Once decoded , these become the basis for all reports UE sends to eNB including CQI, RI, PMI.

Data is random , you cannot deduce channel coefficients from it.

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