How to express this problem with CVX?

The problem is denoted as
I don’t know how to express the constraints C2 and C3

I don’t know what the dimensions are, but the RHS of C2 looks like a 2-norm which is the concatenation of Hk’*Pbar and sigma. You ought to be able to use the same concatenation in CVX as if everything were MATLAB (not CVX) variables.

C3: You could use a for loop with one constraint for each k. Or perhaps use repmat and do it all at once without using for loop. In CVX, matrix >= 0 constrains all elements to be >= 0 (provided not in SDP mode).

I leave the details to you because I don’t know the dimensions of anything.