The problem can be formulated in CVX, so it is convex.
log of concave (or affine) argument is concave. The sum of such terms is concave. Maximization of such a function is a convex optimization problem, presuming the constraints are convex. In your case, the individual terms in the objective function are concave perspeocive functions, and therefore their sum is concave, which can be maximized in a convex optimization problem.
I recommend you read
and read and solve some exercises in at least the first 5 chapters of Convex Optimization – Boyd and Vandenberghe, which is freely downloadable at the author’s website at the link provided.