If E involves trig functions of optimization variables, then an equality constraint involving it is non-convex, and can not be handled by CVX.
As for my above statement, "As you have literally written the problem (perhaps you have typos), the problem is infeasible, because you are (twice) constraining the same thing to be both 1 and 0", I see now that the four equality constraints are with the four different combinations of phi and theta as subscript and superscript, so they are apparently not infeasible. Nevertheless, this appears to be non-convex.
If there is a convex optimization problem, then it's you' responsibility to extract it out of the paper and present it in a self-contained way. And of course you should show it is convex. If you can do all that, then maybe we can help you figure out if there is a way of entering it into CVX. Please read http://ask.cvxr.com/t/why-isnt-cvx-accepting-my-model-read-this-first/570 .