Problem with multiplication of two variables in cvx in matlab

Question

Here is the problem I'm trying to optimize.

where, x,y have non negative elements.

The code I have written for a simple one dimensional variable and not working is as follows

cvx_begin gp
    variable xCVX nonnegative  
    variable yCVX nonnegative  
    Objective = log(1+((8 * xCVX * yCVX)/((4 * xCVX + 2 * yCVX))));
    maximize (Objective)
cvx_end

I know the objective is concave so I used maximization and since there are multiplication, I used gp. but I get the error

Disciplined convex programming error: Illegal operation: {real constant} + {log-concave}

and without gp i get

Error using .* (line 262) Disciplined convex programming error: Invalid quadratic form(s): not a square.

changing the cost function with variable change ui = xi/yi and vi = yi/xi to

(u,v) = \sum_{i = 1}^{N} log(1 + (gi * hi /(gi / ui +hi / vi)) , u,v have non negative elements.

and finally w=1/ui z = 1/vi will lead to

(w,z) = \sum_{i = 1}^{N} log(1 + (gi * hi /(gi * wi +hi * zi)) , w,z have non negative elements.

which will result in Illegal operation: log( {convex} ). here there is no multiplication of w or z

What is the trick to solve this optimization problem?