EDIT: This post is incorrect. I am keeping it only so that the following posts make sense. Please go by my previous post, which was my original, but deleted, and now undeleted post.

Given that you are minimizing, the objective function must be convex in order for the problem to be convex.

if you declared a nonnegative variable `sqrt_ap_power`

instead of `ap_power`

, then you could avoid the `sqrt`

in the objective function. But that would turn the affine (linear) constraints into non-convex quadratic equality constraints involving `sqrt_ap_power^2`

.

Is`channel_est_va`

r channel estimated variance, and therefore nonnegative? Given your taking the square root of `ap_power`

and given the constraints, I presume and will assume `channel_est_var`

is nonnegative. Therefore, both sides of the equality constraints can be squared, resulting in

`sqrt_ap_power(m,:)*sqrt(channel_est_var(m,:)') == 1`

The objective function using `sqrt_ap_power`

in place of `ap_power,`

cab be squared as you have it, but the optimal value of `sqrt_ap_powe`

r will be the same if it is not squared, and then you would have a Linear Programing problem.

So

```
cvx_begin
variable sqrt_ap_power(ap_num,user_num) nonnegative
minimize(sum(sqrt_ap_power(:,k).*channel_est_var(:,k),1));
subject to
for m = 1:ap_num
sqrt_ap_power(m,:)*sqrt(channel_est_var(m,:)') == 1
end
cvx_end
```

I will let you check to make sure I didn’t mess up any parentheses.