# I want to use CVX to formulate and solve the following problem

I have tried to implement codes but they failed. My codes are as follows

the error is about the CVX ruleset violation related to square root in the constraints.

I have tried to convert the MATLAB syntax to use norm but it has an issue with noise variance term. can someone have some idea to sort this issue out ?

Did you try
norm([a_t*w;sigma])

There should be no issue with that.

The main issue is the norm |a_rw|. The constraint |a_rw|-\mathrm{something}\geq 0 will never be convex.

Thanks @Michal_Adamaszek . I was fixated on the norm going the “correct” direction to be used in a convex fashion, and neglected to pay attention to the other term, which, as you point out, is not.

Therefore, the constraints are non-convex, and the problem is non-convex.