How to implement FIR filter power normalization constraints

1

Hello everyone, i’d like to implement FIR filter power normalization constraints.
My code is:

norm(A_FF*shape_pulse) == 1;
where A_FF is Linear matrix. and shape_pulse is my Optimization variable.

The problem is that the DCP doesn’t allow constraint: {convex} == {real constant}, which is not convex;
So how can I implement the constraint without changing my Optimization variable.

Thanks

2

The relaxation, norm(A_FF*shape_pulse) <= 1; is convex, and will be accepted by CVX. You will have to decide if that relaxation is acceptable. If it is not, then use a non-convex solver, such as available under YALMIP.

3

Thank you for your reply, Mark!

The relation norm(A_FF*shape_pulse) <= 1 is not useful for me;

I’ll try the non-convex solver, or change my Optimization variable.

4

Besides, I wonder if there is other affine expression to achieve the same constraint?

5

You can linearize around some point, but that will not be an equivalent model. A non-convex solver may essentially linearize as well, but in an iterative, and for robust solvers, safeguarded way.