Low rank hankel matrix approximation via nuclear norm

i want to solve the problem

where H is a hankel matrix with xi entries , and x’s are the matrix entries with size p by m, what is the easiest to way to do it in cvx,

Between the hankel keyword for variable declaration, norm_nuc, norm(...,'fro'), and square_pos, that should be very straightforward. Perhaps you would benefit from re-reading the CVX Users’ Guide.

but my hankel matrix is populated by block entries unlike scalars, can hankel(c,r) given by cvx handles that

I don’t know. You can figure it out as well as I can. I think you should be able to build up the matrix structure you need by concatenation of blocks (declare the blocks appropriately in CVX), the same as you could in “regular” MATLAB.