Using the cyclic permutation invariance of trace, the objective can be rewritten as square_pos(norm(a'*phi)
), which can be replaced by norm(a'*phi)
because it has the same argmin.
Your semidefintie constraint, as written, is a Bilinear Matrix Inequality (BMI) constraint, which is non-convex and not allowed by CVX.
See my answer to your previous question ERROR:Disciplined convex programming error: Only scalar quadratic forms can be specified in CVX . Did you not learn from that answer?
The link below was also provided in my answer to your previous question. Perhaps you did not read it carefully enough?