Invalid quadratic form(s): not a square (matlab)

Nonconvex
1

Hello guys,

I’m writing a code for convex optimization problem with CVX (matlab)
and I faced DCP errors
how can I solve it?

K = 5;
h = randn(K,1);
h = sort(abs(h));
disp(h)
sigma2 = 0.1; % 잡음 sigma^2
P = 10; % 제약 조건 상수 P

cvx_begin
variable a nonnegative;
variable b(K,1) nonnegative;

% MSE 정의
MSE_1 = cvx(zeros(K,1));
for i = 1:K
    MSE_1 = a * h(i) * b(i) - 1; % sum of squares
end
MSE = sum_square(MSE_1) + sigma2 * square(a);  

minimize(MSE)

|b_k|^2 <= P for all k
subject to
    b.^2 <= P;

cvx_end

the error is
Disciplined convex programming error:
Invalid quadratic form(s): not a square.

오류 발생: * (36번 라인)
z = feval( oper, x, y );

오류 발생: OAC_CVX (17번 라인)
MSE_1 = a * h(i) * b(i) - 1; % sum of squares

and original problem is
image

2

In the offending statement, two CVX variables are multiplied, a and b(i) That is non-convex. So this looks like a non-convex constrained nonlinear least squares problem.