CVX optimization problem, radar signal( Golden code)

Hi there, I have a problem for optimizing sidelobes of Golden code-127 after mismatched filter.

I have just 3 constraints.

first one to neglect trivial solution( work well).

The second for optimizaing sidelobe(work well).

the last one to maintain Loss in Power Gain (LPG) at somepoint.

if I comment the last constrain it gives me signal with sidelobe reduced by 1 dB.

if I put it, it gives me unfeasible solution. where is the mistake??

 cvx_begin
variables q(127,1) t
minimize t
subject to
(s'*q)==(s'*s);
for i=1:length(x_new1(:,1))
(q'*(x_new1(i)')*(x_new1(i))*q)<=t;
end
q'*q <=alpha*(s)*s' ;
cvx_end;

[Walter Roberson]

Note that cvx is a third party toolbox

[xiaopa]

Why can't i solve the value of q?