The paper is concerned with stochastic linear-quadratic (LQ) problems in infinite time horizon with control-dependent diffusions and indefinite cost weighting matrices. A new frequency characteristic for the indefinite stochastic LQ problem is obtained. This characteristic is a complex matrix that can be calculated directly from the given parameters of the LQ problem. The equivalence of the following statements is established: 1) the LQ problem is solvable and has a unique optimal control; 2) the stochastic Riccati equation has a unique solution such that the induced feedback control is stabilizing; 3) the associated optimization problem of the bilinear form is coercive; and 4) the frequency characteristic matrix is uniformly positive definite.