$\bf x$ and $\bf a$ are complex vectors, $\bf C$ is positive definite complex matrix, $\bf B$ is positive-semidefinite complex matrix. What's the objective value? Thanks!
$$\max_{\bf x} \frac{\mathbf{x}^{H} \mathbf{a a}^{H}\mathbf x}{1+\bf x^{H}Bx}$$ $$ {\rm s.t. } ~~ {\mathbf{x}^{H} \mathbf{Cx} } \leq P$$
There is an elegant solution to your problem, involving the principle eigenvector. You find a similar problem with its solution in http://www.fhp.tu-darmstadt.de/nt/fileadmin/nas/Publications/2010/Filter-and-Forward...chen.pdf
In this paper, consider problem (43) with the solution given by (47).