I have this equation, which is similar to SINR somehow but the covariance matrix is a function of vector $\mathbf s$ with length of $M$
$$SINR = \mathbf s^HC^{-1}(\mathbf s)\mathbf s $$
where
$$C(\mathbf s) = S(\mathbf s)WS(\mathbf s) + N $$
and $ S(\mathbf s) $ is covolution matrix of $\mathbf s$.
In simulations, it behaves as it's a concave function, and it's actually easy to show that it's concave in one-dimentional $\mathbf s$. So I tried to prove it with showing that $ g(t) $ is concave, where $$ g(t) = SINR (\mathbf s + t\mathbf v)$$ but getting second derivative of this function even with kronecker product gains nothing and I couldn't prove it. So I want to know if there is any idea to help me how to prove its concavtiy?
edit: matrix $N$ and $W$ are both PSD and $0 \prec W $. Aslo we have: $$ S_{M \times2M-1} = \begin{bmatrix} \mathbf s & 0 & \cdots & 0_{M-1} \\ & \mathbf s & \\ & & \ddots & \\ \mathbf 0_{M-1} & \mathbf 0_{M-2} & & \mathbf s\\ \end{bmatrix} $$ for convolution matrix of $ \mathbf s $