Consider the equation:
$\mathbf{y} = \mathbf{\Lambda_{\epsilon}C\Lambda_{\epsilon}^{\dagger}h}$, where $\mathbf{y}$ and $\mathbf{h}$ are $n$-length complex-vectors, $\mathbf{C}$ is a circulant $n\times n$ complex matrix, and $\mathbf{\Lambda_{\epsilon}}$ is a diagonal matrix with $\mathbf{\Lambda_{\epsilon}}(k) = \exp(i\frac{2\pi \epsilon}{n}k), k =0, 1 \ldots (n-1)$. ($\mathbf{\Lambda_{\epsilon}^{\dagger} = \Lambda_{-\epsilon}}$)
How can we solve for $\epsilon$?