What happens if the noise has no zero mean? I mean, if the exercise is something like: $$y(k) = A x + \eta(k)$$
When I have zero mean, I start from: $$y = A x$$ $$\Rightarrow \hat{y} = A \hat{x}$$ Using algebra, I to get to this equation: $$A^H y = A^H A \hat{x}$$
But what happens if it has no zero mean? I have to use the following inner product, I suppose: $$\langle x,y \rangle = \mathbb{E}[(x-\mathbb{E}[x])^H(x-\mathbb{E}[x])]$$ But I can't see how to get to an equation from that.
Thanks!