# Transmitting over Unknown Fading Channel

I have a system with no diversity and the channel's coefficients change every $T = 10\text{ bits}$ transmitted. The channel estimation system has a flaw and detects the channel's coefficients equal to $h$ while their real values are $h+c$ where $c$ is a constant equal to $1$.

Is there any method I can apply to achieve a better BER than simply using the faulty $h$?

I am using BPSK.

• um, this sounds a bit obvious, but: if you know the error, why don't you simply use the right channel coefficient? – Marcus Müller Dec 9 '17 at 17:32
• the reason i know the error is because it is a simulation. I am looking for a method i can apply in a more realistic scenario, too – Gian Dec 9 '17 at 17:38
• Then don't say it's a fixed constant. We can't read your mind and see what is a "real" problem or not. – Marcus Müller Dec 9 '17 at 17:54

In general scenario, you cannot trust the estimate of $h$, it means that you cannot use coheent detection. Thus try non-coherent detection (detection by energy) : to send bit $0$, use 2 channel uses (2 symbols) $x_0 = [x, x] = [1, 0]$ and to send bit $1$, use $x_1 = [x, x] = [0, 1]$. The receive symbols are $y = [y, y]$
In the well-known Rayleigh flat fading channel, i.e. $y[m] = h[m]x[m]+w[m]$, the optimal detection rule will be \begin{align} \hat{x} &= x_0 \textrm{ if } |y|^2 > |y|^2\\ \hat{x} &= x_1 \textrm{ otherwise} \end{align}