Transmitting over Unknown Fading Channel
The strategy depends heavily your "realistic scenario", e.g. which estimator, which equalizer, which estimation error, etc.

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) $x_0 = [x[0], x[1]] = [1, 0]$ and to send bit $1$, use  $x_1 = [x[0], x[1]] = [0, 1]$. The receive symbols are $y = [y[0], y[1]]$

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} &amp;= x_0 \textrm{ if } |y[0]|^2 &gt; |y[1]|^2\\
\hat{x} &amp;= x_1 \textrm{ otherwise}
\end{align}