matched filtering in GSM
First, please read this answer of mine for a detailed description of matched filters for real-valued signals. In particular, note that what I called the matched filter for a signal $x(t)$ is a(n LTI) filter with
impulse response $h(t) = x(-t)$ which is better described as the time-reversed signal rather than the "inverse" of the impulse response as you call it: to many people, inverse would suggest $[x(t)]^{-1}$ or $-x(t)$
depending on whether they were thinking of multiplicative or additive inverse.. Note also that convolving the channel output with the 
time-reversed channel impulse response does not "cancel" the effect of the channel on the signal at the channel input. In general,
matched filtering distorts the signal being filtered tremendously because
the goal of matched filtering is to produce a peak response at the desired sampling time. This is quite different from the audio enthusiast's desire of
reproducing the input signal with the highest possible fidelity, and
thus using an "inverse" filter to remove all traces of the distortion
caused by the channel filter.  See
the last part of my answer cited above for some pictorial illustrations of how matched filtering distorts the signal so as create a peak response
at the sampling instant.

Second, there are no complex signal in real life; they exist only in the diseased imaginations of DSP engineers.  What we have in real life
is a real-valued bandpass signal
$$x(t) = x_i(t)\cos(2\pi f_0 t) - x_q(t)\sin(2\pi f_0 t)
= \Re\left(x_c(t) e^{j2\pi f_0t}\right)$$
where $x_i(t)$ and $x_q(t)$ are slowly varying signals compared to
the carrier signal of frequency $f_0$ Hz, and 
$x_c(t) = x_i(t) + jx_q(t)$ is called the complex baseband equivalent
of the RF signal $x(t)$. The filter matched to $x(t)$ thus has
impulse response 
\begin{align}
x(-t) &amp;=  x_i(-t)\cos(-2\pi f_0 t) - x_q(-t)\sin(-2\pi f_0 t)\\
&amp;= x_i(-t)\cos(2\pi f_0 t) - [-x_q(-t)]\sin(2\pi f_0 t)\\
&amp;= \Re\left([x_i(-t) -j x_q(-t)]e^{j2\pi f_0t}\right)\\
&amp;= \Re\left([x_c(-t)]^* e^{j2\pi f_0t}\right)
\end{align}
The complex baseband equivalent of the matched filter impulse
response is thus $[x_c(-t)]^*$ and thus when the DSP engineer
proceeds to match-filter the complex baseband equivalent input $x_c(t)$,
she must convolve $x_c(t)$ not with $x_c(-t)$ but rather with 
$[x_c(-t)]^*$, cos doing the former instead of the latter
would result in her being in a state of sin.