Multipath resistance of spread spectrum systems I have been reading about various telecommunications technologies and one thing keeps being repeated many times without a clear explanation - that spread spectrum is not only resistant to multipath interference, but that it can even use it to improve recovery of the data being transmitted. This is frequently mentioned in articles about LTE or DVB-T.

How does this work? I can imagine that something like autocorrelation could be used, but I'm also pretty sure that this is not the way it's done.
The key idea in spread-spectrum communications is to use much more bandwidth than the minimum required for the signal being sent.

Multipath effects occur when the sent signal $s(t)$ and a delayed, attenuated version of it interfere at the receiver:
$$
r(t) = s(t) + \alpha \cdot s(t-\tau)
$$

If $s(t)$ is really narrow band (a sinusoid), and $\alpha = 1$, then 
$$
r(t) = \sin(\omega t) + \sin(\omega(t+\tau))
$$
and if $\omega\tau = \pi$ you can get perfect nulling:
$$
r(t) = \sin(\omega t) + \sin(\omega t + \pi) = 0
$$

If, however, $s(t)$ is not a simple sinusoid, then perfect nulling can be eliminated:
$$
r(t) = [\sin(\omega t) + \sin(\omega_2 t) ] + [\sin(\omega(t+\tau)) + \sin(\omega_2 (t+\tau)) ]
$$
even if  $\omega\tau = \pi$, if $\omega_2$ is chosen well, then $\omega_2\tau \ne \pi$ so there is still some signal to receive.