# 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.

• Thank you, but you appear to have focused on what happens to the signal rather than how it can be reconstructed. I have some idea about how receiving echoes in the signal does not mean that all information is lost, but how do the various devices go about reconstructing the original signal? Especially when the "multi" in multipath means more than two. – JohnEye Mar 31 '16 at 22:20
• I suspect blind deconvolution would be the way to go, but I'm not too sure about the feasibility of such a solution in real-life setup. – JohnEye Mar 31 '16 at 22:37
• @JohnEye Sorry, the title of your post is Multipath resistance of spread spectrum systems so that is what I focused on! :-) – Peter K. Apr 1 '16 at 11:44

LTE uses OFDM. OFDM with a long enough cyclic prefix turns multipath distortion into a large number of flat fading channels at slightly different frequencies. An OFDM system can either dynamically re-assign channels that have faded below some allowed S/N, or use some sort of redundancy (an ECC or error correcting code) across channels.