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The Spread Spectrum technologies such as DSSS and FHSS are successful against frequency-selective fading because the original signal is spread to a larger bandwidth and different frequencies are used a different times.

Do these technologies also mitigate the problems imposed by time-selective fading?

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I hadn't heard the term "time-selective fading" before, and after a bit of research it appears that it refers to the effects of doppler spreading. Given that, the answer is "not really".

DSSS is typically extremely sensitive to carrier offset since the pseudo-random chipping sequence is usually quite long. The long time means that a little carrier offset can lead to destructive interference. This is dealt with by transmitting the data with a pilot. It is easy to search for the pilot across multiple carrier offsets by correlating using FFT techniques.

FHSS does not really have any particular advantages or disadvantages that I am aware of when it comes to handling doppler.

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