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If you are working against background Johnson noise at all frequencies, you have the same output snr as if you stayed on one frequency. You only gain against a jamming station in the case that they would have been on the same frequency as you would have been on without hopping and the other frequencies you hop over have no jamming.
My favorite example is hopping over the 100 channels in the AM brodacast band with a signal that is -6 dB relative to the 100 stations that occupy all 100 channels. You get a -6dB s/j output, you do not get a 20 dB processing gain and a 14 dB s/j output.
In a DSSS system you have a broadband signal and a noise floor which can be equal or even greater than your signal. The despreading of the signal lowers the bandwidth of the signal and thus gives a higher amplitude of your signal (the power remains the same, because the bandwidth is now smaller!)
With respect to the smaller bandwidth you now have more S/N than you had before --> processing gain.
An FHSS modulation does no spreading of the signal, so it's impossible to get a processing gain 8O
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