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I want to understand what actually happens in the direct sequence spread spectrum demodulator ? Why is it said that the signal is recovered from below the noise floor ? Can someone please explain the physical / intuitive interpretation of demodulation in DSSS. ?

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Mathematically, you correlate your received signal with the (known) spreading sequence. That means that a single output of that correlator contains energy from all the sequence, not only from a few signal samples.

That means that if there was signal energy of $e$ in each single sample, and the sequence is $N$ samples long, then the energy of each symbol is $eN$ at the receiver. Noise, which also gets summed up, however, doesn't grow linear with the length $N$ of the sum (unlike the actual TX signal, it isn't correlated with the spreading sequence).

The fact that signal energy grows linear with $N$, but noise doesn't, means that you get an SNR improvement, which can lift the signal, whose power is below the noise power level, above the noise floor.

An SNR improvement incurred by processing the samples (and most commonly, correlating them with something) is called processing gain. You will find that term when you search for "DSSS receiver" very often.

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