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If I am having a 13 bit pattern and sending it at IF frequency on the transmit side. On the receive side after IF conversion I am sending it to ADC. After digitizing the signal and removing the IF by filtering I am passing through a correlator. So if the pattern is 13 bits does SNR increase by $10\text{log}_{10}(13)$ dB? The more the length of the pattern the better the SNR?

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  • $\begingroup$ bit of problem with your terminology: You don't modulate bits onto your IF, you modulate symbols (think of symbols as physical "implementation" of bits or bit groups, makes everything much easier to understand later on). The question of processing gain depends on the number of bits you have per symbol, and the number of samples you take during one symbol duration. Also, it requires a noise process model (for example, white noise), but I don't see a realistic corner case where you get $10\log_{10}(13)\,\text{dB}$ of gain. $\endgroup$ – Marcus Müller Jan 27 at 13:51

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