Combining simultaneous measurements of the same signal for better SNR? I have multiple data sets of the same signal measured using the same hardware and I want to know what sort of techniques I can use to improve the SNR.

I was thinking if I adjust and ensure they have the same phase, i could coherently add them, but I didn't really see an improvement in SNR. I'm guessing the reason for this is because the noise gets added together as well.

It makes me wonder two things:


What are some valid ways to combine like signals, to improve SNR
Is there any way to exploit the similarity in signals to reduce noise?


Thank you
Coherent Gain happens when you have copies of the same signal but different noise. If the noise is independent in each copy, the gain should be $10log N$ dB where $N$ is the number of copies. For a well crafted measurement system, additive electronic noise should be independent. Things like ambient noise will have some correlation provided a reasonable distance between sensors and $5logN$ is a reasonable lower expected gain.

If you don’t see at least $5 log N$ dB, then there is probably something wrong. Coherent Gain works. If it didn’t, many here would not have jobs.  

You might try cross correlating pairs of your copies as a diagnostic. Without knowing your data, I cant say with certainty that you should see a well defined peak but the absence of a well defined peak would be a cause for concern