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Is it common to find systems having signal to noise ratio (SNR) less than 1 i.e. noise is more than signal? I am currently working with SNR of -5db to -20db. And how useful is it to work with sensor readings having negative SNR? I am asking it because the algorithm I am using to solve a problem works well with negative SNR but at positive and higher SNR, it is numerically unstable. This instability arises because of computation of hypergeometric function $_pF_q\left(;;\frac{z}{σ^2}\right)$. At high SNR, i.e. low $σ^2$, the argument $\frac{z}{σ^2}$ becomes very high, making the convergence of hypergeometric function very slow and the algorithm becomes numerically unstable.

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Yes, GPS signals are below the noise floor. Link

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  • $\begingroup$ UWB radars also work below noise floor. $\endgroup$ – learner Jul 14 '14 at 22:43
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It's quite common to work with signals that are below the noise. If you use signal of some length more than 1 you can exploit it to overcome noise impact so it's all right. As I've understood the issue is with algorithm convergence. It's unknown and it's difficult to define what the problem is (write some details if you're allowed). But maybe you should use $\frac{z}{\sigma^2+1}$ instead? So if SNR is pretty low, $\sigma^2$ is the major one and your algorithm will work well as you've written. And while SNR is high the argument will not be very high no more.

If you describe your approach briefly, somebody can probably tell you more about how to improve your algorithm.

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