Noise estimation
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From: Doug on 12 Aug 2010 10:58 Hello, Is there a method to estimate the statistical properties of additive noise from a received signal observation. Assume we have y(k) = x(k) + n(k) and we observe the received signal y(k). I would like to know if there is a way to determine the autocorrelation of the noise process n(k), that is Rnn. This is not a speech problem. x(k) is a digital PAM signal that is corrupted by ISI, it can be assumed cyclostationary. To simplify the problem, we can assume the noise is white Gaussian noise, can we determine the noise variance, sigma^2, and hence Rnn for this simplified case? Ideally I don't want to assume anything about the noise, but if assuming white gaussian noise make things tractable, I take that solution over nothing Thanks in advance -Doug
From: Tim Wescott on 12 Aug 2010 11:19 On 08/12/2010 07:58 AM, Doug wrote: > Hello, > > Is there a method to estimate the statistical properties of additive > noise from a received signal observation. Assume we have > > y(k) = x(k) + n(k) > > and we observe the received signal y(k). I would like to know if > there is a way to determine the autocorrelation of the noise process > n(k), that is Rnn. This is not a speech problem. x(k) is a digital > PAM signal that is corrupted by ISI, it can be assumed > cyclostationary. > > To simplify the problem, we can assume the noise is white Gaussian > noise, can we determine the noise variance, sigma^2, and hence Rnn for > this simplified case? Ideally I don't want to assume anything about > the noise, but if assuming white gaussian noise make things tractable, > I take that solution over nothing > > Thanks in advance > -Doug Is the ISI known? In theory you could demodulate the digital message, remodulate it back to its ideal original, then corrupt it with the ISI to get an estimate of x(k). Then you subtract that out of y(k), and play with n(k) to your heart's content. I imagine that this would only work in practice when n(k) is fairly bad, because otherwise it'll be drowned out by the inaccuracies of the process I mention above. I've never tried this, so I couldn't comment on how well this would work in practice -- other than saying that if you're designing a system from scratch, it may be cheaper to arrange for quiet periods dedicated to measuring the noise that it would be to do all the engineering work to accurately measure the noise in the presence of the signal. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
From: Vladimir Vassilevsky on 12 Aug 2010 11:27 Doug wrote: > Hello, > > Is there a method to estimate the statistical properties of additive > noise from a received signal observation. Assume we have > > y(k) = x(k) + n(k) > > and we observe the received signal y(k). I would like to know if > there is a way to determine the autocorrelation of the noise process > n(k), that is Rnn. This is not a speech problem. x(k) is a digital > PAM signal that is corrupted by ISI, it can be assumed > cyclostationary. > > To simplify the problem, we can assume the noise is white Gaussian > noise, can we determine the noise variance, sigma^2, and hence Rnn for > this simplified case? Ideally I don't want to assume anything about > the noise, but if assuming white gaussian noise make things tractable, > I take that solution over nothing Synchronize to the baud rate and compare the statistics at the end and at the 1/2 of the symbol interval. VLV
From: Doug on 12 Aug 2010 15:09 On Aug 12, 11:19 am, Tim Wescott <t...(a)seemywebsite.com> wrote: > On 08/12/2010 07:58 AM, Doug wrote: > > > > > > > Hello, > > > Is there a method to estimate the statistical properties of additive > > noise from a received signal observation. Assume we have > > > y(k) = x(k) + n(k) > > > and we observe the received signal y(k). I would like to know if > > there is a way to determine the autocorrelation of the noise process > > n(k), that is Rnn. This is not a speech problem. x(k) is a digital > > PAM signal that is corrupted by ISI, it can be assumed > > cyclostationary. > > > To simplify the problem, we can assume the noise is white Gaussian > > noise, can we determine the noise variance, sigma^2, and hence Rnn for > > this simplified case? Ideally I don't want to assume anything about > > the noise, but if assuming white gaussian noise make things tractable, > > I take that solution over nothing > > > Thanks in advance > > -Doug > > Is the ISI known? > > In theory you could demodulate the digital message, remodulate it back > to its ideal original, then corrupt it with the ISI to get an estimate > of x(k). Then you subtract that out of y(k), and play with n(k) to your > heart's content. > > I imagine that this would only work in practice when n(k) is fairly bad, > because otherwise it'll be drowned out by the inaccuracies of the > process I mention above. > > I've never tried this, so I couldn't comment on how well this would work > in practice -- other than saying that if you're designing a system from > scratch, it may be cheaper to arrange for quiet periods dedicated to > measuring the noise that it would be to do all the engineering work to > accurately measure the noise in the presence of the signal. > > -- > > Tim Wescott > Wescott Design Serviceshttp://www.wescottdesign.com > > Do you need to implement control loops in software? > "Applied Control Theory for Embedded Systems" was written for you. > See details athttp://www.wescottdesign.com/actfes/actfes.html- Hide quoted text - > > - Show quoted text - Tim, The ISI or equivalently, the channel impulse response is not known. I need Rnn or at least sigma^2 in order to estimate the channel (long story). There is no way to get reliable symbol decisions; channel estimation must be done first. Thanks! -Doug
From: Doug on 12 Aug 2010 15:13
On Aug 12, 11:27 am, Vladimir Vassilevsky <nos...(a)nowhere.com> wrote: > Doug wrote: > > Hello, > > > Is there a method to estimate the statistical properties of additive > > noise from a received signal observation. Assume we have > > > y(k) = x(k) + n(k) > > > and we observe the received signal y(k). I would like to know if > > there is a way to determine the autocorrelation of the noise process > > n(k), that is Rnn. This is not a speech problem. x(k) is a digital > > PAM signal that is corrupted by ISI, it can be assumed > > cyclostationary. > > > To simplify the problem, we can assume the noise is white Gaussian > > noise, can we determine the noise variance, sigma^2, and hence Rnn for > > this simplified case? Ideally I don't want to assume anything about > > the noise, but if assuming white gaussian noise make things tractable, > > I take that solution over nothing > > Synchronize to the baud rate and compare the statistics at the end and > at the 1/2 of the symbol interval. > > VLV- Hide quoted text - > > - Show quoted text - Vladimir, It is no problem to do symbol synchronization, but I don't understand how comparing the statistics at mid-sym and end-sym will get you anything. Do you have more info or point me to a good reference? Also, I just read that one way get sigma^2 is to find the minimum eigenvalue of Ryy. This makes some sense and given the fact that x(k) has a zero in its power spectral density I think the noise in that region should yield a good result. Does anyone have more information on this technique?? Thanks again -Doug |