Hello, I am finding the amplitude of the signal using complex demodulation (quadrature demodulation). I wanted to know maximum accuracy to which the amplitude of the one of the frequency contained in phase modulated signal(which is the input) can be estimated.The accuracy to which the amplitude obtained should be 10^-8 (between actual and estimated by this method). So i wanted to know if there is any cramer rao bound (accuracy to which amplitude of the signal can be estimated). The SNR of the signal is about 55 to 60 dB. waiting for reply with regards praveen

# Cramer rao bound on estimating amplitude of the signal using complex demodulation

Started by ●July 14, 2003

Reply by ●July 14, 20032003-07-14

praveenkumar1979@rediffmail.com (praveen) wrote in message news:<ff8a3afb.0307140206.15505f8@posting.google.com>...> Hello, > > I am finding the amplitude of the signal using complex demodulation > (quadrature demodulation). I wanted to know maximum accuracy to which > the amplitude of the one of the frequency contained in phase modulated > signal(which is the input) can be estimated.The accuracy to which the > amplitude obtained should be 10^-8 (between actual and estimated by > this method). So i wanted to know if there is any cramer rao bound > (accuracy to which amplitude of the signal can be estimated). The SNR > of the signal is about 55 to 60 dB. > > waiting for reply > with regards > praveenA good lullaby on "Crammer-Rao Bound" by Peter Kootsookos is interesting - see http://www.dspguru.com/comp.dsp/fun/crbound.htm!! From my limited stock I can say, the CR bound provides a lower bound on the estimator variance of an unbiased estimator. If we know your signal's pdf we can calculate Fisher information matrix and its inverse to get variance estimate what is known as CR lower bound. It looks like your SNR is high. I am wondering what accuracy you expect at low SNR- Is it the same? I guess CR bound at low SNR and high SNR may not be same - please correct me if I am wrong. Regards, Santosh

Reply by ●July 15, 20032003-07-15

praveenkumar1979@rediffmail.com (praveen) writes:> I am finding the amplitude of the signal using complex demodulation > (quadrature demodulation). I wanted to know maximum accuracy to > which the amplitude of the one of the frequency contained in phase > modulated signal(which is the input) can be estimated. The accuracy > to which the amplitude obtained should be 10^-8 (between actual and > estimated by this method). So i wanted to know if there is any > cramer rao bound (accuracy to which amplitude of the signal can be > estimated). The SNR of the signal is about 55 to 60 dB.Kay's book ([1], page 542) says that the CRLBs for estimating A, f and phi in: x[n] = A exp( j 2 pi f n ) + complex white Gaussian noise are: var(Ahat) >= sigma^2 / ( 2 N ) var(fhat) >= 6 sigma^2 / ( (2 pi)^2 A^2 N (N^2-1) ) var(phihat) >= sigma^2 ( 2 N - 1 ) / ( A^2 N (N + 1) ) where sigma^2 is the complex noise variance, N is the number of samples of x[n] that you have. [1] S. M. Kay, "Fundamentals of Statistical Signal Processing Vol 1: Estimation Theory", Prentice-Hall, 1993. Ciao, Peter K. -- Peter J. Kootsookos "Na, na na na na na na, na na na na" - 'Hey Jude', Lennon/McCartney

Reply by ●July 15, 20032003-07-15

"Peter J. Kootsookos" <p.kootsookos@remove.ieee.org> wrote> Kay's book ([1], page 542) says that the CRLBs for estimating A, f and phiin:> > x[n] = A exp( j 2 pi f n ) + complex white Gaussian noiseD'oh, I left out phi.... this should read something like: x[n] = A exp( j ( 2 pi f n + phi ) ) + complex white Gaussian noise -- Peter J. Kootsookos "Na, na na na na na na, na na na na" - 'Hey Jude', Lennon/McCartney

Reply by ●July 15, 20032003-07-15

Hello santhosh, You are right, CR bound varies for different SNR. The problem in my case is that amplitude of the frequency is to be estimated with a error of 10^-8. The main problem is because of the noise signal present in it. If the ampliude of the noise is less than 10^-3(when SNR is greater than 90 dB) and less the accuracy estimated is of the order 10^-8. But when SNR is about 60 dB, noise ampltude is greater than 10^-3 and hence estimated amplitude is of the order 10^-5. waiting for reply praveen