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

```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.

with regards
praveen
``` 0  praveenkumar1979
7/14/2003 4:39:48 PM comp.dsp  20333 articles. 1 followers. 2 Replies 429 Views Similar Articles

[PageSpeed] 18

```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 (, 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.

 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
``` 0  p
7/15/2003 8:07:35 AM
```"Peter J. Kootsookos" <p.kootsookos@remove.ieee.org> wrote

> Kay's book (, 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

D'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

``` 0  Peter
7/15/2003 9:15:44 AM