f

#### Cramer Rao Bound and GFSK frequency errors

```Hi,

I know this has been covered extensively in the past but with your
indulgence I'd like to bring up CRLBs again.

My problem is this: I've implemeted a method of measuring ( or rather
estimating ) the carrier frequency errors in GFSK signals from
Bluetooth radios. From many tests on RF IC ATE I have data for the
variance of my measurements. Intuitively it seemed sensible that there
should be a way of relating the SNR of the captured signal I extract
the frequency error from and the measurement variance due to that SNR.
Knowing this I can make an objective judgement about the efficacy of
my implementation and what level of improvement I can hope to make if
necessary. The CRLB seems to fit the bill.

However, I'm going round in circles trying to understand how to work
out an appropriate CRLB. The estimation method I'm using works by
finding the DC offset in the differentiated phase of the 4 bit packet
preamble, equivalent to calculating the mean frequency of the first
four symbols. What's confusing me (I think) is the fact that I'm not
trying to find the frequency of a single tone but the mean frequency
of two alternating tones. Should the bound be calculated for the tones
seperately or using N and T for all for of the tones at once
(difference is 300Hz compared to a few 10s of hz) ?? Does the fact
that the transition between the tones is smooth ( because of the
Gaussian premod filter) make a difference/need to be taken into
account?

Many thanks,
Craig Robinson.

PS: A spooky coincidence - When I initially searched for the CRLB on
the newsgroup the first post I came to was the lyrics to a song. So
I'm reading these lyrics and after the first verse or so the I start
humming the tune too. After another verse I catch on that the tune Im
humming is the same one that is coming from the CD my wife is
listening to. Wierd eh. Reckon the likelihood of that happening is
something like 1/p(Angler catches a salmon in our bath).
```
 0
craig
9/17/2003 7:18:24 PM
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