# equalizer error bias

Started by November 15, 2007
```Hi,
I have a channel with significant ISI with a 3 level (1,0,-1)
transmission. The transmitted data and the receiver data after
quantization have zero mean. The problem is that the error output of
the equalizer after convergence is not zero mean even (it's slightly
positive) though its variance is very low (around 22dB below signal
power). It's been pointed to me that it should be zero mean which
seems reasonable (is it?) but I can't figure out why it's not.
Initially I thought it maybe because of the fixed point implementation
but the floating point shows almost exactly the same mean. The bias
can also be observed at the data output of the equalizer ie. the
histogram of the output shows that the distribution around 0 output
value is not evenly distributed, although 1, -1 values seem balanced.
Another possibility is how I initialize the equalizer. I have a center
tap initialization and always decision directed error calculation but
I'm not sure why this would cause a bias.
Any ideas on why the output could be biased and why it should/shoudn't
be biased would be appreciated.

Thanks.
```
```mk <kal*@dspia.*comdelete> writes:

> Hi,
> I have a channel with significant ISI with a 3 level (1,0,-1)
> transmission. The transmitted data and the receiver data after
> quantization have zero mean. The problem is that the error output of
> the equalizer after convergence is not zero mean even (it's slightly
> positive) though its variance is very low (around 22dB below signal
> power). It's been pointed to me that it should be zero mean which
> seems reasonable (is it?)

Not sure off-the-cuff.

> but I can't figure out why it's not.
> Initially I thought it maybe because of the fixed point implementation
> but the floating point shows almost exactly the same mean. The bias
> can also be observed at the data output of the equalizer ie. the
> histogram of the output shows that the distribution around 0 output
> value is not evenly distributed, although 1, -1 values seem balanced.
> Another possibility is how I initialize the equalizer. I have a center
> tap initialization and always decision directed error calculation but
> I'm not sure why this would cause a bias.
> Any ideas on why the output could be biased and why it should/shoudn't
> be biased would be appreciated.

Here's a couple of very rough thoughts:

1. Have you triple-checked your decision regions? It is easy to see
how an error there would introduce a DC offset.

2. Are you sure your timing is correct? How are you getting timing?
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%%% 919-577-9882                %
%%%% <yates@ieee.org>           % 'Eldorado Overture', *Eldorado*, ELO
http://www.digitalsignallabs.com
```
```On Nov 14, 11:59 pm, mk <kal*@dspia.*comdelete> wrote:
> Hi,
> I have a channel with significant ISI with a 3 level (1,0,-1)
> transmission. The transmitted data and the receiver data after
> quantization have zero mean. The problem is that the error output of
> the equalizer after convergence is not zero mean even (it's slightly
> positive) though its variance is very low (around 22dB below signal
> power). It's been pointed to me that it should be zero mean which
> seems reasonable (is it?) but I can't figure out why it's not.
> Initially I thought it maybe because of the fixed point implementation
> but the floating point shows almost exactly the same mean. The bias
> can also be observed at the data output of the equalizer ie. the
> histogram of the output shows that the distribution around 0 output
> value is not evenly distributed, although 1, -1 values seem balanced.
> Another possibility is how I initialize the equalizer. I have a center
> tap initialization and always decision directed error calculation but
> I'm not sure why this would cause a bias.
> Any ideas on why the output could be biased and why it should/shoudn't
> be biased would be appreciated.
>
> Thanks.

the error output from the EQ is non zero mean and slightly poaitive?

I'll throw out some random ideas...

1) Does the bias change if you use a channel with a different ISI, or
one with no ISI?  or a different data set?  or the mu factor?   i.e.
vary any parameter that you can think of and see what if anything
effects the bias.

2) Does the EQ have an intentional bias to aid convergence or so that
it gradually deacys to a known state with no signal or something like
that?

Mark

```