Randy Yates wrote:

> porterboy76@yahoo.com writes:
> > [...]
> > If the signal and noise are both scaled equally, then
> > how would this affect the BER?
>
> How would that be equalization? Sounds like gain to me.

Thanks for all your answers. Firtsly, Randy, it's equalisation beacuse
the scale is a complex number, and the system is OFDM. In OFDM the
subchannels are decoupled by the FFT/Cyclic Prefix, and each
coefficient of the Frequency domain equaliser is simply the inverses of
the channel FFT coefficent on that subchannel frequency. In fact you
are right it is just a complex gain on any subchannel, but the overall
OFDM equaliser is a bank of N of these gains.

Secondly, I know know why my BER curves are wrong. My colleague kindly
and correctly pointed out to me that the SNR is now different on each
subchannel. While the over all SNR is the arithmetic mean   of the
subchannel SNRs, the bit-error rate is a non-linear function of the
individual subchannel SNRs. SO you cant take an average receiver SNR
and assume a particular BER. It depends on how the subchannel SNRs are
distributed. If there is one particularly bad subchannel, then the
error rate will be high here and will tend to dominate the overall BER
measurement, despite a reasonably good overall SNR at the receiver. As
I suspected, noise enhancement is not such a problem for binary
decisions.

porterboy76@yahoo.com writes:
> [...]
> If the signal and noise are both scaled equally, then
> how would this affect the BER?

How would that be equalization? Sounds like gain to me.
-- 
%  Randy Yates                  % "She tells me that she likes me very much,
%% Fuquay-Varina, NC            %     but when I try to touch, she makes it
%%% 919-577-9882                %                            all too clear."
%%%% <yates@ieee.org>           %        'Yours Truly, 2095', *Time*, ELO  
http://home.earthlink.net/~yatescr

 If the signal and noise are both scaled equally, then
> how would this affect the BER?

The null in the channel attenuates the signal but not the noise  (the
noise is added at the front end of the receiver typically).

Then the equalizer applies gain at those freq where the channel is a
null to make up for the null and therfore amplifies the noise.  It is
really the action of the channel that has degraded the SNR.

Mark

On 19 Oct 2006 09:00:03 -0700, porterboy76@yahoo.com wrote:

>(My question is at the bottom)
>
>======= POST FROM STEFFEN LAST JULY ON COMP. DSP ======
>
>Regarding the noise enhancement after applying the linear zero-forcing
>equalizer I've found some explanation in "digital communications,
>Proakis, 4.Ed, chap.10, p.621" :o). Proakis says:"...the performance of
>the equalizer is poor whenever the folded spectral characteristic
>possesses nulls or takes on small values. This behaviour occurs
>primarily because the equalizer, in eliminating the intersymbol
>interferences, enhances the additive noise. For example, if the channel
>contains a spectral null, or small value, in its frequency response,
>the linear zero-forcing equalizer attempts to compensate for this by
>introducing an infinite, or large, gain at that frequency. But this
>compensates for the channel distortion at the expense of enhancing the
>additive noise.". -> and finally reduces the BER of the uncoded
>OFDM-transmissionsystem.
>
>============ END STEFFENS POST ========================
>
>I also find with a zero-forcing equalizer on OFDM and perfect channel
>kknowledge that I am getting poorer BER than expected. Howeer, I dont
>fully agree that the explanation is noise enhancement, since the data I
>am using is QPSK. If the signal and noise are both scaled equally, then
>how would this affect the BER?


The "noise enhancement" is a reduction in SNR at the output of the
equalizer.   This will naturally degrade the performance somewhat, but
you'll still be way ahead of what it would be without the EQ in the
presence of multipath.

Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org

> I also find with a zero-forcing equalizer on OFDM and perfect channel
> kknowledge that I am getting poorer BER than expected. Howeer, I dont
> fully agree that the explanation is noise enhancement, since the data I
> am using is QPSK. If the signal and noise are both scaled equally, then
> how would this affect the BER?

Are you using some sort of soft (input) decision viterbi decoding in
the scenario that you mention?  If so, the amplification of the low SNR
tone will cause the viterbi metric for that tone to be weighted equally
with those from other tones with higher SNRs.  IMO, this would hurt
performance compared to completely ignoring the metric from the nulled
out tone.

If hard decisions are being made, I am not convinced that a difference
will be seen.

Phil

(My question is at the bottom)

======= POST FROM STEFFEN LAST JULY ON COMP. DSP ======

Regarding the noise enhancement after applying the linear zero-forcing
equalizer I've found some explanation in "digital communications,
Proakis, 4.Ed, chap.10, p.621" :o). Proakis says:"...the performance of
the equalizer is poor whenever the folded spectral characteristic
possesses nulls or takes on small values. This behaviour occurs
primarily because the equalizer, in eliminating the intersymbol
interferences, enhances the additive noise. For example, if the channel
contains a spectral null, or small value, in its frequency response,
the linear zero-forcing equalizer attempts to compensate for this by
introducing an infinite, or large, gain at that frequency. But this
compensates for the channel distortion at the expense of enhancing the
additive noise.". -> and finally reduces the BER of the uncoded
OFDM-transmissionsystem.

============ END STEFFENS POST ========================

I also find with a zero-forcing equalizer on OFDM and perfect channel
kknowledge that I am getting poorer BER than expected. Howeer, I dont
fully agree that the explanation is noise enhancement, since the data I
am using is QPSK. If the signal and noise are both scaled equally, then
how would this affect the BER?