Multipath + AWGN modelling with MATLAB

Hallo everybody,

I've got a little question about the way I'm modelling a multipath-channel
with AWGN using MATLAB for my OFDM-Simulation.

Can anybody tell me whether the way I'm doing it is correct or not?

I've implemented to following code:

%--------------------------------------------------------------------
% tx is the transmitted discrete OFDM-basebandsignal
% which is normalized to an average signalpower of 0 dB independent of
% the chosen subcarrier-modulationscheme (e.g. BPSK, QPSK, 16QAM...)

% [1,0,0,0,0.2] -> multipath with LOS of gain 1 and one reflection of gain
% 0.2

% applying multipath to transmitted OFDM-signal tx
mpath = filter([1, 0, 0, 0, 0.2], 1, tx);

% AWGN with wanted SNR with respect to the normalized signal tx before the

% multipath-filter
rx = awgn(mpath, SNR, 0, 'dB');
%--------------------------------------------------------------------

Is it correct to add the noise (with wanted SNR) to the filtered signal
"mpath" without taking the filtergain into account by using the
transmitted signal "tx" with a signalpower of 0dB as reference for the
awgn(...)-command? If not - how can I take the filtergain into account?
Or do I have to add the noise to the signal "tx" before applying the
multipath-filter?

At the receiver I'm applying a zero-forcing-equalizer in the frequency
domain. When I turn the noise off I get a perfectly equalized signal with
a BER of 0 :o) So the equalizer - which I get from fft([1,0,0,0,0.63], N)
works perfect(I assumed perfect knowledge of the channel impulse
response).
When I turn the multipath off (e.g. perfect channel with impulse response
[1,0,0,...]), the BER-curves perfectly match the theoretical curves of an
OFDM-System under pure AWGN conditions.
So looking at both multipath and AWGN separately everything looks fine! 

But can anybody tell me why I don't get the correct BER-curves when
turning both the multipath-filter and AWGN on and applying equalization at
the receiver?? I think that I must get the same BER-curves as under pure
AWGN conditions since I've perfect knowledge of the channel impulse
response and the equalizer works perfect as I mentioned before?! The
results get even worse as I increase the amplitude of the reflected signal
path in the multipath-filter (e.g. from 0.2 to 0.63).

I'm very thankful for every hint and fruitful conversation.

Many thanks in advance

Steffen





		
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steffen wrote:
> Hallo everybody,
>
> I've got a little question about the way I'm modelling a multipath-channel
> with AWGN using MATLAB for my OFDM-Simulation.
>
> Can anybody tell me whether the way I'm doing it is correct or not?
>
> I've implemented to following code:
>
> %--------------------------------------------------------------------
> % tx is the transmitted discrete OFDM-basebandsignal
> % which is normalized to an average signalpower of 0 dB independent of
> % the chosen subcarrier-modulationscheme (e.g. BPSK, QPSK, 16QAM...)
>
> % [1,0,0,0,0.2] -> multipath with LOS of gain 1 and one reflection of gain
> % 0.2
>
> % applying multipath to transmitted OFDM-signal tx
> mpath =3D filter([1, 0, 0, 0, 0.2], 1, tx);
>
> % AWGN with wanted SNR with respect to the normalized signal tx before the
>
> % multipath-filter
> rx =3D awgn(mpath, SNR, 0, 'dB');
> %--------------------------------------------------------------------
>
> Is it correct to add the noise (with wanted SNR) to the filtered signal
> "mpath" without taking the filtergain into account by using the
> transmitted signal "tx" with a signalpower of 0dB as reference for the
> awgn(...)-command? If not - how can I take the filtergain into account?
> Or do I have to add the noise to the signal "tx" before applying the
> multipath-filter?

I'd say that you add the noise as the last thing you do. You could
simulate a distributed noise field, but that's just adds a lots of
computations fo little if any benefit.

One of the key issues here would be to decide if the power of the
echo goes intot the "S" or the "N" in the SNR. I'd say it should
be counmted as noise, but others may have other opinions. Since the
echo represents coherent and correlated noise, it could mess up your
BER vs SNR curves.

> At the receiver I'm applying a zero-forcing-equalizer in the frequency
> domain. When I turn the noise off I get a perfectly equalized signal with
> a BER of 0 :o) So the equalizer - which I get from fft([1,0,0,0,0.63], N)
> works perfect(I assumed perfect knowledge of the channel impulse
> response).
> When I turn the multipath off (e.g. perfect channel with impulse response
> [1,0,0,...]), the BER-curves perfectly match the theoretical curves of an
> OFDM-System under pure AWGN conditions.
> So looking at both multipath and AWGN separately everything looks fine!

I like that! For some reason, I don't often see that people divides
the problem into se=E5arate tasks and checks that the solution to each
task works.

> But can anybody tell me why I don't get the correct BER-curves when
> turning both the multipath-filter and AWGN on and applying equalization at
> the receiver?? I think that I must get the same BER-curves as under pure
> AWGN conditions since I've perfect knowledge of the channel impulse
> response and the equalizer works perfect as I mentioned before?!

One possible reason for suboptimal results, is that the noise, too,
has been run through your equalizer, so the signal you run through
your matched filter consists of signal, echo and non-white noise.
Thus, the assumptions of the matched filter technique are not met.

> The
> results get even worse as I increase the amplitude of the reflected signal
> path in the multipath-filter (e.g. from 0.2 to 0.63).

Look at the spectra of the equalizing filters. I'd guess they become
increasingly "non-white" as the reflection coefficient increases.

Rune

Hallo Rune,

many thanks for your posting.

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.

So this is the reason why the BER-performance of the uncoded
OFDM-transmissionsystem decreases as the amplitude of the reflected path
of the 2-way-channel increases. Increasing the amplitude of the reflected
path yields "deep-fadings" in the frequency response of the channel ->
representing the small values mentioned by Proakis!!!

What do you think?

Steffen


		
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Hallo Rune,

many thanks for your posting.

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.

So this is the reason why the BER-performance of the uncoded
OFDM-transmissionsystem decreases as the amplitude of the reflected path
of the 2-way-channel increases. Increasing the amplitude of the reflected
path yields "deep-fadings" in the frequency response of the channel ->
representing the small values mentioned by Proakis!!!

What do you think?

Steffen


		
This message was sent using the Comp.DSP web interface on
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steffen wrote:
> Hallo Rune,
>
> many thanks for your posting.
>
> 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.
>
> So this is the reason why the BER-performance of the uncoded
> OFDM-transmissionsystem decreases as the amplitude of the reflected path
> of the 2-way-channel increases. Increasing the amplitude of the reflected
> path yields "deep-fadings" in the frequency response of the channel ->
> representing the small values mentioned by Proakis!!!
>
> What do you think?

Yep, that's more or less what I had in mind. Remember, the reflection
and direct path generate destructive interference. If the reflection
coefficient is +/- 1, there will be complete loss of signals at certain

points, when the travelled distance is an odd or even number of
wavelengths, respectively.

When the signal is completely lost, there isn't much one can do to
recover it.

Rune

As I've read - one option is to use additional techniques like
"channel-coding" with "frequency-interleaving" to improve the BER
performance of the system in the presence of "deep fading".

Many thanks for your hints.

Steffen
		
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As I've read - one option is to use additional techniques like
"channel-coding" with "frequency-interleaving" to improve the BER
performance of the system in the presence of "deep fading".

Many thanks for your hints.

Steffen
		
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www.DSPRelated.com

Rune Allnor wrote:
> steffen wrote:
> > Hallo Rune,
> >
> > many thanks for your posting.
> >
> > 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.
> >
> > So this is the reason why the BER-performance of the uncoded
> > OFDM-transmissionsystem decreases as the amplitude of the reflected path
> > of the 2-way-channel increases. Increasing the amplitude of the reflected
> > path yields "deep-fadings" in the frequency response of the channel ->
> > representing the small values mentioned by Proakis!!!
> >
> > What do you think?
>
> Yep, that's more or less what I had in mind. Remember, the reflection
> and direct path generate destructive interference. If the reflection
> coefficient is +/- 1, there will be complete loss of signals at certain
>
> points, when the travelled distance is an odd or even number of
> wavelengths, respectively.

Try "when the DIFFERENCE in travelled distance is an odd or even number

of wavelengths", and the above makes a little bit more sense.

Rune
> When the signal is completely lost, there isn't much one can do to
> recover it.
> 
> Rune