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Modifying Jakes Method to simulate multipath fading channel

Started by sasuke June 24, 2009
Hello

I have read through Jakes' paper regarding multipath simulation and I have
also gone through the effort of coding it and getting the waveforms like
the autocorrelation function and the power spectral density. Now I want to
take it one step further. I want to modify the Jakes method to simulate a
multipath channel which is not completely dtereministic. Here's what I
intend to do

1. Jakes model have N multiple paths all of which are assumed to arrive at
the receiver at the same time i.e. there are no delays. I intend to add a
random amount of delay to each multipath component.
2. Jakes model assumes the amplitude of the signal which arrives at the
maximum Doppler frequency to be 1/sqrt(2) and the other signals having
frequencies between 0 and max Doppler shift to be all 1. I intend to change
this by choosing an amplitude for each multipath component uniformly
between 0.1 and 1(just an example)
3. The phases in Jakes model are all given by a fixed formula(I wont
repeat it here, but I guess you know which one). I intend to replace that
formula also with a random variable for each multipath component, uniformly
distributed between 0 and 2*pi.

Can someone please tell me if these three modifications are enough to get
a multipath channel. I know that it's not a time varying channel yet, but
once I am sure that this is the right thing, I will bring about variance
with time.

Thanks
Before you go ahead and make any changes, please understand the
original paper first to save your time. Make sure
you know what the assumptions are and how the author start from there
and get the results.

On Jun 24, 10:41=A0pm, "sasuke" <a.ssjg...@gmail.com> wrote:
> Hello > > I have read through Jakes' paper regarding multipath simulation and I hav=
e
> also gone through the effort of coding it and getting the waveforms like > the autocorrelation function and the power spectral density. Now I want t=
o
> take it one step further. I want to modify the Jakes method to simulate a > multipath channel which is not completely dtereministic. Here's what I > intend to do > > 1. Jakes model have N multiple paths all of which are assumed to arrive a=
t
> the receiver at the same time i.e. there are no delays. I intend to add a > random amount of delay to each multipath component. > 2. Jakes model assumes the amplitude of the signal which arrives at the > maximum Doppler frequency to be 1/sqrt(2) and the other signals having > frequencies between 0 and max Doppler shift to be all 1. I intend to chan=
ge
> this by choosing an amplitude for each multipath component uniformly > between 0.1 and 1(just an example) > 3. The phases in Jakes model are all given by a fixed formula(I wont > repeat it here, but I guess you know which one). I intend to replace that > formula also with a random variable for each multipath component, uniform=
ly
> distributed between 0 and 2*pi. > > Can someone please tell me if these three modifications are enough to get > a multipath channel. I know that it's not a time varying channel yet, but > once I am sure that this is the right thing, I will bring about variance > with time. > > Thanks
sasuke <a.ssjgoku@gmail.com> wrote:

>I have read through Jakes' paper regarding multipath simulation and I have >also gone through the effort of coding it and getting the waveforms like >the autocorrelation function and the power spectral density. Now I want to >take it one step further. I want to modify the Jakes method to simulate a >multipath channel which is not completely dtereministic. Here's what I >intend to do
Why have you chosen Jake's model as a starting point? Turin's model seems a good fit for what you are trying to do. Turin, George L., "A statistical model of urban multipath propogation", Trans. Vehicular Technology, 1972. Steve
>sasuke <a.ssjgoku@gmail.com> wrote: > >>I have read through Jakes' paper regarding multipath simulation and I
have
>>also gone through the effort of coding it and getting the waveforms
like
>>the autocorrelation function and the power spectral density. Now I want
to
>>take it one step further. I want to modify the Jakes method to simulate
a
>>multipath channel which is not completely dtereministic. Here's what I >>intend to do > >Why have you chosen Jake's model as a starting point? Turin's model >seems a good fit for what you are trying to do. > >Turin, George L., "A statistical model of urban multipath >propogation", Trans. Vehicular Technology, 1972. > >Steve >
Thanks for the paper on Turin's model. I chose Jakes model because I already have it simulated,the part described in Section 1.7 of the book "Microwave Mobile Communications". I was hoping that I could carry on from there.
>Before you go ahead and make any changes, please understand the >original paper first to save your time. Make sure >you know what the assumptions are and how the author start from there >and get the results. > >On Jun 24, 10:41=A0pm, "sasuke" <a.ssjg...@gmail.com> wrote: >> Hello >> >> I have read through Jakes' paper regarding multipath simulation and I
hav=
>e >> also gone through the effort of coding it and getting the waveforms
like
>> the autocorrelation function and the power spectral density. Now I want
t=
>o >> take it one step further. I want to modify the Jakes method to simulate
a
>> multipath channel which is not completely dtereministic. Here's what I >> intend to do >> >> 1. Jakes model have N multiple paths all of which are assumed to arrive
a=
>t >> the receiver at the same time i.e. there are no delays. I intend to add
a
>> random amount of delay to each multipath component. >> 2. Jakes model assumes the amplitude of the signal which arrives at
the
>> maximum Doppler frequency to be 1/sqrt(2) and the other signals having >> frequencies between 0 and max Doppler shift to be all 1. I intend to
chan=
>ge >> this by choosing an amplitude for each multipath component uniformly >> between 0.1 and 1(just an example) >> 3. The phases in Jakes model are all given by a fixed formula(I wont >> repeat it here, but I guess you know which one). I intend to replace
that
>> formula also with a random variable for each multipath component,
uniform=
>ly >> distributed between 0 and 2*pi. >> >> Can someone please tell me if these three modifications are enough to
get
>> a multipath channel. I know that it's not a time varying channel yet,
but
>> once I am sure that this is the right thing, I will bring about
variance
>> with time. >> >> Thanks > >
From your post I gather that I am missing something from Jakes model. I will once again go through his paper. If you feel something is fundamentally wrong here, please let me know. Thanks
Hi,

sasuke <a.ssjgoku@gmail.com> wrote:
> I want to modify the Jakes method to simulate a multipath channel which is > not completely dtereministic.
There have been several attempts [1, 2] in the past to modify the Jakes model in order to be able to simulate multiple uncorrelated paths. I think [2] in particular also proposes non-deterministic fading in the sense that it depends on parameters determined randomly on initialization. If you want truly uncorrelated, non-deterministic fading processes, however, I recommend you look into IDFT- or FIR-based methods such as those proposed in [3]. Every single Jakes-based method I've seen so far fails to achieve that. The only reason they are still so popular is that they are computationally cheap, and easy to implement. Cheers, Clemens [1] Dent P., Bottomley G.E, Croft T., "Jakes fading model revisited", IEEE Electronic Letters, vol. 29, no. 13, pp. 1162--1163, 1993. [2] Chengshan Xiao, Yahong Rosa Zheng, Beaulieu N.C., "Novel Sum-of-Sinusoids Simulation Models for Rayleigh and Rician Fading Channels", IEEE Trans. on Wireless Comm., vol. 5, no. 12, pp. 3667--3679, 2006. [3] Young D.J., Beaulieu N.C., "On the generation of correlated Rayleigh random variates by inversediscrete Fourier transform", IEEE Conf. on Univ. Pers. Comm., vol. 1, pp. 231--235, 1996.
Clemens Buchacher  <drizzd@aon.at> wrote:

>There have been several attempts [1, 2] in the past to modify the Jakes >model in order to be able to simulate multiple uncorrelated paths. I think >[2] in particular also proposes non-deterministic fading in the sense that >it depends on parameters determined randomly on initialization. > >If you want truly uncorrelated, non-deterministic fading >processes, however, I recommend you look into IDFT- or FIR-based methods >such as those proposed in [3]. Every single Jakes-based method I've seen so >far fails to achieve that. The only reason they are still so popular is that >they are computationally cheap, and easy to implement. > >Cheers, >Clemens > >[1] Dent P., Bottomley G.E, Croft T., "Jakes fading model revisited", IEEE >Electronic Letters, vol. 29, no. 13, pp. 1162--1163, 1993. > >[2] Chengshan Xiao, Yahong Rosa Zheng, Beaulieu N.C., "Novel >Sum-of-Sinusoids Simulation Models for Rayleigh and Rician Fading >Channels", IEEE Trans. on Wireless Comm., vol. 5, no. 12, >pp. 3667--3679, 2006. > >[3] Young D.J., Beaulieu N.C., "On the generation of correlated Rayleigh >random variates by inversediscrete Fourier transform", IEEE Conf. on >Univ. Pers. Comm., vol. 1, pp. 231--235, 1996.
Thanks for this information. But I am still not "getting" why one would use Jake's model as a starting point for modeling an actual channel. I thought the only point of Jake's was to demonstrate that you could still get a Rayleigh distribution from an unrealistically simple model. Is there some deeper motivation for using this model? Steve
Steve Pope <spope33@speedymail.org> wrote:
> But I am still not "getting" why one would use Jake's model as a > starting point for modeling an actual channel. I thought the only > point of Jake's was to demonstrate that you could still get a > Rayleigh distribution from an unrealistically simple model.
Why? It simulates exactly what happens physically -- a superposition of sinusoids with uniformly distributed incidence angels. This converges to a Rayleigh distribution by virtue of the central limit theorem. For a sufficient number of sinusoids (say 20), it works quite well. The autocorrelation function matches the 0th order Bessel function of the first kind exactly (for a few of zero-crossings, which is usually enough in practice). But in many situations you need more than one multi-path or channel. If you add two uncorrelated Jakes fading processes (generated using the techniques described in the papers referenced previously), you would expect to get yet another Jakes fading process. However, the autocorrelation function of this new process is distorted. Ergo, the paths are correlated. Nobody seems to have picked up on that so far in the literature. And I have no idea how to fix it either. OTOH, it's not possible to generate a continuous fading process using the IDFT method. FIR-based methods require ridiculously long filters, and AR models have ill-conditioning issues. So if anyone finds the holy grail of fading simulators, please let me know. Clemens
Clemens Buchacher  <drizzd@aon.at> wrote:

>Steve Pope <spope33@speedymail.org> wrote:
>> But I am still not "getting" why one would use Jake's model as a >> starting point for modeling an actual channel. I thought the only >> point of Jake's was to demonstrate that you could still get a >> Rayleigh distribution from an unrealistically simple model.
>Why? It simulates exactly what happens physically -- a superposition of >sinusoids with uniformly distributed incidence angels. This converges to a >Rayleigh distribution by virtue of the central limit theorem.
As I understand it, Jake's method assumes the incident sinusoids all have the same magnitude. (Correct me if I am incorrect.) This seems unrealistic.
> But in many situations you need more than one multi-path or > channel. If you add two uncorrelated Jakes fading processes > (generated using the techniques described in the papers > referenced previously), you would expect to get yet another Jakes > fading process. However, the autocorrelation function of this > new process is distorted. Ergo, the paths are correlated. Nobody > seems to have picked up on that so far in the literature. And > I have no idea how to fix it either.
Interesting, thanks.
> OTOH, it's not possible to generate a continuous fading process > using the IDFT method. FIR-based methods require ridiculously > long filters, and AR models have ill-conditioning issues.
> So if anyone finds the holy grail of fading simulators, > please let me know.
There is no holy grail, and there are hundreds of models. The Saleh-Valenzuela model, which incorporates clusters arriving at different angles-of-arrival with a given distribution for magnitude and other parameters, is useful. (Perhaps this is considered an FIR model.) I do understand Jake's model is specified in IS-95. I have not seen it used in radio projects I have worked on. Steve
Steve Pope <spope33@speedymail.org> wrote:
> Clemens Buchacher <drizzd@aon.at> wrote:
> >Steve Pope <spope33@speedymail.org> wrote:
> >> But I am still not "getting" why one would use Jake's model as a > >> starting point for modeling an actual channel. I thought the only > >> point of Jake's was to demonstrate that you could still get a > >> Rayleigh distribution from an unrealistically simple model.
> >Why? It simulates exactly what happens physically -- a superposition of > >sinusoids with uniformly distributed incidence angels. This converges to a > >Rayleigh distribution by virtue of the central limit theorem.
> As I understand it, Jake's method assumes the incident sinusoids > all have the same magnitude. (Correct me if I am incorrect.) > This seems unrealistic.
Yes, you are correct. I somehow misread what your original statement. It is indeed unrealistic.
> > But in many situations you need more than one multi-path or > > channel. If you add two uncorrelated Jakes fading processes > > (generated using the techniques described in the papers > > referenced previously), you would expect to get yet another Jakes > > fading process. However, the autocorrelation function of this > > new process is distorted. Ergo, the paths are correlated. Nobody > > seems to have picked up on that so far in the literature. And > > I have no idea how to fix it either.
> Interesting, thanks.
> > OTOH, it's not possible to generate a continuous fading process > > using the IDFT method. FIR-based methods require ridiculously > > long filters, and AR models have ill-conditioning issues.
> > So if anyone finds the holy grail of fading simulators, > > please let me know.
> There is no holy grail, and there are hundreds of models.
> The Saleh-Valenzuela model, which incorporates clusters > arriving at different angles-of-arrival with a given > distribution for magnitude and other parameters, is useful. > (Perhaps this is considered an FIR model.)
> I do understand Jake's model is specified in IS-95. I have > not seen it used in radio projects I have worked on.
The UMTS standard also assume this model (or at least it does not specify anything that would require a more complex model). LTE includes the so-called extended spatial channel model (SCME), which models angles-of-arrival explicitly. I don't think it really makes a difference for receiver design though. Clemens