# power delay profile

Started by December 5, 2005
```Dear All,
I'm given a power delay profile figure, I have to calculate the
corresponding impulse response
values.
How can I do this? Please tell me the steps as I'm doing this problem for
days now..
Thank you
Frank

```
```On Mon, 5 Dec 2005 18:47:20 +0100, "Frank Benett" <frank_b@gmail.com>
wrote:

>Dear All,
>I'm given a power delay profile figure, I have to calculate the
>corresponding impulse response
>values.
>How can I do this? Please tell me the steps as I'm doing this problem for
>days now..
>Thank you
>Frank

Hi Frank,
describe your problem a little more clearly.
I'm not sure what you mean by "power delay profile".
(It sounds like something related to gasoline engines.)

I'm gonna guess that a "power delay profile" is some
sort of graph.  If that's true, what are the dimensions
along the horizontal and vertical axes?

guys here have in providing some useful guidance for you.

[-Rick-]

```
```"Rick Lyons" <R.Lyons@_BOGUS_ieee.org> wrote in message
news:4394c203.339547062@news.sf.sbcglobal.net...
> On Mon, 5 Dec 2005 18:47:20 +0100, "Frank Benett" <frank_b@gmail.com>
> wrote:
>
>>Dear All,
>>I'm given a power delay profile figure, I have to calculate the
>>corresponding impulse response
>>values.
>>How can I do this? Please tell me the steps as I'm doing this problem for
>>days now..
>>Thank you
>>Frank
>
> Hi Frank,
>  I'll bet someone here can help you if you can just
> describe your problem a little more clearly.
> I'm not sure what you mean by "power delay profile".
> (It sounds like something related to gasoline engines.)
>
> I'm gonna guess that a "power delay profile" is some
> sort of graph.  If that's true, what are the dimensions
> along the horizontal and vertical axes?
>
> guys here have in providing some useful guidance for you.
>
http://people.deas.harvard.edu/~vahid/VT-2004-00306.R1.pdf

Has descriptions of several things that might be called power delay profiles
, does yours correspond to one of these?

If so, it seems that you will need to provide some side information before
you can try to get a statistical description of impulse responses that might
create a similar power delay profile and also fit with your local radio
environment in some sense.

Best of Luck - Mike

```
```Thanks for your answer In power deleay profile I mean the plot of the tap
delay (us) on the x axis,
and the corresponding amplitude (dB) on the y axis..
All of the channel models (rural,hilly..etc) are given in this form, and I
need to calculate the impulse response value (h).
thank you,
regard,
Frank

"Mike Yarwood" <mpyarwood@btopenworld.com> az al&#2013265921;bbiakat
&#2013265933;rta a k&#2013266166;vetkez&#2013266165;
h&#2013265933;r&#2013266172;zenetben:
dn2jat\$rr2\$1@nwrdmz02.dmz.ncs.ea.ibs-infra.bt.com...
>
> "Rick Lyons" <R.Lyons@_BOGUS_ieee.org> wrote in message
> news:4394c203.339547062@news.sf.sbcglobal.net...
>> On Mon, 5 Dec 2005 18:47:20 +0100, "Frank Benett" <frank_b@gmail.com>
>> wrote:
>>
>>>Dear All,
>>>I'm given a power delay profile figure, I have to calculate the
>>>corresponding impulse response
>>>values.
>>>How can I do this? Please tell me the steps as I'm doing this problem for
>>>days now..
>>>Thank you
>>>Frank
>>
>> Hi Frank,
>>  I'll bet someone here can help you if you can just
>> describe your problem a little more clearly.
>> I'm not sure what you mean by "power delay profile".
>> (It sounds like something related to gasoline engines.)
>>
>> I'm gonna guess that a "power delay profile" is some
>> sort of graph.  If that's true, what are the dimensions
>> along the horizontal and vertical axes?
>>
>> guys here have in providing some useful guidance for you.
>>
> http://people.deas.harvard.edu/~vahid/VT-2004-00306.R1.pdf
>
> Has descriptions of several things that might be called power delay
> profiles , does yours correspond to one of these?
>
> If so, it seems that you will need to provide some side information before
> you can try to get a statistical description of impulse responses that
> might create a similar power delay profile and also fit with your local
> radio environment in some sense.
>
> Best of Luck - Mike
>
>
>

```
```in article dn3092\$mcm\$1@namru.matavnet.hu, Frank Benett at frank_b@gmail.com
wrote on 12/05/2005 22:24:

> Thanks for your answer In power deleay profile I mean the plot of the tap
> delay (us) on the x axis,
> and the corresponding amplitude (dB) on the y axis..

this is the magnitude of the tap coefficient expressed in dB?  why would
anyone do that?  to show exponential trend as linear?

> All of the channel models (rural,hilly..etc) are given in this form, and I
> need to calculate the impulse response value (h).

so, after throwing away the sign information of h[n], you want to recover
h[n] including the signs of the negative taps?  can we assume that the first
h[n] is > 0?  if so, we might be able to infer zero crossings and toggle the
sign every zero crossing.

--

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

```
```"robert bristow-johnson" <rbj@audioimagination.com> wrote in message
news:BFBA750F.CA9D%rbj@audioimagination.com...
> in article dn3092\$mcm\$1@namru.matavnet.hu, Frank Benett at
> frank_b@gmail.com
> wrote on 12/05/2005 22:24:
>
>> Thanks for your answer In power deleay profile I mean the plot of the tap
>> delay (us) on the x axis,
>> and the corresponding amplitude (dB) on the y axis..
>
> this is the magnitude of the tap coefficient expressed in dB?  why would
> anyone do that?  to show exponential trend as linear?
>
>> All of the channel models (rural,hilly..etc) are given in this form, and
>> I
>> need to calculate the impulse response value (h).
>
> so, after throwing away the sign information of h[n], you want to recover
> h[n] including the signs of the negative taps?  can we assume that the
> first
> h[n] is > 0?  if so, we might be able to infer zero crossings and toggle
> the
> sign every zero crossing.
>
Hi Frank - have you looked through the models and tutorials at
http://itpp.sourceforge.net/3.8.0/index.html   ?

Best of Luck - Mike

```
```"Mike Yarwood" <mpyarwood@btopenworld.com> wrote in message
news:dn4dbv\$64o\$1@nwrdmz03.dmz.ncs.ea.ibs-infra.bt.com...
>
>>
> Hi Frank - have you looked through the models and tutorials at
> http://itpp.sourceforge.net/3.8.0/index.html   ?
>

Mike,

How should we interpret the claim that IT++ is "wildly used"?

Fred

```
```Frank Benett wrote:
> Thanks for your answer In power deleay profile I mean the plot of the tap
>  delay (us) on the x axis,
>  and the corresponding amplitude (dB) on the y axis..
>  All of the channel models (rural,hilly..etc) are given in this form, and I
>  need to calculate the impulse response value (h).
>  thank you,
>  regard,
>  Frank
>
>

If the tap values you are  talking about are in the DFE equalizer, then
I think (I'm not sure) the tap values are simply equal to the channel
impulse response  (in dB of course)

In other words, if the DFE  tap at 5 us is activated at -10 dB, then
the channel has an echo delayed by 5 us that is -10 dB and this (along
with the main path) is the impulse response.

(It's a little more compoicated for an FFE)

No???

Mark

```
```this is the magnitude of the tap coefficient expressed in dB?  why
would
anyone do that?  to show exponential trend as linear?

for the same reasons we typically use dB for SNR etc....

to show a wide dynamic range on a single graph and because the value
relative to the main tap is important..i.e the relative level of the
reflection is important.....

they are typically shown  as dB relative to the main tap...

M

```
```"Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote in message
news:FMednWw5yuHuRgjeRVn-sA@centurytel.net...
>
> "Mike Yarwood" <mpyarwood@btopenworld.com> wrote in message
> news:dn4dbv\$64o\$1@nwrdmz03.dmz.ncs.ea.ibs-infra.bt.com...
>>
>>>
>> Hi Frank - have you looked through the models and tutorials at
>> http://itpp.sourceforge.net/3.8.0/index.html   ?
>>
>
> Mike,
>
> How should we interpret the claim that IT++ is "wildly used"?
>
Hah yes! - english ain't their first language so it's a bit of a hoot in
places but interesting for the different ITU and COST models they've
released.

Best of luck - Mike

```
```"Mark" <makolber@yahoo.com> wrote in message
> yep, the delay profile IS the impulse response...
>
> Mark
>
so what is the average power delay profile?

Best of Luck - Mike

```
```yep, the delay profile IS the impulse response...

Mark

```
```Thanks for your suggestion. If one would use this model in a realistic way,
several factor should be
considered (delay, doppler (fading))..etc). I solved the problem, as I
reduced the complexity of my model:
I consider only the simplest static model which doesn't vary in time. For
this I simply calculated the powers from the
given amplitude which is equivalent to the impulse response h, which i
needed for my matlab simulation!
Frank

"Fred Marshall" <fmarshallx@remove_the_x.acm.org> az al&#2013265921;bbiakat
&#2013265933;rta a
k&#2013266166;vetkez&#2013266165; h&#2013265933;r&#2013266172;zenetben:
d5KdnR2_O4rjjQrenZ2dnUVZ_tudnZ2d@centurytel.net...
>
> "Frank Benett" <frank_b@gmail.com> wrote in message
> news:dn6g0u\$bsc\$1@namru.matavnet.hu...
>> Thanks for all of your answer and effort. I'm wondering why I can't find
>> any information
>> given with in this form.
>> With this power delay profile (PDP) the impulse responses are given with
>> their delay and the
>> corresponding amplitude. (i.e : the average received power).. I have
>> looked the IT++ which
>> was mentioned, it's a really good project and I find channel models
>> there, I hope form this I can figure out the
>> solution, but I'm still curious, if somebody could tell me the
>> mathematics behind this...
>> regards,
>> Frank
>
> Frank,
>
> I'll go out on a limb because I don't generally work in rf comm's and this
> technique is used in that area.  Nonetheless, it seems clear enough what
> the motivation is:
>
> There is a multipath environment which means that signal arrives at a
> receiver perhaps line-of-sight and also by bounce paths and possibly ray
> bending in transmission through a variety of materials.
>
> Now, one method for modeling multipath is to use a delay / attenuation
> value for each path.  When the attenuation values are lined up according
> to delay time you have what looks like a FIR filter in continuous time.
> i.e. the temporal resulution is infinite.  As long as the wavelengths are
> reasonably long relative to the path characteristics then this works fine.
> As the wavelengths get shorter then the temporal location / delay involved
> in any path begins to be difficult to determine relative to a wavelength.
> Rough location is still known of course but the ability to resolve delay
> into phase is lost.
>
> One method for looking at signals in a situation where phase is
> indeterminate is to randomize the phase for each path and look at a large
> sample of possible outcomes to yield system statistics.  I've done this.
>
> But, this doesn't account for the situation where the reflectors in a path
> are distrubuted and perhaps slowly time-varying.  If reflectors are
> distributed they can be modeled as a cluster of reflectors.  With any
> wavelength variation there will now be a distribution of apparent
> reflector amplitudes as well as phases.  With wideband signals it seems
> one can only talk about average reflectivity and random phase.  It's as
> though *each* reflector could be treated as the distributed / stable
> reflector situation above and some statistical measure would make sense.
>
> So, while a FIR model might still apply and the statistical method might
> still be used, is that necessarily the most convenient method for analysis
> purposes?  Often it isn't.  Looking at a curve might be better.
>
> Given that each path has an average strength then it makes some sense to
> measure it in dB and to plot the resulting path / delay structure in dB vs
> time.
> This is no longer a FIR filter representation although it certainly has
> some resemblance.
>
> Make sense?
>
> Fred
>
>
>

```
```"Frank Benett" <frank_b@gmail.com> wrote in message
news:dn6g0u\$bsc\$1@namru.matavnet.hu...
> Thanks for all of your answer and effort. I'm wondering why I can't find
> any information
> given with in this form.
> With this power delay profile (PDP) the impulse responses are given with
> their delay and the
> corresponding amplitude. (i.e : the average received power).. I have
> looked the IT++ which
> was mentioned, it's a really good project and I find channel models there,
> I hope form this I can figure out the
> solution, but I'm still curious, if somebody could tell me the mathematics
> behind this...
> regards,
> Frank

Frank,

I'll go out on a limb because I don't generally work in rf comm's and this
technique is used in that area.  Nonetheless, it seems clear enough what the
motivation is:

There is a multipath environment which means that signal arrives at a
receiver perhaps line-of-sight and also by bounce paths and possibly ray
bending in transmission through a variety of materials.

Now, one method for modeling multipath is to use a delay / attenuation value
for each path.  When the attenuation values are lined up according to delay
time you have what looks like a FIR filter in continuous time.  i.e. the
temporal resulution is infinite.  As long as the wavelengths are reasonably
long relative to the path characteristics then this works fine.  As the
wavelengths get shorter then the temporal location / delay involved in any
path begins to be difficult to determine relative to a wavelength.  Rough
location is still known of course but the ability to resolve delay into
phase is lost.

One method for looking at signals in a situation where phase is
indeterminate is to randomize the phase for each path and look at a large
sample of possible outcomes to yield system statistics.  I've done this.

But, this doesn't account for the situation where the reflectors in a path
are distrubuted and perhaps slowly time-varying.  If reflectors are
distributed they can be modeled as a cluster of reflectors.  With any
wavelength variation there will now be a distribution of apparent reflector
amplitudes as well as phases.  With wideband signals it seems one can only
talk about average reflectivity and random phase.  It's as though *each*
reflector could be treated as the distributed / stable reflector situation
above and some statistical measure would make sense.

So, while a FIR model might still apply and the statistical method might
still be used, is that necessarily the most convenient method for analysis
purposes?  Often it isn't.  Looking at a curve might be better.

Given that each path has an average strength then it makes some sense to
measure it in dB and to plot the resulting path / delay structure in dB vs
time.
This is no longer a FIR filter representation although it certainly has some
resemblance.

Make sense?

Fred

```
```Thanks for all of your answer and effort. I'm wondering why I can't find any
information
given with in this form.
With this power delay profile (PDP) the impulse responses are given with
their delay and the
corresponding amplitude. (i.e : the average received power).. I have looked
the IT++ which
was mentioned, it's a really good project and I find channel models there, I
hope form this I can figure out the
solution, but I'm still curious, if somebody could tell me the mathematics
behind this...
regards,
Frank

"Mark" <makolber@yahoo.com> az al&#2013265921;bbiakat &#2013265933;rta a
k&#2013266166;vetkezo h&#2013265933;r&#2013266172;zenetben:
>
> Frank Benett wrote:
>> Thanks for your answer In power deleay profile I mean the plot of the tap
>>  delay (us) on the x axis,
>>  and the corresponding amplitude (dB) on the y axis..
>>  All of the channel models (rural,hilly..etc) are given in this form, and
>> I
>>  need to calculate the impulse response value (h).
>>  thank you,
>>  regard,
>>  Frank
>>
>>
>
> If the tap values you are  talking about are in the DFE equalizer, then
> I think (I'm not sure) the tap values are simply equal to the channel
> impulse response  (in dB of course)
>
> In other words, if the DFE  tap at 5 us is activated at -10 dB, then
> the channel has an echo delayed by 5 us that is -10 dB and this (along
> with the main path) is the impulse response.
>
> (It's a little more compoicated for an FFE)
>
> No???
>
> Mark
>

```
```"Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote in message
news:FMednWw5yuHuRgjeRVn-sA@centurytel.net...
>
> "Mike Yarwood" <mpyarwood@btopenworld.com> wrote in message
> news:dn4dbv\$64o\$1@nwrdmz03.dmz.ncs.ea.ibs-infra.bt.com...
>>
>>>
>> Hi Frank - have you looked through the models and tutorials at
>> http://itpp.sourceforge.net/3.8.0/index.html   ?
>>
>
> Mike,
>
> How should we interpret the claim that IT++ is "wildly used"?
>
Hah yes! - english ain't their first language so it's a bit of a hoot in
places but interesting for the different ITU and COST models they've
released.

Best of luck - Mike

```
```this is the magnitude of the tap coefficient expressed in dB?  why
would
anyone do that?  to show exponential trend as linear?

for the same reasons we typically use dB for SNR etc....

to show a wide dynamic range on a single graph and because the value
relative to the main tap is important..i.e the relative level of the
reflection is important.....

they are typically shown  as dB relative to the main tap...

M

```
```Frank Benett wrote:
> Thanks for your answer In power deleay profile I mean the plot of the tap
>  delay (us) on the x axis,
>  and the corresponding amplitude (dB) on the y axis..
>  All of the channel models (rural,hilly..etc) are given in this form, and I
>  need to calculate the impulse response value (h).
>  thank you,
>  regard,
>  Frank
>
>

If the tap values you are  talking about are in the DFE equalizer, then
I think (I'm not sure) the tap values are simply equal to the channel
impulse response  (in dB of course)

In other words, if the DFE  tap at 5 us is activated at -10 dB, then
the channel has an echo delayed by 5 us that is -10 dB and this (along
with the main path) is the impulse response.

(It's a little more compoicated for an FFE)

No???

Mark

```
```"Mike Yarwood" <mpyarwood@btopenworld.com> wrote in message
news:dn4dbv\$64o\$1@nwrdmz03.dmz.ncs.ea.ibs-infra.bt.com...
>
>>
> Hi Frank - have you looked through the models and tutorials at
> http://itpp.sourceforge.net/3.8.0/index.html   ?
>

Mike,

How should we interpret the claim that IT++ is "wildly used"?

Fred

```
```"robert bristow-johnson" <rbj@audioimagination.com> wrote in message
news:BFBA750F.CA9D%rbj@audioimagination.com...
> in article dn3092\$mcm\$1@namru.matavnet.hu, Frank Benett at
> frank_b@gmail.com
> wrote on 12/05/2005 22:24:
>
>> Thanks for your answer In power deleay profile I mean the plot of the tap
>> delay (us) on the x axis,
>> and the corresponding amplitude (dB) on the y axis..
>
> this is the magnitude of the tap coefficient expressed in dB?  why would
> anyone do that?  to show exponential trend as linear?
>
>> All of the channel models (rural,hilly..etc) are given in this form, and
>> I
>> need to calculate the impulse response value (h).
>
> so, after throwing away the sign information of h[n], you want to recover
> h[n] including the signs of the negative taps?  can we assume that the
> first
> h[n] is > 0?  if so, we might be able to infer zero crossings and toggle
> the
> sign every zero crossing.
>
Hi Frank - have you looked through the models and tutorials at
http://itpp.sourceforge.net/3.8.0/index.html   ?

Best of Luck - Mike

```