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#### How to obtain Doppler shift and phase delay parameters in multipath time-varying channel at the receiver?

```Hello,

In time-variant multipath channel, in which each path has different time
delay, phase, amplitude and Doppler shift and they all change during every
symbol transmission from transmitter to receiver. Normally the channel
coefficients can be estimated by using the estimation algorithms at the
receiver and roughly it has the channel response as h=(1 0 .9 0 0 0.6
0.1), my question is how can we calculate or obtain the Doppler shift and
visualize this parameter in the channel response h?

Many thanksâ€¦

---------------------------------------
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```
 0
runinrainy
12/21/2016 5:01:08 PM
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```On Wed, 21 Dec 2016 11:01:08 -0600, "runinrainy" <100271@DSPRelated>
wrote:

>Hello,
>
>In time-variant multipath channel, in which each path has different time
>delay, phase, amplitude and Doppler shift and they all change during every
>symbol transmission from transmitter to receiver. Normally the channel
>coefficients can be estimated by using the estimation algorithms at the
>receiver and roughly it has the channel response as h=(1 0 .9 0 0 0.6
>0.1), my question is how can we calculate or obtain the Doppler shift and
>visualize this parameter in the channel response h?

Each reflection can have a different Doppler component depending on a)
the motion of the transmitter, b) the motion of the receiver, c) the
motion of the reflecting surface, d) the direction of the reflection
or ray relative to the Rx antenna (e.g., an LOS ray and a ray
reflected from behind the Rx antenna when facing the Tx can have
opposite signs).

Thinking of the power delay profile, or the channel impulse response,
as a complex-valued array, each reflected ray will be represented by a
tap in the array and may be rotating at a different frequency that
reflected rays at different tap (coefficient index) values.

One thing you said that may not be correct is that the delay, phase,
amplitude and Doppler shift values may all change from
symbol-to-symbol.   If that is actually true then it may be impossible
to ever estimate the channel and successfully recover the signal.
Some non-zero channel coherence time must be sufficiently long to not
only estimate the channel accurately but apply it usefully to enough
symbols to recover information.

```
 0
eric
12/22/2016 12:30:31 AM
```On Wed, 21 Dec 2016 11:01:08 -0600, runinrainy wrote:

> Hello,
>
> In time-variant multipath channel, in which each path has different time
> delay, phase, amplitude and Doppler shift and they all change during
> every symbol transmission from transmitter to receiver. Normally the
> channel coefficients can be estimated by using the estimation algorithms
> at the receiver and roughly it has the channel response as h=(1 0 .9 0 0
> 0.6 0.1), my question is how can we calculate or obtain the Doppler
> on how to visualize this parameter in the channel response h?

I'm not sure you can get there from here.  Even in a perfectly noise-free
environment there may not be enough information, per-symbol, to do what
you want.  The whole channel estimation thing depends, to a great extent,
on building up a picture of what the channel is doing over many symbols.
Add in noise, and life just gets even more difficult.

--
Tim Wescott
Control systems, embedded software and circuit design
I'm looking for work!  See my website if you're interested
http://www.wescottdesign.com
```
 0
Tim
12/22/2016 5:07:58 AM
```>On Wed, 21 Dec 2016 11:01:08 -0600, runinrainy wrote:
>
>> Hello,
>>
>> In time-variant multipath channel, in which each path has different
time
>> delay, phase, amplitude and Doppler shift and they all change during
>> every symbol transmission from transmitter to receiver. Normally the
>> channel coefficients can be estimated by using the estimation
algorithms
>> at the receiver and roughly it has the channel response as h=(1 0 .9 0
0
>> 0.6 0.1), my question is how can we calculate or obtain the Doppler
>> on how to visualize this parameter in the channel response h?
>
>I'm not sure you can get there from here.  Even in a perfectly noise-free

>environment there may not be enough information, per-symbol, to do what
>you want.  The whole channel estimation thing depends, to a great extent,

>on building up a picture of what the channel is doing over many symbols.

>Add in noise, and life just gets even more difficult.
>
>--
>Tim Wescott
>Control systems, embedded software and circuit design
>I'm looking for work!  See my website if you're interested
>http://www.wescottdesign.com

Thanks Tim. In time-variant channel assuming the channel characteristics
change symbol to symbol, then in this case, as far as I know the pilots
are inserted into each symbol and first the channel is estimated by the
when pilots are used to obtain the channel, could you also explain, from
the detected signal taps, how to measure the parameters phase, doppler
shift, angle of arrival of RX antenna?

thnx
---------------------------------------
Posted through http://www.DSPRelated.com
```
 0
runinrainy
12/22/2016 1:22:06 PM
```On Thu, 22 Dec 2016 07:22:06 -0600, runinrainy wrote:

>>On Wed, 21 Dec 2016 11:01:08 -0600, runinrainy wrote:
>>
>>> Hello,
>>>
>>> In time-variant multipath channel, in which each path has different
> time
>>> delay, phase, amplitude and Doppler shift and they all change during
>>> every symbol transmission from transmitter to receiver. Normally the
>>> channel coefficients can be estimated by using the estimation
> algorithms
>>> at the receiver and roughly it has the channel response as h=(1 0 .9 0
> 0
>>> 0.6 0.1), my question is how can we calculate or obtain the Doppler
>>> on how to visualize this parameter in the channel response h?
>>
>>I'm not sure you can get there from here.  Even in a perfectly
>>noise-free
>
>>environment there may not be enough information, per-symbol, to do what
>>you want.  The whole channel estimation thing depends, to a great
>>extent,
>
>>on building up a picture of what the channel is doing over many symbols.
>
>>Add in noise, and life just gets even more difficult.
>>
>>--
>>Tim Wescott Control systems, embedded software and circuit design I'm
>>looking for work!  See my website if you're interested
>>http://www.wescottdesign.com
>
> Thanks Tim. In time-variant channel assuming the channel characteristics
> change symbol to symbol, then in this case, as far as I know the pilots
> are inserted into each symbol and first the channel is estimated by the
> receiver before the deconvolution of the received symbol. At this point,
> when pilots are used to obtain the channel, could you also explain, from
> the detected signal taps, how to measure the parameters phase, doppler
> shift, angle of arrival of RX antenna?
>
> thnx ---------------------------------------
> Posted through http://www.DSPRelated.com

Are you talking about OFDM, and speaking of a "symbol" as one complete

You're still not giving enough information in this case.  Consider a
reflection that's moving quickly enough that it shifts the frequency of
the pilot tone in a given bin into an adjacent data bin -- how do you
distinguish that pilot tone from data?

That's just an example.  You absolutely, positively, have to put bounds
on the situation you anticipate seeing.  If you can't put bounds on what
you anticipate, then you need to put bounds on what situation you're
going to guarantee operation within.  Because there's always a possible
path that's going to be severely distorting enough that you can't deal
with it.

--
Tim Wescott
Control systems, embedded software and circuit design
I'm looking for work!  See my website if you're interested
http://www.wescottdesign.com
```
 0
Tim
12/22/2016 5:57:36 PM
```On Thu, 22 Dec 2016 07:22:06 -0600, "runinrainy" <100271@DSPRelated>
wrote:

>>On Wed, 21 Dec 2016 11:01:08 -0600, runinrainy wrote:
>>
>>> Hello,
>>>
>>> In time-variant multipath channel, in which each path has different
>time
>>> delay, phase, amplitude and Doppler shift and they all change during
>>> every symbol transmission from transmitter to receiver. Normally the
>>> channel coefficients can be estimated by using the estimation
>algorithms
>>> at the receiver and roughly it has the channel response as h=(1 0 .9 0
>0
>>> 0.6 0.1), my question is how can we calculate or obtain the Doppler
>>> on how to visualize this parameter in the channel response h?
>>
>>I'm not sure you can get there from here.  Even in a perfectly noise-free
>
>>environment there may not be enough information, per-symbol, to do what
>>you want.  The whole channel estimation thing depends, to a great extent,
>
>>on building up a picture of what the channel is doing over many symbols.
>
>>Add in noise, and life just gets even more difficult.
>>
>>--
>>Tim Wescott
>>Control systems, embedded software and circuit design
>>I'm looking for work!  See my website if you're interested
>>http://www.wescottdesign.com
>
>Thanks Tim. In time-variant channel assuming the channel characteristics
>change symbol to symbol, then in this case, as far as I know the pilots
>are inserted into each symbol and first the channel is estimated by the

You haven't said so thus far, but what you are describing appears to
be for a multi-carrier system (e.g., OFDM).   In this case you have to
have enough coherence bandwidth (and high enough SNR) that the pilot
tones provide adequate sampling in the frequency domain.   If so, then
interpolation of the bins between the pilots (from the pilot
information) provide the channel estimate.

However, you still have the issue that if the channel is really
changing significantly from symbol-to-symbol, you will be relying
solely on that symbol's pilot tones for channel estimation as well as
phase estimation.   Generally this is very difficult to do unless the
channels are very well-behaved and/or the SNR is very high.   Most
systems rely on averaging channel estimates over many symbols (to
increase the SNR of the estimate), or framing with multiple symbols
dedicated to channel estimation.   In the latter case the channel
estimates must still be done with a period shorter than the coherence
time of the channel or your estimates won't be good enough to
demodulate the signal.

Doppler is a frequency, and frequency requires measurement over time.
e.g., measure the channel at one symbol, measure it later at another,
and the phase changes between the various taps for the reflected rays
will provide estimates of the Doppler for those rays.   You can't
measure frequency from a single symbol, only phase.   A frequency
estimate requires multiple phase estimates over time.

> At this point,
>when pilots are used to obtain the channel, could you also explain, from
>the detected signal taps, how to measure the parameters phase, doppler
>shift, angle of arrival of RX antenna?

Angle of arrival requires beamforming-type computations which require
multiple recieve antennas.