Is Multipath on I and Q at baseband the same as on the Real RF signal?

Hypothetical question...

If I impart 2 identical multipaths onto the I and Q baseband signals, is that the same as imparting one multipath onto the real RF signal?  
Of course I would need to create 2 identical multipths, one for I and one for Q.

At first blush, it would seem these would be the same, but I'm not so sure.  
Done at basband, there is no possible interaction between I and Q.  
Done at RF there may be some cross product?

Thats why I am asking you smart guys   :-)

For logistical reasons, it may be easier to implement a multipath emulation at baseband rather than at RF and I would like to know if the emulation is valid.

thanks

Mark

  

makolber@yahoo.com writes:

> Hypothetical question...
>
> If I impart 2 identical multipaths onto the I and Q baseband signals,
> is that the same as imparting one multipath onto the real RF signal?  

Absolutely not! Is 

  S(t) * cos(w*t) + j * S(t) * sin(w*t) = 
  S(t)            + j * S(t)

?
-- 
Randy Yates
Digital Signal Labs
http://www.digitalsignallabs.com

On Friday, July 10, 2015 at 7:42:10 AM UTC-5, mako...@yahoo.com wrote:
> Hypothetical question...
> 
> If I impart 2 identical multipaths onto the I and Q baseband signals, is that the same as imparting one multipath onto the real RF signal?  
> Of course I would need to create 2 identical multipths, one for I and one for Q.
> 
> At first blush, it would seem these would be the same, but I'm not so sure.  
> Done at basband, there is no possible interaction between I and Q.  
> Done at RF there may be some cross product?
> 
> Thats why I am asking you smart guys   :-)
> 
> For logistical reasons, it may be easier to implement a multipath emulation at baseband rather than at RF and I would like to know if the emulation is valid.
> 
> thanks
> 
> Mark

The multipath propagation occurs at the RF frequency 
and when the RF signal is demodulated into the 
baseband I and Q signals, the multipath signal gets
demodulated also. However, the local reference
carrier signal is assumed to be phase-synchronous with
the main signal, and thus is not phase synchronous with
the multipath signal(s). Thus, the I and Q components
in the multipath signal appear in both the I and the
Q baseband signals.  The **delay** is the same, but
the demodulated baseband I signal is

I(t) = I_{tr}(t) + a [I_{tr}(t-tau) + Q_{tr}(t-tau)]

where I_{tr}(t) is the desired (main) signal and the
rest is the contribution of the multipath signal
(attenuated by factor a and delayed by tau with respect
to the main signal).  Similarly for the baseband Q signal.

Dilip Sarwate

<makolber@yahoo.com> wrote:

>If I impart 2 identical multipaths onto the I and Q baseband signals, is
>that the same as imparting one multipath onto the real RF signal?  
>Of course I would need to create 2 identical multipths, one for I and one for Q.

>At first blush, it would seem these would be the same, but I'm not so sure.  
>Done at basband, there is no possible interaction between I and Q.  
>Done at RF there may be some cross product?

>Thats why I am asking you smart guys   :-)

Most multipath models are derived from the old Turin model,
which assumes the carrier frequency is much larger than other
frequencies of interest (such as bandwidth and baud rate) and
therefore it is valid to assume that each reflection arrives with
a uniformly random phase in the I/Q plane.  The is, the phase
is uniformly random within [0, 2*pi) whereas the magnitude is
defined by the parameters of your model (which could just be
carried over from a real RF model).

If the above assumption is not valid, it is probably best to
use a real model, that is, implement the channel model at RF.

>For logistical reasons, it may be easier to implement a multipath
>emulation at baseband rather than at RF and I would like to know if the
>emulation is valid.

People do this all the time.

Hope this helps.

Steve

dvsarwate  <dvsarwate@yahoo.com> wrote:

>The multipath propagation occurs at the RF frequency 
>and when the RF signal is demodulated into the 
>baseband I and Q signals, the multipath signal gets
>demodulated also. 

Yes

> However, the local reference carrier signal is assumed to be
> phase-synchronous with the main signal, and thus is not phase
> synchronous with the multipath signal(s).

Well, not necessarily.

Some (many) channels do not have a distinct "main" signal that can be 
distinguished from the other reflections.  Also, some (many) scenarios 
do not assume the RX and its demodulator are in any way synchronous 
with the TX (although arranging for this to magically happen may make 
sense when evaluating the multipath behavior in isolation from other 
behaviors such as carrier offset, timing recovery, etc.)
etc.)

> Thus, the I and Q components in the multipath signal appear
> in both the I and the Q baseband signals.  The **delay** is
> the same, but the demodulated baseband I signal is

> I(t) = I_{tr}(t) + a [I_{tr}(t-tau) + Q_{tr}(t-tau)]

> where I_{tr}(t) is the desired (main) signal and the rest is
> the contribution of the multipath signal (attenuated by factor
> a and delayed by tau with respect to the main signal).

This formula is good but it assumes the receiver has successfully 
identified and de-rotated the desired (main) signal, such that it is 
valid to subtract out its associated delay.

Steve

On Fri, 10 Jul 2015 05:42:04 -0700, makolber wrote:

> Hypothetical question...
> 
> If I impart 2 identical multipaths onto the I and Q baseband signals, is
> that the same as imparting one multipath onto the real RF signal?
> Of course I would need to create 2 identical multipths, one for I and
> one for Q.
> 
> At first blush, it would seem these would be the same, but I'm not so
> sure.
> Done at basband, there is no possible interaction between I and Q.
> Done at RF there may be some cross product?
> 
> Thats why I am asking you smart guys   :-)
> 
> For logistical reasons, it may be easier to implement a multipath
> emulation at baseband rather than at RF and I would like to know if the
> emulation is valid.

No, it is not the same, at least not unless you properly take multipath 
delays that are outside of your filter's impulse response time, AND you 
figure that a "multipath" acting on a channel includes a multiply by a 
complex gain.

Such a multipath simulation would have to multiply the I and Q channels 
by some complex number with a magnitude between -2 and +2 and some 
arbitrary phase, as well as correctly taking delays into account that are 
on the order of the low-pass filter's impulse response time, or longer, 
into account.

If I did it that way I'd expect to have a mountain of paper with 
scribbles, and a dozen pages worth of white paper full of analysis to 
explain and justify what I was doing.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

> 
> Such a multipath simulation would have to multiply the I and Q channels 
> by some complex number with a magnitude between -2 and +2 and some 
> arbitrary phase, as well as correctly taking delays into account that are 
> on the order of the low-pass filter's impulse response time, or longer, 
> into account.
>

OK thank you everyone for the replies...

My take after reading these is, yes,    I can implement the MP at I and Q baseband, BUT  for it to be an accurate representation of MP at RF, I cannot simply add the delayed I and Q to the original I and Q but rather i must take the delayed I and Q and feed them into a ___second RF vector modulator___ and then add the RF signals.   The two carrier frequencies would need to be phase locked and the phase of the carrier of the second generator can then be randomized relative to the phase of the "direct" path.... (or i could set it 1 Hz off and have the phase rotate through 360 deg once per second implementing the next levelof complexity, Doppler.)  


thanks

Mark

<makolber@yahoo.com> wrote:

>> Such a multipath simulation would have to multiply the I and Q channels 
>> by some complex number with a magnitude between -2 and +2 and some 
>> arbitrary phase, as well as correctly taking delays into account that are 
>> on the order of the low-pass filter's impulse response time, or longer, 
>> into account.

>OK thank you everyone for the replies...

>My take after reading these is, yes,    I can implement the MP at I and
>Q baseband, BUT  for it to be an accurate representation of MP at RF, I
>cannot simply add the delayed I and Q to the original I and Q but rather
>i must take the delayed I and Q and feed them into a ___second RF vector
>modulator___ and then add the RF signals.   The two carrier frequencies
>would need to be phase locked and the phase of the carrier of the second
>generator can then be randomized relative to the phase of the "direct"
>path.... (or i could set it 1 Hz off and have the phase rotate through
>360 deg once per second implementing the next levelof complexity,
>Doppler.)  

I think you're making it sound more complicated than it is.

Here's the full reference for Turin's model:

G. L. Turin, F. D. Clapp, T. L. Johnston, S. B. Fine, and D. Lavry, 
"A statistical model of urban multipath propagation," IEEE Trans. 
Vehicular Technology, vol. VT-21, no. 1, pp. 1-9, Feb. 1972. 

You to not need to mix back up to RF to introduce the necessary 
multiplication by a arbitrary phase.

Steve

On Mon, 13 Jul 2015 06:24:23 -0700 (PDT), makolber@yahoo.com wrote:

>
>>=20
>> Such a multipath simulation would have to multiply the I and Q channels=
>=20
>> by some complex number with a magnitude between -2 and +2 and some=20
>> arbitrary phase, as well as correctly taking delays into account that are=
>=20
>> on the order of the low-pass filter's impulse response time, or longer,=
>=20
>> into account.
>>
>
>OK thank you everyone for the replies...
>
>My take after reading these is, yes,    I can implement the MP at I and Q b=
>aseband, BUT  for it to be an accurate representation of MP at RF, I cannot=
> simply add the delayed I and Q to the original I and Q but rather i must t=
>ake the delayed I and Q and feed them into a ___second RF vector modulator_=
>__ and then add the RF signals.   The two carrier frequencies would need to=
> be phase locked and the phase of the carrier of the second generator can t=
>hen be randomized relative to the phase of the "direct" path.... (or i coul=
>d set it 1 Hz off and have the phase rotate through 360 deg once per second=
> implementing the next levelof complexity, Doppler.) =20
>
>
>thanks
>
>Mark

Mark,

I *think* I sent you an email last week, because I was travelling and
couldn't post to comp.dsp for some reason (although I could read it).


For each reflected ray the delay, magnitude and phase of the
reflection are independent variables, with the phase typically being
random.   Since the phase of each reflection is random, there's no
need to phase lock anything to the main carrier, if I understand you
correctly. 




Eric Jacobsen
Anchor Hill Communications
http://www.anchorhill.com

> 
> Mark,
> 
> I *think* I sent you an email last week, because I was travelling and
> couldn't post to comp.dsp for some reason (although I could read it).
> 

this email i use to post to usenet is fake


> For each reflected ray the delay, magnitude and phase of the
> reflection are independent variables, with the phase typically being
> random.   Since the phase of each reflection is random, there's no
> need to phase lock anything to the main carrier, if I understand you
> correctly. 
> 
>

understood..

If I want the phase relationship to be STABLE with time then i need to phase lock.

If I don't phase lock, not only will the phase be a random value, but it will also change with time based on the frequency offset between the 2 generators. If the two generators are 1 Hz apart, the phase offset will change 360 deg per sec.   etc.


Mark