Signal multiplication with complex number

>So a complex-valued channel gain per antenna gets multiplied by the
>complex-valued baseband signal received at that antenna.    From this
>perspective the phase is really only relevant to model the phase
>differences between antennas.   For a single antenna system a
>flat-fading channel would only require a scalar amplitude coefficient,
>but for multiple antennas the relative phases matter.

Dear Eric & Steve,

Thanks. I assume that the complex-valued channel gain per antenna is a
single value (one point on complex plane) and not a vector by itself for a
given antenna ...

PS: it is possible that these values could change quasi-dynamically based
on channel conditions and can vary per antenna 
---------------------------------------
Posted through http://www.DSPRelated.com

On Tue, 02 Feb 2016 07:00:45 -0600, "Sharan123" <99077@DSPRelated>
wrote:

>>So a complex-valued channel gain per antenna gets multiplied by the
>>complex-valued baseband signal received at that antenna.    From this
>>perspective the phase is really only relevant to model the phase
>>differences between antennas.   For a single antenna system a
>>flat-fading channel would only require a scalar amplitude coefficient,
>>but for multiple antennas the relative phases matter.
>
>Dear Eric & Steve,
>
>Thanks. I assume that the complex-valued channel gain per antenna is a
>single value (one point on complex plane) and not a vector by itself for a
>given antenna ...

Actually, it can be either.   Generally, basic MIMO processing only
needs independent flat-fading (i.e., single value) channel
coefficients to work.   In practice, there is often multipath where
the channel impulse response has a delay spread that is represented by
a vector rather than a single coefficient.

>PS: it is possible that these values could change quasi-dynamically based
>on channel conditions and can vary per antenna 

Yes.    For MIMO to work the individual channels coefficients for each
antenna must be independent of each other to a high degree.    That
isn't always the case in practice, but often it is.


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

On Tue, 02 Feb 2016 07:00:45 -0600, Sharan123 wrote:

>>So a complex-valued channel gain per antenna gets multiplied by the
>>complex-valued baseband signal received at that antenna.    From this
>>perspective the phase is really only relevant to model the phase
>>differences between antennas.   For a single antenna system a
>>flat-fading channel would only require a scalar amplitude coefficient,
>>but for multiple antennas the relative phases matter.
> 
> Dear Eric & Steve,
> 
> Thanks. I assume that the complex-valued channel gain per antenna is a
> single value (one point on complex plane) and not a vector by itself for
> a given antenna ...

I'm not sure if it's entirely clear from the discussion so far, but the 
underlying process that you're modeling with antenna stuff is that the 
signal goes out from the transmitter, bounces off of random stuff "out 
there", and then various bits of it hit the antenna at various delays.

For delays that are a good portion of a cycle of RF, but are small 
compared to any modulation interval, the best model is a simple phase 
shift and gain (or attenuation).  This, in turn, is best modeled as 
multiplying the signal with a complex gain.

For delays that are a good portion, or more than one, modulation 
interval, then the best model is that delay, plus the afore-mentioned 
complex gain.  This case is going to be most prevalent when you're 
dealing with a spread-spectrum service, because the chipping rate will 
tend to be a much healthier portion of the carrier frequency than the 
underlying bit rate (or analog signal bandwidth).

There's no reason you can't have multiple paths; for how to handle that 
do a search on "rake receiver".

> PS: it is possible that these values could change quasi-dynamically
> based on channel conditions and can vary per antenna

If either your antennas or the things that your signal is reflecting off 
of are moving, then yes.  So definitely yes if the transmitter or 
receiver is mobile (like a cell phone).  Buildings, walls, and towers 
don't generally get up and walk around, so varying multipath isn't as 
much of an issue with fixed stations -- but in a fringe reception area 
you can get significant propagation from airplanes and other moving 
phenomenon.

-- 

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

Dear Eric, Tim, 

Thanks a lot. THis helps a lot
---------------------------------------
Posted through http://www.DSPRelated.com