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how to make a "fading"?

Started by brunomaggi2002 August 9, 2002
Hi
I'm getting into radio channel simulations and I've come across the
following
r = t * c + n
r (received)
t (transmitted)
c fading
n (noise)
where, books say, c is a complex gaussian variable with mean 0 and
variance 0.5 per real dimension. My question is, given that c is
complex, what's the mean and variance of the imaginary dimension?
Cheers
Bruno




I believe you are trying to synthesize Rayleigh fading (as opposed
to Rician), since you are taking the mean value of the real part of
the fading coefficient to be zero. This corresponds to a fading
scenario where you do not have line of sight (LOS) and all you
receive is the reflections from the environment.

In a rayleigh fading scenario, the complex multiplicative coeficient
is referred to as: c(t) = c_r(t) + j.c_i(t), where j=sqrt(-1).

c_r(t) and c_i(t) are real valued random processes, with zero mean,
and 0.5 variance. To achieve this you need to produce two
independenty generated zero mean, unity variance random processes,
scale them by 1/sqrt(2), then combine them as written above to
achieve c(t).

The magnitude of random process c(t), which is equal to sqrt(c_r
(t).^2 + c_i(t).^2) is rayleigh distributed. If you need a rician
fading, you should simply have non-zero mean.

Tansu
--- In matlab@y..., "brunomaggi2002" <brunomaggi2002@y...> wrote:
> Hi
> I'm getting into radio channel simulations and I've come across the
> following
> r = t * c + n
> r (received)
> t (transmitted)
> c fading
> n (noise)
> where, books say, c is a complex gaussian variable with mean 0 and
> variance 0.5 per real dimension. My question is, given that c is
> complex, what's the mean and variance of the imaginary dimension?
> Cheers
> Bruno


Hi,

Assuming that the signal 't' is real (for BPSK modulation),

r = t * c + n

where 'c' is complex gaussian variable with mean 0 and var 0.5 per real
dimension.

'c' can be written as |c| (magnitude which is rayleigh random variable)
and angle(c) (this is uniformly distributed r.v.)

c can also be represented as x + j*y, x = N(0,0.5) and y = N(0,0.5)
where N(a,b) is gaussian r.v. with mean a and variance b.

hope this helps. if u have further doubts, you can check out my homepage
(in my signature below). i have put up some reports on rayleigh fading,
rician fading, etc ...

logesh.

On Fri, 9 Aug 2002, brunomaggi2002 wrote:

> Hi
> I'm getting into radio channel simulations and I've come across the
> following
> r = t * c + n
> r (received)
> t (transmitted)
> c fading
> n (noise)
> where, books say, c is a complex gaussian variable with mean 0 and
> variance 0.5 per real dimension. My question is, given that c is
> complex, what's the mean and variance of the imaginary dimension?
> Cheers
> Bruno >
>
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--
------------------------
Logeshwaran Vijayan
Graduate Student/Research Assistant
EECS Department-The University of Kansas
Lawrence, Kansas.

Office :
Room 339, Raymond Nichols Hall
Information and TeleCommunication Technology Center
Phone No. (785)-864-7799
E-Mail :
URL : www.ittc.ku.edu/~logesh

Residence :
1301 W 24th Street, #o-06,
Lawrence, KS 66046
Phone No. (785)-749-4398
____________________________________________________________
Create a vision of who you want to be and live into that
picture as if it were already true - Arnold Schwarzenegger
------------------------



Hi,
Thanks iceman and Logeshwaran. did not have problems thanks to your
indication - now I'm trying to have parallel channels and i want to
know if it possible to choose the correlation between them.
I mean, something like

function[ch1fading, ch2fading] = makefading(correlation_index)

or I have generate one and repeat the generation of the second until
I obtain the desired correlation

Cheers!!

bruno

--- In matlab@y..., Logeshwaran Vijayan <logesh@i...> wrote:
> Hi,
>
> Assuming that the signal 't' is real (for BPSK modulation),
>
> r = t * c + n
>
> where 'c' is complex gaussian variable with mean 0 and var 0.5 per
real
> dimension.
>
> 'c' can be written as |c| (magnitude which is rayleigh random
variable)
> and angle(c) (this is uniformly distributed r.v.)
>
> c can also be represented as x + j*y, x = N(0,0.5) and y = N(0,0.5)
> where N(a,b) is gaussian r.v. with mean a and variance b.
>
> hope this helps. if u have further doubts, you can check out my
homepage
> (in my signature below). i have put up some reports on rayleigh
fading,
> rician fading, etc ...
>
> logesh.
>
> On Fri, 9 Aug 2002, brunomaggi2002 wrote:
>
> > Hi
> > I'm getting into radio channel simulations and I've come across
the
> > following
> > r = t * c + n
> > r (received)
> > t (transmitted)
> > c fading
> > n (noise)
> > where, books say, c is a complex gaussian variable with mean 0 and
> > variance 0.5 per real dimension. My question is, given that c is
> > complex, what's the mean and variance of the imaginary dimension?
> > Cheers
> > Bruno
> >
> >
> >
> >
> > _____________________________________
> > Note: If you do a simple "reply" with your email client, only the
author of this message will receive your answer. You need to do
a "reply all" if you want your answer to be distributed to the entire
group.
> >
> > _____________________________________
> > About this discussion group:
> >
> > To Join: matlab-subscribe@y...
> >
> > To Post: matlab@y...
> >
> > To Leave: matlab-unsubscribe@y...
> >
> > Archives: http://www.yahoogroups.com/group/matlab
> >
> > More DSP-Related Groups: http://www.dsprelated.com/groups.php3
> >
> > ">http://docs.yahoo.com/info/terms/
> >
> >
>
> --
> ------------------------
> Logeshwaran Vijayan
> Graduate Student/Research Assistant
> EECS Department-The University of Kansas
> Lawrence, Kansas.
>
> Office :
> Room 339, Raymond Nichols Hall
> Information and TeleCommunication Technology Center
> Phone No. (785)-864-7799
> E-Mail : logesh@i...
> URL : www.ittc.ku.edu/~logesh
>
> Residence :
> 1301 W 24th Street, #o-06,
> Lawrence, KS 66046
> Phone No. (785)-749-4398
> ____________________________________________________________
> Create a vision of who you want to be and live into that
> picture as if it were already true - Arnold Schwarzenegger
> ------------------------