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From: cpshah99 on 19 Jan 2010 12:52
Hi All

I have a que regarding narrowband Rician fading, mainly from the
simulations point of view.

Now for flat Rayleigh fading, when we simulate receiver performance in
terms of BER, it is assumed that perfect phase information is availabe at
receiver. So the received signal can be written as

y=x.*abs(a)+n, where a is complex fading process with 0 mean and unit
variance, x is BPSK signal and n is noise.

Now, for flat Rician fading, as it is non zero mean process, the equation
of the received signal is

y=x*c1+x.*abs(a)*c2+n, where c1=sqrt(K/(1+K)), c2=sqrt(1/(1+K)) and K is
Rice factor. The eqn satisfies teh fact that when K=0, it is Rayleigh
fading.

Is the above formulation correct?

Thanks.

Chintan Shah
From: dvsarwate on 19 Jan 2010 14:10
On Jan 19, 11:52 am, "cpshah99" <cpsha...(a)rediffmail.com> wrote:


> y=x*c1+x.*abs(a)*c2+n, where c1=sqrt(K/(1+K)), c2=sqrt(1/(1+K)) and K is
> Rice factor. The eqn satisfies teh fact that when K=0, it is Rayleigh
> fading.


Since c1, c2 and abs(a) are positive constants, in the ordinary
sense with * meaning multiplication, x*c1 + x*abs(a)*c2 + n is
the same as x*c3 + n where c3 = c1 + abs(a)*c2. So there must
be hidden meaning (MATLAB) in the notation x.*abs(a)*c2 where an
extra . is interposed between x and *abs(a).

--Dilip Sarwate

From: cpshah99 on 19 Jan 2010 16:48
>On Jan 19, 11:52=A0am, "cpshah99" <cpsha...(a)rediffmail.com> wrote:
>
>
>> y=3Dx*c1+x.*abs(a)*c2+n, where c1=3Dsqrt(K/(1+K)), c2=3Dsqrt(1/(1+K))
and=
> K is
>> Rice factor. The eqn satisfies teh fact that when K=3D0, it is
Rayleigh
>> fading.
>
>
>Since c1, c2 and abs(a) are positive constants, in the ordinary
>sense with * meaning multiplication, x*c1 + x*abs(a)*c2 + n is
>the same as x*c3 + n where c3 =3D c1 + abs(a)*c2. So there must
>be hidden meaning (MATLAB) in the notation x.*abs(a)*c2 where an
>extra . is interposed between x and *abs(a).
>
>--Dilip Sarwate
>
>

Hello Prof. Sarwate

Thanks for your reply.

As always u r right. The extra '.' was in terms of MATLABI (Matlab)
Language. :-)

But is the eqn correct? Is it fair to multiply the signal with abs(a)
under the assumption that perfect phase is known at the receiver?

If it is wrong then it will be great if you can explain.

I am not matlabi but just use matlab. :-)

Chintan Shah
From: dvsarwate on 19 Jan 2010 17:15
On Jan 19, 3:48 pm, "cpshah99" <cpsha...(a)rediffmail.com> wrote:

>
> But is the eqn correct? Is it fair to multiply the signal with abs(a)
> under the assumption that perfect phase is known at the receiver?
>


In a typical system, the PLL locks on to the specular component
and the signal model is a x1*c1 + x2*c2 + n where x1*c1 is a
BPSK signal of "known" phase that has K/(K+1) of the total signal
energy while x2*c2 is a standard Rayleigh-faded BPSK signal that
contains 1/(K+1) of the energy. I think that the phase of the
Rayleigh-faded BPSK signal is difficult to track separately, but I
am sure that those who have done it will tell you differently soon.
Put another way, if you have a MATLAB simulator for pure BPSK
and another for Rayleigh-faded BPSK, then the Rician signal model
is a weighted sum of the signals in the pure BPSK model and the
Rayleigh-faded BPSK model (IMHO).

--Dilip Sarwate

From: cpshah99 on 20 Jan 2010 04:58
>On Jan 19, 3:48=A0pm, "cpshah99" <cpsha...(a)rediffmail.com> wrote:
>
>>
>> But is the eqn correct? Is it fair to multiply the signal with abs(a)
>> under the assumption that perfect phase is known at the receiver?
>>
>
>
>In a typical system, the PLL locks on to the specular component
>and the signal model is a x1*c1 + x2*c2 + n where x1*c1 is a
>BPSK signal of "known" phase that has K/(K+1) of the total signal
>energy while x2*c2 is a standard Rayleigh-faded BPSK signal that
>contains 1/(K+1) of the energy. I think that the phase of the
>Rayleigh-faded BPSK signal is difficult to track separately, but I
>am sure that those who have done it will tell you differently soon.
>Put another way, if you have a MATLAB simulator for pure BPSK
>and another for Rayleigh-faded BPSK, then the Rician signal model
>is a weighted sum of the signals in the pure BPSK model and the
>Rayleigh-faded BPSK model (IMHO).
>
>--Dilip Sarwate
>
>

Ok.

So I guess this is the way to simulate flat Rician fading channel and
hopefully what I am doing is correct.

Thanks again.

Chintan
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