# how to find the autocorrelation and spectrum of the receiver signal in mobile communication?

Started by November 22, 2004
```Hi all,

I am wondering about the simplest model in mobile communicaiton, multipath.

Suppose the received signal has random uniform [0, 2*pi] phase due to
multipath fading, and also has Rayleigh distribution on its
amplitude(assuming no direct line path), and also has doppler frequency
shift in carrier frequency.

The signal then can be modelled as

r(t)=A*exp(j*2*pi*(f+delta_f)*t + THETA)

where A and THETA are random variables...

How to find its autocorrelation function and then Power Spectrum Density?

Please give me some pointers... thanks a lot!

```
```Hi kiki,

As you have a time domain model of your signal just sample it and
using matlab PSD function (it does the Welch's PSD estimation).
You must have signal long enought.

r[n]=r(delta_t*n)

psd(r[n]);

The above is mixture of mathematics and matlab syntax ... but I think
you got the idea.

penev
-----------------
DSP Forum: www.dsp-bg.info

"kiki" <lunaliu3@yahoo.com> wrote in message news:<cns82k\$j5s\$1@news.Stanford.EDU>...
> Hi all,
>
> I am wondering about the simplest model in mobile communicaiton, multipath.
>
> Suppose the received signal has random uniform [0, 2*pi] phase due to
> multipath fading, and also has Rayleigh distribution on its
> amplitude(assuming no direct line path), and also has doppler frequency
> shift in carrier frequency.
>
> The signal then can be modelled as
>
> r(t)=A*exp(j*2*pi*(f+delta_f)*t + THETA)
>
> where A and THETA are random variables...
>
> How to find its autocorrelation function and then Power Spectrum Density?
>
> Please give me some pointers... thanks a lot!
```
```"Dimitar Penev" <dpenev@yahoo.com> wrote in message
> Hi kiki,
>
> As you have a time domain model of your signal just sample it and
> using matlab PSD function (it does the Welch's PSD estimation).
> You must have signal long enought.
>
> r[n]=r(delta_t*n)
>
> psd(r[n]);
>
> The above is mixture of mathematics and matlab syntax ... but I think
> you got the idea.
>
> penev
> -----------------
> DSP Forum: www.dsp-bg.info
>
>
>
>
>
>
> "kiki" <lunaliu3@yahoo.com> wrote in message
> news:<cns82k\$j5s\$1@news.Stanford.EDU>...
>> Hi all,
>>
>> I am wondering about the simplest model in mobile communicaiton,
>> multipath.
>>
>> Suppose the received signal has random uniform [0, 2*pi] phase due to
>> multipath fading, and also has Rayleigh distribution on its
>> amplitude(assuming no direct line path), and also has doppler frequency
>> shift in carrier frequency.
>>
>> The signal then can be modelled as
>>
>> r(t)=A*exp(j*2*pi*(f+delta_f)*t + THETA)
>>
>> where A and THETA are random variables...
>>
>> How to find its autocorrelation function and then Power Spectrum Density?
>>
>> Please give me some pointers... thanks a lot!

Hi Dimitra,

that's great! I did not know that before... I learned a lot from this
experiment: I did the following:

Fs=1000;
t=[0:1/Fs:20];
A=random('rayleigh', 10, 1, length(t));
THETA=rand(1, length(t))*2*pi;
delta_f=300;
f=1000000;
r=A.*exp(1j*2*pi*(f+delta_f).*t + THETA);
h = spectrum.welch;
psd(h, r, 'Fs', Fs);

----------------------------------

I saw basically a narrow peak centered at delta_f=300 position, it is indeed
very high compared with all other frequency components, which are noisily
flat and small...

I am not sure if my model is correct though...

Can anybody tell me if my following model is correct in simple multipath

>> Suppose the received signal has random uniform [0, 2*pi] phase due to
>> multipath fading, and also has Rayleigh distribution on its
>> amplitude(assuming no direct line path), and also has doppler frequency
>> shift in carrier frequency.
>>
>> The signal then can be modelled as
>>
>> r(t)=A*exp(j*2*pi*(f+delta_f)*t + THETA)

Thanks a lot!

```