- 26th March 2010, 19:05 #1

- Join Date
- Apr 2007
- Posts
- 159
- Helped
- 6 / 6
- Points
- 2,193
- Level
- 10

## AWGN Channel

Hello,

In AWGN channel, how is white noise generated using MATLAB? I mean, I have a code at hand, but I did not understand it. For example, it says somewhere in the code:

y = s + 10^(-Eb_N0_dB(ii)/20)*n;

where s is the transmitted sequence, Eb_N0_dB is the SNR, and n is the additive white noise. Can anyone explain to me the noise term, please? Why do we use the expression 10^(-Eb_N0_dB(ii)/20)*n?

Regards

- 27th March 2010, 10:41 #2

- Join Date
- Apr 2007
- Posts
- 159
- Helped
- 6 / 6
- Points
- 2,193
- Level
- 10

## Re: AWGN Channel

Originally Posted by**mathuranathan**

Actually, I still do not get why we use the expression 10^(-Eb_N0_dB(ii)/20)*n for the noise. Anyway, from the link you gave me, I found a built-in function in MATLAB which is AWGN() function that adds noise depending on the SNR. I tried it as in the following code:

Code:function BER clear; N=10^6; SNRdB=[-3:10]; SNR=10.^(SNRdB/10); b=rand(1,N)>0.5; s=2*b-1; for ii=1:length(SNRdB) y=awgn(s,SNRdB(ii),'measured'); bHat=real(y)>0; Diff=xor(bHat,b); nErr(ii)=length(find(Diff)); end simBER=nErr/N; theoryBER=0.5*erfc(sqrt(SNR)); semilogy(SNRdB,simBER,'k*',SNRdB,theoryBER,'bx'); legend('Simualtion','Theory');

Thanks in advance

- 27th March 2010, 10:41

- 8th April 2010, 09:41 #3

- Join Date
- Apr 2007
- Posts
- 159
- Helped
- 6 / 6
- Points
- 2,193
- Level
- 10

## Re: AWGN Channel

Originally Posted by**mathuranathan**

Regards

- 8th April 2010, 10:25 #4

- Join Date
- Apr 2007
- Posts
- 159
- Helped
- 6 / 6
- Points
- 2,193
- Level
- 10

## Re: AWGN Channel

Originally Posted by**mathuranathan**

1 members found this post helpful.

- 9th April 2010, 13:56 #5

- Join Date
- Apr 2007
- Posts
- 159
- Helped
- 6 / 6
- Points
- 2,193
- Level
- 10

## Re: AWGN Channel

Originally Posted by**mathuranathan**

Thanks in advance

- 9th April 2010, 13:56

- 10th April 2010, 15:08 #6

- Join Date
- Apr 2007
- Posts
- 159
- Helped
- 6 / 6
- Points
- 2,193
- Level
- 10

## Re: AWGN Channel

I have noticed that, when I set the range of errors from 10^-7 up to 0.5, the simulation curve stopped on 10^-6. Why is that?

- 12th April 2010, 15:54 #7

- Join Date
- Apr 2007
- Posts
- 159
- Helped
- 6 / 6
- Points
- 2,193
- Level
- 10

## Re: AWGN Channel - generating noise for required SNR

I think it is clear now the concept of adding AWGN to the transmitted signal over AWGN channel. Let me summarize:

For a specific SNR we need to add a noise term to the transmitted symbol such that the SNR is as specified, i.e.: if the SNR(dB)=15, we need to add a noise term such that the SNR(dB)=15 dB. To do this, we assume that the signal energy is unity (Why?), and then:

Code:y=s+10.^(-15/20)*n

. But, is the assumption that the energy of the signal = 1 is valid?

Now, let us turn to the multipath fading channles. In this case the receiced signal will be:

Code:y=h*s+10.^(-15/20)*n

Shall we assume that the numerator is unity? I.e.: |h|^2*Es =1? Why?

Thanks in advanceLast edited by BlackMamba; 27th August 2010 at 13:19.

- 20th April 2010, 15:00 #8

- Join Date
- Apr 2007
- Posts
- 159
- Helped
- 6 / 6
- Points
- 2,193
- Level
- 10

## Re: AWGN Channel

Originally Posted by**mathuranathan**

Thanks in advance

- 20th April 2010, 15:00

- 23rd April 2010, 16:07 #9

- Join Date
- Apr 2007
- Posts
- 159
- Helped
- 6 / 6
- Points
- 2,193
- Level
- 10

## Re: AWGN Channel - generating noise for required SNR

Originally Posted by**mathuranathan**

Regards

- 10th December 2011, 04:28 #10

- Join Date
- Dec 2011
- Posts
- 6
- Helped
- 0 / 0
- Points
- 203
- Level
- 2

## Re: AWGN Channel - generating noise for required SNR

Is y=s-(20 log(SNR)*n) the same with y = s + 10^(-Eb_N0_dB(ii)/20)*n?

please reply me as soon as possible.

---------- Post added at 05:28 ---------- Previous post was at 05:21 ----------

Is y=s-(20 log(SNR)*n) the same with y = s + 10^(-Eb_N0_dB(ii)/20)*n?

please reply me as soon as possible. And then, i would like to know the value of n?

- 10th December 2011, 17:54 #11

- Join Date
- Jan 2011
- Posts
- 280
- Helped
- 28 / 28
- Points
- 1,898
- Level
- 10

## Re: AWGN Channel - generating noise for required SNR

Is SNR here in dB or linear?

- 10th December 2011, 18:19 #12

- Join Date
- Dec 2011
- Posts
- 6
- Helped
- 0 / 0
- Points
- 203
- Level
- 2

- 10th December 2011, 21:41 #13

- Join Date
- Jan 2011
- Posts
- 280
- Helped
- 28 / 28
- Points
- 1,898
- Level
- 10

## Re: AWGN Channel - generating noise for required SNR

1 members found this post helpful.

- 24th December 2011, 19:35 #14

- Join Date
- Dec 2011
- Posts
- 6
- Helped
- 0 / 0
- Points
- 203
- Level
- 2

## Re: AWGN Channel - generating noise for required SNR

Thank u for ur reply!! but i need to change a little bit. how can i change the equation, y = s + 10^(-Eb_N0_dB(ii)/20)*n to another way? Please tell me! i am not so clear ! Thank u! Is this equation y=s+(1/sqrt(SNR))*n right and same with y = s + 10^(-Eb_N0_dB(ii)/20)*n?

- 26th December 2011, 01:10 #15

- Join Date
- Jan 2011
- Posts
- 280
- Helped
- 28 / 28
- Points
- 1,898
- Level
- 10

- 1st May 2013, 11:43 #16

- Join Date
- Jun 2009
- Location
- Egypt
- Posts
- 14
- Helped
- 1 / 1
- Points
- 767
- Level
- 6

## Re: AWGN Channel - generating noise for required SNR

How to include the path loss exponent and the distance between the source & destination in the channel H???

- 11th May 2013, 23:48 #17

- Join Date
- May 2010
- Location
- assa
- Posts
- 10
- Helped
- 1 / 1
- Points
- 759
- Level
- 6

## Re: AWGN Channel - generating noise for required SNR

i thinck it will be y=s+(1/sqrt(2*SNR))*n not ........ y=s+(1/sqrt(SNR))*n

because σ = √(N0/2)