How is OFDM in AWGN

[cindy]

OFDM is mainly used to combat the multipath effect. But how is its performance in AWGN?

I am doing a simulation with qpsk ofdm system. Before I add OFDM, the BER goes with the theoretic value very well. However, after I add OFDM, the BER degrades dramatically. This is because ifft scales the signal power down by the ifft size N. Therefore, the acuta SNR after adding OFDM is down compared the situation without OFDM.

Is this the correct result? Or the SNR is defined in a different way in OFDM system?

Thanks in advance.

Cindy
[e-mail]

[cindy]

Hi,

I think the signal energy should be the same before and after ifft because the duration for the tansmitted signal is prolonged N times. This means the SNR with and without OFDM should be the same --- the system performance should be the same, in pure AWGN channel.

Please tell me what you think.

Thanks.

Cindy

Pl

[estimation]

Hi Cindy,
you can use the following definiton of IFFT/ FFT pair and you will get correct results for BER.

Normalized IFFT/FFT (signal power is not changed after the transform, and thus SNR is the same):

For length N input vector x, the DFT is a length N vector X,
with elements
N
X(k) = (1/(sqrt(N)) sum x(n)*exp(-j*2*pi*(k-1)*(n-1)/N), 1 <= k <= N.
n=1
The inverse DFT (computed by IFFT) is given by
N
x(n) = (1/(sqrt(N)) sum X(k)*exp( j*2*pi*(k-1)*(n-1)/N), 1 <= n <= N.
k=1

Instead the usual one used in Matlab:

For length N input vector x, the DFT is a length N vector X,
with elements
N
X(k) = sum x(n)*exp(-j*2*pi*(k-1)*(n-1)/N), 1 <= k <= N.
n=1
The inverse DFT (computed by IFFT) is given by
N
x(n) = (1/N) sum X(k)*exp( j*2*pi*(k-1)*(n-1)/N), 1 <= n <= N.
k=1

[cindy]

Thanks.

I have already got the the correct BER by scaling the signal/noise properly after ifft. I figured out the problem by theoretic deriviation, too.

Your method is great, too. I guess many people are doing it based on your methodology, which is easier to understand and manipulate.

Cindy

[cindy]

But, what fft/ifft pair we should use for the channel tansformation?

Cindy

[kader]

The usual one used in matlab

[kader]

The usual one used in matlab is indicated for channel transform

[mohammw4]

hello mi i am also working on ofdm in the same field so plz can u mail me your simulation and program so that i can help you and i have got many thesis on that

[hunter006]

There is a good "tutorial" with a working simulation package available if you search for OFDM on the net. I can't find the link (too lazy), but the filename is OFDM_analy.pdf by Erich Cosby of Virginia Tech. In there is a simulation using AWGN (implemented in a slightly confusing way, but don't be concerned - it is AWGN) that you can use, and defining BER as the number of errors over the total transmission length, you can easily work out the BER for varying modulation schemes. Note that Cosby has allowed for differing SNR values; in my thesis I took a note from his book and also implemented AWGN in transmission, however I used the matlab function to do it. The code I used was:

transmission = ofdm_transmitter( bin_input_stream, modulation );
noisy_trans = awgn( transmission, SNR );
rx_estimated_signal = ofdm_transmitter( noisy_trans, modulation );

As I put a lot of work in to my thesis simulation, I will not release the code, so please don't ask for it as my refusal may offend you.

[cancerman]

Hi,

I understand that the OFDM time signal is generated from the IFFT of the sub carriers in the frequency domain.

If I introduce an AWGN signal to the time signal, how will it affect the individual sub carriers?

Is the total signal energy/power of the AWGN signal the same in both the time and frequency domain? If this is the case, can I take it that the power of the noise added to each sub carrier (when I perform an FFT) is the same?

Thanks

[mido]

when I simulated BPSK under Raleigh fading the simulated results was exactly as theoretical but when I use BPSK in OFDM system the result Untill 15dB like BPSK without OFDM but after that error floor occurred.
Can any one tell me what is the wrong???
PLZ help me

[charan langton]

It may due to the fact that a FFT is used to demodulate. The length of the FFT has a relationship with the resolution. May be, but I have not seen an error floor with OFDM. You may have numerical issue.

[charan langton]

No reason OFDM should perform any worse that QPSK in AWGN. The only problem comes when there are non-linarities present. In which case, is likely to suffer from group delay etc. worse than standard QPSK where reverse is the case in a Rayleigh channel.

Try your analysis by taking out all non-linearities and then do the analysis. You should get same results as QPSK.

[hyper]

Hi Sindy,
I am doing the simulation on OFDM using QPSK, but I can't implemented in matlab, could you please send me the matlab syntax for QPSK in OFDM.
I statrted as follows you can have a look and we can completed together, and this is the program plan.
(((((((((((((((((((Start))))))))))))))))))))))))))))
close all
clc
n=128; %Number of parralel channel;
nofdm=6 % Number of information OFDM symbol
M1=2; % Modulation Level QPSK
fftlen=128; %Length of FFT
gilen=32; % Guard Interval Length
sr=250000; % Synbol Rate
br=sr*M1; % Bit Rate per Carrier
%for SNR=0:2:20;

%(((((((At the Transmitter Generate serial Data )))))))))

serdata=rand(1,n*nofdm*M1)>0.5;

%(((((((Convert the transmitted signal from Parralel to Serial))))))))

paradata=reshape(serdata,n,nofdm*M1);

%(((((((((( QPSK Modulation))))))))))))

[ich qch]=qpskmod1(paradata,n,nofdm,M1);
% I have stoped here we need a QPSK modulation program,......
fmod=1/sqrt(2) % Normalization factor(for QPSK is 1/sqrt(2))
ich1=ich.*fmod;
qch1=qch.*fmod;

%(((((((((((((((((( IFFT )))))))))))))))

%(((((((((((((((((( Guard Interval Inserssion))))))))))))))

%(((((((((((((( Attenuation Calculation )))))))))))))))))))

%(((((((((((((((((( Adding AWGN)))))))))))))))))))))))))))))

%(((((((((((((((((( Guard Interval Removel))))))))))))))))))

%((((((((((((Demodulation))))))))))))))))))))

%(((((((((( Converting Back from Parallel to Serial ))))))))

%(((((((((((( Bit Error Rate Calculation )))))))))))))))