(5 votes, average: 4.8 out of 5)
Loading ...
Let us try to understand simulation of a typical Orthogonal Frequency Division Multiplexing (OFDM) transmission defined per IEEE 802.11a specification.
Orthogonal pulses
In a previous post (here ), we have understood that the minimum frequency separation for two sinusoidals with arbitrary phases to be orthogonal is , where
is the symbol period.
In Orthogonal Frequency Division Multiplexing, multiple sinusoidals with frequency separation is used. The sinusoidals used in OFDM can be defined as (Refer Sec6.4.2 in [DIG-COMM-BARRY-LEE-MESSERSCHMITT]:
, where
correspond to the frequency of the sinusoidal and
is a rectangular window over
.
Using of inverse Fourier Transform
We now have understood that OFDM uses multiple sinusoidals having frequency separation where each sinusoidal gets modulated by independent information. The information
is multiplied by the corresponding carrier
and the sum of such modulated sinusoidals form the transmit signals. Mathematically, the transmit signal is,
The interpretation of the above equation is as follows:
(a) Each information signal multiplies the sinusoidal having frequency of
.
(b) Sum of all such modulated sinusoidals are added and the resultant signal is sent out as .
Update: 29th May 2008
(thanks to the comment by Mr. Mork)
The sampled version of the above equation is,
It is reasonable to understand that above operation corresponds to an inverse Discrete Fourier Transform (IDFT) operation.
Understanding of an OFDM transmission specified per IEEE 802.11a [80211A]
From the Table 79 in [80211A], the symbol duration .
This implies that the used subcarriers are and so on.
The available bandwidth of 20MHz is split into 64 subcarriers. Out of the available 64 subcarriers having indices , the number of used subcarriers is 52. The used subcarriers are having indices from
are used for transmitting information sequence
to
.
To understand in detail the correspondence between the subcarrier index and frequency, one may refer to a previous post (here).
Once the bits in each symbol are assigned to appropriate IDFT inputs (Ref. Figure 109 in [80211A]), the IDFT operation is performed to obtained the time domain signal.
For each symbol, some samples from the end are appended to the beginning of the symbol (referred to as cyclic prefix insertion). We may discuss the pros/cons of cyclic prefix in a future post.
Simulation Model
A simple Octave script where a BPSK modulated signal is transmitted on the 52 used subcarriers, may be used for understanding generation of an OFDM signal. The script is loosely based on 802.11a specification.
Click here to download.
Figure: Spectrum of an OFDM transmission (based on 802.11a specification)
Reference
[DIG-COMM-BARRY-LEE-MESSERSCHMITT]
Hope this helps.
Krishna
Please click here to SUBSCRIBE to newsletter and download the FREE e-Book on probability of error in AWGN. Thanks for visiting! Happy learning.
Related posts
- Inter Carrier Interference (ICI) in OFDM due to frequency offset
- BPSK BER with OFDM modulation
- Peak to Average Power Ratio for OFDM
- Cylcic prefix in Orthogonal Frequency Division Multiplexing
- BER for BPSK in OFDM with Rayleigh multipath channel
D id you like this article? Make sure that you do not miss a new article by subscribing to RSS feed OR subscribing to e-mail newsletter. Note: Subscribing via e-mail entitles you to download the free e-Book on BER of BPSK/QPSK/16QAM/16PSK in AWGN.
{ 1 trackback }
{ 89 comments… read them below or add one }
Hi,
After providing the formula for s(t), you wrote
>It is reasonable to understand that above operation corresponds to an inverse Discrete Fourier Transform (IDFT) operation.
Why? s(t) is a continuous-time signal, so wouldn’t it be the Fourier Series (if anything) rather than the DFT?
Another question: I understand the properties of s(t) as it is, but how can this be implemented efficiently for large values of K? A direct implementation of the formula would require K oscillators at the receiver and the transmitter (to generate the individual sinusoidals), right?
Thanks!
– M
Sorry for the double-posting, but I just happened to find the answer to my question (by pure chance — I’ve been trying to find out for quite a while already).
The relation between s(t) as you wrote it (and as it is widely used) and the actual (I)DFT implementation is looked at in a paper by Lin and Phoong (http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1223555). Summarized very briefly, they find that for general window functions — g(t) in your example — including the commonly used rectangular windows, it is indeed *not* possible to generate the same s(t) using a DFT followed by a DAC. It is possible to generate a signal with the same values at the times t=nT, but the corresponding signal will still be different (and thus have a different PSD, too).
Thanks for your attention
- M
@Mork:Thanks for the valuable comments.
Trying to answer the first comment:
(a) Yes, I agree. I was loosely specifying that a continuous time signal can be represented using IDFT. Infact, I should have added one more step, where I defined s(nT) and then claimed that it can be represented using IDFT.
(b) Yes, direct implementation is K oscillators
Trying to answer the second comment.
Thanks for the link to the paper “OFDM transmitters: analog representation and DFT-based implementation”
(a) From a quick read, the authors are showing that one has to consider the sampled window function g(nT) rather than the contnuous function g(t). I did not follow the full paper, however I was unable to find the reason behind y(t) having more psd than x(t) in region from 0.5 to 0.75 omega_s (ref. figure 5). Any thoughts?
(b) Further, just to note that, in a typical implementation, the output x(nT) will be upsampled followed by a digital filtering, then passed to the DAC. Not of relavence to this discussion, but just to add as FYI.
Thanks again for your comments. You helped me provide a better insight.
Ps. I made a brief update to the post to reflect that s(nT) and not s(t) can be implemented using iDFT.
Hi all,
OFDM is play great role in communication enhancement the understanding of this subject need good acknowledgment in M-arry modulation process and frequency analysis process ,so we can generate OFDM using wavelet Transform instead Fourier Transform.
@Abdul: Can you please point to reference explaining OFDM generation using Wavelet Transform
Note that there is an time extention beofre IDFT.The time that a symbol lasts will be N times than before. So T should be NT while suming N symbols. Is it right?
@kakamilan: Sorry, I did not understand your comment. I do not see a reason why the symbol should be extended before IFFT. Typically the cyclic prefix insertion is done after ifft.
OR where you implying something else?
Hi Krishna,
I read from references that it requires oversampling at least twice, so if you transmitting 2500 bits, it needs at least 1250 zeros in the middle of the sequence. Is it right? I do not see the oversampling in your Matlab script. Thanks
@Filbert: For OFDM case, its a bit different. In OFDM we let aliasing to happen. However, the aliasing does not cause distortion because there are no frequency components in the -ve side of the spectrum. I have discussed in bit detail on the post on Negative Frequency.
URI: http://www.dsplog.com/2008/08/08/negative-frequency/
Ps.
Btw, if its oversampling by 2 (of a bit sequence of 2500bits), we need to insert 2500 bits. You can find details on oversampling and associated filtering (zero-order hold, sinc, raised cosine etc) @
URI: http://www.dsplog.com/2008/04/14/transmit-pulse-shape-nyquist-sinc-rectangular/
URI: http://www.dsplog.com/2008/04/22/raised-cosine-filter-for-transmit-pulse-shaping/
URI: http://www.dsplog.com/2008/05/01/eye-diagram-plot-matlab-raised-cosine-filter/
Hope this helps.
hi Krishna… i hope you are fine and doing well. I am new to this field and would like to post questions starting from a basic level. In matlab why do we need to upsample our data sequence e.g. 4-PAM before sending it to the pulse shaping filter? I read that we need to match their sampling frequencies… but i didn’t understand what its trying to explain. Can you kindly explain this to me that why we need to match the sampling frequencies of both???
thanking in advance…
@kamran: Yes, you are right. The sampling of data sequence and the sampling of the filter should match. If it does not match, then the filtering might not be proper. I have written some posts on transmit pulse shaping filter @
URI: http://www.dsplog.com/2008/04/14/transmit-pulse-shape-nyquist-sinc-rectangular/
URI: http://www.dsplog.com/2008/04/22/raised-cosine-filter-for-transmit-pulse-shaping/
URI: http://www.dsplog.com/2008/05/01/eye-diagram-plot-matlab-raised-cosine-filter/
Hope this helps.
Hi Krishna, how are you? I have some questions about your Matlab code “scriptofdmtx”. Is it right to write:
outputiFFT=64*ifft(inputiFFT,nFFTSize) or just
outputiFFT= ifft(inputiFFT,nFFTSize)?
I get confused if it should be multiplied with nFFTSize or not.
And for [Pxx, W]=pwelch(st,[],[],4096,20)
What is 4096 for? I think it is just nFFT? Why don’t you use 64 instead of 4096?
Thank you
@Filbert: My responses
1. Multiplication by nFFTSize does not really matter. It just enables one to scale the power of the signal, if one desires to do so.
2. The parameter 4096 controls the frequency resolution of the pwelch() function. Yes, I could have used 64, but I just wanted the plot to have more frequency resolution.
Hope this helps.
Sir
i would like to do a project on ’simulation of ofdm using matlab’. also i would like to compare the performance with some other communication system. Which you think is the best one to be compared with ofdm so that i can show the benefits of using ofdm clearly. can you give some help in doing the same?
@sona: You may compare the performance of single carrier 802.11 transmission which is spread spectrum based (data rates of 1Mbps, 2Mbps, 5.5Mbps, 11Mbps) and compare it with 802.11a which is OFDM based (data rates of 6, 9, 12, … 54Mbps).
You may show the performance in multipath for similar data rates. Am expecting that OFDM should offer better immunity for multipath.
Hope this helps.
Hi,
if you would like to use different windowing method (such as hanning), should I use the hanning(x) and multiply the signal and then using the psd() to calculate the PSD (to replace the pwelch function)?
Thanks for your help!
@claire: I think pwelch() by default multiplies by hamming windo before finding the spectrum.
http://www.mathworks.com/access/helpdesk_r13/help/toolbox/signal/pwelch.html
hi sir ,
plz sent some good material about to understand the Doppler shift ;;
sir can you provide the book mentioned below
“L.Hnzo, M.Munster, B.J.Choi, T.Keller, “OFDM and MC-CDMA,”
thank you
IEEE communication socity, March,2004.”
@thiruppathi; I think Digital Communications: Fundamentals and Applications by Bernard Sklar has a good review on Doppler in the chapter on Fading channels (Chapter 15 in my copy).
Hi Krishna,
How are you? I just wonder why the psd in papers i have read the ripple is so smooth (some of them are just flat lines!). When i use your script, there are a lot of ripples. Do you have any idea about this? Thank you
@Filbert: It depends on the parameter passed onto the pwelch() function. Try specifying the window size and overlap factor.
Modify the pwelch() code to
[Pxx,W] = pwelch(st,25,0.01,4096,20);
Hi Mr Pillai,
I have failed to implement OFDM raised cosine windowing. Are you able to give me some matalab hints?
thank you in advance!
@Marwan: As I understand, raised cosine windowing is performed to do transmit filtering without causing ISI. However, in OFDM, as there is cyclic prefix, there wont be any ISI evenif we use a normal filter. Hence may I know the motivation behind using raised cosine filtering for OFDM.
Hi Khrisna,
I have sent you my simulation result, i do hope you can give your opinion about it. And i have another question. You said i should try
[Pxx,W] = pwelch(st,25,0.01,4096,20);
May i know why you chose 25 for window length and 0.01 for overlap factor? Are there any consideration for choosing these parameters?
Thank you
@Filbert: I think smaller window length ensures that the spectrum is smoother. That was one of your objectives, no?
HOLA,
tengo una duda, estoy trabajando en un proyecto y debo usar la ventana hanning, pero resulta que esta me reduce la magnitud de los datos, he leido que para compensar dicha magnitud, estos datos deben ser multiplicados por un factor… pero no tengo conocimiento de como calcular este factor, alguien aquí tiene este dato, o me podrian colaborar con información al respecto. Muchas Gracias
@Omar: (after translating your comment to english thanks to google translate)
“I have a doubt, I’m working on a project and I use the Hanning window, but it is me that this reduces the magnitude of the data, I read that, to compensate for this magnitude, these data should be multiplied by a factor … but I’m not aware of how to calculate this factor, someone here has such information, or do you work with information. Thank you very much”
hmm….how are you applying Hamming window ?
Hi Krishna,
One more doubt,
subcarrierIndex = [-26:-1 1:26];
Here 52 subcarriers are used.
1)Can i use 0 to 51 intstead of negative frequencies and avoid fftshift()?.
2) How do we interpret these subcarrier numbers
0 corresponds to dc value
N/2 ( here 52/2) – corresponds to Nyquist frequency and after this is a replica.
Am i right here ?
Thanks again.
@Kishore: My replies:
(1). Definition of subcarriers from [32:63] in 64-pt FFT is notional. What ever we sent on those subcarriers will get aliased back to [-32:-1]. To understand better, think of the following scenario. Lets say we are sampling a sinusoidal at 11MHz with sampling frequency of 20MHz. From sampling theory, we know that 11MHz gets aliased to 11-20 = -9MHz.
(2) Negative subcarriers can be interpreted as complex sinuosidal e^(-jwt) – with the phase decreasing with increasing time. N/2 is not typically 52/2. Typically we deal with FFT sizes which are powers of 2 – in this example we use 64.
Did you want to look at a post on negative freqency @
http://www.dsplog.com/2008/08/08/negative-frequency/
Hope this helps to give you good pointers. Please revert, if otherwise.
Hi,
while going through “Understanding an OFDM transmission” i have come across few problems,and they are:
1.When the 20 Mhz is divided into 64 subcarriers,then why only 52 are used?is it because we have to provide the guard band in between the siglans???
@Budhaditya: You are right. To be more precise, the null subcarriers are provided to have guard band between signals in adjacent channels.
Hi Mr.Krishna,
I am very happy for your Contributions in solve the problems associated with high data rate as OFDM.I am reseacher and I hope to provide me fundamental code for 16QAM (OFDM) and 16PSK (OFDM).
thanks .
@algenaby: Hope the symbol and bit error rate computation for 16PSK and 16QAM should help you get going
http://www.dsplog.com/2008/03/18/symbol-error-rate-for-16psk/
http://www.dsplog.com/2008/05/18/bit-error-rate-for-16psk-modulation-using-gray-mapping/
http://www.dsplog.com/2007/12/09/symbol-error-rate-for-16-qam/
http://www.dsplog.com/2008/06/05/16qam-bit-error-gray-mapping/
hello
i want to ask whether there is any difference between taking n-point ifft
and then fft for OFDM Vs taking ifft and then n-point fft in matlab.
the difference i get is the signal with n-point ifft and then fft has a
spectrum which do not have good resolution
regard.
@zingas: Is there any specific reason why you mentioned ‘n-point’ specifically?
In general, as long as you undo the effect of what you did at the transmitter at the receiver, you should be able to demodulate correctly the received symbol.
The fft spectral resolution is controlled by sampling frequency (fs) and the size of fft (N). For eg, with fs = 20MHz, and N = 64, the resolution is 312.5kHz. Agree?
Dear Mr Krishna
Regarding your matlab code for OFDM using BPSK over Rayleigh Fading Channels. I tried but i failed to understand how u calculated these parameters.
nFFT = 64; % fft size
nDSC = 52; % number of data subcarriers
nBitPerSym = 52; % number of bits per OFDM symbol (same as the number of subcarriers for BPSK)
nSym = 10^4; % number of symbols
As according to my coding BPSK in OFDM. i have used 256 bits to transmit over 256 symbols i.e. 1 bit/symbol. Using 256 point fft and IFFT. So pls advice me how can i setup my parameters.
Acc to my knowledge in BPSK one bit is transmitted in one symbol and then it is furthur transmitted on the subcarrier.Pls correct me if i am wrong.
@raj: “Acc to my knowledge in BPSK one bit is transmitted in one symbol and then it is furthur transmitted on the subcarrier.Pls correct me if i am wrong.”
This is wrong. In OFDM, depending on the FFT size, there will be more than 1 subcarrier which is used. For eg, in 802.11a systems, we use 64pt FFT and use 52 subcarriers. If each subcarrier is BPSK modulated, then each symbol can carry 52 bits. Hope this helps.
Please refer to posts @ http://www.dsplog.com/tag/ofdm
Hi Krishna,why BER of QAM-OFDM and QAM in AWGN are same?
Dear Krishna Pillai Sir,
Plz give ur email id.
@Bijunair: You may find my details @ http://www.dsplog.com/contact-us/
Dear Mr Krishna
Thanks for ur reply. I want to ask you that
1)if i am not using pilot bits, so is it possible that i can take 52 subcarriers for data bits transmission.
2)Why we use 20 MHz as sampling frequency what is the reason behind it.
3)I have used nSym = 64 while using 52 subcarriers for data transmission is that correct.
4)Can we use EbN0dB in place of EsN0dB in your code for BPSK OFDM in AWGN and Rayleigh Fadig channels.
@raj: My replies:
1/ Yes, you may
2/ Well, sampling frequency of 20MHz was defined by the IEEE TGa standardization committee. In general, it depends on the available spectrum and the number of channel required etc
3/ Well, number of symbols and number of used subcarriers are two independent parameters, agree? OR was there a typo in your comment and you mean nFFT = 64 (instead of nSym = 64)? Even for the latter, your assumption is correct.
4/ For BPSK, Eb/N0 and Es/N0 are same. Agree?
Mr Krishna
Thanks for ur support I want to know that how can i use
hF=fft(ht,64,2); command in place of
hF = fftshift(fft(ht,64,2)); if there is no alternative then pls explain me about these commands
hF = fftshift(fft(ht,64,2));
xt=(nFFT/sqrt(nDSC))*ifft(fftshift(xF.’)).’;
@engineer193: Did not quite follow your question. The fftshift() operator is used to order the output of the fft() such that the spectrum is show with DC at the center. Plz refer to the post on negative frequency for bit more details.
http://www.dsplog.com/2008/08/08/negative-frequency/
sir, i am new to OFDM but i could not understand what is happening to signal after ifft in tranmsission. Whether the tranmission is in frequency domain or time domain. how the signal will look like in spectromter in air. after ifft how the modulation produces multiple frequency. pl explain. I am new to this field. thank you
@krishnakumar: The signal after ifft() is the sum of many complex sinewaves – e^{jwt} + e^{2jwt} + e^{3jwt} + …
The samples are in time domain. The spectrum plot is captured in this post itself.
Plz re-read this post. Hopefully, it should answer some of your queries.
plz, help me to understand why we need to those steps in our code
in script for generting OFDM transmit waveform (loosely based on
IEEE 802.11A specifications)
for ii = 1:nSymbol
inputiFFT = zeros(1,nFFTSize);
% assigning bits a1 to a52 to subcarriers [-26 to -1, 1 to 26]
inputiFFT(subcarrierIndex+nFFTSize/2+1) = ipMod(ii,:);
% shift subcarriers at indices [-26 to -1] to fft input indices [38 to 63]
inputiFFT = fftshift(inputiFFT);
outputiFFT = ifft(inputiFFT,nFFTSize);
% adding cyclic prefix of 16 samples
outputiFFT_with_CP = [outputiFFT(49:64) outputiFFT];
st = [st outputiFFT_with_CP];
end
I can not understand why we need to assign bits a1 to a52 to subcarriers [-26 to -1, 1 to 26]; and not enter our data points directly to ifft like writting
ipMod = [ipMod zeros(1,nBitPerSymbol*nSymbol-nBit)];
ipMod = reshape(ipMod,nFFTSize,length(ipMod )/nFFTSize);
then enters it directly to ifft????????????
@salma: Well, given a sampling frequency of fs and fft order N, we subcarriers defined from [-N/2 to N/2-1]*fs/N. To send information in subcarriers from [-N/2 to -1]*fs/N, we infact send them at [N/2 to N-1] amd due to aliasing, the information gets folded back to [-N/2 to -1]*fs/N.
I have discussed bit more on this topic @
http://www.dsplog.com/2008/08/08/negative-frequency/
Hope this helps.
Ps.
This is a difficult, but important concept to understand in OFDM. Crossing this hurdle is an important step in understanding wireless communication in general and OFDM in particular.
Hi
I am a graduate student, doing a project in water filling algorithm in OFDM. Can any one suggest some material which gives fundamental description of ‘Water filling algorithm’? In many papers, they just mentions it as ‘Applying Water filling algorithm..’ and I could not find a source which explains what it is.
Thanks
Nitya
@Nitya: I quickly recall that water filling algorithm stands for concentrating the transmit power at frequencies where channel is good. Though I have not looked into detail, I found that Chapters 8.5.1 and 8.5.2 in Digital Communication: Third Edition, by John R. Barry, Edward A. Lee, David G. Messerschmitt. discuss about water filling.
Good luck.
In OFDM all the information symbols are convert into parallel form, digital mapping and ifft operation performed.
The output of IFFT is very minimum amplitude in the form of 0.05+i0.253 and so on.Then how to modulate this very minimum amplitude with high carrier frequency. (like interms of MHz)…..
Example
a=randsrc(4,1);
b=diag(a);
c=ifft(b);
d=fft(c,4*8);
plot(abs(d));
@kalidoss: In the example, the signal to be upconverted to ‘RF band’ is c. The upconversion operation is
out = Re{c * exp(j*2*pi*f_carrier*t)}
In the MATLAB script whats the use of fftshift command,why do you perform in the program….
@kalidoss: The output of the N point FFT by default is from [0 to N-1]. However, the frequencies from [N/2 to N-1] gets infact aliased to [-N/2 to -(N-1)]. The fftshift function does the re-arrangement of the N point FFT to do reflect this aliasing.
octave:20> x = [1:16]
octave:21> fftshift(x) = [ 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 ]
Also, try reading the post on negative frequency.
http://www.dsplog.com/2008/08/08/negative-frequency/
1. In the MATLAB script, how to assign the 52 bits to ifftshift variable size of 64 bits. It omits first 6-bits and last 6-bits,remaining bits are filled in the location.
2.In this script where we introduce orthogonality of the signals or how can we visualize the orthogonality.
3. In the program original data bits are 2500, after cyclic prefix total transmitted bits are 3920 instead of 2500. Nearley 56% of increasing data length, it may eat very large bandwidth….
My statements are correct or not….
Sorry for the continuous disturbance…..
@kalidoss: My replies:
1/ In fact using the term sub-carriers might be better. I omit subcarriers from [-32 to -27, 0, 27 to 31]
2/ Orthogonality is introduced because, exp(j*2*pi*k*t/T) are orthogonal. Please refer to the post on Inter Carrier Interference (ICI) in OFDM for a better explanation http://www.dsplog.com/2009/08/08/effect-of-ici-in-ofdm/.
3/ Not correct. Adding cyclic prefix, increases the duration of the symbol on the air. However, this does not increase the bandwidth. Recall, if OFDM we are sending complex sinusoidals. Adding cyclic prefix, means we are sending the same sinusoidals for extra duration, and not sending additional sinusoidals.
hi krishna.. can you help me in designing OFDM system with BPSK using MATLAB Simulink?
@aredeq: Sorry, I do not have Simulink
hello krishna,
i wanted to know how exactly we do the shifting and why is it required..
Also after generating the random symbols,is it that we need to take ifft.. and but when do we modulate it with a carrier like the different carriers that have frequency in multiples for orthogonality..?
please clear my concepts..
thank you..
@vedika: The iFFT takes care of assigning each constellation symbol to different carriers that are orthogonal.
I have 2 doubts..Please help me clear them..
In the script code that you have given–
1.
inputiFFT(subcarrierIndex+nFFTSize/2+1) = ipMod(ii,:);
why have we used the above operation?
Also why do we need to do the below:
–subcarrierIndex+nFFTSize/2+1
2.
How the Cyclic prefix operation has been performed?in the code..Please explain..
thank you..
@vedika:
1. For each row ii, am assigning all columns of ipMod to the variable inputiFFT per the indexing subcarrierIndex+nFFTSize/2+1
2. For inserting cyclic prefix, we take the last 16 samples from the ifft output and pad it to the same variable again.
% adding cyclic prefix of 16 samples
outputiFFT_with_CP = [outputiFFT(49:64) outputiFFT];
Dir krishna,
How do u calculate the sampling frequency and the duration of symbole (34)?
are there limitation for ifft size and number of carriers?
thank you for your helps.
@zizi: Sampling frequency, number of subcarriers etc are chosen based on the system requirements.
For example, in 802.11a specifications, we had a channel of bandwidth 20MHz. So we chose the FFT sampling frequency as 20MHz. Then we chose a 64 point FFT, which resulted in a subcarrier spacing of 312.5kHz (20MHz/64). Had we chosen a higher order FFT, we would have been able to have more subcarriers, but the subcarrier spacing will be narrow.
Some systems like WiMax uses 256/512pt FFT. Some others like DVB etc uses 1024 pt FFT. So, as I see the choices of FFT size, sampling clock etc are engineering choices based on the end design goal.
Dir krishna,
But in your codes matlab you haven’t use the frequency sampling and the duration of symbol (and duration of cyclic prefix) ?
please help me.
thank you.
@zizi: Hmm… I checked. The code assumed a time domain sampling frequency of 20MHz. The duration of the cyclic prefix is 16 samples (0.8us with 20MHz sampling).
Maybe checking out http://www.dsplog.com/2009/10/07/quiz-ieee-80211a-specifications/ might be also be helpful.
Dir krishna,
I have 2 questions :
1-Where are the frequency samling and the duartion symbole mentioned in your code programme.
2-In BER OFDM-multipath simulation if i use the matlab commande ‘rayleigtchan’ ,the curve of BER to be constant, how to equalize the chanal in this cas.
please help me.
thank you.
@zizi: My replies:
1/ Please refer to my previous reply
2/ Divide by the channel in frequency domain.
hi krishna how are u
1, in this script you plotted ofdm spectrum after adding cyclic prefix to ifft output.
i think the iffft output will be the ofdm output is it so sir.
2, you use the function [Pxx, W]=pwelch(st,[],[],4096,20) to plot ofdm spectrum. but in any frequency spectrum it is always between frequency on x axis and magnitude (in dB) on y axis. but by using above function it is PSD on y axis . so does that has same meaning . actually but i did was firstly i take the fft of iffft output and then it taken its absolute value. then i tried to plot dB conversion of absolute value.but i am not getting accurate plot will you plz help me?
@Bhasker: My replies:
1/ Yes. The spectrum which we are concerned is that of the transmit waveform which goes on the air, and that includes the cyclic prefix.
2/ The variable Pxx is in linear. In the plot, I converted to log by 10log10(Pxx) and plotted. Using ifft for one symbol alone might not be a good idea, as it uses very small set of smaples. The pwelch() uses the whole vector and has algorithms to provide the ’smoothed’ spectrum.
You can post your queries. Good luck.
Hi….Guyz..m Implementing OFDM Transmitter using…ifft and i am doing so..by generating random nos. ranging 0 to 3…and i am using QPSK…and…64 pt ifft….but when i am finding its power spectral density its coming out to be a bit unexpected…help me..
clc;
clear all;
x=randsrc(1,50*52,[0,1,2,3]);
M=4;
qpsk=pskmod(x,M);
msg_tx=reshape(qpsk,52,50);
U=msg_tx.’;
st=[];
for j=1:48
temp=ifft(U(j,:),64);
temp2=[temp(49:64),temp];
st=[st,temp2];
end;
fsMHz = 20;
[Pxx,W] = pwelch(st,[],[],4096,20);
plot([-2048:2047]*fsMHz/4096,10*log10(fftshift(Pxx)));
xlabel(’frequency, MHz’)
ylabel(’power spectral density’)
title(’Transmit spectrum OFDM (based on 802.11a)’);
@Raghav: Some comments:
1/ Using modulation values 0 to 3 might not be correct. You might want to use -3,-1, 1, 3 if you want 4PAM
2/ The subcarier loading where edge subcarriers and DC subcarriers are not used is missing.
well sir…i am using… QPSK… which requires….0 to M-1 input values…and M is 4 here…can u throw more light on 2nd point u described..!!
And sir…i got one more problem….i have to implement OFDM…using..fractional fourier transform…
and i need…some matlab codes…of discrete fractional fourier transform..and IDFrFt too…!!
Can you help me with that sir..?
@Raghav: Sorry, I have no posts on fractional Fourier transforms.
Hello Sir,
I am trying to implement ZF frequency equalizer in OFDM for performance analysis through matlab coding.
Please, help me…..if you give me the code then it will be better for me.
@Rupesh Kumar: Please refer to the post http://www.dsplog.com/2008/08/26/ofdm-rayleigh-channel-ber-bpsk/
@Rupesh
zf equalizer should be not a problem,it is just a division in freq.
i implemented LS estimator and MMSE estimator,
i would ask to krishna why for MMSE estimator i have to normalize di RECEIVED QAM Symbols by a factor (fftlenght/numofcarriers)
angelo
@angelo: I have discussed OFDM with ZF equalization in http://www.dsplog.com/2008/08/26/ofdm-rayleigh-channel-ber-bpsk/
If there is no interference, then using ZF equalization is optimal, we might not want to use MMSE. If you are using MMSE, then the scaling factor might have been present to precisely define the noise variance.
Dear Sir,
I have an ambiguity concerning the guard interval;
my question is:
Why we chose the end of the transmitted symbol as guard interval and not the beginning of the symbol, for example?
And thank you in advance.
@Fahmi: Well, we would want to make the symbol + guard interval continuous transmission without any abrupt phase changes. One way to do this is to take the last xx samples and append to the front of the symbol.
Sir, thanks for providing very good articles on OFDM.
I have a doubt regarding the placement of [-26:-1] subcarriers at [38:63].
In the script for generating the OFDM tx symbols, it is given that
//———
% shift subcarriers at indices [-26 to -1] to fft input indices [38 to 63]
//———
What if these [-26:1] are mapped to [27:52] and then [52:63] are filled with zeros.
I understood the aliasing effect but the doubt is why are the -ve indexed carriers are mapped to [38:63] instead of [27:52]
Thanks
Mohan
@mohan: I did not fully understand the motivation behind your query, but to answer you:
the subcarriers mapped to [38 to 63] will get aliased to [-26 to -1]. If you try to map to [27 to 52], then
a) no aliasing on subcarriers mapped from [27 to 31]
b) aliasing on subcarriers mapped from [32 to 52] to [-32 to -12]
Also, please have a look at the post on negative frequency
http://www.dsplog.com/2008/08/08/negative-frequency/
sir,
I got the clariffication for the doubt i raised just now. The 6null carriers at on each side of the band are contributing the DC and 11 zeros.
Thanks
mohan
@mohan: oh, k. good. i just replied anyways
Sir,
is there any particular reason behind “placing the pilot carriers at -21,-7, 7 and 21″. I mean spacing of 14 sub carriers? Can they be placed at any position other than these and if so, what can be the impact on performance etc?
Thanks
mohan
@mohan: I do not think, there is any requirement that ‘have to be spaced 14 subcarriers apart’. But, in general its desirable to have them spread wide apart.
And as FYI. The pilots are used for estimating
a) constant phase shift across subcarriers – caused by residual frequency offset, phase noise
b) linear phase across subcarriers – caused by sampling clock frequency offset
Ok..sir thanks…!!! Well… i’m really trying to understand Discrete Fractional fourier Transform… and i’m doing a Project on OFDM..I think it will be a Big Achievement implementing OFDM with DFrft… Can u too Just take a look on that…and if possible Jss make me Understand its Algorithm..!!
hello krishna
I simulated your code and got the process of it.now i am supposed to design even the receiver part.
I have corrupted the transmitted OFDM using AWGN function and this the following code that i used for receiver part after your code
SNR=20;
Y= AWGN(st,SNR);
[Pyy,W] = pwelch(Y,[],[],4096,20);
figure;
plot([-2048:2047]*fsMHz/4096,10*log10(fftshift(Pyy)));
Y=reshape(Y,49,80);
rt = [];
for ii = 1:nSymbol
% assigning bits a1 to a52 to subcarriers [-26 to -1, 1 to 26]
for j=17:80
inputFFT(subcarrierIndex+nFFTSize/2+1) = Y(ii,j);
end
inputFFT = fftshift(inputFFT);
outputFFT = fft(inputFFT,nFFTSize);
rt = [rt outputFFT]
end
Would u please help further ?
1. i am not able to remove the cyclic prefix that was added,how to get it?
2. how willl recover the original generated samples?
Please do the needful..
Thanks a lot..
hi
i must simulate this paper but i dont know some of blocks in block diagram,such as zero pad,cyclic prefix ,frame status conversion and i dont find these blocks in matlab simulink.plz help me,thanks
http://www.4shared.com/file/220527131/52047ce3/A_Comparative_Performance.html