In this post, let us evaluate the impact of frequency offset resulting in Inter Carrier Interference (ICI) while receiving an OFDM modulated symbol. We will first discuss the OFDM transmission and reception, the effect of frequency offset and later we will define the loss of orthogonality and resulting signal to noise ratio (SNR) loss due to the presence of frequency offset. The analysis is accompanied by Matlab/Octave simulation scripts.

## OFDM transmission

As discussed in the post on Understanding an OFDM transmission, for sending an OFDM modulated symbol, we use multiple sinusoidals with frequency separation is used, where is the symbol period. The information to be send on each subcarrier is multiplied by the corresponding carrier and the sum of such modulated sinusoidals form the transmit signal. 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 .

## OFDM reception

In an OFDM receiver, we will multiply the received signal with a bank of correlators and integrate over the period . The correlator to extract information send on subcarrier is.

The integral,

,

where

takes values from till .

## Frequency offset

In a typical wireless communication system, the signal to be transmitted is upconverted to a carrier frequency prior to transmission. The receiver is expected to tune to the same carrier frequency for down-converting the signal to baseband, prior to demodulation.

**Figure: Up/down conversion**

However, due to device impairments the carrier frequency of the receiver need not be same as the carrier frequency of the transmitter. When this happens, the received baseband signal, instead of being centered at DC (0MHz), will be centered at a frequency , where

.

The baseband representation is (ignoring noise),

, where

is the received signal

is the transmitted signal and

is the frequency offset.

## Effect of frequency offset in OFDM receiver

Let us assume that the frequency offset is a fraction of subcarrier spacing i.e.

.

Also, for simplifying the equations, lets us assume that the transmitted symbols on all subcarriers,

The received signal is,

.

The output of the correlator for sub-carrier is,

.

For ,

The integral reduces to the OFDM receiver with no impairments case.

However for non zero values of , we can see that the amplitude of the correlation with subcarrier includes

- distortion due to frequency offset between actual frequency and the desired frequency .
- distortion due to interference with other subcarriers with with desired frequency . This term is also known as
**Inter Carrier Interference (ICI)**.

## Simulation Model

Click here to download the Matlab/Octave script for computing RMS error with frequency offset. The script performs the following:

1. Generates an OFDM symbol with all subcarriers modulated with .

2. Introduce frequency offset and add noise to result in =30dB.

3. Perform demodulation at the receiver.

4. Find the difference between the desired and actual constellation.

5. Compute the rms value of error across all subcarriers.

6. Repeat this for different values of frequency offset.

**Figure: Error Magnitude vs frequency offset for OFDM**

## Observations

The theoretical results are computed by .

Quite likely the simulated results are slightly better than theoretical results because the simulated results are computed using average error for all subcarriers (and the subcarriers at the edge undergo lower distortion).

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.*

{ 132 comments… read them below or add one }

White tiles are an excellent choice for roofing repairs and replacements.

Paul roofing contractor can get you more information about the large selection of siding options

to choose from. Here are the deailed instructions for installing cloth wallpaper, a home improvement

project for wome who love sophisticated decor.

I visit every day some websites and blogs to read articles or reviews, but this blog provides

quality based posts.

It’s always best to demonstrate your football training drill or fun kids football game to them rather than just tell them.

Although, you have watched the match numerous times in the

television, yet there might never have been a single moment where you do not wish to be inside game.

Have you ever realized that some of thee information you have gathered are irrelevant.

Pretty! This has been an extremely wonderful post.

Thanks for providing these details.

I am really enjoying the theme/design of your blog. Do you ever

run into any web browser compatibility issues? A few of my

blog readers have complained about my blog not operating correctly

in Explorer but looks great in Safari. Do you have any advice to help fix this issue?

Hi, every time i used to check web site posts here early in the dawn, as i like to learn more

and more.

Thɑnkѕ on your marvelous posting! I quite enjoyed reading it, you could be a great author.

I wiull remember to bookmarҡ your blog and will cօme

back freom now on. I want to encourage continue your great work, have

a nice holiԀay weekend!

What’s up colleagues, its wonderful piece of writing about cultureand

entirely defined, keep it up all the time.

Hi there i am kavin, its my first time to commenting anyplace, when i read this paragraph i thought i could also

make comment due to this sensible post.

Hi, for all time i used to check webpage posts here early in the daylight, because i love to gain knowledge of

more and more.

I blog often and I really appreciate your information. This great

article has truly peaked my interest. I will take a note of

your site and keep checking for new details about once a week.

I subscribed to your RSS feed too.

دانلود فیلم,دانلود فیلم,دانلود فیلم,دانلود فیلم,دانلود فیلم,دانلود

فیلم,دانلود فیلم,

Understanding both advantages and disadvantages

are important in order to choose the best internet marketing

strategy. Then consider yourself one of the few, true internet marketers.

The Unit is powered by the Main chip adopting the CORTEX A8

core Sam – Sung S5PV210,and CPU frequency up to

1GHz, Memory 512MB, internal 2G memory space for TV and Internet integration.

Similar is the case with all the customers who have or want to have this

Smar phone. In fact, many users have come to love waterproof cases

for devices with good cameras like the i – Phone because they provide an affordable way to take fun and unique underwater photos.

The integrated full QWERTY key board is fantastic for those that send out

plenty of texts and email messages, whilst another highlight is an

optical track pad to browse through the Black – Berry

Operating-system 6.

you are actually a excellent webmaster. The website loading

pace is amazing. It seems that you are doing any distinctive trick.

Also, The contents are masterpiece. you’ve done a wonderful task on this topic!

Wow that was unusual. I just wrote an very long comment but

after I clicked submit my comment didn’t show up. Grrrr…

well I’m not writing all that over again. Regardless, just wanted to say superb blog!

For latest news you have to go to see world-wide-web and on world-wide-web I found this

web page as a finest web page for most up-to-date updates.

Hi, for all time i used to check webpage posts here in the early hours in the daylight, since i love to find out

more and more.

You can certainly see your expertise within the work you write.

The world hopes for even more passionate writers like you who are not afraid to mention how they believe.

Always go after your heart.

Wonderful goods from you, man. I have consider your stuff prior to and you’re

just extremely wonderful. I really like what you have got here,

really like what you are saying and the way in which you say it.

You’re making it enjoyable and you continue to care for to stay it smart.

I cant wait to read far more from you. That is really a terrific site., funny videos epic fails pranks cats compilation 2014 http://goo.gl/K15dMX

Good day I am so excited I found your website, I really found you by accident, while I was browsing on Digg for

something else, Anyways I am here now and would just like to

say cheers for a marvelous post and a all round interesting blog (I also love the theme/design), I don’t

have time to go through it all at the minute but I have bookmarked it and

also added in your RSS feeds, so when I have time I will be back to read a great deal more, Please

do keep up the great job.

The HSV 1 is distributed through oral secretions or pores and skin sores and one could be contaminated through kissing and

discussing objects like consuming utensils and toothbrushes.

You ought to begin your movie promoting campaign right here.

While you are paying for their services, it is important to realize

that they are specialists in their field and not just paying for their services, but also

knowledge. There are many benefits to hiring an Internet marketing agency to

manage your online marketing efforts.

There is a group of anti viral pills that require to be taken each

day, there has been exploration that presents if

the initial connection with the virus is treated inside a couple of days then your virus can be killed.

Today, I went to the beachfront with my children. I found a sea shell and

gave it to my 4 year old daughter and said “You can hear the ocean if you put this to your ear.”

She put the shell to her ear and screamed. There was a

hermit crab inside and it pinched her ear. She never wants to go back!

LoL I know this is totally off topic but I had to tell someone!, best funny vines compilation 2014 http://goo.gl/mwkepy

If you would like to improve your experience just keep visiting

this web page and be updated with the hottest gossip posted here.

You studied something highly relevant to the job

you’re seeking. Basic education can transform the lives of girls and women,

definitely a better appreciation of their very own potential and rights along with expanded employment opportunities.

It acts physically, emotionally, spiritually, strengthen the mind, frees the creative

capacity, facilitates learning as well as the body becomes healthier.

I was extremely pleased to find this website. I want to to thank you for onws time for this fantastic read!!

I definitely enjoyed every little bit of it and I have you book marked to look at

new stuff in your web site.

Wonderful goods from you, man. I have understand your stuff

previous to and you’re just too great. I actually like what you’ve acquired here, really like what you are stating and the way in which you

say it. You make it entertaining and you still take care of to keep it

smart. I can’t wait to read much more from

you. This is really a terrific site.

The whitening agent is utilized as a gel positioned in a mouthpiece or

as a strip that sticks to your tooth. They dotruly change the overall coloration of your enamel.

For those who avoid these sources of staining, you

could not need one other whitening remedy for 6 to 12 months.

My brother recommended I might like this website.

He was entirely right. This post truly made my day.

You cann’t imagine just how much time I had spent for this

info! Thanks!

Soccer or football as we know it, has been played since ancient times by the

Greeks, Romans, Italians, Chinese, Japanese, Persians etc.

He wasted 15 minutes of his time before he decided

to get a pen and paper and commit our orders to this.

I would say a rental at best, but nothing past

that.

Spot on with this write-up, I absolutely feel this web site needs

a lot more attention. I’ll probably be back again to see more,

thanks for the advice!

Wow, amazing boog layout! How lolng have you been blogging for?

yoou mde blogging look easy. The overall look of your wweb site is excellent, let alone the content!

Excellent beat ! I would like tto apprentice while yoou amend your site,

how can i subscribe for a weblog website? The account

helped me a acceptable deal. I had been a little bit familiar of this your broadcast provided vivid

transparent concept

This design is spectacular! You certainly know hoow to keep a reaader entertained.

Between your wit and your videos, I was almost moved to start my own blog (well, almost…HaHa!)

Excellent job. I really enjoyed what you had to say, and more than that, how you presented it.

Tooo cool!

The virus make a difference the cornea and lead

to keratitis.

Excellent article! We are linking to this great article on our website.

Keep up the great writing., http://goo.gl/c2FWrB

As for the device itself, it is said its screen size will be

3.7 to four.1 inches, which is the standard size in today’s terms.

Why so Well-known?

Undeniably believe that which you said. Your favorite justification appeared to be on the web the easiest thing to be aware of.

I say to you, I certainly get annoyed while people consider worries that they plainly don’t know about.

You managed to hit the nail upon the top as well as defined out

the whole thing without having side effect , people can take a signal.

Will probably be back to get more. Thanks, http://tinyurl.com/l2rbcbu

Asking questions are really fastidious thing if you

are not understanding something completely, however this post provides fastidious understanding yet., http://tinyurl.com/lewp8om

Thanks for sharing your thoughts about ofdm. Regards, http://tinyurl.com/o8jgmoy

For instance, the main characters are both trying very hard to get

into an Ivy League school, and almost fail to do so,

but they both succeed in the end. The worksheet also includes other financial

entries such as:. There are many obvious reasons to have an internet business.

I know this website presents quality based articles and extra information, is there any

other web site which gives these kinds of data

in quality?

Hi, all the time i used to check web site posts here early in the morning, since i enjoy

to learn more and more.

You ought to be a part of a contest for one of the greatest sites on the

internet. I’m going to recommend this website!, http://goo.gl/i2kCey

Our Firm uses the best schemes to draw public consideration to your

Facebook page or a web site. I’ve at all times wanted to have a whole

lot of Fb followers and likes.

Samsung Galaxy S II, Motorola Atrix 2, Motorola Droid Bionic

and etc are among be smartphones with best battery life 2012.

A couple of factors the DROID amazing has observed this sort of a big obtain in

industry share during this interval is on account of two motives.

The boost in battery life assures that you will no longer

need to worry about your i – Phone.

Hmm it appears like your site ate my first comment

(it was super long) so I guess I’ll just sum it up what I wrote and say,

I’m thoroughly enjoying your blog. I as well am an aspiring blog blogger but I’m still new to everything.

Do you have any points for novice blog writers? I’d genuinely appreciate it.

Every weekend i used to pay a quick visit this site, because

i want enjoyment, for the reason that this this web page

conations actually pleasant funny material too.

OK so for this tutorial you will need a PC or Mac with speakers and

the beat making software Dub – Turbo. The hip hop genre has not exactly been known for having a squeaky clean, morally upright, unassailably wholesome image.

But i do agree the fact that during the southern domination of

rap, a lot of rappers came out camouflaged with the crunk thing, and made a lot of money,

but had little or nothing to say; zero lyricism.

Hi Krishna,

A very good work, I always follow you.

Here you discussed a frequency offset, but how would you implement a Doppler effect in OFDM? In the case of frequency offset, you just shift the whole bandwidth of the signal, but in the case of Doppler effect you rather scale the bandwidth of the signal (components of higher frequency are more shifted than components of lower frequency), resulting in a Doppler spread.

How would you model this problem? Maybe by just shifting the signal by fd=(v/c)*f0, where f0=(fc-B/2:fc+B/2), f0 – frequency carrier and B – signal bandwidth.

Thank you in advance. Kind regards.

Great site you’ve got here.. It’s difficult to find hibh quality writing like yours nowadays.

I really appreciate people like you! Take care!!

Thanks for some other informative site. The place else may just I get that kind of information written in such a perfect method?

I have a project that I’m simply now operating on, and I have been on the glance

out for such info.

It’s hard to come by educated people for this subject, but you seem like you know what you’re talking about!

Thanks

Oh my goodness! Impressive article dude! Many thanks, However I

am having issues with your RSS. I don’t know why I am unable to join it.

Is there anyone else having similar RSS problems?

Anyone that knows the solution can you kindly

respond? Thanx!!

Fashion photography is considered as tricky by people but this is the one

which requires fotografia matrimonio to be very

attentive and also very good in each and every photograph he is clicking.

This company is always looking forward to making customer’s friend jealous.

When we go to other people’s wedding or look at the pictures of their wedding we think and talk about how good the photos are and some

where do wish to get the same quality of pictures for our own weddings also.

I think that is one of the so much important information for

me. And i am happy studying your article. However should remark on some basic issues,

The site style is great, the articles is actually great : D.

Just right task, cheers

I’m not that much of a internet reader to be honest but our sites really nice,

keeep it up! I’ll go ahead annd bookmark your site to come back later.

Cheers

whoah this blog is fantastic i really like

studying your articles. Stay up the good work! You recognize, many people are searching around for

this info, you could help them greatly.

wonderful issues altogether, you just received a emblem new reader.

What could you suggest about your submit that you simply made a few days ago?

Any positive?

Excellent write-up. I definitely love this website.

Stick with it!

Last investment Friday was a young investor, or alternatively, they are,

and probably should be chosen as charity of the tennis courts, gymnasium, sauna steam bath, use 2 for

every passenger flying on international ice.

This paragraph presents clear idea designed for the new people of blogging, that really how to do blogging and site-building.

hello sir, m working on ofdm and i am getting problem in ofdm code for ici cancellation technique….i want the code for qpsk and qam for ici cancellation technique in ofdm…It will be greatful if u can help…plssssss rpl positively as early as possible….

please give me idea how change this code of frequency offset will convert for 16 -QAM

hi krishna,

i amwriting the same code for dwt ofdm….but not getting the results can you help me with that….i can mail you my code.

hidden morkov model and selected applications in speech recognition in mat lab implementation . in which i didn,t get an idea that can restructure the model by using matlab code.please can you help me to proceed to write a code in mat lab.and can u help me to modification in the existing hidden model in speech recognition so that we will get benefit .

@mahender: sorry, i have not studied much on the topic of speech recognition

I thank you for your course it s helpful

hello…

i am doing my PG project in ofdm communication…..can u plz give me the matlab code for ICI SELF CANCELLATION SCHEME IN OFDM SYSTEM according to IEEE 802.11a standard….or suggest some reference material…which will help me…..

thanks…..

@tejashri: I ‘ve not not studied that topic. For OFDM related posts, please checkout

http://www.dsplog.com/category/ofdm/

please Krishna i work the 4Pam OFDM AWGN code and the code not run i want ask you what wrong in the program my email:engkareem.aast@hotmail.com:

clc

clear all

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 PAM)

nSym = 10^4; % number of symbols

N = 10^5; % number of symbols

alpha4pam = [-3 -1 1 3]; % 4-PAM alphabets

EbN0dB = [0:10]; % bit to noise ratio

EsN0dB = EbN0dB + 10*log10(nDSC/nFFT) + 10*log10(64/80); % converting to symbol to noise ratio

for ii = 1:length(EbN0dB)

% Transmitter

ipMod = randsrc(1,nBitPerSym*nSym,alpha4pam);

ipMod = reshape(ipMod,nBitPerSym,nSym).’

% Assigning modulated symbols to subcarriers from [-26 to -1, +1 to +26]

xF = [zeros(nSym,6) ipMod(:,[1:nBitPerSym/2]) zeros(nSym,1) ipMod(:,[nBitPerSym/2+1:nBitPerSym]) zeros(nSym,5)] ;

% Taking FFT, the term (nFFT/sqrt(nDSC)) is for normalizing the power of transmit symbol to 1

xt = (nFFT/sqrt(nDSC))*ifft(fftshift(xF.’)).’;

% Appending cylic prefix

xt = [xt(:,[49:64]) xt];

% Concatenating multiple symbols to form a long vector

xt = reshape(xt.’,1,nSym*80);

% Gaussian noise of unit variance, 0 mean

nt = 1/sqrt(2)*[randn(1,nSym*80) + j*randn(1,nSym*80)];

% Adding noise, the term sqrt(80/64) is to account for the wasted energy due to cyclic prefix

yt = sqrt(80/64)*xt + 10^(-EsN0dB(ii)/20)*nt;

% Receiver

yt = reshape(yt.’,80,nSym).’; % formatting the received vector into symbols

yt = yt(:,[17:80]); % removing cyclic prefix

% converting to frequency domain

yF = (sqrt(nDSC)/nFFT)*fftshift(fft(yt.’)).’;

yMod = yF(:,[6+[1:nBitPerSym/2] 7+[nBitPerSym/2+1:nBitPerSym] ]);

% demodulation

r = real(yt); % taking only the real part

ipHat(find(r= 2/sqrt(5))) = 3;

ipHat(find(r>=-2/sqrt(5) & r=0 & r<2/sqrt(5))) = 1;

% converting modulated values into bits

ipBitHat = (ipHat+3)/2;

ipBitHat = reshape(ipBitHat.',nBitPerSym,nSym).';

% counting the errors

nErr(ii) = size(find(ipBitHat – ipMod),2);

end

simBer = nErr/N;

theoryBer = 0.75*erfc(sqrt(0.2*(10.^(Es_N0_dB/10))));

close all

figure

semilogy(Es_N0_dB,theoryBer,'b.-');

hold on

semilogy(Es_N0_dB,simBer,'mx-');

axis([-3 20 10^-5 1])

grid on

legend('theory', 'simulation');

xlabel('Es/No, dB')

ylabel('bit Error Rate of 4 pam OFDM')

title('bit error probability curve for 4-PAM modulation')

@kareem: Are you getting zero BER in no noise case?

How are the bits getting converted to modulation symbols?

Hello,

Can you told me, how to simplify

sum(a^2)/sum(a)

where a is a vector of N complex variables.

@Ahmed: How about sum(a.^2)./sum(a) in matlab ? Note the dot (.)

hi krishna

find here with program for standard OFDM simulator in MATLAB

%%OFDM simulator

ep = [0 .15 .3 ];

% Es/No

EbNo=0:30;

% NS = number of OFDM symbols to transmit

NS = 100;

% Modulation type

modulation = ‘psk’;

M = 4

% N = number of carriers in OFDM symbol

N = 52;

% BPS = number of bits per OFDM symbol

BPS = N*log2(M);

% index for carriers in OFDM symbol

carriers = (1:52) + 2;

% IFFT size

ifftsize = 64;

% Input Bit Stream is normally Distributed

input_bit_stream = sign(randn(1,BPS*NS));

input_bit_stream(input_bit_stream == -1) = 0;

% PERFORM SERIAL TO PARALLEL CONVERSION

parallel_data = reshape(input_bit_stream, log2(M));

% PERFORM MODULATION

modulated_data = dmodce(parallel_data, 1, 1, modulation, M);

% CREATE OFDM SYMBOLS

disp(‘Transmitting OFDM symbols’)

%Normalize

%modulated_data = (modulated_data/max(abs(modulated_data)));

for ll= 1:length(ep)

for l=1:length(EsNo)

k = 1;

for n = 1:NS

ofdm_symbol = zeros(1,ifftsize);

% Map modulated data to FFT bins in OFDM symbol

ofdm_symbol(carriers) = modulated_data(k:k+51);

% Time Signal to transmit

tx_signal = ifft(ofdm_symbol,ifftsize);

% DOPPLER SHIFT

rx_signal = tx_signal.*exp((j*pi*ep(ll)/ifftsize)*(0:ifftsize-1));

noise = sqrt(1/(2*log2(M)*10^(EsNo(l)/10)))*(randn(1,64)+j*randn(1,64));

rx_signal = rx_signal + noise;

% FFT

received_ofdm = fft(rx_signal, ifftsize);

% Extract data from carriers in OFDM symbol

received_symbols(k:k+51) = received_ofdm(carriers);

k = k + 52;

end

% PERFROM DEMODULATION

received_data = ddemodce(received_symbols, 1, 1, modulation, M);

%PERFORM PARALLEL TO SERIAL CONVERSION

output_bit_stream = reshape(received_data, log2(M));

% CALCULATE BER

BER(ll,l)= sum(xor(input_bit_stream, output_bit_stream))/length(input_bit_stream);

end

end

===================================================

i am experiencing problem in reshape. if you can rectify then i will be highly oblige.

send me reply on my mail : nbnadoda@yahoo.co.in

@nanu: Am sure you will be able to identify the problem in reshape() yourself

I am surprised as well Krishna, its the non-linear dynamics of the laser. I am still analyzing now. thanks anyway

@Thavamaran: Ok, good luck

Krishna, thanks for the quick reply. I dont get your question on linearly varying phase? But the constellation always has 45 or 135 or 225 or 315 degree of phase shift, so it has about 90 degree difference between them.

Anyway symbol timing synch has a lot of method, which method can I look into, do you have any code referring to timing synch?

For receiver portion, im using correlator receiver, not PLL cause I feel its pointless cause correlator works extremely well for my back-to-back.

@Thavamaran: Not sure why you are seeing a fixed phase shift. Kinda surprising.

hello please I try to estimate frequency offset in mimo ofdm using pn sequences have you an exaples for matlab codes could help me i make acquistion and tracking please advise it’s important .thanks

@eng_dina: Sorry, I do not have the matlab codes.

Hi Krishna, this is my first post in your website. This is a very straight forward example. I have built my OFDM system and my back-to-back works perfectly fine. But when I perform optical OFDM, which is part of my work, at the receiver, the constellation point shifted by 45 degree, then I just compensate the phase, but end up I realize that its nonlinear phase shift.

But I dont think I have a problem with CFO, cause its ideal. Do you think I need timing symbol synchronization? Please advise. Thanks.

@Thavamaran: Are you having a linearly varying phase across subcarriers? If yes, it might be related to the symbol timing synchronization.

Hi krishna

Kindly tell me why are we doing this: theoryErr = (theoryErr-1);

Regards

Obaid

Thank you for replying, I will see the post then I will back to discuss you.

@Shaimaa: Ok

The simulated curve was around 50% and increased slightly as EbNo increases.

Is it necessary to compensate for frequency offset before demodulating the bpsk symbols as in Rayleigh fading channel??????????

@Shaimaa: Typically, receivers will have a circuit for compensating frequency offset prior to attempting demodulation. I have written a brief post on how to estimate frequency offset with short preamble defined in 802.11a

http://www.dsplog.com/2008/03/03/frequency-offset-estimation-using-80211a-short-preamble/

I added the code

% Adding frequency offset

xt = xt.*exp(j*2*pi*freqOffsetkHz_v*(1e3/20e6)*[0:length(xt)-1]);

with freqOffsetkHz_v values=10 or 20 kHz

in your script_ber_bpsk_ofdm then run the program but the simulated curve was so bad. Is that expected

@Shaimaa: If there is frequency error, then the intercarrier interference can result in poor BER. However, I have not done the simulations to see how much bad it can get.

hi…

what are the problems are occur in high PAPR?

@PRIYA: Power amplifier efficiency is comprimised

please reply my massege it’s really important

thanks

Hi krishna,

I hope you are doing fine and great. I have seen your code and its great. here you have supposed that all the input symbols are modulated like ak=1, if I am right for this reason you are generating all ones as the input i.e.

ipBit = ones(1,nBitPerSym*nSym) > 0.5; (kindly correct me if I am wrong)

My point is that when we generate random bits i.e. ones and zeros, then the simmulated error is higher than the theoretical error …

kindly help in this regard …

@invizible: Oh, is it. I have not tried that.

Idon’t try to simulte cfo for mimo system only but for mimo ofdm I propose a new scheme that targets MMIO OFDM systems which have unsynchronized oscillators such that CFO of individual paths have to be estimated separately. This scheme may also apply to OFDM systems with multi-user access. The new method, which is similar to Moose’s method, estimates the CFO by measuring the carrier phase difference between 2 identical successive training sequences embedded in the preambles. In order to make CFO estimates be more time efficient,I allow 2 transmitter antennas transmit their training sequence concurrently in every time period, except the first and the last period. I use Frank-Zadoff code with different phase shifts in the training sequences in different antennas. Due to the good correlation property of Frank-Zadoff code, it helps reduce the interference caused by the concurrent transmissions from other antennas.

please helpppppppppppppppppppppppp

please reply me it’s urgent Ineed the code it’s really important and thanks alot

@eng_dina: Good luck with you are algorithm investigation. Hope you have made the simulations and obtained satisfactory results.

Could you help me to find the theoretical BER of OFDM with Walsh-Hadamard over the multipath transmission

@Ahmed: Sorry, I do not have the required information

Idon’t try to simulte cfo for mimo system only but for mimo ofdm I propose a new scheme that targets MMIO OFDM systems which have unsynchronized oscillators such that CFO of individual paths have to be estimated separately. This scheme may also apply to OFDM systems with multi-user access. The new method, which is similar to Moose’s method, estimates the CFO by measuring the carrier phase difference between 2 identical successive training sequences embedded in the preambles. In order to make CFO estimates be more time efficient,I allow 2 transmitter antennas transmit their training sequence concurrently in every time period, except the first and the last period. I use Frank-Zadoff code with different phase shifts in the training sequences in different antennas. Due to the good correlation property of Frank-Zadoff code, it helps reduce the interference caused by the concurrent transmissions from other antennas.

cfo for mimo only but for mimo ofdm system

please helpppppppppppppppppppppppp

Idon’t try to simulte cfo for mimo system only but for mimo ofdm I propose a new scheme that targets MMIO OFDM systems which have unsynchronized oscillators such that CFO of individual paths have to be estimated separately. This scheme may also apply to OFDM systems with multi-user access. The new method, which is similar to Moose’s method, estimates the CFO by measuring the carrier phase difference between 2 identical successive training sequences embedded in the preambles. In order to make CFO estimates be more time efficient,I allow 2 transmitter antennas transmit their training sequence concurrently in every time period, except the first and the last period. I use Frank-Zadoff code with different phase shifts in the training sequences in different antennas. Due to the good correlation property of Frank-Zadoff code, it helps reduce the interference caused by the concurrent transmissions from other antennas.

cfo for mimo only but for mimo ofdm system

please helpppppppppppppppppppppppp

Idon’t try to simulte After examining some synchronization I propose a new scheme that targets MMIO OFDM systems which have unsynchronized oscillators such that CFO of individual paths have to be estimated separately. This scheme may also apply to OFDM systems with multi-user access. The new method, which is similar to Moose’s method, estimates the CFO by measuring the carrier phase difference between 2 identical successive training sequences embedded in the preambles. In order to make CFO estimates be more time efficient,I allow 2 transmitter antennas transmit their training sequence concurrently in every time period, except the first and the last period. I use Frank-Zadoff code with different phase shifts in the training sequences in different antennas. Due to the good correlation property of Frank-Zadoff code, it helps reduce the interference caused by the concurrent transmissions from other antennas.

cfo for mimo only but for mimo ofdm system

please helpppppppppppppppppppppppp

thanks for your your graet work

please I study for my master in frequency synchronization in mimo ofdm system but i have problem with the matlab code to simulate to find out if estimation of the CFO on one path is affected by the CFO values of the adjacent paths and examine the estimator accuracy in term of its mean and variance

please help me it’s urgent and necessary

f_max = f_Tofdm/(M_sub*T_s); % f_max =maximal Doppler frequency (Hz),M_sub*T_s = OFDM Symbol period (sec),

%f_ndopp = f_max*M_sub*T_s % Normalized Maximum Doppler Spread Freq.

% Area parameter

% ra Rural Area

% tu Typical Urban

% bu Bad Urban

% ht Hilly Terrain

% no no fading

AREA = ‘no’ ;

% start simulation loops

for ee = 1 : length(EcNo)

ee

[theo_fo_var, rfo_var, rfo] = FOE_mimo_fading(EcNo(ee), tfo_array, NTX, NRX, M_sub, N, f_max, AREA, T_s, model, L);

plot_theo_fo_var(:,:,ee)=theo_fo_var;

plot_rfo_var(:,:,ee)=rfo_var;

plot_theo_rfo(:,:,ee)=tfo_array;

plot_rfo(:,:,ee)=rfo;

end

% plot results

for ii_tx = 1 : NTX

for ii_rx = 1 : NRX

% rearrange array order for easier plotting

vect_plot_theo_rfo = permute(plot_theo_rfo(ii_tx,ii_rx, , [2 3 1]);

vect_plot_rfo= permute(plot_rfo(ii_tx,ii_rx, , [2 3 1] ) ;

vect_plot_theo_fo_var= permute(plot_theo_fo_var(ii_tx,ii_rx,:),[2 3 1]);

vect_plot_rfo_var= permute(plot_rfo_var(ii_tx,ii_rx, , [2 3 1]);

%plot mean

figure;

plot(EcNo, vect_plot_theo_rfo, ‘:’ , ‘Linewidth’,2) ;

hold;

plot(EcNo, vect_plot_rfo,’o-’,'MarkerSize’ , 6,’Linewidth’, 1) ;

grid on;

t_str=sprintf(‘New_ Theo and Est Freq Offset %s M=%d N=%d %dx%d path:tx%d-rx%d fo=%1.3f’,AREA,M_sub,N,NTX,NRX,ii_tx,ii_rx,tfo_array(ii_tx,ii_rx));

title(t_str);

xlabel(‘EcNo SNR range and step (in dB)’);

ylabel(‘Norm Freq Offset’) ;

legend(‘Theo’,'Est’,'Location’,'Northeast’);

% save graph

fstr=sprintf(‘new_m%d_%dx%dp%d%d_%s’,M_sub,NTX,NRX,ii_tx,ii_rx,AREA);

hgsave(fstr);

% plot variance

figure;

semilogy(EcNo, vect_plot_theo_fo_var,’:',’Linewidth’,2);

hold;

semilogy(EcNo, vect_plot_rfo_var,’o-’,'MarkerSize’,6,’Linewidth’,1);

grid on;

grid minor;

t_str=sprintf(‘New_ Est Var and CRLB %s M=%d N=%d %dx%d path:tx%d-rx%d fo=%1.3f’,AREA,M_sub,N,NTX,NRX,ii_tx,ii_rx,tfo_array(ii_tx,ii_rx));

title(t_str);

xlabel(‘EcNo (in dB)’);

ylabel(‘Variance’);

legend(‘CRLB’,'Est’,'Location’,'Northeast’);

% save graph

fstr=sprintf(‘new_y%d_%dx%dp%d%d_%s’,M_sub,NTX,NRX,ii_tx,ii_rx, AREA) ;

hgsave(fstr);

end

end

% rename variables for export

new_plot_theo_fo_var=plot_theo_fo_var;

new_plot_rfo_var=plot_rfo_var ;

new_plot_theo_rfo=plot_theo_rfo;

new_plot_rfo=plot_rfo;

% save all variables

fstr=sprintf(‘new_f%d_%dx%d_%s.mat’,M_sub,NTX,NRX,AREA);

save(fstr);

% save variables for plotting

fstr=sprintf(‘new_p%d_%dx%d_%s.mat’,M_sub,NTX,NRX,AREA);

save(fstr,’new_plot_theo_fo_var’,'new_plot_rfo_var’,'new_plot_theo_rfo’,'new_plot_theo_rfo’);

% end of file

and this is the core of the code

@eng_dina: How are you modeling the CFO for MIMO systems?

If all the chains have a common RF clock, then all the chains will have similar CFO and the estimate from all the chains can be combined to improve the accuracy of the CFO estimation.

If the chains have independent RF clock, then we need to estimate CFO on each chain independently.

thanks alot for your helpful work please I work in my master in frequency synchronization in mimo ofdm and I have problem in the matlab code try to examine the estimator accuracy in term of its mean and variance and find out if estimation of the CFO on one path is affected by the CFO values of the adjacent paths

Hello,

can You explain why is sample frequency (20e6) in the term freqOffsetkHz_v(ii)*(1e3/20e6) necessary ? We need delta_f so it shall be actually -200:200kHz and not delta_f*sample_time …

best regards

Hi krishna

Can you please provide any references (books or web links) for SNR loss calculations (analytical) for AWGN and dispersive channels.

Regards.

Obaid

Sir,

I want to find BER for 4QAM in OFDM using AWGN. If i take the difference between reciver’s demodulated symbols and actual symbols(at transmitter) and devide the difference by the length of actual symbols, can i get the BER?

Thanks.

Hello Sir!

i gone through above code.it is useful to understand ici. but i have queery that how to cancel ici due to phase offset due to local oscillator frequency offset.

will you please help me.

thank you.

Can i think, delay spread is equal to total number of multiple paths in the system

@r.kalidoss: Delay spread is computed using the amplitude of the taps and their delay values.

Hi there…for one more question..

ipBit = ones(1,nBitPerSym*nSym) > 0.5; % random 1′s and 0′s

if i change “ones” to “rand”, the result seems to have differences. Can you explain it?

Thanks very much

@cyrus:

With ak’s randomly distributed, the interference term slightly changes. How much difference did you see?

1.I would like to know that why we need to have 1e3 in the following expression.

% Adding frequency offset

xt = xt.*exp(j*2*pi*freqOffsetkHz_v(ii)*(1e3/20e6)*[0:length(xt)-1]);

2.As you mentioned about,choosing -5 to 5 as subcarriers outside that range has negligible interference.I still have a bit of confuse about it.Can i change to others values?

@cyrus:

1/ To convert kHz to Hz

2/ Sure, you can.

Hi there,

I’m a bit confused about the theorical results calculation..

theoryErr =sum(1./(j*2*pi*([-5:5]+delta)).*(exp(j*2*pi*([5:5]+delta))-1));

could someone explain to me please how ([-5:5]+delta) relates to (k-m+delta)? Well I of course get the delta part just not sure how -5:5 was chosen?

Would really appreciate any reply

T

@Treasa: I just chose -5 to 5 as subcarriers outside that range has negligible interference.

referring to last line of this post:

why the subcarriers at the edge undergo lower distortion ???

@Obaid: Well, at the edge there will be subcarriers only at the left or right and not both. Hence there will be lower interference.

Hi krishna,

thank you so much for ur help and posts in this website,

i am working on Next generation WLAN 802.11n Simulation.

I need ur help

i would like get the simulation for MIMO OFDM with MMSE equalizer .and also with MIMO OFDM STBC codes.

pls help me .i would greatful if you help me.

thank you once again.

Sk.khaja rasool.

Pls: do reply to this mail ID khajarasool_17@yahoo.com

@Khaja Rasool: Though I have not disucssed MIMO + OFDM or STBC + OFDM, I have discussed MIMO, STBC, and OFDM independently. You may refer

http://www.dsplog.com/tag/mimo

http://www.dsplog.com/tag/stbc

http://www.dsplog.com/tag/ofdm

Good luck.

Can i think, due to change of frequency i.e. m/T to m+q/T (Frequency offset) orthogonality of the signal change?

@kalidoss: Yes, you are right.

Krishna, Can we think frequency offset is due to doppler shift…..apart from carrier mismatch in the receiver….

@kalidoss: I have not discussed Doppler in this post. I guess the effect of Doppler might not be as simple to understand as is the case with frequency offset. I will write about Doppler soon.

First time i saw the frequency offset problem in OFDM with simple example.Its fine working. Then to how to mitigate this problem.

Any method available to solve this issue.

@kalidoss: You may checkout the post on Frequency offset estimation using 802.11a short preamble

http://www.dsplog.com/2008/03/03/frequency-offset-estimation-using-80211a-short-preamble/

Krishna,

I stand self-corrected. I realized that the term “[0:length(xt)-1]/Fs” corresponds to time, i.e t in the expression

exp(1i*2*pi*freqOffsetkHz_v(ii)*1e3*t), and you are simply shifting the spectrum by multiplying the two time-domain signals.

Sorry, I didn’t know what I was thinking.

Urbie

@Urbie: No problem. Glad that you have solved it.

{ 2 trackbacks }