Orthogonal Frequency Division Multiplexing Frequency Offset Correction full report
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26042010, 10:16 AM
Orthogonal Frequency Division Multiplexing Frequency Offset Correction.pdf (Size: 273.83 KB / Downloads: 234) A Technique for Orthogonal Frequency Division Multiplexing Frequency Offset Correction Abstract: The Orthogonal Frequency Division Multiplexing (OFDM) is a Multi Carrier Modulation technique employing Frequency Division Multiplexing of orthogonal subcarriers. It is also sometimes called as discrete multitone modulation (DMT). It is better than CDMA in high bit rate and Broadband Communications .It is a multi carrier technique, which is very sensitive to Frequency Offset between transmitter and receiver. This paper discusses the effects of frequency offset on the performance of OFDM digital communications. The main problem with frequency offset is that it introduces interference among multiplicity of carriers in the OFDM signal. It is shown that to maintain signal to interference ratios of 20 dB or greater for the OFDM carriers, offset is limited to 4% or less of the intercarier spacing. Also the paper describes a method to estimate frequency offset using a repeated data symbol. A maximum likelihood estimation (MLE) algorithm is used. Since the intercarrier interference energy and signal energy both contribute coherently to the estimate, the algorithm generates extremely accurate estimates even when the offset is far too great to demodulate the data values. Also, the estimation error depends only on total symbol energy so it is insensitive to channel spreading and frequency selective fading. Presented By: Mr.S.KATHIRAVAN Mr. P.PONMANI IIIYR ECE IIIYR CSE MEPCO SCHLENK ENGG.COLLEGE. Introduction: Orthogonal frequencydivision multiplexing (OFDM), also sometimes called discrete multitone modulation (DMT), is a transmission technique based upon the idea of frequency division multiplexing (FDM). In FDM, multiple signals are sent out at the same time, but on different frequencies. Most people are familiar with FDM from the use of radio and television: normally, each station is designated to broadcast at a particular frequency or channel. OFDM takes this concept further: In OFDM, a single transmitter transmits on many different orthogonal (independent) frequencies (typically dozens to thousands). (Because the frequencies are so closely spaced, each one only has room for a Narrowband signal). This, coupled with the use of advanced modulation techniques on each component, results in a signal with high resistance to interference. Application: OFDM is used in many communications systems such us: ADSL, Wireless LAN, DAB, DVB, UWB and PLC. Characteristics: An OFDM baseband signal is the sum of a number of orthogonal subcarriers, with data on each subcarrier being independently modulated commonly using some type of quadrature amplitude modulation (QAM) or phaseshift keying (PSK). This composite baseband signal is typically used to modulate a main RF carrier. The benefits of using OFDM are many, including high spectrum efficiency, resistance against multipath interference (particularly in wireless communications), and ease of filtering out noise (if a particular range of frequencies suffers from interference, the carriers within that range can be disabled or made to run slower).. The above figure represents theOFDM signals.Here there are 5 carriers.when any one of the carrier is in positive peak , all the others are at zero.thus only one signal is received at a particular frequency.Thus the ICI is reduced. Frequency offset: The frequency offset in the OFDM symbols represents the frequency shift between the transmitted and the received symbols.This case arises as a result of frequency change in the receivers during transmission.As a result of this frequency offset problem, there arises a condition where the orthogonality of the individual carriers is affected. Thus the inter symbol interference (ICI) arises. In the figure ,the frequency offset Af is present.as a result , at the output sampling is affected.This leads to the reduction in the performance of the OFDM system. Method: The method used in this paper has been developed to correct frequency offset errors in digital communication systems employing OFDM as the method of modulation. There are two deleterious effects caused by frequency offset; one is the reduction of signal amplitude in the output of signal amplitude in the output of the filters matched to each of the carriers and the second is introduction of ICI(intercarrier interference) from the other carriers which are no longer orthogonal to the filter. Because, in OFDM, the carriers are inherently closely spaced in frequency compared to the channel bandwidth, the tolerable frequency offset becomes a very small fraction of the channel bandwidth. Maintaining sufficient open loop frequency accuracy can become difficult in links, such as satellite links with multiple frequency translations. We have presented the algorithm to estimate frequency offset from the demodulated signals in the receiver. The algorithm extends to OFDM, with important differences, a method for single carrier MPSK. The technique involves the repetition of a data symbol and comparison of the phases of each of the carriers between the successive symbols. Since the modulation phase values are not changed, the phase shift of each of the carriers between successive repeated symbols is due to the frequency offset. The offset is estimated using a maximum likelihood estimate (MLE) algorithm. The basic block diagram of OFDM is in the Figure: Generalized OFDM System Model: I/p data Symbol Mapping Serial to Parallel IFFT Parallel to Serial Fig3:Baseband Model of OFDM system Channel Parallel to Serial FFT Serial to Parallel Frequency offset estimation using MLE algorithm) In an OFDM transmission symbol is repeated, one receives, in the absence of noise , the 2 N point sequence K rn=(1/N)[ZXkHke2njn(k+e)/N] k=K n=0,1,...,2N1. The kth element of the first N points of the above equation is N1 Rik=[Zrne2njnk/N] n=0 k=0,1,2,..N1 and the kth element of the second half of the sequence is 2N1 R2k=[Zrne2njnk/N] n=0 2N1 =[Zrn+Ne2njnk/N] n=0 k=0,1,..,N1. From the first equation r =r e2nJe >R =R e2nje rn+N=rne >R2k=R1ke including the AWGN one obtains Y1k=R1k+W 1k; Y2k=R1ke2nje+W2k; K=0,1,2,...,N1. It is found that between the first and second DFT's both the ICI and the signal are altered in exactly the same way, by a phase shift proportional to frequency offset. Therefore, if offset e is estimated using observations, it is possible to obtain accurate estimates even when the offset is too large for satisfactory data demodulation. The maximum likelihood estimate (MLE) of e is given by K e1=(1/2n)tan1[ZIm(Y2kY*1k)/ k=K K [ZRe(Y2kY*1k)] k=K in the absence of noise the angle of Y2kY*1k is 2IIe. Statistical properties of the estimate: The conditional mean and variance of e given e and {Rk} can be approximated as follows. Consider the complex products Y2kY 1k from which we estimate e. For a given e, subtract the corresponding phase, 2IIe, from each product to obtain the tangent of the phase error. K tan[2n(e1e)]= [ZIm(Y2kY*1ke2nje)/ k=K K [ZRe(Y2kY*ike2nje)] k=K For Ie1eI<<1/2n, the tangent can be approximated by its argument so that e1e~ K[ZIm(R1k+W2ke2nje)(R*1k+W*1k)]/ k=K K ZRe(R1k+W2ke 2nje)(R*1k+W*1k)] k=K At high signal to noise ratios, a condition compatible with successful communications signaling, may be approximated by K e1e~ [ZIm(W2k R* 1ke2nje+R1kW* 1k)]/ k=K K [ZRe(R1k2)] k=K From which we find that E[eeIe,{Rk}]=0. Therefore, for small errors the estimate is conditionally unbiased. The conditional variance of the estimate is easily determined for above equation. Var[eIe,{Rk}]=1/{(2n)2(Es/No)} Where N1 Es=(T/N)ZIrJ2 n=0 is the total symbol energy. Since the total energy is the sum of the energies of the 2K+1 carriers, the error variance of the offset estimate will in practice be very low. Acquisition: In the event that the frequency offset is greater than + or 1/2 of the carrier spacing, a strategy for initial acquisition to bring the offset within the limits of the algorithm must be developed. A continuous symbol stream occurs in the applications such as digital audio broadcast. A second possibility is that OFDM communications such as digital radio. Here we envision that the session interval will include one or more repeated symbols. The basic strategy for initial frequency offset acquisition, in either case, is to shorten the dft's and use larger carrier spacings such that the phase shift doesnot exceed +or  n. The frequency offset in Hz is 8=e/T=eAf where Af is the inter carrier spacing and T is the symbol interval. Let us assume that the initial frequency offset is not greater than + or5max. Then Af initial>2Smax determines the minimum initial carrier spacing, and the corresponding dft lengths. If the average power of the shortened symbols is kept the same, the variance of the estimate of einitial will be larger than for the longer data symbols,since it estimates the fraction of carrier spacing, corresponds to a proportionately larger fractional offset for the longer data symbols. However, the MLE estimate is so accurate that in practice the initial estimate still may be adequate. If not, it is refined by following the shortened repeated symbols by a repetition of the first full length data symbol. Codes: 1.calculation of frequency offset: clc; clear all; close all; x1= randint(1,1020);%generating a random number for i=1:1020 if (x1(i)>0.5) x1(i)=1; else x1(i)=0; end end disp(x1); x2=reshape(x1,4,255);%to convert 1 by 1020 to 255 by 4 for n=1:4 x3(:,n)=ifft(x2(:,n),255);%ifft of the random signal end y=awgn(x3,10);%adding the awgn noise for p=1:4 xx(:,p)=fft(x3(:,p),255);%taking fft of transmitted signal end x7=reshape(xx,1,1020); x8=abs(x7); for v=1:1020 if (abs(x8(v))abs(x1(v)))<=0.5%to convert into a 1 or 0 x8(v)=0; end end q=0; for c=1:1020 if(x1©==x8©) q=q+1;%number of error free signals end end disp(q);%displays the number of signals without error xy=xx.*exp(i*2*pi*.005);%taking fft after introducing a phase shift figure(2); subplot(2,2,1); plot(xx);%fft value without phase shift title('normal fft'); subplot(2,2,2); plot(xy);%fft value with phase shift title('fft after a phase shift'); xx=reshape(xx,1,1020); xy=reshape(xy,1,1020); z1=[zeros(1,1020)]; y1=[zeros(1,1020)]; for k=1:1:1020 if k==1 y1(1)=imag(xy(k)*conj(xx(k)));%calculating the %estimate phase shift according to the algorithm z1(1)=real(xy(k)*conj(xx(k))); else y1(k)=imag(y1(k1))+imag(xy(k)*conj(xx(k))); z1(k)=real(z1(k1))+real(xy(k)*conj(xx(k))); end end e2=(1/(2*pi))*atan(imag(y1)/real(z1));%estimated phase %shift z2=[zeros(1,1020)]; y2=[zeros(1,1020)]; for b=1:1:1020 if b==1 y2(1)=imag(xx(b)+(conj(xx(b))*exp(2*pi*i*.005))); %calculating the difference in phase shifts betweeen %the estimated and the actual phase shifts z2(1)=(abs(xx(b)).A2); else y2(b)=imag(y2(b1))+imag(xx(b)+(conj(xx(b))*exp(2*pi*i*.005))); z2(b)=z2(b1)+(abs(xx(b)).A2); end end e1=(1/(2*pi))*(y2/z2);%difference in phase shiftsof estimated and the actual disp(e1) e=e2e1;%the phase shift disp(abs(e)); freqoff=.2*1.5;%frequency offset for a phase shift of %0.2 hz and inter carrier spacing of 1.5 hz disp(freqoff); 2.generation of OFDM symbols: clc; x1= randint(1,150);%generating a random number figure(1); subplot(4,1,1); plot(x1);%plots the random signal title('random signal'); x2=x1';%converting 1 by 150 to 150 by 1 x3=ifft(x2,150);%taking ifft y=awgn(x3,30);%adding the awgn noise disp(y); x4=fft(y,150);%taking fft of the received signal x5=abs(x4'); disp(x5); for p=1:1:150 if x5(p)>0.5 x5(p)=1; elseif x5(p)<0.5 x5(p)=0;%converting complex to 1 and 0 end end q=0; for i=1:1:150 if (x1(i)x5(i))==0 q=q+1;%counting the number of error free signals end end disp(q); subplot(4,1,2); plot(x5);%plots the output of the receiver title('received signal'); Conclusions: An algorithm for maximum likelihood estimate (MLE) of frequency offset using the dft values of a repeated data symbol has been presented. It has been shown that for small error in the estimate is conditionally unbiased and is the sense that the variance is inversely proportional to the number of the carriers in the OFDM signal. Furthermore, both the signal values and the ICI, contribute coherently to the estimate so that it is possible to obtain very accurate estimates even when the offset is too great, that is there is too much ICI to demodulate the data values. Since the estimate error depends only on total symbol energy, the algorithm works well in the multipath channels. However, it is required that the frequency offset as well as the channel impulse response be constant for a period of two consequtive symbols. References: 1. .R.W.Chang," synthesis of band limited orthogonal signals for multi channel data transmission", Bell syst.Tech. J, vol 45, pp. 17751796, Dec 1966. S.Darling, "On digital sideband modulators, IEEE Trans. Circuit 2. Theory, vol CT17, pp. 409414, Aug. 1970. 3. S.B.Weinstein and P.M.Ebert, "Data transmission by frequency division multiplexing using the discrete Fourier transform", IEEE Trans. Commn. Technol., vol. COM19, p.p.628634, Oct.1971. 4. J.A.Cbingham,"Multicarrier modulation for data transmission: An idea whose time has come", IEEE Commn. Mag., vol. 28, PP. 1725, Mar.1990. Use Search at http://topicideas.net/search.php wisely To Get Information About Project Topic and Seminar ideas with report/source code along pdf and ppt presenaion



project report helper Active In SP Posts: 2,270 Joined: Sep 2010 
16102010, 03:35 PM
35772324ofdm.pdf (Size: 170.69 KB / Downloads: 110) OFDM  Orthogonal Frequency Division Multiplex, OFDM  Orthogonal Frequency Division Multiplex, the modulation concept being used for many wireless and radio communications radio applications from DAB, DVB, WiFi and Mobile Video. This OFDM tutorial is split into several pages each of which addresses a different aspect of OFDM operation and technology: [1] OFDM basics tutorial [2] OFDM synchronization Orthogonal Frequency Division Multiplex or OFDM is a modulation format that is finding increasing levels of use in today's radio communications scene. OFDM has been adopted in the WiFi arena where the 802.11a standard uses it to provide data rates up to 54 Mbps in the 5 GHz ISM (Industrial, Scientific and Medical) band. In addition to this the recently ratified 802.11g standard has it in the 2.4 GHz ISM band. In addition to this, it is being used for WiMAX and is also the format of choice for the next generation cellular radio communications systems including 3G LTE and UMB. If this was not enough it is also being used for digital terrestrial television transmissions as well as DAB digital radio. A new form of broadcasting called Digital Radio Mondiale for the long medium and short wave bands is being launched and this has also adopted COFDM. Then for the future it is being proposed as the modulation technique for fourth generation cell phone systems that are in their early stages of development and OFDM is also being used for many of the proposed mobile phone video systems. OFDM, orthogonal frequency division multiplex is a rather different format for modulation to that used for more traditional forms of transmission. It utilises many carriers together to provide many advantages over simpler modulation formats. OFDM concept An OFDM signal consists of a number of closely spaced modulated carriers. When modulation of any form  voice, data, etc. is applied to a carrier, then sidebands spread out either side. It is necessary for a receiver to be able to receive the whole signal to be able to successfully demodulate the data. As a result when signals are transmitted close to one another they must be spaced so that the receiver can separate them using a filter and there must be a guard band between them. This is not the case with OFDM. Although the sidebands from each carrier overlap, they can still be received without the interference that might be expected because they are orthogonal to each another. This is achieved by having the carrier spacing equal to the reciprocal of the symbol period. 


seminar surveyer Active In SP Posts: 3,541 Joined: Sep 2010 
20102010, 04:15 PM
Prepared by: Mary Ann Ingram OFDM.pdf (Size: 136.74 KB / Downloads: 132) OFDM Advantages OFDM is a spectrally efficient modulation technique 


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05032011, 10:32 AM
orthogonalfrequencydivisionmultiplexing.sho.DOC (Size: 1.05 MB / Downloads: 37) ABSTRACT: OFDM otherwise called orthogonal frequency division multiplexing is a modulation and a multiple access technique that can be applied to mobile communications. OFDM or Multitone modulation as it is sometimes called is the basis for several commercial wireless applications. In OFDM the segments are according to frequency there by dividing the spectrum into a number of equally spaced tones, which are orthogonal with each other and carries a portion of user information on each tone. As the mobile cellular wireless system operates under harsh and challenging channel conditions, the wireless channel is distinct and much more unpredictable than the wired because of the factors such as multipath fading, shadow fading, Doppler spread and time dispersion or delay spread. OFDM over comes the ISI (intersymbol interference) in a multipath environment. In order to combat these effects the modern wireless systems employ a variety of signal processing techniques, which include the factors such as equalization, error correction coding, spread spectrum, interleaving and diversity. The sinusoidal waveforms making up the OFDM tones have the very special property of being the only eigen functions of a linear channel. With this property and the incorporation of small amount of guard time, called the cyclic prefix to each symbol enables the orthogonality between tones to be preserved in the presence of multipath. The cyclic prefix allows the tones to be realigned at the receiver thus regaining orthogonality and is used to absorb transients from previous bursts caused by multipath. Thus OFDM eliminates the effect of multipath, ISI (intersymbol interference), ICI (intercarrier interference) in Mobile channels. INTRODUCTION: OFDM represents a different systemdesign approach. It can be thought of as a combination of modulation and multipleaccess schemes that segments a communications channel in such a way that many users can share it. Whereas TDMA segments are according to time and CDMA segments are according to spreading codes, OFDM segments are according to frequency. It is a technique that divides the spectrum into a number of equally spaced tones and carries a portion of a user's information on each tone. A tone can be thought of as a frequency, much in the same way that each key on a piano represents a unique frequency. OFDM can be viewed as a form of frequency division multiplexing (FDM), however, OFDM has an important special property that each tone is orthogonal with every other tone. FDM typically requires there to be frequency guard bands between the frequencies so that they do not interfere with each other. OFDM allows the spectrum of each tone to overlap, and because they are orthogonal, they do not interfere with each other. DEFINITION: Orthogonal frequency division multiplexing (OFDM) is a communications technique that divides a communications channel into a number of equally spaced frequency bands. A subcarrier carrying a portion of the user information is transmitted in each band. Each subcarrier is orthogonal (independent of each other) with every other subcarrier, differentiating OFDM from the commonly used frequency division multiplexing (FDM). OVERVIEW OF OFDM: This paper describes OFDM and its application to mobile communications. OFDM is a modulation and multipleaccess technique that has been explored for more than 20 years. Only recently has it been finding its way into commercial communications systems, as Moore's Law has driven down the cost of the signal processing that is needed to implement OFDM–based systems. OFDM, or multitone modulation as it is sometimes called, is presently used in a number of commercial wired and wireless applications. On the wired side, it is used for a variant of digital subscriber line (DSL). For wireless, OFDM is the basis for several television and radio broadcast applications, including the European digital broadcast television standard, as well as digital radio in North America. OFDM is also used in several fixed wireless systems and wireless localarea network (LAN) products. A system based on OFDM has been developed to deliver mobile broadband data service at data rates comparable to those of wired services, such as DSL and cable modems. OFDM enables the creation of a very flexible system architecture that can be used efficiently for a wide range of services, including voice and data. For any mobile system to create a rich user experience, it must provide ubiquitous, fast, and userfriendly connectivity. OFDM has several unique properties that make it especially well suited to handle the challenging environmental conditions experienced by mobile wireless data applications. OFDM FOR MOBILE COMMUNICATIONS: OFDM represents a different systemdesign approach. It can be thought of as a combination of modulation and multipleaccess schemes that segments a communications channel in such a way that many users can share it. Whereas TDMA segments are according to time and CDMA segments are according to spreading codes, OFDM segments are according to frequency. It is a technique that divides the spectrum into a number of equally spaced tones and carries a portion of a user's information on each tone. A tone can be thought of as a frequency, much in the same way that each key on a piano represents a unique frequency. OFDM can be viewed as a form of frequency division multiplexing (FDM), however, OFDM has an important special property that each tone is orthogonal with every other tone. FDM typically requires there to be frequency guard bands between the frequencies so that they do not interfere with each other. OFDM allows the spectrum of each tone to overlap as shown in the fig1, and because they are orthogonal, they do not interfere with each other. By allowing the tones to overlap, the overall amount of spectrum required is reduced. 


ashish229 Active In SP Posts: 1 Joined: Mar 2011 
17032011, 10:29 PM
send me seminar and presentation report on this topic



amadkki Active In SP Posts: 1 Joined: May 2011 
19082011, 12:00 AM
Respected Sir,
I have gone through your report and I have a very important question, xy=xx.*exp(i*2*pi*.005) this 0.005 is it e?? the offset.. secondly the final e=e2e1;%the phase shift disp(abs(e)); freqoff=.2*1.5;%frequency offset for a phase shift of %0.2 hz and inter carrier spacing of 1.5 hz In this one , the e is coming out = 1.4171e022 and then you have written that phase shift of 0.2 Hz and deltaf=1.5. so the offset =0.3.. how phase shift is 0.2 hz ...i mean where in the coding we found phase shift to be 0.2 Hz.. plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz it will be a great help....thanks Kind regards AMad tariq amadkki@hotmail.com Respected Sir, I have gone through your report and I have a very important question, xy=xx.*exp(i*2*pi*.005) this 0.005 is it e?? the offset.. secondly the final e=e2e1;%the phase shift disp(abs(e)); freqoff=.2*1.5;%frequency offset for a phase shift of %0.2 hz and inter carrier spacing of 1.5 hz In this one , the e is coming out = 1.4171e022 and then you have written that phase shift of 0.2 Hz and deltaf=1.5. so the offset =0.3.. how phase shift is 0.2 hz ...i mean where in the coding we found phase shift to be 0.2 Hz.. plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz it will be a great help....thanks Kind regards AMad tariq amadkki[at]hotmail.com Reference: topicideashowtoorthogonalfrequencydivisionmultiplexingfrequencyoffsetcorrectionfullreport?pid=54967#pid54967#ixzz1VPH0ABQ2 


