# Tutorial de Orthogonal Frequency Division Multiplexing

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Orthogonal Frequency Division Multiplexing

0.8

Normalized Amplitude --->

0.6

0.4

0.2

0

-0.2 -6 -4 -2 0 2 Normalized Frequency (fT) ---> 4 6

By, Vijaya Chandran Ramasami KUID 698659

TABLE OF CONTENTS ABSTRACT .................................................................................................................................................. 5 OVERVIEW OF THE REPORT ................................................................................................................ 6 1. OFDM SYSTEM MODEL....................................................................................................................... 7 1.1. INTRODUCTION ..................................................................................................................................... 7 1.2. OFDM USING INVERSE DFT ................................................................................................................ 7 1.3. GUARD TIME AND CYCLIC EXTENSION............................................................................................... 10 1.4. RAISED COSINE WINDOWING ............................................................................................................. 11 1.5. OFDM GENERATION .......................................................................................................................... 11 1.6. OFDM SYSTEM DESIGN ..................................................................................................................... 12 2. ADVANTAGES OF OFDM................................................................................................................... 14 2. 1. MULTI-PATH DELAY SPREAD TOLERANCE ........................................................................................ 14 2.2. EFFECTIVENESS AGAINST CHANNEL DISTORTION............................................................................... 14 2.3. THROUGHPUT MAXIMIZATION (TRANSMISSION AT CAPACITY) .......................................................... 15 2.4. ROBUSTNESS AGAINST IMPULSE NOISE .............................................................................................. 15 2.5. FREQUENCY DIVERSITY...................................................................................................................... 16 3. THE PEAK POWER PROBLEM IN OFDM ...................................................................................... 16 3.1. POWER AMPLIFIER LINEARITY ........................................................................................................... 16 3.2. CLIPPING ............................................................................................................................................ 17 3.3. ERROR-CONTROL CODING.................................................................................................................. 18 3.4. PEAK CANCELLATION......................................................................................................................... 18 3.5. PAR REDUCTION CODES .................................................................................................................... 18 3.6. SYMBOL SCRAMBLING TECHNIQUES .................................................................................................. 19 4. SYNCHRONIZATION IN OFDM SYSTEMS .................................................................................... 19 4.1. SYNCHRONIZATION USING CYCLIC EXTENSION .................................................................................. 19 4.2. SYNCHRONIZATION USING TRAINING SEQUENCES .............................................................................. 21 4.3. OPTIMAL TIMING IN THE PRESENCE OF MULTI-PATH.......................................................................... 21 5. MULTI-CARRIER CDMA ................................................................................................................... 22 5.1. SYSTEM MODEL ................................................................................................................................. 22 5.2. ADVANTAGES OF MC-CDMA............................................................................................................ 23 6. APPLICATIONS OF OFDM ................................................................................................................ 24 6.1. DIGITAL AUDIO BROADCASTING (DAB) ............................................................................................ 24 6.2. DIGITAL VIDEO BROADCASTING (DVB) ............................................................................................ 25 6.3. WIRELESS LANS ................................................................................................................................ 25 6.4. OFDMA............................................................................................................................................. 26 CONCLUSION ........................................................................................................................................... 26 REFERENCE: ............................................................................................................................................ 27

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LIST OF FIGURESFIGURE 1 : A OFDM MODULATOR .............................................................................................................. 8 FIGURE 2 : THREE SUBCARRIERS WITHIN AN OFDM SYMBOL ................................................................... 9 FIGURE 3: SPECTRA OF INDIVIDUAL SUB-CARRIERS ................................................................................... 9 FIGURE 4 : GUARD TIME AND CYCLIC EXTENSION - EFFECT OF MULTIPATH ......................................... 10 FIGURE 5 : OFDM SYTEM BLOCK DIAGRAM ............................................................................................ 12 FIGURE 6 : SYNCHRONIZATION USING CYCLIC EXTENSION ...................................................................... 20 FIGURE 7 : SYNCHRONIZATION USING TRANING SEQUENCES ................................................................... 21 FIGURE 8 : A MULTI-CARRIER CDMA TRANSMITTER ............................................................................. 22 FIGURE 9 : A MULTI-CARRIER CDMA RECEVIER.................................................................................... 23

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LIST OF TABLESTABLE 1 : DIGITAL AUDIO BROADCASTING (OFDM PARAMTERS) .......................................................... 24 TABLE 2 : WLAN - OFDM PARAMETERS ................................................................................................. 26

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AbstractMulti-Carrier Modulation is a technique for data-transmission by dividing a high-bit rate data stream is several parallel low bit-rate data streams and using these low bit-rate data streams to modulate several carriers. Multi-Carrier Transmission has a lot of useful properties such as delay-spread tolerance and spectrum efficiency that encourage their use in untethered broadband communications. OFDM is a multi-carrier modulation technique with densely spaced sub-carriers, that has gained a lot of popularity among the broadband community in the last few years. This report is intended to provide a tutorial level introduction to OFDM Modulation, its advantages and demerits, and some applications of OFDM.

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Overview of the ReportThis report is organized as follows: The first section of the report presents the OFDM System Model. Details of

generation and demodulation of OFDM are presented, along with system design issues. The second section of the report presents some of the important advantages of OFDM that suit its use in Broadband communications. The third section of the report discusses the Peak Power Problem in OFDM and some techniques used to overcome the problems of Power Amplifier Non-Linearity. The fourth section of the report discusses Synchronization Issues associated with OFDM and some synchronization methods commonly used in OFDM. The fifth section of the report discusses a relatively new technique of combining OFDM with CDMA called Multi-Carrier CDMA (MC-CDMA). Transmitter and Receiver structures for MC-CDMA and some of the advantages offered by MCCDMA are discussed. The final section of the report presents some of the applications of OFDM for broadband communications. Applications such as DAB, DVB and WLAN are considered in some detail.

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1. OFDM System ModelOFDM is a multi-channel modulation system employing Frequency Division Multiplexing (FDM) of orthogonal sub-carriers, each modulating a low bit-rate digital stream. 1.1. Introduction In older multi-channel systems using FDM, the total available bandwidth is divided into N non-overlapping frequency sub-channels. Each sub-channel is modulated with a separate symbol stream and the N sub-channels are frequency multiplexed. Even though the prevention of spectral overlapping of sub-carriers reduces (or eliminates) Interchannel Interference, this leads to an inefficient use of spectrum. The guard bands on either side of each sub-channel is a waste of precious bandwidth. To overcome the problem of bandwidth wastage, we can instead use N overlapping (but orthogonal) subcarriers, each carrying a baud rate of 1/T and spaced 1/T apart. Because of the frequency spacing selected, the sub-carriers are all mathematically orthogonal to each other. This permits the proper demodulation of the symbol streams without the requirement of nonoverlapping spectra. Another way of specifying the sub-carrier orthogonality condition is to require that each sub-carrier have exactly integer number of cycles in the interval T. It can be shown that the modulation of these orthogonal sub-carriers can be represented as an Inverse Fourier Transform. Alternatively, one may use a DFT operation followed by low-pass filtering to generate the OFDM signal. The details of this method are explained in the next section. It must be noted that OFDM can be used either as a modulation or a multiplexing technique. 1.2. OFDM using Inverse DFT The use of Discrete Fourier Transform (DFT) in the parallel transmission of data using Frequency Division Multiplexing was investigated in 1971 by Weinstein and Ebert [1]. Consider a data sequence d0, d2, , dN-1, where each dn is a complex symbol. (The data

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sequence could be the output of a complex digital modulator, such as QAM, PSK etc). Suppose we perform an IDFT on the sequence 2dn (the factor 2 is used purely for scaling purposes), we get a result of N complex numbers Sm (m = 0,1,N-1) as:N 1 nm S m = 2 d n exp( j 2 ) = 2 d n exp( j 2 f n t m ) [m = 0,1,..N-1] ------(2.1) N n=0 n =0 N 1

Where,n and t = mTs -------(2.2) NTs Where, Ts represents the symbol interval of the original symbols. Passing the real part of fn =

the symbol sequence represented by equation (2.1) thorough a low-pass filter with each symbol separated by a duration of Ts seconds, yields the signal,

e j 2f1tmxsm

dn

Serial To Parallel Converter

+

e j 2f N 1tmx

Figure 1 : A OFDM Modulator n N 1 y (t ) = 2 Re d n exp( j 2 t ), for 0 t T -------(2.3) T n =0 Where, T is defined as NTs. The signal y(t) represents the baseband version of the OFDM signal.

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1 0.8 0.6 0.4

Amplitude --->

0.2 0 -0.2 -0.4 -0.6 -0.8 -1

0

0.1

0.2

0.3

0.4 0.5 0.6 0.7 Normalized Time (t/T) --->

0.8

0.9

1

Figure 2 : Three Subcarriers within an OFDM symbol

0.8

Normalized Amplitude --->

0.6

0.4

0.2

0

-0.2 -6 -4 -2 0 2 Normalized Frequency (fT) ---> 4 6

Figure 3: Spectra of Individual Sub-Carriers

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It is easy to note from (2.3), that The length of the OFDM signal is T.

The spacing between the carriers is equal to 1/T. The OFDM symbol-rate is N times the original baud rate. There are N orthogonal sub-carriers in the system.

The signal defined in equation (2.3) is the basic OFDM symbol. 1.3. Guard Time and Cyclic Extension One of the main advantages of OFDM is its effectiveness against the multi-path delay spread frequently encountered in Mobile communication channels. The reduction of the symbol rate by N times, results in a proportional reduction of the relative multi-path delay spread, relative to the symbol time. To completely eliminate even the very small ISI that results, a guard time is introduced for each OFDM symbol. The guard time must be chosen to be larger than the expected delay spread, such that multi-path components from one symbol cannot interfere with the next symbol. It the guard time is left empty, this may lead to inter-carrier interference (ICI), since the carriers are no longer orthogonal to each other. To avoid such a cross talk between sub-carriers, the OFDM symbol is cyclically extended in the guard time. This ensures that the delayed replicas of the OFDM symbols always have an integer number of cycles within the FFT interval as long as the multi-path delay spread is less than the guard time.

guard

Symbol

guard

guard

Symbol

guard

Multipath component that does not cause ISI

guard

Symbol Multipath component that causes ISI

guard

Figure 4 : Guard Time and Cyclic Extension - Effect of Multipath

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1.4. Raised Cosine Windowing If the ODFM symbol were generated using equation (2.3), the power spectral density of this signal would be similar to the one shown in Fig (psd). The sharp-phase transitions caused by phase modulation results in very large side-lobes in the PSD and the spectrum falls off rather slowly (according to a sinc function). If the number of sub-carries were increased, the spectrum roll-off will be sharper in the beginning, but gets worse at frequencies a little further away from the 3-dB cut-off frequency. To overcome this problem of slow spectrum roll-off, a windowing may be used to reduce the side-lobe level. The most commonly used window is the Raised Cosine Window given by [2]:

0.5 + 0.5 cos( + t /( Tr )), w(t ) = 1.0, 0.5 + 0.5 cos ((t-T ) /( T )), r r

0 t Tr

Ts t Tr Ts t (1 + )Tr

Here Tr is the symbol interval which is chosen to be shorter than the actual OFDM symbol duration, since the symbols are allowed to partially overlap in the roll-off region of the raised cosine window. Incorporating the windowing effect, the OFDM symbol can now be represented as:N 1 n y (t ) = 2 Rew(t ) d n exp( j 2 t ), for 0 t T T n=0

It must be noted that filtering can also be used as a substitute for windowing, for tailoring the spectrum roll-off. But windowing is preferred to filtering because, it can be carefully controlled. With filtering, one must be careful to avoid rippling effects in the roll-off region of the OFDM symbol. Rippling causes distortions in the OFDM symbol, which directly leads to less-delay spread tolerance. 1.5. OFDM Generation Based on the previous discussions, the method for generating an ODFM symbol is as follows. First, the N input complex symbols are padded with zeros to get Ns symbols that are

used to calculate the IFFT. The output of the IFFT is the basic OFDM symbol.

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Based on the delay spread of the multi-path channel, a specific guard-time must be

chosen (say Tg). A number of samples corresponding to this guard time must be taken from the beginning of the OFDM symbol and appended at the end of the symbol. Likewise, the same number of samples must be taken from the end of the OFDM symbol and must be inserted at the beginning. The OFDM symbol must be multiplied with the raised cosine window to remove the power of the out-of-band sub-carriers. The windowed OFDM symbol is then added to the output of the previous OFDM symbol with a delay of Tr, so that there is an overlap region of Tr between each symbol. Figure (modem) shows the block diagram of an OFDM transmitter and receiver.

Input Bits

Channel Coding

Symbol Mapping

Serial To Parallel

IFFT

Parallel To Serial Cylic Extension Raised Cosine Window RF-TX Module

DAC

Output Bits

Channel Decoder

Symbol Demap

Parallel To Serial

FFT

Serial To Parallel Remove Cylic Extension Timing & Frequenc Sync

RF-RX Module

Frequency Corrected Signal

ADC

Figure 5 : OFDM Sytem Block Diagram 1.6. OFDM System Design OFDM system design, as in any other system design, involves a lot of tradeoffs and conflicting requirements. The following are the most important design parameters of an12

OFDM system. The following parameters could be a part of a general OFDM system specification: Bit Rate required for the system.

Bandwidth available. BER requirements. (Power efficiency). RMS delay spread of the channel.

Guard Time Guard time in an OFDM system usually results in an SNR loss in an OFDM system, since it carries no information. The choice of the guard time is straightforward once the multi-path delay spread is known. As a rule of thumb, the guard time must be at least 2-4 times the RMS delay spread of the multi-path channel. Further, higher-order modulation schemes (like 32 or 64 QAM) are more sensitive to ISI and ICI than simple schemes like QPSK. This factor must also be taken into account while deciding on the guard-time. Symbol Duration To minimize the SNR loss due to the guard-time, the symbol duration must be set much larger than the guard time. But an increase in the symbol time implies a corresponding increase in the number of sub-carriers and thus an increase in the system complexity. A practical design choice for the symbol time is to be at least five times the guard time, which leads to an SNR loss that is reasonable. Number of Sub-carriers Once the symbol duration is determined, the number of sub-carriers required can be calculated by first calculating the sub-carrier spacing which is just the inverse of the symbol time (less the guard period). The number of sub-carriers is the available bandwidth divided by the sub-carrier spacing. Modulation and Coding Choices The first step in deciding on the coding and modulation techniques is determining the number of bits carried by an OFDM symbol. Then, a suitable combination of modulation and coding techniques can be selected to fit the input data rate into the OFDM symbols and, at the same time, satisfying the bit-error rate requirements. The choice of modulation

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and coding techniques are lot easier now, since each channel is assumed to almost AWGN and one doesnt need to worry about the effects of multi-path delay spread.

2. Advantages of OFDMOFDM possesses some inherent advantages for Wireless Communications. This section glances on few of the most important reasons on why OFDM is becoming more popular in the Wireless Industry today. 2. 1. Multi-path Delay Spread Tolerance As discussed earlier, the increase in the symbol time of the OFDM symbol by Ntimes (N being the number of sub-carriers), leads to a corresponding increase in the effectiveness of OFDM against the ISI caused due to multi-path delay spread. Further, using the cyclic extension process and proper design, one can completely eliminate ISI from the system. 2.2. Effectiveness against Channel Distortion In addition to delay variations in the channel, the lack of amplitude flatness in the frequency response of the channel also causes ISI in digital communication systems. A typical example would be the twister-pair used in telephone lines. These transmission lines are used to handle voice calls and have a poor frequency response when it comes to high frequency transmission. In systems that use single-carrier transmission, an equalizer might be required to mitigate the effect of channel distortion. The complexity of the equalizer depends upon the severity of the channel distortion and there are usually issues such as equalizer non-linearities and error propagation etc that cause additional trouble. In OFDM systems on the other hand, since the bandwidth of each sub-carrier is very small, the amplitude response over this narrow bandwidth will be basically flat (of course, one can safely assume that the phase response will be linear over this narrow bandwidth). Even in the case of extreme amplitude distortion, an equalizer of very simple structure will be enough to correct the distortion in each sub-carrier.

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2.3. Throughput Maximization (Transmission at Capacity) The use of sub-carrier modulation improves the flexibility of OFDM to channel fading and distortion makes it possible for the system to transmit at maximum possible capacity using a technique called channel loading. Suppose the transmission channel has a fading notch in a certain frequency range corresponding to a certain sub-carrier. If we can detect the presence of this notch by using channel estimation schemes and assuming that the notch doesnt vary fast enough compared to the symbol duration of the OFDM symbol, it can be possible to change (scale down/up) the modulation and coding schemes for this particular sub-carrier (i.e, increase their robustness against noise), so that capacity as a whole is maximized over all the sub-carriers. However, this requires the data from channel-estimation algorithms. In the case of single-carrier systems, nothing can be done against such fading notches. They must somehow survive the distortion using errorcorrection coding or equalizers. 2.4. Robustness against Impulse Noise Impulse noise is usually a burst of interference caused usually caused in channels such as the return path HFC (Hybrid-Fiber-Coaxial), twisted-pair and wireless channels affected by atmospheric phenomena such as lightning etc. It is common for the length of the interference waveform to exceed the symbol duration of a typical digital communication system. For example, in a 10 MBPS system, the symbol duration is 0.1 s , and a impulse noise waveform, lasting for a couple of micro-seconds can cause a burst of errors that cannot be corrected using normal error-correction coding. Usually complicated ReedSolomon codes in conjunction with huge interleaves are used to correct this problem. OFDM systems are inherently robust against impulse noise, since the symbol duration of an OFDM signal is much larger than that of the corresponding single-carrier system and thus, it is less likely that impulse noise might cause (even single) symbol errors. Thus, complicated error-control coding and interleaving schemes for handling burst-type errors are not really required for OFDM Systems simplifying the transceiver design.

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2.5. Frequency Diversity. OFDM is the best place to employ Frequency Diversity. In fact, in a combination of OFDM and CDMA called the MC-CDMA transmission technique (section 5), frequency diversity is inherently present in the system. (i.e, it is available for free) Even though, OFDM provides a lot advantages for Wireless Transmission, it has a few serious disadvantages that must be overcome for this technology to become a success. The following sections discuses two serious problems associated with OFDM transmission.

3. The Peak Power Problem in OFDMOne of the most serious problems with OFDM transmission is that, it exhibits a high peak-to-average ratio. In other words, there is a problem of extreme amplitude excursions of the transmitted signal. The OFDM signal is basically a sum of N complex random variables, each of which can be considered as a complex modulated signal at different frequencies. In some cases, all the signal components can add up in phase and produce a large output and in some cases, they may cancel each other producing zero output. Thus the peak-to-average ratio (PAR) of the OFDM system is very large.

The problem of Peak-To-Average Ratio is more serious in the transmitter. In order to avoid clipping of the transmitted waveform, the power-amplifier at the transmitter frontend must have a wide linear range to include the peaks in the transmitted waveform. Building power amplifiers with such wide linear ranges is a costly affair. Further, this also results in high power consumption. The DACs and the ADCs must also have a wide range to avoid clipping. There has been a lot of research put into the study of overcoming the PAR problem in OFDM [4,5,6,7]. The following sections discuss some of the most common and important of those techniques as well as other issues. 3.1. Power Amplifier Linearity Practical Power Amplifiers have an input power range over which they have a linear transfer curve. Usually the linearity of non-ideal power amplifiers is measured using a

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term called the 1 dB compression point. It is defined as the input power at which the output power of the amplifier is 1 dB less than the output power obtained with an ideal amplifier. The figure(power) shows a typical response curve of a non-ideal power amplifier. 3.2. Clipping One important feature of the peak-to-average ratio in the OFDM is the fact that the percentage of symbols have a very large peak-power is less (and the percentage decreases with an increase in the number of sub-carriers). Thus in this case, the simplest possible solution to the peak-power problem would be Clipping, i.e., limiting the peak amplitude to some maximum level. Although simple, this method has a few disadvantages. Clipping produces a kind of self-interference that causes some degradation in the

BER performance. The non-linear distortion caused due to clipping increases the amount of out-of-band radiation. The increase in the out-of-band radiation is basically because of the fact that the clipping operation is a multiplication of the OFDM symbol with a rectangular function that is 1 if the amplitude is below a threshold and a smaller value if the amplitude is above the threshold. This rectangular waveform increases the out-of-band radiation, and as a result, the spectrum has a roll-off that is inversely proportional to the frequency.

The problem of slow spectrum roll-off can be overcome to some extent, by windowing the rectangular clipping waveform. Several windows are proposed in literature. Some of the most common ones are Gaussian, Cosine, Hamming, Kaiser etc. Simulation results show a slight degradation in BER with clipping. When windowing is applied the BER performance is still worse, since a large portion of the signal is affected by windowing than by clipping alone.

The required back-off for the power amplifier can be determined by specifying the amount of attenuation for the out-of-band spectral components, relative to the in-band spectral components. It has been shown that windowing offers a 3-dB gain in the required back-off when compared to clipping alone.

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3.3. Error-Control Coding One of the problems with clipping is the degradation in BER. Specifically, the symbols that have a large PAR ratio are vulnerable to errors. To reduce this effect, forward error correction (FEC) can be applied across several OFDM symbols. When FEC is applied, the errors caused due to large PAR in particular symbols can be corrected by the surrounding symbols. 3.4. Peak Cancellation Another method of removing the peaks in a OFDM signal is to subtract a time-shifted and scaled reference function such that each subtracted reference function reduces the peak power of at least one signal sample. It is desirable to choose a signal with approximately the same bandwidth as the transmitted signal. The most commonly used peak-canceling function is the sinc function because of its desirable frequency-domain properties. The sinc function can be time-limited by multiplying by a raised-cosine window. It can be shown that the peak cancellation technique will result in a lesser outof-band interference than the clipping and windowing techniques. A further advantage of the peak-cancellation technique is the fact that it can be digitally implemented, following the IFFT in the transmitter. 3.5. PAR Reduction Codes A more elegant solution to the PAR problem is the use of coding techniques. The PAR can be reduced by using a code that only produces OFDM symbols for which the PAR is below some desired level. The more the reduction in the PAR, the smaller is the coding rate. It has been shown that (pg 138) it is possible to construct codes with a code rate of that provides a maximum PAR of 3 dB. Another interesting result in this direction is the fact (pg 139) that the correlation properties of complementary sequence can translate into a relatively small PAP ratio of 3-dB when these codes are used to modulate an OFDM Symbol. All these results have lead to the usage of Golay-Complementary sequences for generating these codes. Golay complementary sequences are sequence pairs for which the sum of auto-correlation function is zero for all delay shifts that are not equal to zero. A lot of research papers have been published on the usage of Golay Codes for OFDM transmission, that deal with the efficient generation of these code and the optimal and sub-optimal decoding and other interesting properties.18

3.6. Symbol Scrambling Techniques The basic idea of these techniques is that, for each OFDM symbol, the input sequence is scrambled by a certain number of scrambling sequences. The output signal with the smallest PAR is transmitted. If the PAR for one OFDM symbol has a probability p of exceeding a certain level without scrambling, the probability that it will exceeding with scrambling (given a set of k scrambling codes) is pk. Thus scrambling hopes to reduce the probabilitiy of occurrence of high PARs, rather than reducing the levels of these PARs.

4. Synchronization in OFDM SystemsAnother important issue in OFDM transmission is synchronization. There are basically three issues that must be addressed in synchronization. The receiver has to estimate the symbol boundaries and the optimal timing instants that minimize the effects of inter-carrier interference (ICI) and inter-symbol interference (ISI). In an OFDM system, the sub-carriers are exactly orthogonal only if the transmitter! "

and the receiver use exactly the same frequencies. Thus receiver has to estimate and correct for the carrier frequency offset of the received signal. Further, the phase information must be recovered if coherent demodulation is employed. Another associated problem with OFDM systems is the effect of phase noise. Phase noise is present in all practical oscillators and it manifests itself in the form of random phase modulation of the carrier. Both phase-noise and frequency offset cause significant amount of ICI in an OFDM receiver. The effect these are worse in OFDM than single carrier systems. The use of efficient frequency and phase estimation schemes can help reduce these effects. Some of the common methods used to achieve synchronization in OFDM systems are: 4.1. Synchronization using Cyclic Extension Since a Cyclic extension is added to every OFDM symbol, the first Tg seconds of the OFDM symbol is identical to the last part. This property can be exploited for both timing and frequency synchronization using a scheme depicted in figure (1).

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This scheme correlates Tg seconds of the OFDM symbol with a part that is T seconds delayed (T being the symbol time, less the guard period Tg). The output of the correlator can be written as: y (t ) = r (t )r (t T )d0 Tg

The symbol timing is estimated from the correlation peaks at the output of the correlator. The characteristics of the correlation peaks (in terms of the correlation side-lobe levels and the standard deviation of the correlation magnitude) are better if the correlation is performed over a large number of independent samples. Since the number of independent samples is proportional to the number of sub-carriers, this cyclic extension correlation method is efficient only if a large number of sub-carriers are present (more than 100). In the case of less number of sub-carriers, the side-lobe to peak ratio of the correlator output will be high and sometimes this might lead to wrong timing. Once the timing is established using the correlation output, the frequency offset can be directly estimated. The phase of the correlator output is equal to the phase drift between samples that are T seconds apart. Hence the frequency offset can be estimated as the correlation phase divided by 2T .Frequency Offset

T

Conjugation Estimate Phase

xOFDM Signal

Integrate over Tg

Find Max Correlation

Timing

Figure 6 : Synchronization using Cyclic Extension The cyclic extension technique is basically used for blind synchronization where it is not possible to use a training sequence.

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4.2. Synchronization using Training Sequences In cases like packet data transmission in which a training sequence is available, a much more efficient method of timing recovery is to correlate the received signal with the known training sequence and to find the peaks in the correlator output. This method is illustrated in fig (corr). Here T is the sampling interval and ci are the matched filter coefficients, which are in turn, the complex conjugates of the known training sequence. From the correlation peaks in the output signal, both the symbol timing and the frequency offset can be estimated.

T

T

T

x

x

x

+

Find Max

Symbol Timing

Figure 7 : Synchronization using Traning Sequences 4.3. Optimal Timing in the Presence of Multi-path The effect of multi-path is the introduction of ICI and ISI in the OFDM symbol. These effects are significant only if the delay spread of the channel exceeds the guard interval. ICI is caused mainly because the FFT interval is no longer flat (because the roll-off regions due the multi-path components interfere with the flat region of the FFT interval). ISI is caused mainly because of the overlap between the previous OFDM symbol and the current OFDM symbol in the FFT interval. The solution to this timing problem is to find the delay window with a width equal to the guard time-that contains the maximum signal power. The optimal FFT starting time is then equal to the starting delay of the found delay window, plus the delay that occurs between a matched filter peak output from a single OFDM pulse and the delay of the last sample from the flat part of the OFDM signal envelope, minus the length of the FFT interval.

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5. Multi-Carrier CDMARecently a new proposal for a system based on a combination of CDMA and OFDM has gained increasing attention in the research community. This system is called the MultiCarrier CDMA (MC-CDMA) system and it combines the advantages offered by both OFDM and CDMA. This section describes the basic architecture and the advantages of this system: 5.1. System Model A MC-CDMA transmitter spreads the data signal using a given spreading code in the frequency domain. In other words, each chip of the signal is transmitted over a separate sub-carrier. The block diagram of a basic OFDM transmitter is shown in figure (trans). In the MC-CDMA transmitter, the input data stream is first converted into a parallel symbol stream (of width P), using a serial to parallel converter. Each data symbol is spread using a spreading code K. All the data in total ( P K ), are now transmitted in parallel using sub-carrier modulation (OFDM).

Spreading

Datastream

Serial To Parallel

IDFT

Spreading

Figure 8 : A Multi-Carrier CDMA Transmitter

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In the MC-CDMA receiver, after down-conversion, the K sub-carrier components corresponding to the received users data is first coherently detected with the DFT and combined (using various diversity combining strategies) to yield the received data.

Weighting (Diversity)

Despreading

Received Signal

FFT

Parallel To Serial

Symbol Stream

Weighting (Diversity)

Despreading

Figure 9 : A Multi-Carrier CDMA Recevier 5.2. Advantages of MC-CDMA Combining OFDM with CDMA has a lot of advantages when compared to using DSCDMA alone. Some of them are discussed in this section: The transmitted symbol duration is much larger than the chip duration of DS-CDMA,# $ % &

this makes the job of synchronization much easier. Provided there is an adequate guard interval provided, the multi-path correction in the form of RAKE combining is not necessary. The OFDM-CDMA system provides inherent frequency diversity, since a single symbol is spread over a wide range of frequencies that may fade independently and a diversity combiner can be used to improve the fading performance of the system. Finally, it must be noted that all these advantages are in addition, to what is already offered by CDMA.

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6. Applications of OFDMA lot of applications that use OFDM technology have spawned over the last few years. In this section, one such application will be described in detail, while a introduction to the other applications will be provided. 6.1. Digital Audio Broadcasting (DAB) DAB is an European standard for digital broadcasting that is intended to replace the current analog technologies such as AM and FM. It was standardized by the European Telecommunications Institute (ETSI) in 1995 [8]. DAB has got four transmission modes with different parameters as shown in the table below: Mode I # of sub-carriers Sub-carrier Spacing Symbol Time Guard Time Carrier Frequency Transmitter Separation Table 1 : Digital Audio Broadcasting (OFDM Paramters) The DAB transmitted data consists of number of audio signals sampled at a rate of 48 kHz with a 22-bit resolution. This audio signal is then compressed at rates ranging from 32 to 384 kbps, depending upon the desired signal quality. The resulting digital data is then divided into frames of 24 ms. DAB uses differential QPSK modulation for the sub-carriers. A null-symbol (or a silence period that is slightly greater than the OFDM symbol length) is used to indicate the start of the frame. A reference OFDM symbol is then sent to serve as a starting point for the differential decoding of the QPSK subcarriers. Differential Modulation avoids the use of complicated phase-recovery schemes. 1.246 ms 246 us < 375 MHz < 96 km 311.5 us 61.5 us < 1.5 GHz < 24 km 155.8 us 30.8 us