Orthogonal frequency division multiplexing seminar 2004
ORTHOGONAL FREQUENCY DIVISION MULTIPLPLEXING
SEMINAR REPORT
2004
Done by
Arun Mohan .V
Department of Electronics & Communication Engineering
GovernmentEngineeringCollege
Thrissur
ACKNOWLEDGMENT
I would like to thank everyone who helped to see this seminar to completion. In particular, I would like to thank my seminar coordinator Mrs. Muneera.C.R for her moral support and guidance to complete my seminar on time. Also I would like to thank Mr. C. D. Anil Kumar for his invaluable help and support.
I would like to take this opportunity to thank Prof. Indiradevi, Head of the Department, Electronics & Communication Engineering for her support and encouragement.
I express my gratitude to all my friends and classmates for their support and help in this seminar.
Last, but not the least I wish to express my gratitude to God almighty for his abundant blessings without which this seminar would not have been successful.
ABSTRACT
Multi-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. It has found immense applications in communication systems. This report is intended to provide a tutorial level introduction to OFDM Modulation, its advantages and demerits, and some applications of OFDM.
TABLE OF CONTENTS
ABSTRACT ...... …….3
1.HISTORYOFOFDM………………………….………….....5
2. OFDM SYSTEM MODEL...... 7
3.ADVANTAGESOFOFDM...... 22
4. THE PEAK POWER PROBLEMINOFDM...... 25
5.SYNCHRONIZATIONINOFDMSYSTEMS...... 30
6. MULTI-CARRIER CDMA...... 33
7. APPLICATIONS OF OFDM...... 36
8. CONCLUSION ...... 41
REFERENCE ...... 42
1. HISTORY OF OFDM
The concept of using parallel data transmission by means of frequency division multiplexing (FDM) waspublished in mid 60s. Some early development can be traced back in the 50s. A U.S. patent wasfilled and issued in January, 1970. The idea was to use parallel data streams and FDM with overlappingsub channels to avoid the use of high speed equalization and to combat impulsive noise, and multipathdistortion as well as to fully use the available bandwidth. The initial applications were in the militarycommunications. In the telecommunications field, the terms of discrete multi-tone (DMT), multichannelmodulation and multicarrier modulation (MCM) are widely used and sometimes they areinterchangeable with OFDM. In OFDM, each carrier is orthogonal to all other carriers. However, thiscondition is not always maintained in MCM. OFDM is an optimal version of multicarrier transmission
schemes.
Figure 1: comparison of band width between FDM and OFDM
For a large number of sub channels, the arrays of sinusoidal generators and coherent demodulatorsrequired in a parallel system become unreasonably expensive and complex. The receiver needs precisephasing of the demodulating carriers and sampling times in order to keep crosstalk between sub channelsacceptable. Weinstein and Ebert applied the discrete Fourier transform (DFT) to parallel datatransmission system as part of the modulation and demodulation process. In addition to eliminating thebanks of subcarrier oscillators and coherent demodulators required by FDM, a completely digitalimplementation could be built around special-purpose hardware performing the fast Fourier transform(FFT). Recent advances in VLSI technology enable making of high-speed chips that can perform largesize FFT at affordable price.
In the 1980s, OFDM has been studied for high-speed modems, digital mobile communicationsand high-density recording. One of the systems used a pilot tone for stabilizing carrier and clockfrequency control and trellis coding was implemented. Various fast modems were developed fortelephone networks.
In 1990s, OFDM has been exploited for wideband data communications over mobile radio FMchannels, high-bit-rate digital subscriber lines (HDSL, 1.6 Mb/s), asymmetric digital subscriber lines(ADSL, 1,536 Mb/s), very high-speed digital subscriber lines (VHDSL, 100 Mb/s), digital audiobroadcasting (DAB) and HDTV terrestrial broadcasting.
2. OFDM SYSTEM MODEL
2.1 INTRODUCTION
In older multi-channel systems using FDM, the total available bandwidth is divided into N non-overlappingfrequency sub-channels. Each sub-channel is modulated with aseparate symbol stream and the N sub-channels are frequency multiplexed. Even though the prevention of spectral overlapping of sub-carriers reduces (or eliminates) Inter channel Interference, this leads to an inefficient use of spectrum. The guard bands on either side of each sub-channel are a waste of precious bandwidth. To overcome the problem of bandwidth wastage, we can instead use N overlapping (but orthogonal) sub carriers, 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. Thispermits the proper demodulation of the symbol streams without the requirement of non overlapping 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. The idea in OFDM is to define a symbol sequence in the frequency domain, transmit it in the time domain, and map the received samples back into the frequency domain.
In high speed data transfer, Quality of service is an important criterion. Therefore modulation techniques must be good enough for quality data transfer, which modulation can compromise all contradicting requirements in the best manner. Usingadaptive equalization techniques at the receiver could be the solution, but there are practical difficulties in operating this equalization in real-time at several Mb/s with compact, low-cost hardware. A promising candidate that eliminates a need for the complex equalizers is the OFDM. Here methods generation, properties, merits and demerits of the technique are discussed.
It is an important feature of the OFDM system design that the bandwidth occupied is greaterthan the correlation bandwidth of the fading channel. A good understanding of the propagation statisticsis needed to ensure that this condition is met. Then, although some of the carriers are degraded bymultipath fading, the majority of the carriers should still be adequately received. OFDM can effectivelyrandomize burst errors caused by Rayleigh fading, which comes from interleaving due to parallelization.So, instead of several adjacent symbols being completely destroyed, many symbols are only slightlydistorted. Because of dividing an entire channel bandwidth into many narrow sub bands, the frequencyresponse over each individual subband is relatively flat. Since each subchannel covers only a smallfraction of the original bandwidth, equalization is potentially simpler than in a serial data system. Asimple equalization algorithm can minimize mean-square distortion on each subchannel, and theimplementation of differential encoding may make it possible to avoid equalization altogether. Thisallows the precise reconstruction of majority of them, even without forward error correction (FEC).
2.2 Mathematical description of OFDM
After the qualitative description of the system, it is valuable to discuss the mathematical definition of themodulation system. This allows us to see how the signal is generated and how receiver must operate, andit gives us a tool to understand the effects of imperfections in the transmission channel. As noted above,OFDM transmits a large number of narrowband carriers, closely spaced in the frequency domain. Inorder to avoid a large number of modulators and filters at the transmitter and complementary filters anddemodulators at the receiver, it is desirable to be able to use modern digital signal processing techniques,such as fast Fourier transform (FFT).
Mathematically, each carrier can be described as a complex wave:
The real signal is the real part of sc(t). Both Ac(t) and fc(t), the amplitude and phase of the carrier, canvary on a symbol by symbol basis. The values of the parameters are constant over the symbol durationperiod t.
Figure 2: Single and multi bit channel spectrum
OFDM consists of many carriers. Thus the complex signals ss(t)is represented by:
Where,
This is of course a continuous signal. If we consider the waveforms of each component of the signal overone symbol period, then the variables Ac(t) and fc(t) take on fixed values, which depend on the frequencyof that particular carrier, and so can be rewritten:
If the signal is sampled using a sampling frequency of 1/T, then the resulting signal is represented by:
At this point, we have restricted the time over which we analyse the signal to N samples. It is convenientto sample over the period of one data symbol. Thus we have a relationship:
If we now simplify the equation for signal, without a loss of generality by letting w0=0, then the signal becomes:
Now above eqn can be compared with the general form of the inverse Fourier transform:
In simplified, the function is no more than a definition of the signal in the sampled frequencydomain, and s(kT) is the time domain representation. Above eqns are equivalent if:
This is the condition that was required for orthogonality. Thus, one consequence of maintaining orthogonality is that the OFDM signal can be defined by using Fouriertransform procedures.
The Fourier transform allows us to relate events in time domain to events in frequency domain. There are several version of the Fourier transform, and the choice of which one to use depends on the particular circumstances of the work. The conventional transform relates to continuous signals which are not limited to in either time or frequency domains. However, signal processing is made easier if the signals are sampled. Sampling of signals with an infinite spectrum leads to aliasing, and the processing of signals which are not time limited can lead to problems with storage space. To avoid this, the majority of signal processing uses a version of the Discrete Fourier Transform (DFT). The DFT is a variant on the normal transform in which the signals are sampled in both time and the frequency domains. By definition, the time waveform must repeat continually, and this leads to a frequency spectrum that repeats continually in the frequency domain. The Fast Fourier Transform (FFT) is merely a rapid mathematical method for computer applications of DFT. It is the availability of this technique, and the technology that allows it to beimplemented on integrated circuits at a reasonable price, that has permitted OFDM to be developed as far as it has. The process of transforming from the time domain representation to the frequency domain representation uses the Fourier transform itself, whereas the reverse process uses the inverse Fourier transform.
2.3OFDM USING IDFT
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. Consider a data sequence d0, d2… dN-1,
Where each dn is a complex symbol. (The data 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:
Where, Ts represents the symbol interval of the original symbols. Passing the real part of 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,Where, T is defined as NTs. The signal y(t) represents the base band version of the OFDM signal.
Figure 3: OFDM modulator
It is easy to note from (2.3), that
1 The length of the OFDM signal is T.
2. The spacing between the carriers is equal to 1/T.
3. The OFDM symbol-rate is N times the original baud rate.
4. There are N orthogonal sub-carriers in the system.
The signal defined in equation (2.3) is the basic OFDM symbol.
Figure 4: Three sub carriers within an OFDM signal
Figure 5: Spectra of individual carriers
2.5GUARD TIME AND CYCLIC EXTENSION
The main problem with reception of radio signals is fading caused by multipath propagation. Also, there are intersymbolinterference (ISI), shadowing, and interference. This makes link quality vary. Further constraints are limited bandwidth, low power consumption, network management and multi-cellular operation.
As a result of the multi-path propagation, there are many reflected signals, which arrive at the receiver at different times. Delayed signals are the result of reflections from terrain features such as trees, hills or mountains, or objects such as people, vehicles or buildings. These echoes cause ISI. Combined, these signals can produce fading.
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, relativeto 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. If 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.
2.6 . 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 fall off rather slowly (as the 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
The most commonly used window is the Raised Cosine Window, W (t)
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 OFDMsymbol can now be represented as:
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.
2.7. OFDMGENERATION
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.
Based on the delay spread of the multi-path channel, a specific guard-time must be chosen (say Tg). 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 r T b between each symbol.
Figure 6: OFDM transmitter and receiver
2.8OFDM SYSTEM DESIGN
OFDM system design, as in any other system design, involves a lot of tradeoff’s and conflicting requirements. The following are the most important design parameters of an OFDM system. The following parameters could be a part of a generalOFDM 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. Naturally, the addition of the guard interval reduces the data capacity by an amount dependent on its length. The concept of a guard interval could in principle be applied to a single-carrier system, but the loss of data capacity would normally be prohibitive.
EachOFDM symbol is preceded by a periodic extension of the signal itself. The total symbol duration isT Total=Tg+T, where Tg is the guard interval and T is the useful symbol duration. When the guard intervalis longer than the channel impulse response or the multipath delay, the ISI can be eliminated.However, the ICI, or in-band fading, still exists. The ratio of the guard interval to useful symbol durationis application-dependent. Since the insertion of guard interval will reduce data throughput, Tg is usuallyless than T/4.With a guard interval included in the signal, the tolerance on timing the samples is considerably more relaxed