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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 system-design approach. It can be thought of as a combination of modulation and multiple-access 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 multiple-access 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 local-area 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 user-friendly 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 system-design approach. It can be thought of as a combination of modulation and multiple-access 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
OVERVIEW OF THE WIRELESS ENVIRONMENT:
Mobile cellular wireless systems operate under harsh and challenging channel conditions. The wireless channel is distinct and much more unpredictable than the wireline channel because of factors such as multipath and shadow fading, Doppler spread, and time dispersion or delay spread. Multipath is a phenomenon that occurs as a transmitted signal is reflected by objects in the environment between the base station and a user. These objects can be buildings, trees, hills, or even trucks and cars. The reflected signals arrive at the receiver with random phase offsets, because each reflection generally follows a different path to reach the user's receiver. The degree of cancellation, or fading, will depend on the delay spread of the reflected signals, as embodied by their relative phases, and their relative power
Internet Time dispersion represents distortion to the signal and is manifested by the spreading in time of the modulation symbols. This occurs when the channel is band-limited, or, in other words, when the coherence bandwidth of the channel is smaller than the modulation bandwidth. Time dispersion leads to intersymbolinterference, or ISI, where the energy from one symbol spills over into another symbol, and, as a result, the BER is increased. It also leads to fading.
Internet In many instances, the fading due to multipath will be frequency selective, randomly affecting only a portion of the overall channel bandwidth at any given time. Frequency selective fading occurs when the channel introduces time dispersion and when the delay spread exceeds the symbol period. When there is no dispersion and the delay spread is less than the symbol period, the fading will be flat, thereby affecting all frequencies in the signal equally. Flat fading can lead to deep fades of more than 30 decibels (dB).
Internet Doppler spread describes the random changes in the channel introduced as a result of a user's mobility and the relative motion of objects in the channel. Doppler has the effect of shifting, or spreading, the frequency components of a signal. The coherence time of the channel is the inverse of the Doppler spread and is a measure of the speed at which the channel characteristics change. This in effect determines the rate at which fading occurs. When the rate of change of the channel is higher than the modulated symbol rate, fast fading occurs. Slow fading, on the other hand, occurs when the channel changes are slower than the symbol rate. The statistics describing the fading signal amplitude are frequently characterized as either Rayleigh or Ricean. Rayleigh fading occurs when there is no line of sight (LOS) component present in the received signal.
If there is a LOS component present, the fading follows a Ricean distribution. There is frequently no direct LOS path to a mobile, because the very nature of mobile communications means that mobiles can be in a building or behind one or other obstructions. This leads to Rayleigh fading but also results in a shadow loss. These conditions, along with the inherent variation in signal strength caused by changes in the distance between a mobile and cell site, result in a large dynamic range of signals, which can easily be as much as 70 dB.
OVERVIEW OF TRADITIONAL MOBILE WIRELESS SYSTEMS:
All modern mobile wireless systems employ a variety of techniques to combat the aforementioned effects. Some techniques are more effective than others, with the effectiveness depending on the air-interface and the system-architecture approach taken to satisfy the requirements of the services being offered. As mobile systems evolved from analog to digital, more sophisticated signal-processing techniques have been employed to overcome the wireless environment.
These techniques include equalization, channel or error-correction coding, spread spectrum, interleaving, and diversity. Diversity has long been used to help mitigate the multipath-induced fading that results from users' mobility. The simplest diversity technique, spatial diversity, involves the use of two or more receive antennae at a base station that are separated by some distance, say on the order of five to 10 wavelengths. The signal from the mobile will generally follow separate paths to each antenna. This relatively low- cost approach yields significant performance improvement by taking advantage of the statistical likelihood that the paths are not highly correlated with each other. When one antenna is in a fade, the other one will generally not be. Spread spectrum systems employ a form of diversity called frequency diversity.
Here the signal is spread over a much larger bandwidth than is needed for transmission and is typically greater than the coherence bandwidth of the channel. A wideband signal is more resistant to the effect of frequency selective fading than is a narrowband signal, because only a relatively small portion of the overall bandwidth use is likely to experience a fade at any given time. There are two forms of spread spectrum, code division multiple access (CDMA) and frequency hopping (FH).
OPERATION OF OFDM:
The sinusoidal waveforms making up the tones in OFDM have the very special property of being the only Eigen-functions of a linear channel. This special property prevents adjacent tones in OFDM systems from interfering with one another, in much the same manner that the human ear can clearly distinguish between each of the tones created by the adjacent keys of a piano. This property, and the incorporation of a small amount of guard time to each symbol, enables the orthogonality between tones to be preserved in the presence of multipath. This is what enables OFDM to avoid the multiple-access interference that is present in CDMA systems. The frequency domain representation of a number of tones, shown in Figure 1 highlights the orthogonal nature of the tones used in the OFDM system. Notice that the peak of each tone corresponds to a zero level, or null, of every other tone. The result of this is that there is no interference between tones. When the receiver samples at the center frequency of each tone, the only energy present is that of the desired signal, plus whatever other noise happens to be in the channel.
Internet To maintain orthogonality between tones, it is necessary to ensure that the symbol time contains one or multiple cycles of each sinusoidal tone waveform. This is normally the case, because the system numerology is constructed such that tone frequencies are integer multiples of the symbol period, as is subsequently highlighted, where the tone spacing is 1/T. Viewed as sinusoids. The below figure shows three tones over a single symbol period, where each tone has an integer number of cycles during the symbol. .
Internet In absolute terms, to generate a pure sinusoidal tone requires the signal start at time minus infinity. This is important, because tones are the only waveform than can ensure orthogonality. Fortunately, the channel response can be treated as finite, because multipath components decay over time and the channel is effectively band-limited. By adding a guard time, called a cyclic prefix, the channel can be made to behave as if the transmitted waveforms were from time minus infinite, and thus ensure orthogonality, which essentially prevents one subcarrier from interfering with another (called intercarrier interference, or ICI). Multipath causes tones and delayed replicas of tones to arrive at the receiver with some delay spread. This leads to misalignment between sinusoids, which need to be aligned as in fig shown below to be orthogonal. The cyclic prefix allows the tones to be realigned at the receiver, thus regaining orthogonality.
Internet The cyclic prefix is sized appropriately to serve as a guard time to eliminate ISI. This is accomplished because the amount of time dispersion from the channel is smaller than the duration of the cyclic prefix. A fundamental trade-off is that the cyclic prefix must be long enough to account for the anticipated multipath delay spread experienced by the system. The amount of overhead increases, as the cyclic prefix gets longer. The sizing of the cyclic prefix forces a tradeoff between the amount of delay spread that is acceptable and the amount of Doppler shift that is acceptable.
CONCLUSION:
This tutorial highlights the unique design challenges faced by mobile data systems that result from the vagaries of the harsh wireless channel, the wide and varied service profiles that are enabled by data communications, and the performance of wireline-based protocols, such as TCP/IP, with the realities of wireless links. OFDM has been shown to address these challenges and to be a key enabler of a system design that can provide high-performance mobile data communications. OFDM is well positioned to meet the unique demands of mobile packet data traffic. Nevertheless, to seamlessly unwire all the IP applications inherent in the wired Internet and intranets (including interactive data applications and peer-to-peer applications), all layers of the OFDM air interface need to be jointly designed and optimized from the ground up for the IP data world. .
BIBLOGRAPHY:
Wireless Digital Communications, Modulation and Spread Spectrum applications, by Dr.Kamilo Feher, Prentice-Hall, India.
Mobile Cellular Tele Communications Analog And Digital Systems, by William C.Y.Lee, McGraw Hill, Second Edition.
Wireless Communications Principles And Practice, by Theodore S.Rappaport, Pearson Education, Second Edition Digital Communications, by J.Proakis, New York: McGraw-Hill
Tutorials on Ofdm http://ieconline/tutorials/ofdm.html

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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. OFDM is a multi-channel modulation system employing Frequency Division Multiplexing (FDM) of orthogonal sub-carriers, each modulating a low bit-rate digital stream. In FDM, the prevention of spectral overlapping of sub-carriers reduces Interchannel Interference, but 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 this problem, OFDM uses 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. This permits 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. 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. It must be noted that OFDM can be used either as a modulation or a multiplexing technique.
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 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,
OFDM Modulator
Where, T is defined as NTs. The signal y(t) represents the baseband version of the OFDM
Three Subcarriers within an OFDM symbol Spectra of Individual Sub-Carriers
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. 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.
Guard time and cyclic extension-Effect of Multipath
OFDM Generation
The generation of OFDM 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). 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 r T ?between each symbol.
Figure shows the block diagram of an OFDM transmitter and receiver.
OFDM System Block Diagram
The following are the most important design parameters of an OFDM system.
¢ Guard Time
¢ Symbol Duration
¢ Number of Sub-carriers
Advantages of OFDM
OFDM 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.
¢ Multi-path Delay Spread Tolerance
¢ Effectiveness against Channel Distortion
¢ Throughput Maximization (Transmission at Capacity)
¢ Robustness against Impulse Noise
Synchronization in OFDM Systems
Synchronization in OFDM system is achieved by the following methods
¢ Synchronization using Cyclic Extension
¢ Synchronization using Training Sequences
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.
Synchronization using cyclic extension
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:
The symbol timing is estimated from the correlation peaks at the output of the correlator.
The characteristics of the correlation peaks 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 T p 2 .
Multi-Carrier CDMA
Recently 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 Multi-Carrier CDMA (MC-CDMA) system and it combines the advantages offered by both OFDM and CDMA.
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 ( K P ´ ), are now transmitted in
parallel using sub-carrier modulation (OFDM).
Multi-carrier CDMA Transmitter Multi-carrier CDMA receiver
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.
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 alreadyoffered by CDMA.
Applications of OFDM
A 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.
Digital Video Broadcasting (DVB)
Digital Video Broadcasting (DVB) is a standard for broadcasting Digital Television over satellites, cables and thorough terrestrial (wireless) transmission. DVB was standardized by the ETSI in 1997 [9]. The following are some important parameters of DVB: _ DVB has two modes of operation: the 2k mode with 1705 sub-carriers and the 8k modes with 6817 sub-carriers.
¢ _ DVB uses QPSK, 16-QAM or 64-QAM sub-carrier modulation.
¢ _ DVB uses a Reed-Solomon outer code (204,188,t=8) and a inner convolutional code with generator polynomials (177,133 octal) combined with two layers of interleaving for error-control.
¢ _ Pilot Sub-carriers are used to obtain reference amplitudes and phases for coherent
demodulation. Two-dimensional channel estimation is performed using the pilot
sub carriers, which aids in the reception of the OFDM signal.
Wireless LANs
Wireless LANs are one of the most important applications of OFDM. A lot of standards have been proposed for Wireless LANs during the past decade, most of then based on spread-spectrum schemes. In July 1998, IEEE Wireless LAN standardization group IEEE 802.11 standardized a scheme based on OFDM operating in the 5-GHz band. It is interesting to note that this standard is one of the first packet-based one to use OFDM. The parameters of this WLAN standard are given in table
WLAN-OFDM Parameters
One of the main reasons for using OFDM for Wireless LANs is relatively small amount of delay spread encountered in such applications. In the case of indoor environments, the delay spread is still much less and the efficiency of OFDM in such environments is very high. In outdoor-environments however, directional antennas need to be employed if the same guard interval were used
OFDMA
Finally, it is also possible to use OFDM for multiple-access too. This technique is called OFDMA and is implemented by providing each user with a small number of sub-carriers. Even though this technique is similar to FDMA, it avoids the use of large guard bands that are used to prevent adjacent channel interference.
Conclusion
OFDM has several interesting properties that suit its use over Wireless channels and hence many Wireless standards have started to use OFDM for modulation and multiple access. The various methods of generation and demodulation of OFDM and specific issues such as linearity and synchronization were analyzed. Application of OFDM such MC-CDMA, DAB, DVB , WLAN etc, were also discussed in detail.

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