ORTHOGONAL FREQUENCY DIVISION MULTIPLEXER

                                                           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.

                                                                   

 

       Fig 1. Time Delayed multipath signals

    Courtesy: 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.

 

                                                               

Fig2. Demonstration of multipath reflections

Courtesy: 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).

                                                                 

 Fig3. Demonstration of time varying fading

Courtesy: 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.

                                                                    

Fig4. Two-dimensional illustration of ofdm channel resource

Courtesy: 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.

                                          .

                                      

      Fig5. Time- and frequency-domain representation

  Courtesy: Internet

                                                                 

 

Fig6. Integer number of sinusoid periods

Courtesy: 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.

                                                             

                                                               

Fig7. Cyclic extension of sinusoid

Courtesy: 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.