# Frequency Division Multiplexing

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Frequency Division Multiplexing (FDM)

Frequency Division Multiplexing (FDM), a parallel data transmission technique which transmits different number of signals simultaneously over a single transmission line, such as a wired or wireless system. Each signal travels within its own unique frequency range, which is modulated by the data (text, voice, video, etc.). [1]

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Conventional FDM Spectrum

The basic idea behind (FDM) is to divide the available bandwidth into different number of sub channels (carriers), each of which is spaced with suitable guard band to reduce interference, whereas each sub channel is transmitted simultaneously.

Orthogonal Frequency Division Multiplexing (OFDM)

Orthogonal Frequency Division Multiplexing (OFDM), a digital transmission technique that uses the concept of sub carriers overlapping and each sub carrier is spaced a multiple of 1/T apart in frequency. In this way a large number of carriers are used for single transmission channel, being spaced apart at slightly different frequencies.

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Conventional OFDM Spectrum

The basic idea behind (OFDM) is to occupy significantly lesser bandwidth than (FDM) technique, efficiently by using non overlapping (In Frequency only) orthogonal carriers each of a different frequency, The frequency spacing of the carriers is chosen in such a way that the modulated carriers are orthogonal and do not interfere with one another. Therefore guard bands are not required between individual sub channels (carriers), providing the facility for using the available bandwidth in a more efficient manner.

What Is Orthogonal Frequency Division Multiplexing (OFDM)?

OFDM is one of the most recently introduced digital modulation scheme that modulates digital data onto a radio frequency (RF) signal, then divides the data in different sub parts. OFDM efficiently uses different number of carriers for different number of modulated data packets, each sub carrier can transmit a lower-speed signal, all of which are converted back in the receiver into the original higher-speed signal. All of the data packets are transmitted simultaneously over these sub carriers.

Each packet of data is transmitted over a carrier that is spaced apart at precise frequency from other carrier carrying another packet of modulated data. This spacing provides the "orthogonality" in this technique which prevents the demodulators from recovering the signals with frequencies other than their predefined frequency. Therefore in OFDM multiple high speed digital signals are send in parallel on orthogonal carrier frequencies.

By using this updated form of multi carrier modulation technique (OFDM), one can use the whole bandwidth more efficiently as well as system can be less affected by noise, and other interferences.

Preface

A single-carrier system modulates information onto a single carrier using one of the most common techniques used in signal processing i.e., by varying frequency, phase, or amplitude of carrier. As digital signals are quantized in the form of bits and symbols, and these bits and symbols are in greater number so digital signals require higher bandwidth. Consequently the time period of these bits and symbols become shorter and shorter which causes interference between these bits or symbols. This type of interference is commonly known as Intersymbol Interface (ISI), when the reciprocal of the system rate is significantly smaller than the time dispersion. Actually ISI is caused by multi-path delays. This is the result of receiving not one, but several copies of the signal, due to multiple reflections (i.e., Multipath), say, off buildings, airplanes, etc., of the transmitted signal. In such a case, a channel equalizer is employed at the receiver to compensate for the channel distortions. The figure below shows a simple representation of a Single-carrier modulation system.

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Single-carrier modulation system

In telecommunication systems, intersymbol interference (ISI) is a form of distortion of a signal in which one symbol interferes with subsequent symbols. In this way all the symbols have similar effect as noise. Therefore system becomes more susceptible to loss of information from impulse noise, harmonic noise, timing jitter; frequency offset, and signal reflections. All of these noise factors can make it difficult for the receiver to recover all the symbols in their original form as they were sent by the transmitter.

Frequency division multiplexing (FDM) is next advancement after the concept of single carrier modulation by using large numbers of sub carriers within the same single channel transmission. The total data stream to be sent is divided among a large number of sub carriers in the same single transmission channel. There is no compulsion that the data stream to be sent has to be divided evenly also they don't have to be originated from a single information source. FDM data transmission usually requires a suitable guard interval between modulated sub carriers in order to prevent the collapse between the spectrums of each sub carrier. By inserting the guard intervals between each sub carrier, overall system's effective information rate as well as system efficiency decreases by comparing FDM with a single carrier modulation system.

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In order to increase system's effective information rate as well as its efficiency, which was not maintained by the FDM, an upgraded modulation system known as Orthogonal Frequency Division Multiplexing (OFDM) was introduced. Generally OFDM uses a combination of sub carriers which are orthogonal in frequency; in this way the guard intervals that were used to prevent the spectrum overlapping of various sub carriers and to recover the individual carriers in an FDM system would no longer be necessary in OFDM. By using the orthogonality concept, each sub carrier allows the neighboring sub carriers to overlap, without loosing their spectral information and energy. If and if only this orthogonality in OFDM system is maintained, it's very possible to recover each and individual sub carrier despite of their overlapping spectrums. The figure below shows a simple representation of an OFDM multi carrier system.

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A simple OFDM generator.

Description

Earlier the approach was to design a bandwidth-efficient communication system in the presence of channel distortion i.e., to subdivide the available channel bandwidth into a number of equal-bandwidth sub channels, where the bandwidth of each sub channel is sufficiently narrow so that the frequency response characteristics of the sub channels are nearly ideal. Such a subdivision of the overall bandwidth into smaller sub channels is illustrated in Figure below. Thus, we create *K = B/∆f *sub channels, where different information symbols can be transmitted simultaneously in the *K *sub channels. Consequently, the data is transmitted by frequency-division multiplexing (FDM). [6]

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Subdivision of the channel bandwidth *W* into narrowband sub channels of equal width *∆f.*

With each sub channel, we associate a carrier:

*X*_{k}* (t) = sin 2*_{∏ }*f*_{k }*t,k= 0, 1 …… k-1*

In OFDM system suppose there are *K *sub channels, the symbol rate of the entire sub carriers is reduced by a factor of *N* as compared to the symbol rate of a single carrier modulation system that uses the entire bandwidth *B* and transmits data at the same rate as OFDM. Hence, the symbol interval in the OFDM system is *T*= *KT*_{s}*, *where as *T** _{s}* is the symbol interval in the single-carrier transmission system. By increasing

*K*, the symbol interval

*T*can be made significantly larger than the time period of the channel-time dispersion. Thus, intersymbol interference (ISI) can be further reduced by selection of

*K.*In other words, each sub channel has a fixed frequency response.

*C (f*_{k}*), k = 0, 1…... K - 1.* [6]

As long as the orthogonality among the sub carriers is kept constant, then by using the OFDM system, different number of bits/symbol combination can be modulated on each sub carrier. Hence, sub carriers that yield a higher SNR due to a lower attenuation can be modulated to carry more bits/symbol than sub channels that yield a lower SNR (high attenuation). As QAM, PSK, QPSK, FSK and other modulation schemes with different constellation sizes can be used in an OFDM system.

History

In the early-1960s the idea was to use parallel data transmission carriers and was named as Frequency Division Multiplexing (FDM). OFDM; sometimes called multi-carrier or discrete multi-tone modulation was the idea proposed in the late 1960s, according to which each sub carrier overlapped to its adjacent sub carriers with minimum frequency spacing in between, and this spacing was carefully designed so that each sub carrier is orthogonal to the other sub carriers. The OFDM technique was used in several high frequency military systems in the early days of its invention, named as under.

- KINEPLEX

- ANDEFT

- KATHRYN

In the early-1970's, Weinstein and Ebert used Discrete Fourier Transform (DFT) technique in parallel data transmission systems for the purpose of modulation and demodulation.

- FFT-based OFDM.

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Examples of our workIn the early-1980's, OFDM was used in high-speed digital modems, in digital mobile and wireless communication, and in high-density efficient recording.

- Pilot tone was used to stabilize and control carrier and frequency.

- Trellis code is implemented.

- COFDM

In 1980, Hirosaki suggested an equalization algorithm and by using, it can suppress both inter-symbol (ISI) and inter-carrier interference (ICI) caused by the channel impulse response, and phase or frequency mismatch. In the late 1980's, Hirosaki also introduced the (IDFT and DFT) based implementation of 8-QAM OFDM system.

In the 1990s, OFDM was exploited for wideband data communications.

- Mobile radio FM channels.

- Fix-wire network.

- High bit rate digital subscriber line. (HDSL)

- Asymmetric digital subscriber line. (ADSL)

- Very high speed digital subscriber line. (VDSL)

- Digital audio broadcasting. (DAB)

- Digital video broadcasting. (DVB)

- High definition television (HDTV)

The three different mechanisms used for the digital terrestrial television broadcasting system in major world portion are as under.

- In Europe

- (COFDM)

- In North America

- (8-VSB)

- In Japan

- (BST-OFDM)

- Wireless LAN

The three different mechanisms used for the wireless LAN system in major world portion are as under.

- HIPERLAN2 (In Europe)

- IEEE 802.11a (In U.S.A)

- IEEE 802.11g (In U.S.A)

Implementation

Overview

OFDM is a special form of multi carrier modulation. An efficient way to implement OFDM as suggested by Weinstein in 1971, by means of an Inverse Discrete-time Fourier Transform (IDFT) and Discrete-time Fourier Transform (DFT) combination as a modulation technique. The mathematical complexity was reduced by implementing OFDM using a combination of Inverse Fast Fourier Transform (IFFT) and Fast Fourier Transform (FFT). However, due to some budget constraints appeared in implementing large size FFT's, OFDM was not affectively implemented at that time. Recent advances in VLSI solved that problem, and now use of large size integration techniques enabled faster and cheaper implementation of IFFT and FFT based OFDM systems. [11]

There are several digital techniques used to implement OFDM in practice. However in modern systems, the Modulation/Demodulation scheme followed by OFDM is a combination of fast Fourier Transform (FFT) and inverse fast Fourier Transform (IFFT) or Discrete fast Fourier Transform (DFFT) and inverse Discrete fast Fourier Transform (IDFFT), whichever used.

The complete block diagram of an OFDM system implemented using Discrete-time Fourier Transform (DFT) and Fast Fourier Transform (FFT) techniques,

Serial to Parallel, And Parallel to Serial Buffer, D/A converter

Before performing the Inverse Discrete Fourier Transform (IDFT), the incoming data is first converted from a serial stream to parallel sets of data, making it easier for IDFT block in time domain conversion. Each set of data contains one symbol, representing each sub carrier. The signal samples *X** _{n}* generated after computing the IDFT are passed through a serial to parallel converter, in which parallel sets of data are converted into serial stream again. The serial stream of OFDM data is then passed from a digital-to-analog (D/A) converter, whose output, ideally is the OFDM signal waveform

*X(t).*

Inverse Discrete Fourier Transform (IDFT)

An OFDM system treats the source symbols (e.g., the QPSK or QAM symbols that would be present in a single carrier system) at the transmitter as though they are in the frequency-domain. These symbols are used as the inputs to an IDFT block that brings the signal into the time domain. The IDFT takes in *N* symbols at a time where *N* is the number of subcarriers in the system. Each of these *N* input symbols has a symbol period of *T* seconds. Recall that the basis functions for an IDFT are *N* orthogonal sinusoids. These sinusoids each have a different frequency and the lowest frequency is DC. Each input symbol acts like a complex weight for the corresponding sinusoidal basis function. Since the input symbols are complex, the value of the symbol determines both the amplitude and phase of the sinusoid for that sub carrier. The IDFT output is the summation of all *N* sinusoids. Thus, the IDFT block provides a simple way to modulate data onto *N* orthogonal subcarriers. The blocks of *N* output samples from the IDFT make up a single OFDM symbol. After some additional processing, the time-domain signal that results from the IDFT is transmitted across the channel. [5]

Discrete Fourier Transform (DFT)

At the receiver side, a DFT (Discrete Fourier Transform) block is used to recover the modulated signal and then convert it into the frequency domain. Generally, the output of DFT block is the collection of original symbols that were sent as in input to the IDFT (Inverse Discrete Fourier Transform) at the transmitter side. When DFT output is plotted in the complex plane, the output samples form a constellation graph, such as 32-QAM. However, there will be no constellation graph for the time-domain signal. Instead of constellation graph, a scatter plot is formed with an irregular shape, when time-domain signal is plotted on the complex plane. Therefore every receiver who's processing is based upon the concept of a constellation (such as symbol slicing), must have to work in the frequency domain. The block diagram in Figure below illustrates the signal transformation between frequency-domain and time domain in an OFDM system. [5]

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A/D Converter, Serial to Parallel, and Parallel to Serial Buffer

Before performing the Discrete Fourier Transform (DFT), the incoming analog OFDM data is first converted into digital data stream, then this serial digital data stream splits into parallel data stream, making it easier for DFT block for conversion from time domain to frequency domain and the magnitudes of the frequency components correspond to the original data. Finally, the parallel to serial block converts these parallel sets of data into a serial stream, hence recovering the original input data.

Cyclic Prefix

The time period of each symbol in OFDM modulation scheme is long. Therefore to remove Intersymbol Interference (ISI), its necessary to insert cyclic prefix to each block of *N *signal samples. The cyclic prefix for the block of samples consists of the samples *X*_{N - m }*, X*_{N - m + 1}*, …..., X** _{N - 1}*. These samples are appended to the beginning of the block, thus, creating a signal sequence of length

*N + m*samples.

^{[6]}Cyclic prefix creates a guard band around individual OFDM symbols, which greatly minimizes the effects of Intersymbol Interference (ISI), and maintaining the orthogonality in between the symbols.

At the receiver side the cyclic prefix between the individual orthogonal signals is removed then converted into time domain, using DFT.

Applications

Almost all the standards used in broadband, wireless and high speed data transmission and connectivity in present age are based upon multi-carrier modulation. i.e., Orthogonal Frequency Division Multiplexing (OFDM). The future enhancements of the wireless broadband communication are completely based on the concept of increasing the available data rate to provide the best coverage and quality communication to the mobile user. This will enable value added services that are not possible with current state of the art mobile wireless radio systems. While an increase in data rate could be achieved by combining techniques in the form of multi mode terminals (e.g. UMTS and wireless LAN). [8]

The Wireless World Research Forum (WWRF) and IEEE have chosen OFDM best suited modulation scheme for various current and future communications system projects, and researches all over the world. OFDM is well suited for systems in which the channel characteristics make it difficult to maintain adequate communications link performance. OFDM is especially suitable for high-speed communication due to its resistance to Inter Symbol Interference (ISI). OFDM has its wide acceptance in wireless as well as wired communications as an appropriate broadband modulation scheme

Wired Applications

Early advances made in OFDM opened a whole new era of bandwidth efficient systems by providing the benefits of OFDM in data transferring over phone lines, modems, networks, digital radio, and digital televisions.

- ADSL and VDSL broadband access via POTS copper wiring.

- Power line communication (PLC).

- Multimedia over Coax Alliance (MoCA) home networking. [10]

- Cable modem.

- Multipoint multi channel distribution services. (MMDS)

Wireless Applications

In the early days of OFDM invention the users had limited speed of wireless networking ranging less than 11Mbps. After a lot of research and advancements OFDM is introduced to wireless broadband network, after which the wireless standards like IEEE 802.11a and 802.11g are running the real-world wireless LAN speed ranges to 50Mbps and above.

Typically, OFDM, is a spread-spectrum technology that gives wireless networking a new physical (PHY) layer, is implemented in embedded chipsets made up of radio transceivers, Fast Fourier Transform (FFT) processors, system input/output (I/O), serial to parallel and back again translators and OFDM logic.[9]

Recent advancement and up gradation of wireless communication systems tends to adopt OFDM systems in below listed applications:

- The wireless LAN radio interfaces.

- IEEE 802.11a, and 802.11g

- HIPERLAN/2.

- The digital radio systems

- DAB/EUREKA 147, DAB+

- Digital Radio Mondiale

- HD Radio, T-DMB and ISDB-TSB

- The terrestrial mobile TV systems

- DVB-H, T-DMB

- ISDB-T and Media FLO forward link

- More than 3G cellular communication techniques

- Flash-OFDM and

- 3GPP Long Term Evolution (LTE)

- The Wireless LAN / Fixed broadband wireless access (BWA) standards

- IEEE 802.16 (or WiMAX)

- HIPERLAN

- Mobile Broadband Wireless Access (MBWA) standards

- IEEE 802.20

- IEEE 802.16e (Mobile WiMAX)

- WiBro

- Wireless Personal Area Network (PAN) Ultra wideband (UWB) IEEE 802.15.3a proposed by WiMedia Alliance. [10]

- Anti-Jamming, Military applications.

- MIMO-OFDM system for Wireless LAN.

References

[1].OFDM Tutorial.

Available at: http://www.wave-report.com/tutorials/OFDM.html

[2].http://dictionary.zdnet.com/definition/OFDM.html

[3].Programmable Logic Facilitates the Implementation of OFDM Based Systems.

By: Tapan A. Mehta, Product Marketing Manager, Altera Corporation.

Available at: http://archive.chipcenter.com/pld/pldf092.htm

[4].Multiple Access Schemes for OFDM.

S-72.4210. Post-Graduate Course in Radio Communications.

By: Alexis Dowhuszko.

Dated, 21.03.2006

[5]. signal processing, the principles of OFDM.

By: Louis Litwin and Michael Pugel. Page # 30.

January 2001.

Available at: www.rfdesign.com

[6].Communication Systems Engineering.

2^{nd} Edition. Page #556-558

By: John G Proakis and Masoud Salehi.

PEARSON−Prentice Hall.

ISBN 81-7758-428-6

[7].Chapter 1.

Introduction to Orthogonal Frequency Division Multiplexing Technique.

By:CCU. Wireless Access Tech Lab.

[8].

WWRF/WG4/Subgroup on New Air Interfaces

Broadband Multi-Carrier Based Air Interface

By: Stefan Kaiser1, Uwe-Carsten Fiebig1, Naoto Matoba2, Andy Jeffries3, Marc de Courville4, Arne Svensson5

[9].OFDM: Old Technology for New Markets

By: Steven J. Vaughan-Nichols

November 14, 2002

Available at: www.wi-fiplanet.com/tutorials/article.php/1500651.html

[10].Multi Carrier Digital Communications: Theory and Applications of OFDM

Bahai, A. R. S., Saltzberg, B. R., Ergen, M. (2004)., Springer, 2004.

[11].Orthogonal Frequency Division Multiplexing for Wireless Communications

By: Hua Zhang

School of Electrical and Computer Engineering.

Georgia Institute of Technology,

Dated November 11, 2004