# Orthogonal Frequency Division Multiplexing And Bandwidth Usage Computer Science Essay

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Orthogonal frequency division multiplexing (OFDM) has become one of the sought modulation technique for wireless communications. The reason for which is its ability to provide high data rate, better bandwidth utilization and robustness in to channel impairments. However OFDM is also subjected to few disadvantages like its sensitivity to frequency offset, large dynamic range or in other words high peak to average ratio and its sensitivity to channel fading. In this thesis, we study the effects of frequency offset on the performance of OFDM channels. Here we infer through mathematical simulations that to maintain signal to interference ratios of minimum 20 dB for the OFDM sub channels, the offset should be limited to less than 4% of the intercarrier spacing. Also we estimate the frequency offset by using maximum likelihood estimation (MLE) algorithm.

1. INTRODUCTION

With the tremendous growth in the communication industry, the need for the efficient utilization of bandwidth is very important. Apart from bandwidth shortage, the need for high data rates for different multimedia modes such as video, voice, data has paved way for research in various multiplexing technologies. One such evolution is the Orthogonal Frequency Division Multiplexing which uses multicarrier modulation.

OFDM is a special case of multicarrier transmission, where a single datastream is transmitted over a number of lower rate subcarrier and these subcarriers are orthogonal to each other. Other than aforementioned reasons for the development of OFDM, the main reason to use OFDM is to increase the robustness against frequency selective fading or narrowband interference [1].

(More to write here )

The study of history of OFDM shows that it was first introduced in 1950s and was primarily used for military communications [2]. [11] Presents a brief history of the introduction and evolution of OFDM applications. An example of the early OFDM applications was the AN/GSC-10(KATHRYN) variable rate data modem built for the high-frequency radio. 34 parallel low rate channels were generated by using PSK modulation by a frequency multiplexed set of subchannels. Orthogonal frequency assignment was carried with a channel spacing of 82 Hz which acted as a guard interval between successive signalling elements. OFDM was also used in other high-frequency military systems, such as KINEPLEX [12] and ANDEFT [13]. It was in the 1980's that OFDM was explored for high speed modems, digital mobile communications. [14] realized the OFDM techniques for multiplexed QAM using DFT. [15] also designed the commonly used 19.2 kbps voiceband data modem using multiplexed QAM where pilot tone was used for stabilizing carrier and clock frequency control. Later in the 1990's area of the OFDM was explored for wideband data communications over mobile radio FM channels, HDSL, ADSL, VHDSL and DAB.

Dr. Douglas Jones, Professor of Electrical and Computer Engineering at University of Illinois at Urbana-Champaign explains better the reason of underlining multiplexing and parallel transmission utilized in OFDM. He says if we have to transmit 1,000,000 bits per second, then it in a single carrier transmission, it is transmitted one at a time, each taking one microsecond to be transmitted. A delay spread longer than one microsecond would cause delayed reflections from multipath to overlap the direct signal for the next bit, thus causing ISI. If instead 1000 bits are transmitted in parallel at a time on 1000 separate OFDM subchannels, then the bits can be transmitted 1000 times slower; that is, one millisecond to send them. A multipath delay spread of 1 microsecond would only overlap 1/1000th of the transmission interval for any given bit, thus causing hardly any interference.

However the feature of multicarrier in OFDM makes it susceptible to synchronization errors between transmitter and receiver local oscillator frequencies. This error is known as the carrier frequency offset (CFO) and causes ICI and also destroys the orthogonality between the subcarriers. In this literature we study the effects that CFO can cause to the SNR in an OFDM system, estimate the amount of frequency offset and also methods to overcome the effects/loss. There are number of research papers which proposes different methods to combat ICI in OFDM [3] - [7] (Complete this !! )

This report is organized as follows. Part 2 gives a brief description of the standard OFDM system.

b. Background and Literature Survey

There are numerous publications and books based on OFDM digital communication systems. [1] by Richard Van Nee and Ramjee Prasad provides a comprehensive introduction to OFDM, to understand the implementation of OFDM, its benefits and applications. This is used as a base document for the discussion of an OFDM system in this thesis. [2] Discusses about the effects of frequency offset in OFDM

2. OFDM System

The conventional frequency multiplexing approach, the frequency band is divided into N non-overlapping frequency sub-bands and each of these subchannels are modulated with a separate information signal and these N sub-bands are frequency multiplexed. This technique avoids interchannel interference but at the cost of inefficient consumption of the bandwidth. To overcome this, OFDM was designed such that it uses N overlapping frequency sub-bands and each would carry a signalling rate and each would be placed apart by the same rate (to avoid usage of high speed equalization and to avoid noise distortion). The OFDM carriers would have orthogonality between them in a symbol interval if simulated such that the carriers are spaced in frequency at the reciprocal of the symbol rate. [2]

In an OFDM system, the input bit stream is multiplexed into N parallel symbol streams each with symbol period Ts using a serial to parallel convertor. Each of these parallel symbols is modulated with different sub-carriers which are placed 1/NTs apart in frequency. As the sub-carriers are 1/NTs apart, they are orthogonal over the interval (0, Ts)

The block diagram of a general OFDM system is given as figure 1. The serial to parallel port groups the input bit streams from the encoder into groups of log2M bits, where M is size of the digital modulation scheme for each of the carrier. Thus N such symbols - Xm are formed, which are mapped to bins of an inverse fast Fourier transform. These IFFT bins correspond to the orthogonal sub-carriers in the OFDM symbols [3]. Hence the OFDM symbol can be expressed as

xn = (1/N) Xm e (j2Ï€nm/N)

Encoder

S/P

IFFT

P/S

D/A

Channel

## +

A/D

S/P

FFT

P/S

Decoder

AWGN

Wn

XÌƒm

Ym

yn

Output Bit Stream

Input Bit Stream

Xm

xn

Baseband OFDM transceiver system

Here Xm 's are the baseband symbols on each sub-carrier. These are passed onto a D/A converter which would create an analog signal to be transmitted through the channel.

At the receiving end, the signal is converted back to digital N point sequence y(n) for each sub-carrier. This digital signal is demodulated using a N-point FFT. The demodulated signal is given as

Y(m) = y(n) e (-j2Ï€nm/N) + W(m)

Here W(m) is the FFT samples of w(n) which is the additive white Gaussian noise entering the channel.

OFDM Features:

OFDM is special case of parallel transmission system where high bit rate data is split into lower rate streams, each of this substream is modulated onto a separate subcarrier. Since OFDM signals are transmitted at low data rates simultaneously on a number of subcarriers, which means the symbol duration is more. Now since the symbols are not close to each other, there is lesser interference due to multipath delay spread.

A multipath distortion causes ISI in a single carrier or a narrow band signal but in an OFDM system, ISI is avoided by inserting cyclic prefix in every OFDM symbol. The period in which the cyclic prefix is inserted is called as the guard interval/guard time.

The cyclic prefix is actually a periodic extension of the end of the OFDM symbol which is added to the beginning of the symbol before being transmitted. This overload is then removed at the receiver before demodulation. (Mathematically the Cyclic Prefix / Guard Interval converts the linear convolution with the channel impulse response into a cyclic convolution. This results in a diagonalised channel, which is free of ISI and ICI interference. )

The advantage of cyclic prefix could be better understood in the figure 2a where there is no guard interval inserted and due to which the ISI occurs between two consecutive symbols. There is interference in symbol 2 from symbol 1 which could be due to the multipath delay, this result in signal distortion/loss. Whereas in figure 2b, a guard interval containing the cyclic prefix is inserted and the interference occurs during that time period which means there is no net loss of signal or information.

## Symbol 1

## Symbol 2

## Symbol 3

## Symbol 1

## Symbol 2

## Symbol 3

ISI from

symbol 1

ISI from

symbol 2

Figure 2a: OFDM transmission without cyclic prefix

## Symbol 3

## GI

## Symbol 2

## GI

## Symbol 1

## Symbol 3

## GI

## Symbol 2

## GI

## Symbol 1

ISI from

symbol 2

ISI from

symbol 1

Figure 2b: OFDM transmission with a cyclic prefix

But the cyclic prefix had some disadvantages, one of which is the wastage of the time period which is the reason for the loss in Signal to Noise ratio given as :

## )

1

## (

log

10

10

T

Tcp

SNR

loss

## ï€

## ï€

## ï€½

Here T is the total length of the transmitted signal and Tcp is the length of the cyclic prefix, hence there should be a limit for the length of the cyclic prefix.

But there are numerous studies carried out to utilize the ideal guard interval for other purposes like spectrum sensing [8] and [9].

For an OFDM system design, the parameters to be considered are [2]:

Number of subcarriers

Guard time

Symbol duration

Sub-carrier spacing

Modulation type per subcarrier

Type of forward error correction coding

The values of the above parameters depend on system requirements such as available bandwidth, required bit rate, tolerable delay spread.

Advantages of OFDM:

OFDM or parallel data transmissions/multiplexing were introduced for better usage of bandwidth and OFDM particularly hugely succeeds in doing so.

OFDM is more resistant to frequency selective fading than single carrier system as the channel is divided into narrow flat fading subchannels.

http://sna.csie.ndhu.edu.tw/~cnyang/MCCDMA/tsld021.htm

OFDM is a very efficient method to deal with multipath, the complexity for its implementation is much lesser than that for a single carrier system which needs an equaliser. [2]

For a slow time-varying channels, using OFDM we can enhance the capacity by adapting the data rate per sub-carrier according to the signal-to-noise ratio for that sub-carrier.

Disadvantages of OFDM;

OFDM is sensitive to frequency offset (which is studied in this paper)

OFDM has a large dynamic range or peak-to-average ratio and hence requires RF power amplifiers with a high peak to average ratio.

Applications of OFDM

One of the most revolutionary applications of OFDM is digital audio broadcasting (DAB). It was the first OFDM based standard, more about DAB is mentioned below

OFDM is widely used in ADSL where high bit rates are transmitted over twisted-pair copper wires.

OFDM is also used in terrestrial digital video broadcasting (DVB - T)

It is used in Wireless LAN Networks such as

HIPERLAN/2

IEEE 802.11a

IEEE 802.11g

// http://140.123.106.13/~wl/ofdm/pdfnew/Chapter%208%20OFDM%20Applications.pdf

Digital Audio Broadcast:

DAB is a replacement for the current analogue audio broadcasting based on AM and FM. DAB promises better sound quality, more number of stations, smaller portable receivers and also much higher spectrum efficiency. Another interesting feature of DAB is that it can carry text, images as well as sound. DAB was standardized in 1995 by ETSI and the first ever standard of OFDM [2].

The Wikipedia.org shows a brief comparison of the various mobile internet standards [6]. The important and commonly used standards are summarized below:

StandardÂ Â

FamilyÂ Â

Primary UseÂ Â

Radio TechÂ Â

Downlink (Mbit/s)Â Â

Uplink (Mbit/s)Â Â

NotesÂ Â

LTE

UMTS/4GSM

General 4G

OFDMA/MIMO/SC-FDMA

360

80

LTE-Advanced update to offer up to 1 Gbit/s fixed speeds.

WiMAX

802.16e

Mobile Internet

MIMO-SOFDMA

144

35

WiMAX update IEEE 802.16m to offer up to 1 Gbit/s fixed speeds.

Flash-OFDM

Flash-OFDM

Mobile Internet

mobility up to 200mph (350km/h)

Flash-OFDM

5.3

10.6

15.9

1.8

3.6

5.4

Mobile range 18miles (30km)

extended range 34 miles (55km)

HIPERMAN

HIPERMAN

Mobile Internet

OFDM

56.9

56.9

Wi-Fi

802.11

(11n)

MobileÂ Internet

OFDM/MIMO

288.9

(Supports 600Mbps@ 40MHz channel width)

Antenna, RF front end enhancements and minor protocol timer tweaks have helped deploy long range P2P networks compromising on radial coverage, throughput and/or spectra efficiency (310km & 382km).

iBurst

802.20

MobileÂ Internet

HC-SDMA/TDD/MIMO

95

36

Cell Radius: 3-12 km

Speed: 250kmph

Spectral Efficiency: 13 bits/s/Hz/cell

Spectrum Reuse Factor: "1"

EDGE Evolution

GSM

MobileÂ Internet

TDMA/FDD

1.9

0.9

3GPP Release 7

UMTS-TDD

UMTS/3GSM

Mobile Internet

CDMA/TDD

16

16

Reported speeds according to IPWireless using 16QAM modulation similar to HSDPA+HSUPA

EV-DOÂ 1xÂ Rev.Â 0

EV-DOÂ 1xÂ Rev.A

EV-DOÂ Rev.B

CDMA2000

Mobile Internet

CDMA/FDD

2.45

3.1

4.9xN

0.15

1.8

1.8xN

Rev B note: N is the number of 1.25 MHz chunks of spectrum used.

Study of OFDM systems with Carrier Frequency Offset (CFO)

This project will investigate the performance of OFDMA systems in the presence of carrier frequency offset.

A frequency offset can come from a number of sources; one of them is a Doppler shift or frequency mismatch in the modulator and the demodulator oscillators. Doppler effect arises when there is relative motion between transmitter and receiver. In this case, the frequency shift is given by

Î”f = fc

Here v is the relative velocity between transmitter and receiver, c is the speed of light, and fc is the carrier frequency. Generally Doppler shifts are negligible, for example, with a carrier frequency fc = 5 GHz and a velocity of 100 km/h, the offset value is Î”f = 1.6 kHz which is very much less significant compared to the carrier spacing of 312.5 kHz (Table 1)

The other source of frequency offset is due to frequency errors in the oscillators.

In an OFDM system, it is very important that the oscillator frequencies of all users and the base station be synchronous. Practically this requirement is very difficult to implement and hence there exist some frequency offset between multiple transceivers [4]. The IEEE 802.11a standard requires that the oscillators to have frequency errors within 20 ppm(parts per million). To compare with the effects of doppler shift, let us consider the same example for a carrier of 5 GHz, the maximum frequency error of

Î”fmax = 2Ã-20Ã-10-6Ã-5Ã-109 = 200 KHz

Here the factor of '2 'is to compensate for errors in both the transmitter and the receiver with opposite signs. This value of 200 KHz is large compared to the frequency carrier spacing of 312.5 KHz.

The frequency offset disturbs the orthogonality of the sub-carriers and eventually gives rise to lower SNR and ISI which affects the overall performance of the OFDM system. Thus a frequency offset reduces the signal amplitude and gives rise of inter carrier interference from neighbouring sub-carriers. Hence it is very important that we estimate error and compare their performances is affected and ideas to reduce/eliminate them.

## Frequency offset in Single carrier systems.

Single carrier modulation systems are less sensitive to frequency errors than OFDM systems. But single carrier systems are sensitive to timing offset errors whereas OFDM exhibits good performance in the presence of timing errors.

Estimation of Frequency Offset:

At the receiver of an OFDM system, it performs two synchronization tasks; firstly it checks for the symbol boundaries and the optimal timing instants so as to minimize both ISI and the ICI. Secondly, it tries to estimate and correct frequency errors. To overcome the effects of frequency offset such as loss of orthogonality, ISI and ICI it is important to have frequency synchronization [16]. Generally the synchronization process is divided into two phases acquisition and tracking. In the acquisition phase, a rough estimate of the frequency offset is obtained and corrected. The residual small deviations are then corrected in the tracking mode. Furthermore, conditions are not static in a real system, this causes small deviations in frequency offset that the tracking stage should estimate and correct. The synchronization stage can be either non-data-aided, when no extra information is included in the transmitted data, or data-aided, when they employ periodically transmitted training symbols and/or known pilot sub-carriers [17]. Here we implement acquisition by using a data aided algorithm which was introduced in [2] by P. H. Moose.

## Implementation and Experimental Results:

The implementation was carried out with reference to figure 3 shown below. This is extracted out from the basic OFDM transceiver system shown in figure 1.

S/P Converter

IFFT

P/S Converter

## Transmitter

Input

Noise

Frequency Offset

## Channel

## Receiver

S/P Converter

FFT

P/S Converter

## Algorithm:

## STEP1:

Define all the essential parameters

N=256;

K=96;

## STEP2:

Generate X{k}

Where X{k} is the modulated values, here 8PSK modulation is used. It is generated using direct Matlab command

## STEP3:

Simulate channel H(k)

The channel can be AWGN, Rayleigh or RIchian etc.

## STEP4:

Find the mean and variance of X(k) and H(k).

## STEP5:

Simulate the equation given below ([2], eq (4)).

Here H(k) is the transfer function of the channel at the frequency of k th sub-carrier

## Using the expression

Find the values of and form step 4 .

For a given value of , find the value of

## STEP6:

For each value of n, generate with variance obtained form

## STEP7:

Again use step 5 to obtain the new values of SNR for different values of .

## STEP8:

Plot (, SNR)

## Theoretical Plot

## Simulation Plot

## The curve is shifted by some 25 dB.

## This may be because of UNKNOWN channel characteristics. And in the relative frequency offset formula, the absolute frequency is known to us.

## With reference to the figure ,the loss of orthogonality causing ICI is shown in Figure 5. The areas, colored with yellow, show the ICI. When the centers of adjacent subcarriers are shifted because of the frequency offset, the adjacent subcarriers nulls are also shifted from the center of the other subcarrier. The received signal contains samples from this shifted subcarrier, leading to ICI [4].

Figure 5. Illustration of ICI (From Ref. 4. )

The destructive effects of the frequency offset can be corrected by estimating the frequency offset itself and applying proper correction. This calls for the development of a frequency synchronization algorithm. Due to the increasing importance of OFDM de-modulation in wireless and uncertain channels, a number of techniques have been devel-oped.

Typically, three types of algorithms are used for frequency synchronization: algo-rithms that use pilot tones for estimation (data-aided), algorithms that process the data at

10

the receiver (blind), and algorithms that use the cyclic prefix for estimation [5]. Among these algorithms, blind techniques are attractive because they do not waste bandwidth to transmit pilot tones [4]. However, they use less information at the expense of added complexity and degraded performance [4].

The CFO introduces an extra term Î´f to the received signal which is difficult to demodulate and cause high bit error rate. To compensate for this, there are a number of approaches discussed in [ ] to [ ]. [ ] and [ ] generates a symbol clock and a frequency offset estimate at the receiver by using pilot symbols. [ ] maximises the average log-likelihood function [ML Estimation of Time and Frequency Offset in OFDM Systems,Jan-Jaap van de Beek, Student Member, IEEE, Magnus Sandell, Student Member, IEEE,and Per Ola BÂ¨orjesson, Member, IEEE]

[2] By P.H. Moose was one of the first papers which studied the effects of frequency offset on the performance of OFDM communication systems. It concludes that in order to maintain signal to interference of 20 dB or more for the subcarriers in an OFDM then the frequency offset should be limited to not more than 4% of the intercarrier spacing. It also discusses a method to estimate the frequency offset by a data driven technique which is shown in this literature.

System Design:

According IEEE 802.11a specifications, the following are the values of the parameters we have used for the implementation of OFDM [7].

## Parameter

## Value

NSD : Number of data subcarriers

48

NSP : Number of pilot subcarriers

3

Size of FFT

64

NST : Total number of used subcarriers

52

Î”f : Subcarrier spacing

.3125 MHz (20 MHz/64)

TFFT : FFT/IFFT period

3.2 Î¼s (1/.3125)

TGI Guard Interval duration

.8 Î¼s (TFFT /4)

TSYM :Total symbol duration

4 Î¼s (TGI + TFFT )

Used subcarrier index

{ -26 to -1, +1 to +26 }

The relation between Symbol energy and bit energy is gives as:

In this section, we study the degradation that frequency offset can cause to the SNR of an OFDM system.

Plots :

Relation between estimated frequency offset and the frequency offset.