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OFDM AND OFDM CHANNEL

ESTIMATION

Abhishek Gupta (06102298)

Supervised By: Mr. Ashish Goel

May - 2010

Submitted in partial fulfillment of the Degree of

Bachelor of Technology

DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING

JAYPEE INSTITUTE OF INFORMATION TECHNOLOGY UNIVERSITY,

NOIDA
http://www.jiit.ac.in/jiit/index.htm

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CHAPTER 1

Probability Distributions

1.1 Weibull distribution

In probability theory and statistics, the Weibull distribution [1] is a continuous

probability distribution. The probability density function of a Weibull random variable x

is:

where k> 0 is theshape parameterand > 0 is thescale parameterof the distribution.Its complementary cumulative distribution function is a stretched exponential function.

The Weibull distribution is related to a number of other probability distributions; in

particular, it interpolates between the exponential distribution (k= 1) .

Fig 1.1,Weibull probability distribution function

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1.2 Normal Distribution

In probability theory and statistics, the normal distribution [2] orGaussiandistribution is a continuous probability distribution that often gives a good description of

data that cluster around the mean. The graph of the associated probability density

function is bell-shaped, with a peak at the mean, and is known as the Gaussian function

orbell curve. Probablity distribution of Normal distribution of random variable x whose

mean is and variance is given by:

Fig 1.2,Normal probability distribution function

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1.3 Gamma Distribution

In probability theory and statistics, the gamma distribution [3] is a two-parameter

family of continuous probability distributions. It has a scale parameter and a shape

parameter k. The gamma distribution is frequently a probability model for waiting times;

for instance, in life testing, the waiting time until death is a random variable that is

frequently modeled with a gamma distribution. The probability density function of the

gamma distribution can be expressed in terms of the gamma function parameterized in

terms of a shape parameterkand scale parameter. Both kand will be positive values.

The equation defining the probability density function of a gamma-distributed random

variablex is

i If is a positive integer, then

Fig 1.3, Gamma Probability Distribution Function

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4 Exponential Distribution

In probability theory and statistics, the exponential distributions [4] are a class of

continuous probability distributions. They describe the times between events in a Poisson

process, i.e. a process in which events occur continuously and independently at a constant

average rate. Probability distribution for random variable x is given by:

Here > 0 is the parameter of the distribution, often called the rate parameter.

Fig 1.4, Exponential probability distribution function

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1.5 Rayleigh Distribution

In probability theory and statistics, the Rayleigh distribution [5] is a continuous

probability distribution. As an example of how it arises, the wind speed will have a

Rayleigh distribution if the components of the two-dimensional wind velocity vector are

uncorrelated and normally distributed with equal variance. The distribution is named after

Lord Rayleigh.The Rayleigh probability density function is

Fig 1.5,Rayleigh Probability Distribution Function

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.6 Rician Distribution

probability theory and statistics, the Rice distribution orRician distribution [6],In

named after Stephen O. Rice, is a continuous probability distribution.

The probability density function is

Fig 1.6, Probability Distribution function

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CHAPTER 2

Orthogonal Frequency Division Multiplexing

.1 OFDM Definition-division multiplexing (OFDM) is a frequency-division

g parallel data transmission by means of frequency division

2

Orthogonal frequency

multiplexing (FDM) scheme utilized as a digital multi-carrier modulation method. A

large number of closely-spaced orthogonal sub-carriers are used to carry data. The data is

divided into several parallel data streams or channels, one for each sub-carrier. Each sub-

carrier is modulated with a conventional modulation scheme (such as quadrature

amplitude modulation or phase shift keying) at a low symbol rate, maintaining total data

rates similar to conventionalsingle-carriermodulation schemes in the same bandwidth.

2.2 OFDM History

The concept of usin

multiplexing (FDM) was published in mid 60s. Some early development can be traced

back in the 50s. A U.S. patent was filled and issued in January, 1970. The idea was to use

parallel data streams and FDM with overlapping subchannels to avoid the use of high

speed equalization and to combat impulsive noise, and multipath distortion as well as to

fully use the available bandwidth. The initial applications were in the military

communications. In the telecommunications field, the terms of discrete multi-tone

(DMT), multichannel modulation and multicarrier modulation (MCM) are widely used

and sometimes they are interchangeable with OFDM. In OFDM, each carrier is

orthogonal to all other carriers. However, this condition is not always maintained in

MCM. OFDM is an optimal version of multicarrier transmission schemes.

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2.3 ORTHOGONALITY

carriers means that each carrier has an integer number ofThe orthogonality [9] of the

cycles over a symbol period. Due to this, the spectrum of each carrier has a null at the

centre frequency of each of the other carriers in the system. This results in no interference

between the carriers, allowing them to be spaced as close as theoretically possible. This

overcomes the problem of overhead carrier spacing required in FDMA. Each carrier in

an OFDM signal has a very narrow bandwidth (i.e. 1 kHz), thus the resulting symbol rate

is low. This results in the signal having a high tolerance to multipath delay spread, as the

delay spread must be very long to cause significant inter-symbol interference (e.g. > 100

ms).

Fig 2.1,Frequency Response Of OFDM transmitted signal

.4 Why We Need OFDM ?

o transmit all

worse as the channel bandwidth becomes narrower, and the frequency band increases.

2

In FDMA each user is typically allocated a single channel, which is used t

the user information. The bandwidth of each channel is typically 10kHz-30kHz for voice

communications. However, the minimum required bandwidth for speech is only 3kHz.

The allocated bandwidth is made wider then the minimum amount required to prevent

channels from interfering with one another. This extra bandwidth is to allow for signals

from neighboring channels to be filtered out, and to allow for any drift in the centre

frequency of the transmitter or receiver. In a typical system up to 50% of the total

spectrum is wasted due to the extra spacing between channels. This problem becomes

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TDMA partly overcomes this problem by

sed by several users. Multiple users access the same channel by transmitting in their

nge over between users due totime slotting on the channel. A change over

annels (typically 100-8000). The carriers

using wider bandwidth channels, which are

u

data in time slots. Thus, many low data rate users can be combined together to transmit in

a single channel that has a bandwidth sufficient so that the spectrum can be used

efficiently.

There are however, two main problems with TDMA. There is an overhead associated

with the cha

time must be allocated to allow for any tolerance in the start time of each user,due to

propagation delay variations and synchronization errors. This limits the number of usersthat can be sent efficiently in each channel. In addition, the symbol rate of each channel is

high (as the channel handles the information from multiple users) resulting in problems

with multipath delay spread.

OFDM overcomes most of the problems with both FDMA and TDMA. OFDM splits the

available bandwidth into many narrow band ch

for each channel are made orthogonal to one another, allowing them to be spaced very

close together, with no overhead as in the FDMA example. Because of this there is no

great need for users to be time multiplex as in TDMA, thus there is no overhead

associated with switching between users.

2.4.1Comparison Of Bandwidth Of FDM and OFDM

Fig2.2 [11]

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2.5 OFDM Model Used

Fig2.3,OFDM Communication Block

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OFDM model comprises of following parts-:

1) OFDM transmitter

2) Channel

3) OFDM Receiver

2.5.1 OFDM transmitter: The transmitter section converts digital data to be

transmitted, into a mapping of subcarrier amplitude and phase. It then transforms this

spectral representation of the data into the time domain using an Inverse Discrete Fourier

Transform (IDFT). It comprises of following blocks-:

1) Serial to Parallel converter-:As our channel is divided in into various sub channel

and data to be transferred is loaded on these channel so we required to convert our serial

data into parallel streams one for each sub channel.

2) Differential modulation-: Once each subcarrier has been allocated bits for

transmission, they are mapped using a modulation scheme to a subcarrier amplitude and

phase, which is represented by complex In-phase and Quadrature-phase (IQ) vector.

3) Inverse Fourier transform An IFFT is required to convert data into time domain as

physical signal you transmit must be in the tim

broken up into N subcarriers,

te that is Nc times lower than the single carrier transmission. This

rate makes OFDM naturally resistant to effects of Inter-Symbol Interference

ltipath propagation. Multipath propagation is caused by the radio

ansmission signal reflecting off objects in the propagation environment, such as walls,

g

tly different times, changing the

received subcarrier vector. Adding a guard period allows time for the transient part of the

-:

e domain.

4) Guard Band-: In OFDM the system bandwidth is

resulting in symbol ra

low symbol

(ISI) caused by mu

tr

buildin s, mountains, etc. These multiple signals arrive at the receive at different times

due to the transmission distances being different. In multipath environments ISI causes

spreading of the energy between the symbols, resulting in transient changes in the

amplitude and phase of the subcarrier at the start of the symbol. The transient signal is a

result of each multipath component arriving at sligh

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signal to decay, so that the FFT is taken from a steady state portion of the symbol. This

eliminates the effect of ISI.

Mathematical Equations

Transmitted data:

OFDM symbol starting at t= can be written as-:

=Number of subcarrier

T=symbol duration

=Complex Modulated Symbol

=Carrier frequency

Generation of time domain signal using IFFT:

The IFFT of transmitted signal is given by:

2.5.2 OFDM Channel-:A channel model is then applied to the transmitted signal. Themod , and peak power clipping to be

controlled. The signal to noise ratio is set by adding a known amount of white noise to

the transmitted signal. Multipath delay spread then added by simulating the delay spread

using an FIR filter. The length of the FIR filter represents the maximum delay spread,

while the coefficient amplitude represents the reflected signal

el allows for the signal to noise ratio, multipath

magnitude.

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ally does the reverse operation to the

oved. The FFT of each symbol is then taken to find

le of each transmission carrier is then

eval y demodulating the received phase. The

data words are then combined back to the same word size as the original data.

2.5.3 OFDM Receiver-: The receiver basic

transmitter. The guard period is rem

the original transmitted spectrum. The phase ang

uated and converted back to the data word b

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CHAPTER 3

FADING

.1 FADING

wireless communications, fading[13] is deviation of the attenuation that a carrier-

unication signal experiences over certain propagation media. The

ding may vary with time, geographical position and/or radio frequency, and is often

odeled as a random process.

fading channel is a communication channel that experiences fading. In wireless

s, fading may either be due to multipath propagation, referred to as multipath

duced fading, or due to shadowing from obstacles affecting the wave propagation,

metimes referred to as shadow fading.

ENT

adio waves propagate from a transmitting antenna and travel through free space

ndergoing absorption, reflection, refraction, diffraction, and scattering. They are greatly

affected by the ground terrain, the atmosphere, and the objects in their path, such as

buildings, bridges, hills, and trees. These multiple physical phenomena are responsible

for most of the characteristic features of the received signal. In most of the mobile or

cellular systems, the height of the mobile antenna may be smaller th

structures. Thus, the existence of a e-of-sight (LOS) path between the

transmitter and the receiver is highly unlik se, propagation comes from

reflection and scattering from the buildings and diffraction over or around them. Thus, in

practice, the transmitted signal arrives at the receiver via several paths, with different

ting a multipath situation.

3

In

modulated telecomm

fa

m

A

system

in

so

3.2 FADING IN A WIRELESS ENVIRONM

R

u

an the surrounding

direct or lin

ely. In such a ca

time delays crea

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FADING

Fig 3.1, Multipath Propogation [13]

At the receiver, these multipath waves with randomly distributed amplitudes and phases

combine to give a resultant signal that fluctuates in time and space. Therefore, a receiver

at one location may have a signal that is much different from the signal at another

location only a short distance away because of the change in the phase relationship

among the incoming radio waves. This situation causes significant fluctuations in

the signal amplitude. This phenomenon of random fluctuations in the received signal

vel is termed asfading.

Whereas the short-term fluctuation in the signal amplitude caused by the local multipath

is called small-scale fading[13], and is observed over distances of about half a

wavelength, long-term variation in the mean signal level is called large-scale fa

The latter effect is a result of movement over distances large enough to cause gross

variations in the overall path between the transmitter and the receiver. Large-scale fading

is also known asshadowingbecause these variations in the mean signal level

are caused by the mobile unit moving into the shadow of surrounding objects, such as

buildings and hills. Because of multipath, a moving receiver can experience several fades

in a very short duration. In a more serious case, the vehicle may stop at a location where

le

ding.

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FADING

the signal is in deep fade; in such a situation, maintaining good communication becomes

an issue of great concern.

Small-scale fading can be further classified as flat or frequency selective, and slow or

fast. A received signal is said to undergo flat fadingif the mobile radio channel has a

constant gain and a linear phase response over a bandwidth larger than the bandwidth of

the transmitted signal. Under these conditions, the received signal has amplitude

fluctuations as a result of the variations in the channel gain over time caused by

multipath. However, the sp ed signal remain intact at

the receiver. If the mobile radio channel ha a constant gain and linear phase response

ference

tion between the transmitter and the receiver, Doppler spread is

troduced in the received signal spectrum, causing frequency dispersion. If the Doppler

idth

ectral characteristics of the transmitt

s

over a bandwidth smaller than that of the transmitted signal, the transmitted signal

is said to undergofrequency selective fading. In this case, the received signal is distorted

and dispersed because it consists of multiple versions of the transmitted signal, attenuated

and delayed in time. The result is time dispersion of the transmitted symbols within the

channel arising from these different time delays bringing about intersymbol inter

(ISI) [13].

When there is relative mo

in

spread is significant relative to the bandwidth of the transmitted signal, the received

signal is said to undergo fast fading. This form of fading typically occurs for very low

data rates. However, if the Doppler spread of the channel is much less than the bandw

of the baseband signal, the signal is said to undergoslow fading. The work reported here

will be confined to flat fading.

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FADING

3.3 Fading basic terms

3.3.1 Doppler spread

When a user (or reflectors in its environment) is moving, the users velocity causes a shift

in the frequency of the signal transmitted along each signal path. This phenomenon is

known as the Doppler shift. Signals travelling along different paths can have different

Doppler shifts, corresponding to different rates of change in phase. The difference in

Doppler shifts between different signal components contributing to a single fading

he channel to become uncorrelated from its previous value.

ignal changes. The coherence time is a measure of the

inimum time required for the magnitude change of the channel to become uncorrelated

om its previous value.

Slow fading arises when the coherence time of the channel is large relative to thedelay constraint of the channel. In this regime, the amplitude and phase change

imposed by the channel can be considered roughly constant over the period of

channel tap is known as the Doppler spread[13]. Channels with a large Doppler spread

have signal components that are each changing independently in phase over time.

3.3.2 Coherence Time

The coherence time [13] is a measure of the minimum time required for the magnitude

change of t

3.3.3 Coherence bandwidth

As the carrier frequency of a signal is varied, the magnitude of the change in amplitude

will vary. The coherence bandwidth [13] measures the separation in frequency after

which two signals will experience uncorrelated fading.3.4 Slow versus fast fading

The termsslow andfastfading refer to the rate at which the magnitude and phase change

imposed by the channel on the s

m

fr

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FADING

shadowing, where a large

e

e.

ovide robustness to fading. OFDM divides the wideband signal

into many slowly modulated narrowband subcarriers, each exposed to flat fading rather

than re

3.6 Fad

Rayleigh fading Rician fading Nakagami fading Weibull fading

use. Slow fading can be caused by events such as

obstruction such as a hill or large building obscures the main signal path between

the transmitter and the receiver..

Fast fading occurs when the coherence time of the channel is small relative to thedelay constraint of the channel. In this regime, the amplitude and phase change

imposed by the channel varies considerably over the period of use.

3.5 Flat versus frequency-selective fading

In flat fading [13], the coherence bandwidth of the channel is larger than the bandwidthof the signal. Therefore, all frequency components of the signal will experience the sam

magnitude of fading.

In frequency-selective fading, the coherence bandwidth of the channel is smallerthan the bandwidth of the signal. Different frequency components of the signal

therefore experience decorrelated fading

Since different frequency components of the signal are affected independently, it ishighly unlikely that all parts of the signal will be simultaneously affected by a deep fad

Certain modulation schemes such as OFDM and CDMA are well-suited to employing

frequency diversity to pr

f quency selective fading

ing model

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FADING

3.6. R

The m

number s, the phases

es a random

variable. In the case of an unmodulated carrier, the transmitted signal at frequency wc

1 ayleigh Fading

obile antenna, instead of receiving the signal over one LOS path, receives a

of reflected and scattered waves. Because of the varying path length

are random and, consequently, the instantaneous received power becom

reaches the receiver via a number of paths, the Ith path having an amplitude a i and a

phase i. If it is assumed that there is no direct path or LOS component, the received

signal s(t) can be expressed as

where N is the number of paths. The phase depends on the varying path lengths,

changing by when the path length changes by a wavelength. Therefore, the phases are

uniformly distributed over [0,2 ].When there is relative motion between the transmitter

and the receiver, Eq must be modified to include the effects of motion-induced frequency

and phase shifts. The ith reflected wave with amplitude and phase arrive at the receiver

from an angle relative to the direction of motion of the antenna. The Doppler shift of this

wave is given by

Where v is the velocity of the mobile, c is the speed of light (3 *10 m/s),and is are

niformly distributed over[ 0,2]. The received signal can now be written as:u

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FADING

Expressing the signal in in phase and quadrature form:

Where the in phase and quadrature components are respectively given as

3.6.2 Rician Fading

The Rician distribution [13] is observed when, in addition to the multipath components,

there exists a direct path between the transmitter and the receiver.

In the presence of such a path, the transmitted signal can be written as

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CHAPTER 4

CHANNEL ESTIMATION TECHNIQUES

The method of least squares [7] is a standard approach to the approximate solution of

ver determined systems, i.e. sets of equations in which there are more equations than

the sum of the

squares of the errors made in solving every single equation.

The least-squares line uses a straight line

oximate the given set of data (

4.1 Least Square Technique

o

unknowns. "Least squares" means that the overall solution minimizes

y=a+bx

to appr ), ),., where . The best

fitting curve f(x) has the least square error, i.e.,

Please note that a and b are unknown coefficients while all and are given. To obtain

the least square error, the unknown coefficients a and b must yield zero first derivatives.

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Expanding the above equations, we have:

The unknown coefficients a and b can therefore be obtained:

stands for .

Fig 4.1,Least square technique [7]

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4.2 Mean Square Technique

In statistics, the mean square error or MSE [8] of an estimator is one of many ways toquantify the difference between an estimator and the true value of the quantity being

estimated. MSE measures the average of the square of the "error." The error is the

amount by which the estimator differs from the quantity to be estimated. The difference

occurs because of randomness or because the estimator doesn't account for information

The MSE of an estimator with respect to the estimated parameter is defined

that could produce a more accurate estimate.

The MSE is equal to the sum of the variance and the squared bias of the estimator

The MSE thus assesses the quality of an estimator in terms of its variation and

4.3 Minimum mean square technique

In statistics and signal processing, a minimum mean square error (MMSE) estimator

describes the approach which minimizes the mean square error (MSE), which is a

common measure of estimator quality.

MSE =E[(X - c)]

the value ofc that will minimize the MSE.

c=E[x]

is the choice that minimizes the MSE. The MSE is then called the Minimum Mean

Square Error (MMSE) and is clearly equal to the variance ofX.

unbiasedness

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ata

e of

nd the

e

4.4.1 Linear Interpolation

Linear interpolation is a simple technique used to estimate unknown values that lie

between known values. The concept of linear interpolation relies on the assumption that

the rate of change between the known values is constant and can be calculated from

he two

known points can be calculated using one of the points and the rate of change.

Generally, linear interpolation takes two data points, say (

4.4 Interpolation Techniques

Interpolation is the process of using known data values to estimate unknown d

values. Various interpolation techniques are often used in channel estimation . On

the simplest methods, linear interpolation, requires knowledge of two points a

constant rate of change between them. With this information, you may interpolat

values anywhere between those two points.

these values using a simple slope formula. Then, an unknown value between t

, ) and ( ), and the

interpolant is given by:

at the point (x,y)

Linear interpolation is quick and easy, but it is not very precise.

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CHAPTER 5

OFDM CHANNEL ESTIMATION

5.1

A ency selective and time variant.For anOFDM mobile communication system, the channel transfer function at different

in both frequency and time domains. Therefore, a dynamic

is necessary. Pilot-based approaches are widely used toestimate the channel properties and correct the received signal. In this chapterwe have

i


wideband radio channel is normally frequ

subcarriers appears unequal

estimation of the channel

nvestigated two types of pilot arrangements.

Fig5.1,Block type pilot arrangement Fig5.2,Comb type pilot arrangement

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OFDM CHANN

The first kind of pilot arrangement shown in Figure 5.1 is denoted as block-type

pilot arrangement. The pilot signal assigned to a particular OFDM block, which is sent

periodically in time-domain. This type of pilot arrangement is especially suitable forslow-fading radio channels. Because the aining block contains all pilots, channel

ot required. Therefore, this type of pilot

rrangement shown in Figure 5.2 is denoted as comb-type pilot arrangement. The pilot

lock-type pilot arrangement system.

.2 CHANNEL ESTIMATION BASED ON BLOCK-TYPE PILOT

RRANGEMENT

block-type pilot-based [15] channel estimation, as shown in Figure 5.1, OFDM channel

estimation symbols are transmitted periodically, and all subcarriers are used as pilots. The task

here is to estimate the channel conditions (specified by

EL ESTIMATION

tr

interpolation in frequency domain is narrangement is relatively insensitive to frequency selectivity. The second kind of pilot

a

arrangements are uniformly distributed within each OFDM block. Assuming that the

payloads of pilot arrangements are the same, the comb-type pilot arrangement has ahigher re-transmission rate. Thus the comb-type pilot arrangement system is provides

better resistance to fast-fading channels. Since only some sub-carriers contain the pilot

signal, the channel response of non-pilot sub-carriers will be estimated by interpolatingneighboring pilot sub-channels. Thus the comb-type pilot arrangement is sensitive to

requency selectivity when comparing to the bf

5

A

In

or ) given the pilot signals (specified

by vector ) and received signals (specified by ), with or without using certain knowledge of

the channel statistics. The receiver uses the estimated channel conditions to decode the received

data inside the block until the next pilot symbol arrives. The estimation can be based on least

square (LS), minimum mean-square error (MMSE), and modified MMSE.

If inter symbol interference is eliminated by the guard interval, we write in matrix notation:

Y=XFh+ W

= XH +W

Where,

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5.2.1 Least Square Error (LSE) Estimation

We have to minimize

For minimization of J we have to differentiate J with respect to H

Where H = Transfer Function

5.2.2Minimum Mean Square Error (MMSE) Estimation

MSE (mean square error) is expresses as

Frequency domain estimate of H is given by

Time domain estimate of h is given by

\

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5.3 CHANNEL ESTIMATION BASED ON COMB-TYPE PILOT

ARRANGEMENT

ormly inserted

into X(k) according to following equation:

L = number of carriers/Np

xp(m) is the mthpilot carrier value

e define {Hp(k) k = 0, 1, . . . Np} as the frequency response of the channel atpilot sub-carriers. The estimate of the channel at pilot sub-carriers based on LS

estimationis given

In comb-type[16] based channel estimation, the Np pilot signals are unif

W

by:

Yp(k) andXp(k) are output and input at the kthpilot sub-carrier respectively. Since LS estimate is

susceptible to noise and ICI, MMSE is proposed while compromising complexity. Since MMSE

includes the matrix inversion in each iteration, the simplified linear MMSE estimator is suggestedin which the inverse is only needed to be calculated once.

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Simulation Results

.1 OFDM simulation results

odulation

pared with the transmitted bits and BER curve was obtained.

CHAPTER 6

6

Number of Symbols taken =10000

IFFT =1024 point

Modulation Scheme : Differential M

SNR was varied from 1 db to 12 db.The model followed is shown in figure 2.3 chapter 2

Received bits were com

Fig 6.1, OFDM Transmitted data

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Simulation Results

Fig6.2,OFDM Received data in Polar Form

Fig6.3, Bit error rate plot

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Simulation Results

6.2 Fading Model Simulation Results

The Mathematical equations followed for implementation are mentioned in chapter 3under heading 3.6.1.

Two cases were considered .

1) Stationary Mobile2) Mobile moving at a speed of 25 m/sec. In this case Doppler effect will

come into consideration

For both the cases the carrier frequency was taken to be 900 MHz and thenumber of paths were varied from 4 to 40.

Fig 6.4, Rf Signal for stationary mobile in Rayleigh Fading model

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Simulation Results

Fig 6.5 RF Signals for mobile moving at velocity 25 m/sec in Rayleigh Fading Model

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Simulation Results

6.3 LS Technique Implementation

Least Square Technique was implemented. Four random data points were taken and aequation of line was generated such that the sum of squares of error of these data points

from the line is least.

Title : plot of LS technique

Fig 6.6,LS technique implementation

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Simulation Results

6.4 OFDM channel estimation using LS estimation technique

as calculated as shown below.

Number of Subcarriers : 64umber of iteration per SNR :200N

Procedure for LS EstimationA channel was assumed and channel matrix was generated.

Modulation Scheme used is BPSK.

or LS estimation H wF

Expected Transmitted data were calculated using

X(expected)= Inv(H) * Y

Where Y was Received data

This X(Expected) was compared with Generated data that was transmitted and a plot of

Symbol Error Rate Vs Signal to Noise Ratio was obtained

Fig 6.7

.5 OFDM Channel Estimation using MMSE Technique

or MMSE Technique the transfer function was calculated using the formula

,Plot of SER vs SNR for LS estimation

6

F

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Simulation Results

trix of Y

Expected Transmitted data were calculated usingX(expected)= Inv(H) * Y

here Y was Received dataata that was transmitted and a plot of

nal to Noise Ratio was obtained

Where R = Auto-covariance mayyY = Received Data matrix

R = Cross- Covariance matrix between h and YhYh = Impulse response of the channel

WThis X(Expected) was compared with Generated d

Symbol Error Rate Vs Sig

Fig 6.8,Plot of SER VS SNR for MMSE estimation technique

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Simulation Results

6.6 Comparison of LS and MMSE Technique

s compared for LS technique and MMSE

e.

than MMSE.

Signal Error Rate Vs Signal to Noise Ratio wa

technique.MMSE Techniques was found to be better than LS techniqu

ue was moreFor a given SNR Value of SER for LS techniq

Fig 6.9,Comaprison of SER vs SNR plot for LS and MMSE

36

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Conclusion

FDM Model was implemented and Various Fading Models were Studied. Bit Error rate

gh Model was implemented with

SE technique were

he techniques

nd it was found that the MMSE technique is better than LS techniqueS Estimation technique is susceptible to noise and inter carrier interference, so MMSE

proposed while compromising complexity since MMSE includes Matrix Inversion at

ach iteration.

O

plot was studied for OFDM Model.

ffect of Fading on signal was studied and RayleiEDoppler spread and without Doppler spread.

Channel Implementation was studied and LS technique and MMimplemented.

ignal Error Rate Vs SNR plot was implemented and compared for both tS

aL

is

e

37

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Appendix

Equations used

1

OFDM1.1Transmitted data:

OFDM symbol starting at t= can be written as-:

=Number of subcarrier

T=symbol duration

=Complex Modulated Sym

bol

=Carrier frequency

1.2Generation of time domain signal using IFFT:The IFFT of transmitted signal is given by:

2 Channel Estimation2.1Channel estimation Using LS technique

Transfer Function for channel is given by-:

Where

X=Transmitted data matrix

Y=Received data matrix

38

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Appendix

ation using MMSE technique

Transfer Function for channel is given by-:2.2 Channel estim

Where RhY =Cross -Covariance matrix of G(impulse response of channel)

RYY= Auto-covariance matrix of g

Y=Received data matrix

39

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REFERENCES

on

[2] on

[3] n.wikipedia.org/wiki/Gamma_distribution

[4] .wikipedia.org/wiki/Exponential_distribution

[5] ipedia.org/wiki/Rayleigh_dis ution

[6] n.wikipedia.org/wiki/Rician_distribution[7]

[8] n_squares

[9] Savo Glisic Advanced Wireless Communications 4G Technologies , John Wiley &

Sons Ltd , 2004[10] K.Fazel and S. Kaiser Multi-Carrier and Spread Spectrum Systems , John Wiley

& Sons Ltd , 2003

[11] Henrik Schulze and Christian Luders Theory and Applications of OFDM and

CDMA wideband wireless communications , John Wiley & Sons Ltd , 2005

[12] Ramjee Prasad Ofdm for wireless communication systems , Artech House, Inc.

Boston London,2004

[13] Gayatri S. Prabhu and P. Mohana Shankar Senior Member, IEEE , Simulation of Flat

Fading Using MATLAB ,IEEE TRANSACTIONS ON EDUCATION, VOL. 45, NO.

1, FEBRUARY 2002

[14] MEHMET KEMAL OZDEMIR, LOGUS BROADBAND WIRELESS

SOLUTIONS, INC. AND HUSEYIN ARSLAN, Channel Estimation For Wireless

OFDM Systems,IEEE Communications Surveys ,2ND QUARTER 2007, VOLUME 9,

NO. 2.

[15] Seongwook Songand and Andrew C.Singer, Pilot Aided OFDM Channel

Estimation in Presence of the Guard Band IEEE TRANSACTIONS ON

OMMUNICATIONS, VOL. 55, NO. 8, AUGUST 2007

6] Athina Petropulu , Ruifeng Zhang, Member, IEEE, and Rui Lin Blind OFDM

Channel Estimation through Simple Linear Processing , IEEE TRANSACTIONS ON

WIRELESS COMMUNICATIONS, VOL. 3, NO. 2, MARCH 2004

[1] http://en.wikipedia.org/wiki/Weibull_distributi

http://en.wikipedia.org/wiki/Normal_distributi

http://e

http://en

http://en.wik trib

http://e

http://en.wikipedia.org/wiki/Least_squares

http://en.wikipedia.org/wiki/Mea

,

C

[1

40

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[17]AleksandarJeremic,TimothyA.T EE,andAryeNehorai,Fellow,IEEE,

OFDM Channel Estimation in presence of Interference ,IEEE TRANSACTIONS ON

ER 2004

ember, IEEE, and Georgios B.

ier Block Transmissions, IEEE

NO. 3, MARCH 2004

homas,Member,IE

SIGNAL PROCESSING, VOL. 52, NO. 12, DECEMB

[18] Zhengdao Wang, Member, IEEE, Xiaoli Ma, M

Giannakis, Fellow, IEEE OFDM or Single-Carr

TRANSACTIONS ON COMMUNICATIONS, VOL. 52,

41

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i

TABLE OF CONTENTS

Topic Page No.

Certificate from the supervisor III

Acknowledgement IV

Summary V

List of Figures VI

Abstract VIII

Chapter 1 Probability distribution

1.1 Weibull Distribution 1

1.2 Normal Distribution 2

1.3 Gamma Distribution 3

1.3 Exponential Distribution 4

1.4 Rayleign Distribution 5

1.5 Rician Distribution 6

Chapter 2 OFDM

2.1 OFDM Definition 7

2.2 OFDM History 7

2.3 Orthogonality 8

2.4 Why we need OFDM 8

2.4.1 Comparison of bandwidth of OFDM and FDM 9

2.5 OFDM Model Used 10

2.5.1 OFDM Transmitter 11

2.5.2 OFDM Receiver 13

2.5.3 OFDM Channel 13

Chapter 3 Fading

3.1 Fading definition 14

3.2 Fading in wireless environment 14

3.3 Fading Basic Terms 16

3.3.1 Doppler spread 16

3..3.2 Coherence Time 17

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3

cy Selective Fading

g

.2 20

hapter 4 chniques

2

Technique

4.4

4.4.1 e 24

onChapter 5

5.2 timation based on block type 26

on

5.3 timation based on comb type 27

hapter 6

ults

ethod

6.6 f LS and MMSE Technique

Resume

40

3..3. Coherence Bandwidth 17

3.4 Slow vs Fast Fading 17

3.5 Flat vs Frequen 18

3.6 Fading Model 18

3.6.1 Rayleigh Fadin 18

3.6 Rician Fading

C Channel Estimation Te

4.1 Least Square Technique 21

4.2 Mean Square Technique 3

4.3 Minimum Mean Square 23

Interpolation Technique 24

Linear Interpolation Techniqu

OFDM Channel Estimati

5.1 OFDM channel estimation

OFDM channel es

25

pilot arrangement

5.2.1 Least Square Error (LSE) Estimation 27

5.2.2 Minimum Mean Square Error (MMSE) Estimati 27

OFDM channel es

pilot arrangement

C Simulation Results

6.1 OFDM simulation result 29

6.2 Fading Model Simulation Res 31

6.3 Ls Technique Implementation 336.4 OFDM Channel Estimation using lS method 34

6.5 OFDM Channel Estimation using MMSE m 34

Comparison o 36

Conclusion 37

Appendix 38

Reference

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CERTIFICATE

ersity, Noida has been carried out

under my supervision. This work has not been submitted partially or wholly to any other University

r Institute for the award of this or any other degree or diploma.

o ______

enior Lecturer, Department of ECE

Date :

This is to certify that the work titled OFDM And OFDM Channel Estimation submitted by

Abhishek Gupta (06102298) in partial fulfillment for the award of degree of Bachelor of

Technology of Jaypee Institute of Information Technology Univ

o

Signature of Supervis r : ______________

Name of Supervisor : Mr.Ashish Goel

Designation : S

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ACKNOWLEDGEMENT

e not only showed us the right direction but also tried to provide us with all the

necessary resources. We are highly grateful for all the time and effort he has put in for discussions

nd reviews.

k Gupta (6102298)

ate:

I would like to express our gratitude towards our project supervisor Mr. Ashish Goel,

Senior lecturer, Department of ECE for his ideas, encouragement and guidance in all phases of

our project .H

a

_____________________

Abhish

D

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SUMMARY

6 (WiMAX)

and as the core technique for the fourth-generation (4G) wireless mobile communications. with high

The Project OFDM And OFDM Channel Estimation helped in learning about OFDM and its

The Bit Error Rate curve was simulated and attempt was made to send the bits with minimum error

parameter. A procedure was studied and simulated to see

the effect of channel on transmitted data.. The channel have some effect on the transmitted data and

n attempt was made to study that effect.

he simulation were done in Matlab and results were studied.

_____________________ ___________________

ment of ECE

OFDM is becoming widely applied in wireless communications systems due to its high rate

transmission capability.It has been used in digital audio broadcasting (DAB) systems, digital videobroadcasting (DVB) systems, digital subscriber line (DSL) standards, and wireless LAN standards

such as the American IEEE Std. 802.11 (WiFi) and its European equivalent HIPRLAN/2. It has

also been proposed for wireless broadband access standards such as IEEE Std. 802.1

bandwidth efficiency and its robustness with regard to multi-path fading and delay .

importance in forthcoming Technologies.

from transmitter to receiver.

Channel Estimation is another important

a

T

Abhishek Gupta (0612298) Mr Ashish Goel,

Date: Senior Lecturer,

Depart

Date:

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Figure No. Page No.

Chapte

Fig. 3.1 Plot of Weibull distribution 1Fig 1.3

ion

ig 1.6 ayleigh distribution

Chapter 2

transmitted signal

Fig. 2.2 dwidth comparison

Fig. 2.3

h propogation 12

smitted signal

F

mation technique

Chapter 5

Fig 5.1 Block type pilot arrangement 25

Fig 5.2 ngement 25

Chapter 6 Simulation results

Topic

r 1 Probability distribution

Plot of Normal distributionn 2

Fig 1.4 Plot of Gamma distribution. 3

Fig 1.5 Plot of exponential distribut 4

F Plot of R 5

Fig 1.8 Plot of Recian distribution 6

OFDM

Fig. 2.1 Frequency Response Of OFDM 8

OFDM and FDM ban 9

OFDM Communication Block 10

Multipat

Effect of multipath on tran 13

Chapter 3 Fading

ig. 3.1 Multipath Propogation 15

Chapter 4 OFDM Channel esti

Fig 4.1 Least Square technique 22

Chanel Estimation

Comb type pilot arra

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a

ceived data

Fig 6.4al for stationary mobile in Rayleigh Fading 31

ng at velocity 25 m/sec 31

VS SNR for MMSE estimation 35

Fig 6.9 Comaprison of SER vs SNR plot for lS and MMSE 36

Fig6.1 Plot of OFDM Transmitted dat 29

Fig 6.2 Plot of OFDM Re 29

Fig 6.3 Bit error rate plot 30

Fig 6.4 Plot of Power Spectral density

Rf Sign

30

model

RF Signals for mobile movi Fig 6.5

in Rayleigh Fading Model

Fig 6.6 Ls Technique Implementation 33

Fig 6.7 Plot of SER vs SNR for ls estimation

Plot of SER

34

Fig 6.8

technique

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ABSTRACT

In FDMA each user is typically allocated a single channel, which is used to transmit all the user

information. The bandwidth of each channel is typically 10kHz-30kHz for voice communications.

However, the minimum required bandwidth for speech is only 3kHz. The allocated bandwidth is

made wider then the minimum amount required to prevent channels from interfering with one

another. This extra bandwidth is to allow for signals from neighbouring channels to be filtered out,

and to allow for any drift in the centre frequency of the transmitter or receiver. In a typical system

up to 50% of the total spectrum is wasted due to the extra spacing between channels. This problem

sent efficiently in each channel.

In addition, the symbol rate of each channel is high (as the channel handles the information from

ther, with no overhead

becomes worse as the channel bandwidth becomes narrower, and the frequency band increases.

There are two main problems with TDMA. There is an overhead associated with the change over

between users due to time slotting on the channel. A change over time must be allocated to allow

for any tolerance in the start time of each user, due to propagation delay variations and

synchronization errors. This limits the number of users that can be

multiple users) resulting in problems with multipath delay spread.

OFDM overcomes most of the problems with both FDMA and TDMA. OFDM splits the available

bandwidth into many narrow band channels (typically 100-8000). The carriers for each channel are

made orthogonal to one another, allowing them to be spaced very close toge

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as in th

This report contains knowledge about OFDM and also how to estimate channel. Various

parameter are considered that effect the transmitted data in real life. The report also contains some

knowledge about fading and how it effects the transmitted data

e FDMA example. Because of this there is no great need for users to be time multiplex as in

TDMA, thus there is no overhead associated with switching between users.

rep2ort

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