MARCH 14, 2009 Telecom Engineering Research Lab, INHA University, Korea S.M.R. Islam Channel Estimation Techniques Based on Pilot Arrangement in OFDM Systems

MARCH 14, 2009 Telecom Engineering Research Lab, INHA University, Korea S.M.R. Islam

Channel Estimation Techniques Based on Pilot Arrangement in OFDM Systems

Authors: Sinem Coleri, Mustafa Ergen


Outline

• Motivation for OFDM

• OFDM System Architecture

• Channel Estimation Techniques

• Performance Analysis

• Conclusion


Motivation for OFDM

• Disadvantages of FDMA– Bad Spectrum Usage

• Disadvantages of TDMA– Multipath Delay spread problem


OFDM: Use of Frequency Spectrum

• Efficient use of spectrum– Overlap in frequency spectrum of subcarriers

• Null point of all other subcarriers at the center frequency of any particular subcarrier

Frequency spectrum of the subcarriers


Multipath Delay Spread

• Multi-path delay spread definition– Time spread between the arrival of the first and last

multipath signal, seen by the receiver.• Received radio signal consisting of a direct signal, plus

reflections from objects

• Multi-path delay spread effect– Inter-Symbol Interference (ISI) when the delayed

multipath signal overlaps with the symbols following it


OFDM: Eliminating ISI

• Cyclic Prefix– Prepend the last part of the signal to the beginning of the

signal• Duration of the CP larger than multipath delay spread• Orthogonality of the carriers not affected.


OFDM Overview

• Divides high-speed serial information signal into multiple lower-speed sub-signals.– Transmits simultaneously at different frequencies in

parallel.

• Modulation ( BPSK, PSK,QPSK,16QAM, …).

• Pilot subcarriers used to prevent frequency and phase shift errors.


Benefits of OFDM

• Higher data rates– Overlap of subcarriers

• Lower bandwidth than spread spectrum.– High spectral efficiency

• Lower multi-path distortion– Usage of cyclic prefix


Our OFDM System Assumptions

Usage of cyclic Prefix

Impulse response of the channel shorter than Cyclic Prefix.

Slow fading effects so that the channel is time-invariant over the symbol interval.

Rectangular Windowing of the transmitted pulses

Perfect Synchronization of transmitter and receiver

Additive, white, Gaussian channel noise


System Architecture-1


1,...,2,1,0

Nn

kXIDFTnx

1,...,1,0,

1,...,1,,

Nnnx

NNnnNxnx gg

f nwnhnxy ff

1,...,1,0 Nnnyny f

1,...,2,1,0

Nk

nyDFTkY

1,...,1,0

Nk

kWkIkHkXkY 1,...,1,0 NkkH

kYkX

ee

1

76

54

32

System Architecture-2Input to Time Domain

Guard Interval Channel

Guard Removal Output to Frequency Domain

Output Channel EstimationICI AWGNChannel Estimated Channel


Pilot Arrangement

• Block Type– All sub-carriers

reserved for pilots with a specific period

• Comb Type– Some sub-carriers are

reserved for pilots for each symbol


Channel Estimation @Block-Type

1

0

110

1

.

.

.

,...,,

N

N

LS

y

y

y

xxxdiagXwhere

yXh

LS estimate MMSE estimate

MMSEMMSE

kHH

ggH

yy

HHgg

Hgy

yygyMMSE

kN

nj

nkN

yygyMMSE

TN

NT

N

Fgh

nEXFXFRyyER

XFRgyER

yRRg

eN

W

F

whereyRFRh

gaussianmeanzeroiidnnnn

gDFThhhh

nXFgy

]|[|][

][

1

.

.

.

.

.

.

.

,,,],...,,[

)(],...,,[

2

1

2

1

110

110

...

.

.

...

1N1NNW

01NNW

1N0NW

00NW


Channel Estimation @ Block-Type

Block Type Decision Feedback Interpolation

1,...,1,0 NkkH

kYkX

ee

1,...,0 NkkX

kYkH

puree

He -kth sub-carrier Channel Response Estimated

Xe(k) -> signal demapper -> signal mapper -> Xpure(k)

Use same channel estimation for the whole symbol duration


Channel Estimation @ Comb-Type Pilot

•Np pilot signals uniformly inserted in X(k)•L=Number of Carriers/Np

•{Hp(k) k=0,1,…,Np} , channel at pilot sub-carriers•Xp input at the kth pilot sub-carrier•Yp output at the kth pilot sub-carrier

LMS EstimateLS Estimate

0,

1,...,1,.inflmpx

Lldata

lmLXkX

1,...,1,0 p

p

pp Nk

kX

kYkH


Interpolation @ Comb-Type

•Linear Interpolation

•Second Order Interpolation

•Low pass Interpolation

•Spline Cubic Interpolation

•Time Domain Interpolation


Ll

mHL

lmHmH

lmLHkH

ppp

ee

0

1

Linear Interpolation Second Order Interpolation

Nl

mpHcmpHcmpHc

c

c

c

where

lmLHkH ee

/

11011

,2

1

1

,110

,2

1

1

Low Pass Interpolation (interp in MATLAB)

Interpolation @ Comb-Type

Time Domain Interpolation

Spline Cubic Interpolation (spline in MATLAB)

•Insert zeros into the original sequence

•Low-pass filter while passing original data unchanged

•Interpolation such that mean-square error between ideal and interpolated values min.


OFDM SetupParameter Specifications

FFT Size 1024

Number of Carriers 128

Pilot Ratio 1/8

Guard Length 256

Guard Type Cyclic Extension

Sample rate of OFDM signal

44.1kHz

Bandwidth 17.5kHz

Signal Constellation BPSK, QPSK, DQPSK, 16QAM


Channels

Delay (OFDM samples) Gain Phase(rad)

0 0.2478 -2.5649

1 0.1287 -2.1208

3 0.3088 0.3548

4 0.4252 0.4187

5 0.49 2.7201

7 0.0365 -1.4375

8 0.1197 1.1302

12 0.1948 -0.8092

17 0.4187 -0.1545

24 0.317 -2.2159

29 0.2055 2.8372

49 0.1846 2.8641

Delay Amplitude

0 1

2 0.3162

17 0.1995

36 0.1296

75 0.1

137 0.1

Channel 1 Channel 2

nwnahnh 1

Time Varying Channel (AR Model)

ATTC (Advanced Television Technology Center)

and the Grande Alliance DTV laboratory`s ensemble E model

Simplified version of (Digital Video Broadcasting) DVB-T channel model


Simulation-1

Modulation BPSK

Channel Rayleigh Fading

H(n) Channel 1

Doppler Frequency

70Hz


Modulation QPSK


H(n) Channel 1

Doppler Frequency

70Hz

Simulation-2


Modulation 16QAM


H(n) Channel 1

Doppler Frequency

70Hz

Simulation-3


Modulation DQPSK


H(n) Channel 1

Doppler Frequency

70Hz

Simulation-4


Simulation-5

Modulation 16QAM

Channel AR Fading

H(n) Channel 1

Doppler Frequency

70Hz


Modulation 16QAM


H(n) Channel 2

Doppler Frequency

70Hz

Simulation-6


Modulation 16QAM


H(n) Channel 1

SNR 40dB

Simulation-7


Conclusion•OFDM System•Block Type

•Direct or Decision Feedback•Comb Type

•LS or LMS estimation at pilot frequencies•Interpolation Techniques

•Linear•Second Order•Low Pass•Spline•Time Domain

•Modulation •BPSK,QPSK,16QAM,DQPSK

•Results:•Comb Type performs better since it tracks fast fading channels.•Low-pass interpolation performs better since mean square error between the interpolated points and their ideal values is minimized.

Documents

MARCH 14, 2009 Telecom Engineering Research Lab, INHA University, Korea S.M.R. Islam Channel Estimation Techniques Based on Pilot Arrangement in OFDM Systems