Channel Estimation in OFDM Systems

Zhibin WuYan Liu

Xiangpeng Jing

OUTLINE OFDM System Introduction

Channel Estimation Techniques

Performance Evaluation

Conclusion

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 sub-carriers used to prevent frequency and phase shift

errors. Usage of cyclic prefix for lower multi-path distortion Controlled overlapping of bands in one channel Max spectral efficiency (Nyquist rate) Easy implementation using inverse FFTs Easy time-freq. Synchronization Modulate by switching between time and frequency domain

Introduction to OFDM Systems

Time-Frequency View

Some 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

System Architecture (cont’d)1. Input to time domain2. Guard Interval 3. Channel4. Guard Removal5. Output to frequency

domain

6. Output

7. Channel Estimation

1,...,2,1,0 NnkXIDFTnx

1,...,1,0,

1,...,1,,

Nnnx

NNnnNxnx gg

f

nwnhnxy ff

1,...,1,0 Nnnyny f

1,...,2,1,0 NknyDFTkY

1,...,1,0

Nk

kWkIkHkXkY

ICI AWGNChannel

1,...,1,0 NkkH

kYkX

ee

Estimated Channel

Pilot for Channel EstimationTim

e

Carriers

Tim

e

Carriers

Comb Type: Part of the sub-

carriers are always reserved as pilot for each symbol

Block Type: All sub-carriers is

used as pilot in a specific period

Block-type Channel Estimation

LS: Least Square Estimation

1

0

110

1

.

.

.

,...,,

N

N

LS

y

y

y

xxxdiagXwhere

yXh

Comb-type Estimation

0,

1,...,1,.inflmpx

Lldata

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

xp(m) is the mth pilot carrier value

{Hp(k) k=0,1,…,Np} , channel at pilot sub-carriersXp input at the kth pilot sub-carrierYp output at the kth pilot sub-carrier

LS Estimate

1,...,1,0 pp

pp Nk

kX

kYkH

LMS Estimate

Xp(k) LMS + e(k)-

Yp(k)

Interpolation for Comb-type Linear Interpolation

Second Order Interpolation

Ll

mHL

lmHmH

lmLHkH

ppp

ee

0

1

Nl

mpHcmpHcmpHc

c

c

c

where

lmLHkH ee

/

11011

,2

1

1

,110

,2

1

1

Simulation ParametersParameter Specifications

FFT Size 64

Number of Carriers 64

Pilot Ratio 1/16

Guard Length 16

Guard Type Cyclic Extension

data rate of OFDM signal 1Mbps/sub-carrier

Signal Constellation 16QAM

System structure in MATLAB Simulation

OFDM Transmitter

OFDM Receiver

Received and Recovered Signals

Received signal phases are distorted by multi-path fading

Comb-LS Estimation Combating multipath rayleigh fading with RLS adaptive

equalization A detail simulation with MATLAB 20 multipath, random phase, and weibull distribution of

amplitutde

Sym

bol Err

or

Rate

Comb-LS Estimation

Filter length .vs. Sample Rate

1. Keep the ratio of F/S, increase S

2. Keep S, increase F.

Observed Symbol error rate with F ( filter length ) and

S ( samples per symbol)

Conclusion OFDM System Introduction Block Type

Direct or Decision Feedback Comb Type

LS or LMS estimation at pilot frequencies Interpolation Techniques

Linear Second Order Time Domain

Modulation BPSK,QPSK,16QAM,DQPSK

Some Results: Comb Type performs better since it tracks fast fading channels. RLS algorithm vs. LMS algorithm