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Channel Estimation for IEEE 802.16a OFDM Downlink Transmission

Student: Student: 王依翎王依翎 Advisor: Dr. David W. LinAdvisor: Dr. David W. Lin

2006/02/23

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Outline

Introduction to IEEE 802.16aDownlink channel estimation methodsSimulation

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Reference

(1) Ruu-Ching ChenRuu-Ching Chen, “IEEE 802.16a TDD OFDMA Downlink Pilot-Symbol-Aided Channel Estimation: Techniques and DSP Software Implementation ,“ M.S. thesis, Department of Electronics Engineering, National Chiao Tung University, Hsinchu ,Taiwan, R.O.C., June 2005. (2) IEEE Std 802.16a-2003, IEEE Standard for Local and Metropolitan Area Networks - Part 16: Air Interface for Fixed Broadband Wireless Access Systems – Amendment 2: Medium Access Control Modifications and Additional Physical Layer Specifications for 2-11GHz. New York: IEEE, April 1, 2003.

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Outline

Introduction to IEEE 802.16aDownlink channel estimation methodsSimulation

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Primitive Parameters

Primitive parameters characterize the OFDMA symbol: (1) BW : the nominal channel bandwidth, it equals 10 MHz in the system . (2) Fs/BW : the ratio of “sampling frequency" to the nominal channel bandwidth. It is set to 8/7. (3)Tg/Tb : the ratio of CP time to “useful" time. We use 1/8 in the system. (4) NFFT : the number of points in the FFT. The OFDMA PHY defines this value to be 2048.

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Derived Parameters

The following parameters are defined in terms of the primitive parameters.

(1)Fs = (Fs/BW)‧BW = sampling frequency.

The value equals 10X8/7 = 11.42 MHz.

(2)Δf = Fs/NFFT = carrier spacing = 5.57617 KHz.

(3)Tb = 1/Δf = useful time = 179.33 μs.

(4)Tg = (Tg/Tb)‧Tb = CP time = 22.4 μs.

(5)Ts = Tb + Tg = OFDM symbol time = 201.9μs.

(6) 1/Fs = sample time = 87.5657 ns.

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Types of carriers

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Pilot Allocation

varLocPilotk = 3L + 12Pk , Pk={0,1,2,……,141}

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Data Carrier Allocation

The exact partitioning into subchannels is according to the following equation called a permutation formula:

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Carrier Allocation

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Data Modulation

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Pilot Modulation

•The polynomial for the PRBS generator is

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Outline

Introduction to IEEE 802.16aDownlink channel estimation

methodsSimulation

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DL Channel Estimation Methods

Our interpolation schemes work in both frequency and the time domains.

(1)Linear and second-order interpolation are

applied in the frequency domain

(2)2-D interpolation and LMS (least mean

square adaptation) optimize their

performance in the time domain.

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Least-Square (LS) Estimator

An LS estimator minimizes the squared error :

where Y : the received signal

X : a priori known pilots

Channel matrix considering pilot carriers only:

2ˆ XHY LS

11

22

11

00

,

,

,

,

...0...0...0

0...0...0...0

0......0...0

0...0......0

0...0...0...

ˆ

pNpNmm

mm

mm

mm

LS

H

H

H

H

H

2ˆ XHY LS → iLS mmmXmHmY ,)()(ˆ)(2

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Least-Square (LS) Estimator (cont.)

The estimate of pilot signals, based on one observed OFDM symbol, is given by

where N(m) is the complex white Gaussian noise on subcarrier m The LS estimate of Hp based on one OFDM symbol only is susceptible to Gaussian noise, and thus an estimator better than the LS estimator is preferable.

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Linear Minimum Mean Squared Error (LMMSE) Estimator

The mathematical representation for the LMMSE estimator of pilot signals is

where the covariance matrices are defined by

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Linear Interpolation

Mathematical expression:

where Hp(k); k = 0, 1,…,Np, are the channel frequency responses at pilot subcarriers, L is the distance between the two given data,the pilot sub-carriers spacing, and 0 ≦ l < L.

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Second-Order Interpolation

Also called Gaussian second order estimation. The interpolation is obtained using three successive pilot

subcarriers signal as follows :

where

)1()()1(

)()(

101

mcmcmc

lmk

HHHHH

ppp

ee

L

l

c

c

c

2

)1(

)1)(1(2

)1(

1

0

1

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Time Domain Improvement Methods

We can only use 166 pilots in one symbol to interpolate the channel in the frequency domain.

It is not sufficient because the pilot spacings are too wide in our system.

Since the channel does not change abruptly over time, we propose two methods to improve the performance.

(1) Two-Dimensional Interpolation (2) Least Mean Square (LMS) Adaptation

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Two-Dimensional Interpolation

Index of a variable location pilot :

The maximum number of pilot locations that we can use is :

Since the equivalent number of pilots becomes 568/166 = 3.421 times that of the original case, better

estimation is expected.

}141 2,....., 1, 0,{

3,... 1, 2, 0,

123var

k

kk

P

L

PLLocPilot

568324)8142(

4)(

tsFixLocPilosPilotsCoincidenttsVarLocPilo NNN

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Two-Dimensional Interpolation (cont.)

One possible way of interpolation (extrapolation) is

where , n = 0, 1, … , 7, are the channel frequency

responses at pilot carriers in the nth previous symbol.

When dealing with fading channels, we consider replacing the formula above with

)(~

fh pn

)(~

2

1)(

~

2

1)(

~

2

1)(

~

2

1

)(~

2

1)(

~

2

1)(

~

2

1)(

~

2

1)(

~

7362

51402

4

fhfhfhfh

fhfhfhfhfh

pppp

pppppextrapDsets

)(~

4

3)(

~

4

7)(

~

2

1)(

~

2

3

)(~

4

1)(

~

4

5)(

~)(

~

7362

5102

4

fhfhfhfh

fhfhfhfh

pppp

ppppextrapDsets

(formula 1)

(formula 2)

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Least Mean Square (LMS) Adaptation

The LMS algorithm is the most widely used adaptive filtering algorithm in practice for its simplicity.

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Outline

Introduction to IEEE 802.16aDownlink channel estimation methodsSimulation

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Comparison Between Formula 1 and Formula 2 Using Linear Interpolation

SER :

(symbol error rate)

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Comparison Between Formula 1 and Formula 2 Using Linear Interpolation (cont.)

• MSE of :|ˆ| ii HH

(mean square error)

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Comparison Between Formula 1 and Formula 2 Using 2nd-Order Interpolation

SER

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Comparison Between Formula 1 and Formula 2 Using 2nd-Order Interpolation (cont.)

• MSE of : |ˆ| ii HH