Performance Evaluation of Channel Estimation Based on Adaptive Filters and Adaptive Guard Interval for Mobile Wimax

7/30/2019 Performance Evaluation of Channel Estimation Based on Adaptive Filters and Adaptive Guard Interval for Mobile W

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PERFORMANCE EVALUATION OF CHANNEL ESTIMATION BASED ON

ADAPTIVE FILTERS AND ADAPTIVE GUARD INTERVAL FOR MOBILE

WIMAX

Quang Nguyen-Duc[1], Thang Nguyen-Manh[1] and Lien Pham-Hong[2][1]

Ho Chi Minh City University of Technology, Vietnam[2]

Ho Chi Minh City University of Technology Education, Vietnam

Email: [email protected], [email protected] , [email protected]

Abstract. In this paper, the channel estimation

algorithms are studied for mobile WiMAX standard.

The comb-pilot structure is used for channel

estimation algorithms. We constructed an channel

estimation algorithm based on two adaptive filters:

Kalman and extended Kalman. Then we combined

them with adaptive GI (guard interval) optimization

algorithm. A performance analysis showed that

depending on complex or simple computation, we can

choose EKF (Extended Kalman Filter) estimator,

adaptive GI with Kalman estimator or adaptive GI

with LS( Least squared) estimator.

Keywords: Kalman fl ter, adaptive Guard inserti on,

estimation channel, mobil e WiMAX.

I. INTRODUCTION

Mobile WiMAX is a rapidly growing broadband wirelessaccess technology based on IEEE 802.16-2004 and IEEE

802.16e-2005 air-interface standards [1]. The OFDM has

been chosen to be used in WiMAX since it shows many

advantages. OFDM divides the overall frequency band

into a number of sub-band and transmits a low-rate data

stream in each sub-band.In addition, OFDM allows

overlap of the sub-channels but keeps the orthogonality of

the sub-carriers. Therefore, high spectral efficiency is

achieved [2].

This article focuses on channel estimation system formobile WIMAX The channel estimation can beperformed by inserting pilot tones into OFDM symbol

[3],[4]. In this paper, channel estimation is studied for

comb-type pilot. The comb-type pilot channel estimation

consists of algorithms to estimate the channel at pilot

frequencies and to interpolate the channel. The

interpolation of the channel for comb-type can use one of

the different interpolation methods such as linear

interpolation, second order interpolation, low-pass

interpolation, spline cubic interpolation, and time domain

interpolation [5].

We construct the algorithm of channel estimation based

on adapive filters which are Kalman and EKF. Next, we

continue optimizing the upper estimators by anotheralgorithm to have an optimal GI.

Fig 1. Effect of small GI

To counteract the ISI, the high-efficiency OrthogonalFrequency Division Multiplexing (OFDM) modulation

first splits the high-rate data stream into a number of

parallel sub-streams and modulates them onto different

orthogonal sub-carriers and thus lower the symbol rate,

and then add a GI to the head of each symbol to reducethe influence of adjacent symbol interference. Fixed GI

may force devices that encounter smaller delay spread to

use unnecessarily large GI length, which in turn, causes a

considerable loss in spectral efficiency and waste

transmitter energy of the system. An Optimal GI will

provides the ability to reliably send information at the

lowest possible power level, which has advantage of

extending the battery life of mobile devices. With the

reasons as describing above, optimizing GI is also

important in a WiMAX system. The authors in [8]

presented optimization of GI for mobile WiMAX standard

over multi-path channels by using different GIs, whereasthe authors in [9] presented the study of different GIs to

improve the BER performance of fixed WiMAX. Another

author in [10] presented an algorithm to optimize GI for

OFDM systems.

In this paper, we construct the algorithm of channel

estimation based on LS estimator, kalman and EKF

estimator with fixed GI (256 for mobile WiMAX) . Then

we use this result to have guard interval optimization to

have adaptive GI. Finally, we compare performance

between estimators with fixed GI and with adaptive GI

using GI optimization algorithm .II. SYSTEM MODEL

OFDM converts serial data stream into parallel blocks of

size N and modulates these blocks using inverse fast

Fourier transform (IFFT). Time domain samples of an

OFDM symbol can be obtained from frequency domain

data symbols as Fig. 2 shows a typical block diagram of

OFDM system with pilot signal assisted. The binary

information data are grouped and mapped into multi-

amplitude multi-phase signals.

Fig 2. OFDM system model

The binary information is first grouped and mapped

according to the modulation in signal mapper. After

inserting pilots either to all sub-carriers with a specific

period or uniformly between the information data


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sequence, IFFT block is used to transform the data

sequence of length N {X(k)} into time domain signal

{x(n)} with the following equation:

( ) ( ){ } ( )

( )11,2,1,0

21

0

=

==

=

Nn

ekXkXIFFTnx Nkn

jN

k

K

Where N is FFT length

Following IFFT block, guard time, which is chosen to belarger than the expected delay spread, is inserted to

prevent inter-symbol interference. This guard time

includes the cyclically extended part of OFDM symbol in

order to eliminate inter-carrier interference (ICI). The

total OFDM symbol is given as follows:

( )( )

( )( )2

1,1,0,

1,,1,,

=+=+

=Nnnx

NNnnNxnx

gg

fL

L

where Ng is the length of the guard interval.

Signal after the conversion from parallel to serial will be

passed through the frequency selective fading channel and

change over time, and added noise. At the receiver, the

receiver signal is

)()()()( nwnhnxny ff += (3)where w(n) is additive white Gaussian noise and h(n) is

the channel impulse response.

Following FFT block, the pilot signals are extracted

and the estimated channel He(k) for the data sub-channelsis obtained in channel estimation block. Then the

transmitted data is estimated by:

( )( )( )

( )41,1,0 == NkkH

kYkX

e

e L

Then the binary information data is obtained back in

signal demapper block

III. CHANNEL ESTIMATION BASED ON

ADAPTIVE FILTERS

A. Estimation channel based on kalman filter withcomb-type pil ot

1. Kalman fil ter in troduction

In statistics, the Kalman filter is a mathematical method

named after Rudolf E. Kalman. Its purpose is to use

measurements observed over time, containing noise and

other inaccuracies, and produce values that tend to be

closer to the true values of the measurements and their

associated calculated values [11]. Kalman estimator is one

of the adaptive estimation algorithms that are used to

estimate the fading process in OFDM systems [12]. We

can estimate channel response H from the following

equation:

H(n+1)= F(n+1,n) H(n) +v1(n) (5)

H(n) is the frequency response of the channel of pilots at

the nth OFDM symbols.

F(n+1,n) is (Np x Np) state matrix relating the state of

the system between the (n+1)th and nthOFDM symbol.

v1(n) is zero mean white noise process with correlation

matrix. Besides, in Kalman estimator, we also have the

measurementequation: Y(n)=C(n).H(n)+v2(n) (6)

where v2(n) is zero mean white noise measurement withcorrelation matrix. C(n) is aNp x Np diagonal matrix with

pilot symbols on its diagonal.

Fi

g.3 Kalman estimator model2. The proposed algori thm of estimati on channel based

on kalman fil ter

+ At the fir st OFDM symbol:

We determine matrix H1 based on LS (least square)

estimator:

p

P

X

YH =1 (7)

With YP is the pilot signal at the receiver, XP is the pilot

signal at the transmitter.

+ At other OFDM symbols:

Step 1: We calculate state matrix F:HH WMWnHnHEnnF

=+=+)}().1({),1( (8)

Where : n= 1m; m is the number of OFDM symbols

W is DFT matrix of channel response h and

dd ITfJM *)2(0 = (9)fd is the maximum Doppler frequency, T is the symbol

OFDM duration, Id is the unit matrix (Np x Np) with NP is

pilot length.

J0 is the Bessel function of the first-kind and zero order.

Step 2:we can construct Kalman estimator to calculate

matrix G(n) and (n) as follows:

1

2 )]()()1,()()[()1,(),1()(++= nQnCnnKnCnCnnKnnFnG HH

(10)

)()()()( nHnCnYn = (11)

)()()]1,()()()1,()1,()[,1(),1( 1 nQnFnnKnCnGnnFnnKnnFnnKH

++=+(12)

with G(n) is Gain Kalman, )(n is innovation process.

K(n+1,n) is the predicted state-error correlation matrix.

C(n) is the Np x Np diagonal matrix with pilot symbols on

its diagonal.

Q1(n) and Q2(n) are defined by the following equations:

(13)

Q1(n) is correlation matrix of process noise.

Q2(n) is correlation matrix of measurement noise.

In the simulation , we choose Q1=0.012 * Id , Q2=0.1.

Step 3: We determine matrix H (this is frequency channel

response at pilot-carrier) from the upper information.

)()()()()1( nnGnHnFnH +=+ (14)Step 4: We interpolate frequency channel response at

datacarrier by interpolation algorithms. In this paper, we

use linear interpolation algorithm. Finally, after this step,

we already has channel response in all sub-carriers and

this is channel response in frequency domain.


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B. Channel estimation based on extended kalman f il ter

with comb-type pil ot

1.Extended Kalman I ntroductionThe extended Kalman filter (EKF) is the nonlinear version ofthe Kalman filter which linearizes about the current mean and

covariance. The EKF has been considered the standard in thetheory of nonlinear state estimation, navigation system ,GPS.

Unlike Kalman filter, state space model in EKF is nonlinear

Gaussian. We can estimate channel response H from thefollowing equation:

H(n+1)= f( H(n)) +v1(n) (15)Y (n)= c(H(n)) +v2(n) (16)

With f(H), c(H) can both be nonlinear

2. The proposed algori thm of channel estimati on based

on extended kalman fi lter

Assume)()( nienH =

(17)

With (n) is unknown function depends on the variable n

+ At the fi rst OFDM symbol:

We determine matrix H1 based on LS (least square)

estimator:

p

P

X

YH =1

With YP is the pilot signal at the receiver, XP is the pilot

signal at the transmitter.Following matrix H1, we can determine

iH /)ln( 11 = (18)+ At other OFDM symbols:

To estimate the quantity (n) using an EKF in each

OFDM frame, the state equation is built as (n) = (n-1)Step 1: We calculate state matrix F and C:

dnn If

F =

= = )1( (19)

Id is the unit matrix (Np x Np) with NP is pilot length.

)()()(

)().()( nin

i

n iXeXeHXYnC

==== ==

(20)Step 2: we can construct Extended Kalman estimator to

calculate matrix G(n) and (n) as Kalman estimator.

Step 3: We determine matrix H (this i s frequency channel

reponse at pilot-carrier) from the upper information.

))().(Re()1()( nnKnFn += (21))()( nienH =

Step 4: We interpolate frequency channel response atdatacarrier by interpolation algorithms. In this paper, we

use linear interpolation algorithm. Finally, after this step,

we already has channel response in all sub-carriers and

this is channel response in frequency domain.

IV. GUARD INTERVAL OPTIMIZATION

ALGORITHM

The algorithm is composed of the following steps:

+ Step 1:Based on the upper result of estimation channel,

calculating RMS delay spread:

In order to change the length of the cyclic prefix

adaptively, we must estimate the Ts normalized RMSdelay spread:

2

2

2

2

22

|)(|

|)(|

|)(|

|)(|

=

l

l

l

lRMS

lh

llh

lh

llh

(22)

From Eq.(22), we can see that with the estimation of the

CIRhthat we calculated by using LS or adaptive filters,

we can calculate the estimation of the RMS delay spread

RMS .

+ Step 2: Setting Guard Interval for the next OFDM

symbols:

In our simulation, we will change the length of the GI

based on the estimation results. In the step 1 above, we

have derived the estimation structure of RMS . After we

got the value RMS , we can set the duration of the GI of

the next transmission two times of delay spread RMS

according to the designing rule.

+ Step 3:Sending the information of next GI length back

to transmitter:

In the OFDM with adaptive GI, the receiver must send

back the chosen GI length which can be done by using thesignalling field in the data packet. The number of the GI

sample can be presented in a few bits; this will not add

much burden to the system.

The transmitter will set GI with new length which is

signalled by the receiver in the next OFDM symbols.

Fig 4. Block diagram of the OFDM transceiver with adaptive GI

V. MOBILE WiMAX STANDARD

The channel models can be classified into two main

categories: statistical and empirical models. Empirical

models are based on measurements performed in real

environments, while the statistical models estimate the

channels characteristics through mathematical relations.

Two empirical models are generally used for describing a

WiMAX system: the SUI (Stanford University Interim)

channel model, which is used for simulating an IEEE802.16-2004 system (a fixed WiMAX system) [13] and

the ITU-R (International Telecommunication Union-

Radio communication) channel model. This type of model

is used for the simulation of an IEEE 80216e-2005 system

(a mobile WiMAX system). The ITU wideband channel,

is described based on a tapped delay line model, with a

maximum number of 6 taps [14]. Channel model ITU-R

for 3 environments: indoor, pedestrian, vehicular and

empirical model (channel B) is used to describe multi-

path channel. In this paper , we use indoor and pedestrian

model for our algorithms.


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Channel A Channel BTap

Delay(ns) Power

(dB)

Delay

(ns)

Power

(dB)

1 0 0 0 0

2 50 -3 100 -3.6

3 110 -10 200 -7.2

4 170 -18 300 -10.8

5 290 -16 500 -18

6 310 -32 700 -25.2

Table 1. Indoor channel model

Channel A Channel BTap

Delay

(ns)

Power (dB) Delay (ns) Power

(dB)

1 0 0 0 0

2 110 -9.7 200 -0.9

3 190 -19.2 800 -4.9

4 410 -22.8 1200 -8

5 - - 2300 -7.8

6 - - 3700 -23.9

Table.2. Pedestrian channel model

VI. SIMULATION RESULTS

A. Simulati on parameters

The paper uses parameters of IEEE 802.16e to simulate

mobile WiMAX standard.

We simulate at the frequency of 2.5 GHz with bandwidth

of 20 MHz in two environment: indoor model and

pedestrian model. FFT size is 1024, the number of usedsub-carriers is 840, LS estimator, Kalman and EKF

estimator use fixed GI size of 256 which is in IEEE

802.16e. Our adaptive GI size is calculated by guardinterval optimization algorithm.

At the physical layer of standard IEEE 802.16e, the

adaptive modulation is used with modulations such as: 4-

QAM, 16-QAM, 64-QAM, depending on environment

conditions. In this paper, we use 3 modulation schemes:

4-QAM, 16-QAM and 64-QAM for simulation.

Mobile WiMAX Parameter

Number of Sub-carrier 840

FFT size 1024

Modulation4-QAM, 16-QAM,64-QAM

Number of pilot -carrier 210

Rayleigh Fading Channel Model ITU-R channel B

Fixed Guard Interval 256

License frequency 2.5 GHz

Bandwidth 20 MHz

Table 3. Simulation parameters

In this paper, we use BER (Bit Error Rate) parameter to

compare estimation methods such as LS (Least Square)

estimator, Kalman estimator and extended Kalman

estimator, LS estimator with adaptive GI, Kalman

estimator with adaptive GI and EKF (Extended Kalman

Filter) estimator with adaptive GI.

B. BER compari son between L S (least square) estimator

with fixed GI and adaptive GI algorithm with LS

estimator

Figure 5, 6 show the BER performance of the systemwith adaptive GI and the conventional non-adaptivesystem with fixed GI in fading environment such as:

indoor model with mobile speed of 1 km/h, pedestrian

model with mobile speed of 5 km/h. From BER

performance of two figures, we can see how fading

impact the system. With all these results, adaptive GI

length show better performance than fixed GI length in

three figures. BER results still depend on the order of

QAM modulation. BER result of fixed GI with 4-QAM is

still better than adaptive GI with 16-QAM.

0 5 10 15 20 25 30 35 4010

-4

10-3

10-2

10-1

100

SNR[dB]

BER

Comparison between adaptive GI and fixed GI

adaptive GI,4-QAM

fixed GI,4-QAM

adaptive GI,16-QAM

fixed GI,16-QAMadaptive GI,64-QAM

fixed GI,64-QAM

Figure 5: BER for indoor model with,mobile speed of 1km/h

ISI from fading makes the system have lowperformance in pedestrian model (figure 6). We can see

with adaptive GI, we have good performance by removing

ISI such as BER results of adaptive GI with 16-QAM is

really better is fixed GI with 4-QAM when SNR is higher

than 25dB, BER results of adaptive GI with 64-QAM is

really better is fixed GI with 16-QAM when SNR is

higher than 30 dB.

0 5 10 15 20 25 30 35 4010

-3

10-2

10-1

100

SNR[dB]

BER

Comparison between adaptive GI and fixed GI

adaptive GI,4-QAM

fixed GI,4-QAM

adaptive GI,16-QAM

fixed GI,16-QAM

adaptive GI,64-QAM

fixed GI,64-QAM

Figure 6: BER for pedestrian model with mobile speed of 5 km/h.


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These results show that adaptive GI algorithm with LS

estimator really enhance performance better than LS with

fixed GI. However, the system will have higher

computation.

C. BER compari son between LS estimator wit h fi xed GI,

Kalman estimator wi th fi xed GI and adaptive GI wi th

Kalman estimator.

Figure 7 is the result for indoor model with mobile speedof 2 km/h. We can see with Kalman estimator, we have

much better performance than LS estimator in almost

modulation schemes. With all three methods, Kalman

estimator with adaptive GI has better performance than

LS estimator and Kalman estimator with fixed GI.

However, the BER results of Kalman estimator and

Kalman estimator with adaptive GI are nearly the same.

0 5 10 15 20 25 30 35 4010

-5

10-4

10-3

10-2

10-1

100

B

ER

SNR[dB]

BER

4QAM with LS estimator

4QAM with kalman estimator

4QAM with adaptive GI



16QAM with a daptive GI



64QAM with a daptive GI

Fig 7. BER for indoor model, mobile speed of 2 km/h

Figure 8 is the BER result of pedestrian model for mobile

speed of 5 km/h. In 4-QAM modulation, we can see

Kalman estimator with adaptive GI is better than Kalman

estimator from 0 dB to 25 dB. In 16-QAM and 64-QAM

modulation, Kalman estimator with adaptive GI had betterperformance than LS estimator and Kalman estimator.

This is more clearly when SNR is higher. Besides, with

all three modulations, Kalman estimator has better BER

than LS estimator in all SNR range.These results prove that Kalman with adaptive GI has

good performance when SNR is high or the quality

system is rather good for pedestrian model.

0 5 10 15 20 25 30 35 4010

-5

10-4

10-3

10-2

10-1

100

BER

SNR[dB]

BER










Fig 8. BER for pedestrian model, mobile speed of 5 km/h

With the upper results, we can conclude that Kalman

esitmator with adaptive GI enhance performance in all

simulation models. However, the system will have more

complex computation with Kalman algorithm and

adaptive GI optimization algorithm.

D. BER comparison between Kalman estimator and

Extended Kalman estimator

Figure 8 is the result for indoor model with mobilespeed of 2 km/h. We can see with EKF estimator, we have

much better performance than kalman estimator in almost

modulation schemes. In 4-QAM modulation, the result is

clearly. However, with 16-QAM and 64-QAM

modulation, the BER results of Kalman estimator and

Extended Kalman estimator is not significantly changed

from 0 to 15 dB.

0 5 10 15 20 25 30 3510

-5

10-4

10-3

10-2

10-1

100

BER

SNR[dB]

BER

4QAM with kalman

4QAM with extended kalman

16QAM with kalman


64QAM with kalman


Fig 9. Simulation BER for indoor model, mobile speed of 2 km/h

Figure 9 is the BER result of pedestrian model for

mobile speed of 4 km/h. In 4 QAM modulation, EKFestimator is better than Kalman estimator in the range

from 0 to 20 dB, but when SNR is higher 20dB, EKF

gives results that are not good. With 16-QAM, 64-QAM,

EKF estimator has better result with higher SNR.

0 5 10 15 20 25 30 35 4010

-5

10-4

10-3

10-2

10-1

100

BER

SNR[dB]

BER

4QAM with kalman


16QAM with kalman


64QAM with kalman


Fig 10. BER for pedestrian model , mobile speed o f 4 km/h


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With these results, we can show that EKF (Extended

Kalman Filter) have better performance than Kalman

estimator. The system of EKF estimator is more complex

computation but nearly the same as Kalman estimator.

E. BER comparison between EKF estimator with f ixed

GI and adaptive GI with kalman and EKF estimator.

With BER results from figure 11 and 12, adaptive GI

with Kalman and EKF estimator does not enhanceperformance when comparing with EKF estimator.

0 5 10 15 20 25 30 35 4010

-4

10-3

10-2

10-1

100

SNR[dB]

BER

Comparison between EKF estimator and adaptive GI algorithm

EKF estimator-4QAM

adaptive GI with Kalman-4QAM

adaptive GI with EKF-4QAM

EKF estimator -16QAM



EKF estimator-64QAM



Fig 11. BER for indoor model, mobile speed of 2 km/h

0 5 10 15 20 25 30 35 4010

-4

10-3

10-2

10-1

100

SNR[dB]

BER

Comparison between EKF estimator and adaptive GI algorithm

EKF estimator-4QAM



EKF estimator -16QAM



EKF estimator-64QAM



Fig 12. BER for pedestrian model, mobile speed of 4 km/h

The upper results can show that EKF estimator is the best

choice in this case because the system of adaptive GI with

Kalman and EKF estimator do not enhance performance

but it has much higher computation than EKF estimator

with fixed GI.

VII. CONCLUSION

The paper evaluates performance of channel estimation

based on adaptive filters under fixed GI and adaptive GI

with GI optimization algorithm. Simulation parametersused in the paper are followed by mobile WiMAX

standard. With fixed GI system, EKF estimator had the

best performance. With adaptive GI system using GI

optimization algorithm, Kalman estimator is the better

choice than EKF estimator with the advantage of lower

computation. For the lowest computation, we can choose

adaptive GI with LS estimator which also had good

performance, nearly the same as Kalman estimator.

For future researches, we can evaluate more with other

adaptive filters so that we can have an optimal algorithm

with hybrid solutions between adaptive filters.

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Documents

Performance Evaluation of Channel Estimation Based on Adaptive Filters and Adaptive Guard Interval for Mobile Wimax