Performance of a Novel Fuzzy-Based Code Allocator for Two-Dimensional Spreading OFCDM Communication...

International Journal of Fuzzy Systems, Vol. 10, No. 4, December 2008 231

Performance of a Novel Fuzzy-Based Code Allocator for Two-Dimensional

Spreading OFCDM Communication Systems

Yung-Fa Huang, Neng-Chung Wang, Tan-Hsu Tan, and Chih-Pin Tsai

Abstract1 Moreover, the two-dimensional (2-D) spreading codes, spreading on both time and frequency domain, has been applied to OFDM system [5-6]. Using the orthogonality property between the 2-D codes, the orthogonal fre-quency coded division multiplexing (OFCDM) is per-formed in the downlink for mobile communication sys-tems [7-8]. The diversity gain can be obtained from fre-quency domain or time domain, respectively referring frequency diversity and time diversity. The frequency diversity depends on the correlation of the combining elements in frequency bands while the time diversity depends on the correlation of the combining elements in time slices. From the 2-D codes, the diversity gain can be obtained from frequency domain which the spreading codes are all spread in the subcarriers for the multi-carrier CDMA systems [8]. However, the 2-D codes could also be spread in the time-domain to obtain the time diversity [9]. As we know that the both fre-quency and time diversity gain depend on the 2-D spreading codes and the response of the frequency and time selective fading channels [10]. Moreover, the time diversity not only depends on the time spreading factor in the 2-D spreading codes but also related with the Doppler shift incurred by the speed of mobiles. There-fore, with the flexibility to the diversity effects, the 2-D spreading codes are proposed to perform the future 4G wireless mobile communication systems.

In this paper, we investigate the multi-user per-formance in a two-dimensional (2-D) spreading or-thogonal frequency coded division multiplexing (OFCDM) communication system over frequency and time selective fading channels. To compromise be-tween diversity gain and multiple access interference (MAI), we propose an adaptive fuzzy inference sys-tem to infer adequate 2-D spreading factors and to assign the orthogonal variable spreading factor (OVSF) codes to active users for OFCDM mobile communication systems. Simulation results show that the proposed fuzzy-based code allocation (FBCA) scheme not only suppresses the MAIs induced by non-orthogonality but also exploit the diversity gain over time and frequency selective fading channels and then outperforms the orthogonal code allocation (OCA) scheme at all system loads.

Keywords: OFCDM systems, 2-D OVSF code, diversity gain, fuzzy inference system, time and frequency selec-tive fading channel.

1. Introduction

The orthogonal frequency division multiplexing (OFDM) supports high rate data transmission. The con-ventional direct-sequence code-division multiple-access (DS-CDMA) can give a high potential capacity for the multiple access communication systems [1]. Therefore, the combined technique of OFDM and CDMA, multi-carrier code-division multiple-access (MC-CDMA) communication technique, which exploits the spreading feature of CDMA but without the adverse effect of in-creasing frequency selectivity in the channel, has re-ceived much attention among researchers and been adored as a favorite candidate for 4th generation cellular communication systems [2-4].

However, when multiple users simultaneously access the system the code orthogonality among users in MC-CDMA systems is highly distorted by the instanta-neous frequency response of the channel. Moreover, the Doppler effects due to the mobile moving depict a fast fading channel. Thus, the orthogonality of 2-D codes spreading in the time-domain may be degraded due to the Doppler shift of the moving mobile station. There-fore, the multiple access interference (MAI) due to the frequency selectivity in fading channels or the time se-lectivity in Doppler shift channels degrades the per-formance of 2-D spreading OFCDM communication systems. Then, the bit error rate (BER) is degraded due to the MAI in multi-user access systems. The MAI due to the out-orthogonality among the multiple access in-creases with the active number of users. Therefore, the performance of the OFCDM system can be improved by adequately selecting the 2-D spreading codes to com-promise the diversity gain maximization and the MAIs

Corresponding Author: Yung-Fa Huang is with the Department of Information and Communication Engineering, Chaoyang University of Technology, 168 Jifong E. Rd., Wufong Township, 41349, Taichung County, Taiwan. E-mail: [email protected] Manuscript received 28 Aug. 2008; revised 1 Nov. 2008; accepted 21 Dec. 2008.

© 2008 TFSA


Fig. 2 shows the block diagram of the downlink transmission of OFCDM wireless communication sys-tems, in which the transmitter and receiver models are depicted in Fig. 2(a) and 2(b) respectively. In OFCDM, the N-bit binary data stream of the k-th user is modulated with BPSK, 1,...,2,1,0,, −= Njb jk . Each symbol dura-tion T consisted with the effective symbol period Te and guard period Tg, i.e. gc TTT += . Through S/P block, the further spreading data stream spreading by 2-D codes is denoted by dm,i, m=(j+1)mod(Nc/SFF)+mj,

1,,2,1,0 −= Fj SFm , iTFc

mSFSFN

ji +⋅⎥⎦

⎥⎢⎣

⎢ +=

/1

,

1,,2,1,0 −= Ti SFm .

minimization. The fuzzy logic developed by Zadeh [11] has drawn a

great deal of attention because of its universal approxi-mation ability in the nonlinear problem. The adaptive fuzzy controller can adapt time-varying uncertainties [12]. Thus, the fuzzy inference systems (FIS) have been applied to a variety of fields, such as rotor systems [13], face detection and recognition [14], ocean salinity and temperature variations prediction [15], and so on. Moreover, in previous works, the FIS was used to effec-tively improve the performance of partial parallel inter-ference cancellation in DS-CDMA systems [16] and MC-CDMA systems [17], respectively. Therefore, in this paper, we propose an adaptive FIS to infer adequate or-thogonal variable spreading factor (OVSF) codes to compromise the diversity effects and MAIs, and thus to improve the downlink system capacity for the 2-D spreading OFCDM communication systems.

Thus, the baseband transmitted symbol waveform in the m-th subcarrier can be expressed by

2. System Models

The description of OFCDM system in this paper here

focuses on the downlink system. A synchronous downlink system is performed for simplicity of the sin-gle cell system model. With the 2-D spreading codes from OVSF codes as shown in Fig. 1 [6], we have the time-spreading coefficients and the frequency-domain spreading coefficients by SFT and SFF, respectively. Then the 2-D spreading factor is obtained by SF=SFT×SFF. Moreover, in the OVSF codes, the codes of l-th level is expressed by , v = 1,2,…, 2l, where

SF=2l. Then, in this paper the 2-D spreading codes ex-pressed by . The 2-D spreading codes are composed by

and

, respectively,

where is the frequency spreading factor and SFT is the time spreading factor.

vlC ,2

},{ ,, FT SFSFSFSFSF CCC =

},...,,...,,{ 21,

T

TTTTT

SFSF

vTSFSFSFSFSF cccc=C

},...,,...,,{ 21,

F

FFFFF

SFSF

vFSFSFSFSFSF cccc=C

FSF

∑∑= =

−⋅⋅⋅=K

k

N

i

tfjvFkSF

vTkSFimkikm

Dm

FTiTtpeccdPtS

1 1

2,,,,, )()( π ,

(1)

where Pk,i and dk,m,i are the average power of symbols and the i-th data symbol of the k-th user, respectively, p(t) is the impulse response of pulse-shaping filter,

em Tmf /= is the center frequency of the m-th subcar-rier, )mod()1( FSFmvF += , . The Nc components of the subcarriers are scrambled by ap-plying frequency interleaving in order to eliminate the correlation among fading between adjacent sub-carriers. Then the transmitted signal after IDFT is obtained as

)mod()1( TSFivT +=

∑=

=cN

mm tStS

1)()( (2)

Then, the summation of Nc components is followed by inserting a guard interval, which is greater than the mul-tipath delay spread, Tm of the radio channel. Then, the transmitter model for OFCDM with 2-D spreading codes is shown in Fig. 2 (a).

The broadband signal transmitted to the frequency se-lective fading channel can be received at receiver and be sampled with matched filter with symbol rate. As a fre-quency selective Rayleigh fading channel, we assume a wide-sense stationary uncorrelated scattering (WSSUS) channel [10] with multipath frequency-selective fading. Then, the received signal of base station can be ex-pressed as

Figure 1. An OVSF code tree.

)()()]()(cos[

)(1 1

,,,

,,,

tniTtpit

hccdPtr

Tmip

i

K

k

N

mim

vFkSF

vTkSFimkik

c

FT

+−⋅+−×

⋅⋅⋅= ∑ ∑∑∞

−∞= = =

θτω, (3)

where hm,i is the sub-channel gain at the i-th time dura-

Y.-F. Huang et al.: Performance of a Novel Fuzzy-Based Code Allocator for Two-Dimensional Spreading OFCDM Communication Systems 233

tion on the m-th subcarrier, which exhibits a Rayleigh distribution, n(t) is an additive white Gaussian noise (AWGN) process with zero mean and two-sided power spectral density (PSD) No/2, τi is the propagation delay at the i-th time duration on the m-th subcarrier, and

is a random variable with uniform distribution on (0, 2π). After discrete Fourier transform (DFT) operation and deinterleaver, the received signal for the m-th sub-carrier during the i-th data interval at nth symbol is ex-

pressed by

)(imθ

)()()(1

1

0

,,,,,,, nnccndAnr m

K

k

N

m

vFkSF

vTkSFimkimkim

c

FT+⋅⋅= ∑ ∑

=

−

=, (4)

where Ak,m,i and are the received signal ampli-tude and AWGN with two-sided power spectral density (PSD) No/2, for nth symbol of the m-th subcarrier, re-spectively.

)(nnm

IDFT

Serial/Parallel Converter

• • •

• • •

⊗

⊗ ⊗

⊗

• • •

∑

d1,1

cos(2π0Δft)

Guard Interval Insertion

cos(2πfct)

⊗ S(t)

Data Stream of bk,j

dNm,Ni

2-D Spreading Codes Controller

• • •

⊗

⊗

• • •

kSFSF T,C

Duplicator in Tim

e-slices

kSFSF F,C

Duplicator in Sub-carriers

• • •

• • •

cos(2π(Nc-1)Δft)

dm,i’

• • •

)(0 tS

)(tSm

⊗ ⊗

⊗

• • •

• • •

)(tScN

Interleaver

s0,i

sm,i

sNc-1,i

• • •

Multiplexing

• • •

• • •

Other Users

(a)

DFT

S / P

• • •

⊗

⊗⊗

⊗

• • •

∑

cos(2π0Δft)

Guard Interval Remove

cos(2πfct)

⊗ r(t)

jkb ,ˆ

2-D Spreading Codes Controller k

SFSF T,C

P/S

kSFSF F,C

• • •

cos(2π(Nc-1)Δft)

)(0 tS

)(tSm

⊗⊗

⊗

• • •

• • •

)(tScN

• • •

• • •

• • •

DeInterleaver

s0,i

∑

• • •

Sgn

• • •

⊗

⊗

• • •

• • •

⊗

• • •

sm,i

sNc-1,i

im,G

Combiner (b)

Figure 2. Block diagram for OFCDM communication systems with 2-D spreading codes: (a) transmitter (b) MRC receiver for the k-th user.


In OFCDM systems, the orthogonal VSF code is per-formed to spread the transmitted symbol on both the time and the frequency domains simultaneously, as shown in Fig. 3. In Fig. 3, the spreading factor is set 16 and when SFT*SFF=16*1, it means the spreading factor is all on time with 16. Then it is called MC-DS-CDMA scheme. However, when SFT*SFF=1*16, where the spreading is all on frequency with 16. Thus, it is called MC-CDMA scheme.

To obtain the advantage of diversity gain, the maximal ratio combining (MRC) techniques [10] is performed in this paper. Thus, the receiver model for OFCDM systems is illustrated in Fig. 2(b). Therefore, the decision statistic for the m-th subcarrier during the i-th data duration for conventional MRC receivers is thus obtained as

[ ])()()( *,

,,,,, nhccnrnZ im

vFkSF

vTkSFimimk FT

⋅⋅⋅ℜ= , (5)

where , SFF is the frequency spreading factor and , SFT is the time spreading factor. Furthermore, the symbol decision for the j-th symbol is thus obtained by combining the 2-D spreading sub-channels as

)mod()1( FSFmvF +=)mod()1( TSFivT +=

⎥⎥⎦

⎤

⎢⎢⎣

⎡= ∑ ∑

= =

F

j

T

i

SF

m

SF

mimkjk iZb

1 1,,, )(sgn , (6)

where ,

,

jFFc mSFSFNjm +⋅= )]/(mod[

1,,2,1,0 −= Fj SFm iTFc

mSFSFN

ji +⋅⎥⎦

⎥⎢⎣

⎢ +=

/1 ,

. 1,,2,1,0 −= Ti SFm

3. Fuzzy-Based Code Allocation Scheme To examine the characteristics of diversity gain ob-

tained from 2-D spreading, the orthogonal VSF codes [9] are generated with the processing gain 16. In OFDM systems, the frequency synchronization error will result in the devastated inter-carrier interference (ICI) to de-grade the BER performance. Therefore, in order to focus much attention on the BER variations on the different 2-D spreading, we assume perfect subcarrier synchroni-zation with no frequency offset and no nonlinear distor-tion and perfect subcarrier amplitude/phase estimation for OFCDM systems. The combination of OFDM sig-naling and CDMA scheme has one major advantage that it can lower the symbol rate in each subcarrier so that a longer symbol duration makes it easier to quasi-synchronize the transmissions [5]. Therefore, in this paper, we assume a synchronous downlink channel, and then we discuss the BER performance of MC-CDMA systems with OVSF codes over frequency

selective fading channels. When multiple users are active, the OVSF codes can

be allocated to users sequentially by C16,1, C16,2,…, and C16,16. We call it sequential code allocation (SCA) scheme. However, due to the orthogonalization distorted in frequency and time selective channels, the BER is degraded due to the MAI in multi-user access systems. The MAI due to the out-orthogonality among the multi-ple access increases with the active number of users. Therefore, the performance of the OFCDM system can be improved by adequately selecting the 2-D spreading codes to compromise the diversity gain maximization and the MAIs minimization.

To maintain the orthogonality between the active users, an orthogonalized code allocation (OCA) scheme was proposed to improve the SCA scheme in previous work [18]. In the OCA, the code allocated to the k-th user is according to the time spreading factor SFT. The OVSF codes are allocated to users by C16,1, C16,q+1, C16,2q+1,…, and C16,16, where q= SFT. Thus, even though the or-thogonality among user SFT+1, SFT+2, …, SF would be destroyed, the orthogonality among user 1, 2, …, SFT can be maintained to suppress the MAIs.

Furthermore, as we know that the diversity gain in the decision statistic in (5) can be obtained from the fre-quency and time diversity depending on the 2-D spread-ing codes and the response of the frequency and time selective fading channels. The frequency diversity de-pends on the frequency spreading factor SFF in the 2-D spreading codes with the frequency interleaving on the subcarriers. Moreover, the time diversity not only de-pends on the time spreading factor SFT in the 2-D spreading codes but also related with the Doppler shift incurred by the speed of mobiles. Therefore, we further study the compromise between the maximization of the diversity gain and minimization of the MAIs.

The FIS is a decision-making logic which employs a set of fuzzy IF-THEN rules. It has drawn a great deal of attention because of its universal approximation ability in nonlinear problems [12-17]. Therefore, the optimal 2-D spreading factors of the adaptive code allocation (ACA) schemes can be easily determined by an FIS with sufficient rules. We can establish these fuzzy rules by matching input-output pairs through an adaptation pro-cedure. Here, for the practical implementations, we es-tablished both membership functions (MBFs) and rules by the heuristic basis and the knowledge about the in-put-output relations to find the optimal time spreading factor SFT for each user.

It is easy to know that to increase diversity, the fre-quency spreading factor becomes can be larger as the number of user K decreases. Moreover, as the MAI in-creases with the active number of users K, the SFT should be set to a larger value to decrease the interfer-


ence. On the other hand, if the Doppler shift is high due to the high speed of mobiles, the SFT should be set a smaller value to remain the orthogonality in time domain. Therefore, the optimal SFT inferred by the FIS in the fuzzy-based code allocation (FBCA) scheme should be adapted to the compromise on benefits of the diversity gain over the frequency- and time-selective fading channels and the sufferings of the MAI due to the multi-user access and the out of orthogonality.

We choose five Gaussian MBFs to cover the entire universe of discourse of two inputs, K and fD,k, and one output SFT,k. The five linguistic terms, very slow (VS), slow (S), medium (M), fast (F) and very fast (VF), are chosen to cover the universe of discourse for the fD,k of the desired user as shown in Fig. 3(a). The five terms, very few (VF), few (F), medium (MED), many (M) and a great many (GM), are chosen to cover the universe of discourse for the active number of users as shown in Fig. 3(b). As for the terms of the SFT,k, the five terms, very small (VS), small (S), medium (MED), large (L), and very large (VL), are chosen to cover its universe of dis-course as shown in Fig. 3(c). The Gaussian MBF of the fuzzy set in each interval [ , ] of the universe of discourse U can be expressed by

liF −

iC +iC

(a)

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛ −−=

2

21exp)( l

i

lii

iF

xxxl

i σμ , (7)

where l = 1, 2, …, 5, i = 1, 2, 3, [ ]+−∈ iii CCx , , and lix

and are the mean and standard deviation of the Gaussian MBF, respectively. In this paper, we consider the fuzzy control rules of a two-input-single-output fuzzy system as

liσ

(b)

R j: IF fD,k is AND K is , 11lF 2

2lF

THEN SFT,k = , (8) 33lF

where , and are the linguistic terms of the input variables fD,k, K and the output variable SFT,k, respectively, and l1, l2 , l3 = 1, 2, …, 5, and the index of rule j = 1, 2, …, 25. The rule base, shown in Table 1, including 25 fuzzy IF-THEN rules, can be established heuristically by the experimental results, which infer the relations between the adequate SFT of users to accom-modate their diversity with MAIs.

11lF 2

2lF 3

3lF

There are many defuzzification methods available. However, the following centroid calculation, which re-turns the center of area under the aggregated MBFs curve, is being employed here:

SFT,k (c)

Figure 3. The membership functions of the input variables (a) fD,k, and (b)K, and output variable (c) SFT,k for the proposed

FBCA scheme.


Table 1. The rule base of FBCA scheme.

K

fD,k VF F MED M GM

VS VS S MED L VL

S VS S MED L VL

M VS S MED L VL

F VS S L VL VL

VF VS S VL VL VL

SFT,

k

fD,k (Hz) fD,k (Hz)Figure 4. The 3-D inferring diagram for FBCA scheme in

OFCDM systems.

∑

∑

=

=⋅

= q

iiF

q

iiFi

kT

z

zzSF

l

l

1

1,

)(

)(

3

3

μ

μ, (9)

Then, the inference 3-D results for the SFT can be ob-tained as shown in Fig. 4. In consequence, the proposed FIS can be performed to assist in the 2-D code allocation for OFCDM communication systems as shown in Fig. 5, the block diagram of an FBCA transmitter over a fre-quency- and time-selective fading channel. where q is the number of quantization levels of the out-

put area under the aggregated MBFs, zi is the amount of the inference output at the quantization level i and

)(3

iF zlμ is its membership value in the output fuzzy set

. lF3

FBCAFBCA Mulri-user of 2-D SpreadingCodes Controller

Mulri-user of 2-D SpreadingCodes Controller

2-D SpreadingOFCDM diagram2-D Spreading

OFCDM diagram

ΣΣ

IDFT(2 0 )cos ftπ

(2 ( 1) )ccos N ftπ −

GuardIntervalInsertion

GuardIntervalInsertion

P/SP/S

(2 )ccos f tπ

( )S t

MuX&Σ

MuX&Σ

1, jb

2, jb

3, jb

,K jb #K


OFCDM diagram

#k,k jb


OFCDM diagram#3

#2

#1

K Df

TSF

Figure 5. The block diagram of an FBCA transmitter for OFCDM systems over a frequency- and time-selective fading channel.


4. Simulation Results

To examine the characteristics of diversity gain ob-tained from 2-D spreading, the OVSF codes [9] are gen-erated with the processing gain 16. In order to focus much attention on the BER variations on the different 2-D spreading, we assume perfect subcarrier synchroni-zation with no frequency offset and no nonlinear distor-tion and perfect subcarrier amplitude/phase estimation for OFCDM systems. The combination of OFDM sig-naling and CDMA scheme has one major advantage that it can lower the symbol rate in each subcarrier so that a longer symbol duration makes it easier to quasi-synchronize the transmissions [5]. Therefore, in this paper, we assume a synchronous downlink channel, and then we discuss the BER performance of MC-CDMA systems with OVSF codes over frequency selective fading channels. To investigate the multi-user performance of ACA schemes in the 2D spreading OFCDM systems as shown in Fig. 2, we performed computer simulation in which the simulation parameters are listed in Table 2.

We compare the BER performance of FBCA and OCA schemes for OFCDM systems with SNR = 9dB and K= 4 as shown Fig. 6. From Fig. 6, we observed that with the lower MAIs of K=4, the system BER can be improved by increasing the SFT for higher mobile speed to gain more time diversity. However, the proposed FBCA can adapt the speed of active mobile units to allocate the suitable SFT,k of OVSF codes to users and then maxi-mize the benefits of diversity gain with minimizing the MAIs.

Table 2. The parameters of computer simulation.

Number of sub-carriers, Nc 4096

Data modulation BPSK

Spreading factor, SF 16

2-D spreading code OVSF code

Doppler shift, fD 10-100 (Hz)

OFDM symbol duration 1 ms

Combining techniques MRC

To investigate the capacity performance of the ACA

schemes, Fig. 7 shows the BER performance comparison of FBCA and OCA schemes for OFCDM systems with fixed speed fD,k = 10 Hz and SNR = 9dB. From Fig. 7, we

observed that when the number of users increases, the performance is degraded due to the increasing MAIs. Even though, the MAIs of the number of users K = 4 is compensated by the frequency diversity gain of SFT =1. When the number of users increases to 16, the BER per-formance is degraded by the dominated MAIs. Then, with the minor out-orthogonality, the performance of SFT =16 is the best than other small SFT. Furthermore, Fig. 8 shows the BER performance comparison of FBCA and OCA schemes for OFCDM systems with varying speed fD,k from 10 to 100 Hz and SNR = 9dB. From Fig. 8, we observed that the proposed FBCA robustly outperforms the OCA schemes with different SFT of OVSF codes for all number of users with different speed from 10 to 100 Hz. Therefore, no matter what speed of the mobiles, or the number of users, the proposed FBCA scheme can robustly allocate the adequate 2-D OVSF cods to users for varying system load.

Figure 6. BER performance comparison of FBCA and OCA schemes for OFCDM systems with SNR = 9dB and K= 4.

Figure 7. BER performance comparison of FBCA and OCA

schemes for OFCDM systems with varying speed fD,k = 10 Hz and SNR = 9dB.


Figure 8. BER performance comparison of FBCA and OCA schemes for OFCDM systems with varying speed fD,k = [10,

100] Hz and SNR = 9dB.

5. Conclusions

In this paper, an FIS is proposed to improve the

multi-user performance for 2-D spreading OFCDM sys-tems over frequency selective fading channels. Simula-tion results show that the proposed FBCA scheme can suppress the MAIs induced by the non-orthogonality over time and frequency selective fading channels. Con-sequently, the FBCA scheme outperforms the OCA scheme in varying speed and number of users.

Acknowledgment

This work is supported by National Science Council, Taiwan, Republic of China, under Grant NSC 96-2221-E-324 -003.

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Yung-Fa Huang received the Dip-lom-Eng. in electrical engineering from National Taipei University of Technology, Taipei, in 1982, M.Eng. degree in electrical engineering from National Tsing Hua University, Hsinchu, Taiwan, in 1987 and Ph.D. degree in electrical engineering from National Chung Cheng University, Chiayi, Taiwan, in 2002. During 1987-2002, he was an in-

structor in Chung Chou Institute of Technology, Yuanlin, Tai-wan. From February 2002 to July 2004, he was with the De-partment of Electrical Engineering, Chung Chou Institute of Technology, as an Associate Professor. From August 2004 to July 2007, he was an Associate Professor in Graduate Institute of Networking and Communication Engineering, Chaoyang University of Technology, Taichung, Taiwan. From August 2007 to July 2008, he was the Department Head of Computer and Communication Engineering and the Institute Chair of the Graduate Institute of Networking and Communication Engi-neering, Chaoyang University of Technology. Since Aug. 2008, he has been the Department Head of Information and Communication Engineering, Chaoyang University of Tech-nology. His current research interests include multiuser detec-tion in OFDM-CDMA cellular mobile communication systems, communication signal processing, fuzzy systems and wireless sensor networks.

Neng-Chung Wang received the B.S. degree in Information and Computer Engineering from Chung Yuan Christian University, Taiwan, in June 1990, and the M.S. and Ph.D. degrees in Computer Science and Information Engineering from National Cheng Kung University, Taiwan, in June 1998 and June 2002, respectively. He joined the faculty of the Department of Computer Science and

Information Engineering, Chaoyang University of Technology, Taiwan, as an assistant Professor in August 2002. From Au-gust 2006 to July 2007, he was an Assistant Professor at the Department of Computer Science and Information Engineer-ing, National United University, Taiwan. Since August 2007, he has become an Associate Professor at the Department of Computer Science and Information Engineering, National

United University, Taiwan. His current research interests in-clude computer networks, wireless networks, and mobile computing. Dr. Wang is a member of the IEEE Computer So-ciety, IEEE Communications Society, and Phi Tau Phi Society.

Tan-Hsu Tan received the B.S. degree from National Taiwan Institute of Technology and M.S. degree from Na-tional Tsing Hua University, in 1983 and 1988, respectively, both in electri-cal engineering, and the Ph.D. degree in electronics engineering from National Chiao Tung University, Hsinchu, Tai-wan, in 1998. Since 1988, he has been f Electrical Engineering at the National

Taipei University of Technology, Taipei, Taiwan, R. O. C., where he is currently an associate professor. His research in-terests include mobile radio communications, optimization algorithms, and innovative applications of RFID technology.

with the Department o

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