Further performance analysis of the generalized MC DS-CDMA system in Nakagami-m fading channels

Computers and Electrical Engineering 35 (2009) 1–8

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Further performance analysis of the generalized MC DS-CDMA system in Nakagami-m fading channels Seher Sener a, Ibrahim Develi b,*, Nurhan Karaboga b a b

Institute of Science and Technology, Erciyes University, 38039 Kayseri, Turkey Department of Electrical and Electronics Engineering, Faculty of Engineering, Erciyes University, 38039 Kayseri, Turkey

a r t i c l e

i n f o

Article history: Received 22 December 2006 Received in revised form 27 November 2007 Accepted 27 March 2008 Available online 6 May 2008 Keywords: Spread spectrum communications Generalized MC DS-CDMA Rate of average power decay BER performance analysis Optimum normalized subcarrier spacing

a b s t r a c t The generalized multicarrier direct sequence code-division multiple-access (MC DS-CDMA) is a well known model that can be extended to different MC DS-CDMA schemes by simply varying a single parameter called as normalized subcarrier spacing. In this paper, the effect of the rate of average power decay on the bit error rate (BER) performance of the generalized MC DS-CDMA system is presented. Two specific schemes known as multitone DS-CDMA and orthogonal MC DS-CDMA are considered for the BER performance analysis. Simulation results show that the rate of average power decay has an important effect on the BER performance comparisons between the multitone DS-CDMA system and the orthogonal MC DS-CDMA system. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction Recently, the combination of multicarrier (MC) modulation and code-division multiple-access (CDMA) signaling has been widely studied due to the possible benefits carried out from both techniques [1–7]. The two common forms of this scheme are the multitone direct sequence (DS) CDMA [8] and the orthogonal MC DS-CDMA [9–14]. In a multitone DS-CDMA system the subcarrier frequencies are chosen to be orthogonal harmonics of each other with minimum frequency separation among them before spreading. Therefore, in multitone DS-CDMA systems, the spacing D between two adjacent subcarrier frequencies is D = 1/Ts, where Ts represents the symbol duration of the multitone DS-CDMA signal. On the contrary, in an orthogonal MC DS-CDMA system, the subcarrier frequencies are chosen to satisfy the orthogonality condition with the minimum possible frequency separation after spreading. For an orthogonal MC DS-CDMA system, the D between two adjacent subcarrier frequencies is D = 1/Tc where Tc is the chip duration of spreading codes. It is well known that the Nakagami-m distribution spans via the m parameter the widest range of fading figure [15,16]. For instance, it includes the one-sided Gaussian distribution (m = 1/2) and the Rayleigh distribution (m = 1) as special cases. In the limit as m ? 1, the Nakagami-m fading channel converges to a nonfading additive white Gaussian noise (AWGN) channel. Similarly, when m > 1, allowing the Nakagami-m distribution to closely approximate the Rician distribution. It should be noted that the Nakagami-m distribution often gives the best fit to land-mobile and indoor-mobile multipath propagation, as well as scintillating ionospheric radio links [16]. In a recent paper [17], Yang and Hanzo have proposed a class of generalized MC DS-CDMA schemes and evaluated its performance over multipath Nakagami-m fading channels. In the proposed scheme, both the multitone DS-CDMA system and the orthogonal MC DS-CDMA system can be viewed as a member of the class of generalized MC DS-CDMA systems having * Corresponding author. Tel.: +90 352 437 49 01/32 205; fax: +90 352 437 57 84. E-mail address: [email protected] (I. Develi). 0045-7906/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compeleceng.2008.03.001

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S. Sener et al. / Computers and Electrical Engineering 35 (2009) 1–8

arbitrary subcarrier spacing of k. As it is remarked in [17], the generalized MC DS-CDMA system model includes a number of specific MC DS-CDMA schemes, and the results generated can be extended to different MC DS-CDMA systems by simply varying a single parameter, k. Interested readers may refer to [17] for the influence of the subcarrier spacing k on the bit error rate (BER) performance of the MC DS-CDMA system. The performance analysis performed in [17] considers only one specific rate of average power decay. As an extension of [17], the BER performance of the multitone DS-CDMA systems for transmissions over Nakagami-m fading channels has been successfully presented in [18]. In order to better understanding the BER performance of the generalized MC DS-CDMA, the effect of the rate of average power decay on the BER performance of the generalized MC DS-CDMA is investigated in the present study [19]. The remainder of this paper is organized as follows. In the following section, a brief description of the generalized MC DSCDMA system which was originally introduced in [17] is presented. This section also includes the descriptions of the multitone DS-CDMA and the orthogonal MC DS-CDMA schemes. In Section 3, performance of the multitone DS-CDMA and the orthogonal MC DS-CDMA is analyzed and compared. Finally, some conclusions are drawn in Section 4. 2. The generalized MC DS-CDMA system In this section, a brief description of the generalized MC DS-CDMA system [17] is presented. At the transmitting side of the generalized MC DS-CDMA system, the binary data stream having bit duration of Tb is serial-to-parallel converted to U parallel substreams. Therefore, the symbol duration is Ts = UTb. After serial-to-parallel conversion, the uth substream modulates a subcarrier frequency fu using binary phase-shift keying (BPSK) for u = 1, 2, . . . , U. Then, the U subcarrier-modulated substreams are added in order to form the complex modulated signal. Finally, spectral spreading is imposed on the complex signal by multiplying it with a spreading code. Therefore, the transmitted signal of user k can be expressed as sk ðtÞ ¼

U pffiffiffiffiffiffi X 2P bku ðtÞck ðtÞ cosð2pfu t þ /ku Þ

ð1Þ

u¼1

where U is the number of subcarriers and P is the transmitted power per subcarrier. bku(t) and ck(t) represent the binary data stream and the spreading waveform, respectively. fu is the uth subcarrier frequency and /ku denotes the phase angles introduced in the carrier modulation process. The processing gain, Ne, of the subcarrier signal can be written as [17, Eq. (6)] N e ¼ UN 1 

ðU  1Þk 2

ð2Þ

where N1 is the spreading gain of a corresponding single-carrier DS-CDMA system and k is the normalized subcarrier spacing. In this study, it is assumed that the channel between the kth transmitter and the corresponding receiver is a multipath Nakagami-m fading channel [15]. The complex low-pass equivalent representation of the impulse response experienced by subcarrier u of user k is given by   LX p 1 ðkÞ jw ðkÞ ulp ð3Þ aulp dðt  sklp Þe hku ðtÞ ¼ lp ¼0 ðkÞ aulp ,

ðkÞ

where sklp and wulp represent the attenuation factor, delay and phase-shift for the lpth multipath component of the channel, respectively, while d(t) is the Kronecker–Delta function. The total number of diversity paths, Lp, is given by [17, Eq. (8)]   2N e ðL1  1Þ þ1 ð4Þ Lp  2N e þ ðU  1Þk where L1 denotes the number of resolvable paths in the context of the corresponding single-carrier DS-CDMA signal. It is ðkÞ assumed that the phases fwulp g in Eq. (3) are independent identically distributed (i.i.d) random variables uniformly distribðkÞ uted in the interval [0, 2p), while the Lp multipath attenuations faulp g are independent Nakagami random variables with a probability density function of     ðkÞ ðkÞ ðkÞ p aulp ¼ M aulp ; m; Xulp ð5Þ 2mm R2m1 ðm=XÞR2 MðR; m; XÞ ¼ e CðmÞXm where C() is the gamma function and m is the Nakagami-m fading parameter, which is equal to m ¼ E2 bðaulp Þ2 c=Varbðaulp Þ2 c ðkÞ ðkÞ and ranges from 1/2 to 1. The parameter Xulp in Eq. (5) is the second moment of aulp . The multipath intensity profile (MIP) distribution considered in this paper is an exponential MIP defined by ðkÞ

ðkÞ

ðkÞ

Xulp ¼ Xu0 expðglp Þ ðkÞ Xu0

8lp ¼ 0; . . . ; Lp  1

ðkÞ

ð6Þ

is the average signal strength corresponding to the first resolvable path and g represents the rate of average power where decay. It is useful to note that the exponential MIP is a more realistic profile model where the average power decays exponentially as the path delay increases [20–22].

S. Sener et al. / Computers and Electrical Engineering 35 (2009) 1–8

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Consider K asynchronous CDMA users in the system, where all of them use the same U and Ne values, with perfect power control. Consequently, when K signals obeying the form of Eq. (1) are transmitted over the fading channels, the received signal at the base station can be expressed as rðtÞ ¼

p 1 pffiffiffiffiffiffi K X U LX   X ðkÞ ðkÞ 2P aulp bku ðt  sklp Þck ðt  sklp Þ  cos 2pfu t þ uulp þ nðtÞ

ð7Þ

k¼1 u¼1 lp ¼0 ðkÞ

ðkÞ

where uulp ¼ /ku  wulp  2pfu sklp , which is assumed to be an i.i.d random variable having a uniform distribution in [0, 2p), while n(t) represents the AWGN with zero mean and double-sided power spectral density of N0/2. At the receiver, according to the decision variable Zv, v = 1, 2, . . . , U, the current data bit of the vth substream is decided to be 0 or 1, depending on whether Zv is higher than zero. When we assume that the first L, 1 6 L 6 Lp, number of resolvable paths are combined by the receiver, than Zv, can be written as [17, Eqs. (11) and (12)] L1 X

Zv ¼ Z vl ¼

Z vl ; l¼0 Z T s þsl

v ¼ 1; 2; . . . ; U

ð8Þ

rðtÞ  avl cðt  sl Þ cosð2pfv t þ uvl Þdt

ð9Þ

sl

Finally, the U number of parallel data substreams are parallel-to-serial converted, in order to output the serial data bits. Based on the detailed performance analysis presented in a previous study, the average BER for the generalized MC DS-CDMA system is given by [17, Eq. (47)] !m Z 2 L1 1 p=2 Y m sin h dh ð10Þ Pb ¼ 2 p 0 cc egl þ m sin h l¼0 where cc ¼

" 1  #1 X0 Eb 2ðKLp  1Þð1  egLp Þ 1  þ þ ðU  1ÞI M N0 Lp ð1  eg Þ 3N e

ð11Þ

and    U X U X 1 Ne 2pðu  vÞk  1  sinc 2 2 UðU  1Þ v¼1 u¼1 2p2 ðu  vÞ k Ne

IM ¼

ð12Þ

u–v

2.1. Orthogonal MC DS-CDMA scheme The orthogonal MC DS-CDMA scheme does not include serial-to-parallel data conversion either. However, each subcarrier signal is DS spread using a common spreading sequence ck(t). Therefore, the symbol duration of the multicarrier DS-CDMA signal is the same, as that of the input data bit duration. The transmitted signal of user k in the orthogonal MC DS-CDMA system can be expressed as rffiffiffiffiffiffi U 2P X sk ðtÞ ¼ bk ðtÞck ðtÞ cosð2pfu t þ /ku Þ ð13Þ U u¼1 where P is the transmitted power of the orthogonal MC DS-CDMA signal, U is the number of subcarriers, while bk(t) and ck(t) are the baseband data sequence and the spreading waveforms, respectively. Finally, fu for u = 1, 2, . . . , U are the subcarrier frequencies and /ku for u = 1, 2, . . . , U are the initial phases introduced by the subcarrier-modulation. In the orthogonal MC DSCDMA system the subcarrier frequencies are usually chosen to be orthogonal to each other after spreading, which can be formulated as Z

Tc

cosð2pfi t þ /i Þ  cosð2pfj t þ /j Þdt ¼ 0

for i–j

ð14Þ

0

where Tc is the chip duration. In this scheme, the minimum spacing D between two adjacent subcarriers satisfies D = 1/Tc. The spectral gain is then given by [23, Eq. (17.6)] SG ¼

Uð2=T c Þ ðU þ 1Þð1=T c Þ

ð15Þ

The receiver block diagram of the orthogonal multicarrier DS-CDMA system is shown in Fig. 1 [23]. In the orthogonal MC DSCDMA system frequency diversity is achieved by combining the U correlator’s outputs associated with the U subcarriers. The receiver provides a correlator for each of the U subcarriers, and the outputs of the U correlators are combined to produce a

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S. Sener et al. / Computers and Electrical Engineering 35 (2009) 1–8

×

×

Tb

1 0

cos(2π f t + ϕ )

g [1] T

Received Signal

×

cos( 2π f t + ϕ )

gk[2]

×

×

cos( 2π f t + ϕ )

2 0

∑

Zk

• • •

• • •

×

b

U 0

g [U]

Fig. 1. The receiver block diagram of the orthogonal MC DS-CDMA system [23].

processing gain comparable to that of a single-carrier DS system, provided that the spacing between two adjacent subcarriers is D = 2/Tc. The system has a number of advantages. Firstly, the orthogonal MC DS-CDMA system is robust to multipath fading due to the frequency diversity achieved over the subcarriers. Secondly, the orthogonal MC DS-CDMA system exhibits narrowband interference suppression capability due to the DS spreading. Thirdly, in an orthogonal MC DS-CDMA system having U subcarriers the entire bandwidth of the system is divided into U equi-width frequency bands. Thus each subcarrier frequency is modulated by a spreading sequence having a chip duration, which is U times as long as that of the corresponding single-carrier DS-CDMA system [23,24].

2.2. Multitone DS-CDMA scheme The multitone DS-CDMA transmitter spreads the serial-to-parallel converted data streams with the help of a given spreading code in the time domain, so that the spectrum of each subcarrier prior to the spreading operation can satisfy the orthogonality condition with the minimum frequency separation. Therefore, it is possible to produce strong spectral overlap among the different subcarrier signals after DS spreading. At the transmitter side of the multitone DS-CDMA, the binary data stream having a bit duration of Tb is serial-to-parallel converted to U parallel substreams. The new bit duration on each subcarrier, which defines the modulated symbol duration is Ts = UTb. The ith substream modulates the subcarrier frequency fi, i = 1, 2, . . . , U. The multitone signal is produced by the addition of the different subcarriers’ signals. Then, spectrum spreading is imposed on the multitone signal by multiplying it with a spreading code. The transmitted signal of user k can be expressed as sk ðtÞ ¼

U pffiffiffiffiffiffi X 2P bku ðtÞck ðtÞ cosð2pfu t þ /ku Þ

ð16Þ

u¼1

where P represents the transmitted power of each subcarrier, bku(t) represents the data sequence modulating the uth subcarrier, ck(t) is the spreading code of user k, while fu and /ku are the uth subcarrier frequency and modulation phase, respectively. In the multitone DS-CDMA system the subcarrier frequencies are selected to be orthogonal to each other with minimum frequency separation before spreading, which can be formulated as Z Ts cosð2pfi t þ /i Þ  cosð2pfj t þ /j Þdt ¼ 0 for i–j ð17Þ 0

The receiver block diagram of the multitone DS-CDMA system is shown in Fig. 2 [23]. The receiver is composed of U RAKE combiners, each of which has the same form as the single-carrier DS-CDMA RAKE receiver. It is useful to note that this is an optimum receiver for an AWGN channel. Unfortunately, the multitone DS-CDMA scheme suffers from inter-subcarrier interference and requires a high-complexity RAKE based receiver. However, as compared to the spreading codes assigned to a corresponding single-carrier DS-CDMA scheme, the capability to use longer spreading codes results in the reduction of self-interference and multiple-access interference. The multitone DS-CDMA scheme uses longer spreading codes than the corresponding single-carrier DS-CDMA scheme. Also, the relative code-length extension is in proportion to the number of subcarriers. Thus, the multitone DS-CDMA system can support more users [23].

5

×

1 Rake Combiner

Z

2nd Rake Combiner

Z

U Rake Combiner

Z

< > 0

1

< > 0

2

cos(2π f t + ϕ )

×

Received Signal

×

• • •

• • •

cos(2π f t + ϕ ) < > 0

U

Parallel-to-Serial Converter

S. Sener et al. / Computers and Electrical Engineering 35 (2009) 1–8

Data

cos(2π f t + ϕ ) Fig. 2. The receiver block diagram of the multitone DS-CDMA system [23].

3. Performance analysis and results In this section, the BER performance of the generalized MC DS-CDMA system for transmission over Nakagami-m fading channels with an exponential MIP is presented. The simulations are realized for the multitone DS-CDMA system and the

10-1 Multitone Orthogonal Optimu m

BER

10-2

10-3

10-4 0

2.5

5

10

15

20

25

30

Fading parameter, m 10 -1

10

Multitone Or thogonal Optimum

-2

BER

10 -3

10 -4

10 -5

10 -6 0

3.8 5

10

15

20

25

30

Fading parameter, m Fig. 3. BER of the multitone DS-CDMA system and the orthogonal MC DS-CDMA system versus the fading parameter, m, for a low rate of average power decay (g = 0.2), when: (a) Eb/N0 = 8 dB and (b) Eb/N0 = 12 dB.

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S. Sener et al. / Computers and Electrical Engineering 35 (2009) 1–8

orthogonal multicarrier DS-CDMA system. Suggestions from the literature helped guide our choice of parameter values for the simulation. Except from the values employed for g, the parameter values used in the simulation are similar to those used in previous studies [17,23]. The system parameters and the computer simulation conditions which are not changed during the simulation are summarized as follows: the spreading gain and the number of resolvable paths of the corresponding single-carrier DS-CDMA system are N1 = 128 and L1 = 32, respectively. The number of subcarriers used in this section is U = 32. The number of simultaneous users and the number of diversity branches used by the receiver are assumed as K = 10, and L = 5, respectively. The signal to noise ratio (SNR) per bit is assumed as Eb/N0 = 8 dB and Eb/N0 = 12 dB. In order to emphasize the effects of two extreme scenarios, the rate of average power decay g is set to 0.2 (a low rate of average power decay) and 0.9 (a high rate of average power decay). In each figure, three curves are provided. We use dotted lines, broken lines, and solid lines to show the BER performance achieved by the multitone DS-CDMA system, the orthogonal MC DS-CDMA system, and the MC DS-CDMA system having optimum spacing, respectively. Figs. 3 and 4 show the BER versus the fading parameter, m, for the multitone DS-CDMA and the orthogonal MC DS-CDMA. It should be noted that the BER curves obtained by the MC DS-CDMA system having optimum spacing, are denoted as ‘‘optimum” in all figures. In Fig. 3a and b, the BERs for the multitone DS-CDMA and the orthogonal MC DS-CDMA are compared for a low rate of average power decay which equals to g = 0.2. As can be seen, the performance of multitone DS-CDMA scheme is somewhat better than the performance of orthogonal MC DS-CDMA scheme, when the channel fading is severe. The effect of the SNR per bit on the performance of these schemes is also evident. It can be observed that the orthogonal MC DS-CDMA scheme starts to outperform the multitone DS-CDMA at different fading values as m = 2.5 and m = 3.8 for Eb/N0 = 8 dB and Eb/ N0 = 12 dB, respectively. Fig. 4a and b show the BERs achieved by the multitone DS-CDMA and the orthogonal MC DS-CDMA when a high rate of average power decay is employed (g = 0.9). These results mainly match the trends shown in Fig. 3a and b. It can be

10 -1 Multitone Orthogonal Optimum

BER

10 -2

10 -3

10 -4 0

10

5

15

20

25

30

Fading parameter , m 10 -1 Multitone Orthogonal Optimum

BER

10 -2

10 -3

10 -4

10 -5 0

5

10

15

20

25

30

Fading parameter, m

Fig. 4. BER of the multitone DS-CDMA system and the orthogonal MC DS-CDMA system versus the fading parameter, m, for a high rate of average power decay (g = 0.9), when: (a) Eb/N0 = 8 dB and (b) Eb/N0 = 12 dB.

S. Sener et al. / Computers and Electrical Engineering 35 (2009) 1–8

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observed that the performance of the multitone DS-CDMA scheme is superior to that of the orthogonal MC DS-CDMA scheme in a wide range of fading parameter, 0 6 m < 15. However, the orthogonal MC DS-CDMA scheme begins to achieve better performance than the multitone DS-CDMA at the same fading value, m = 15, for both Eb/N0 = 8 dB and Eb/N0 = 12 dB. It is well known that as the rate of average power decay increases, a main path signal should have larger average power than a multipath signal. Thus, the amount of received power in each faded path will be decreased. This is the reason why we observe two different interchanges as a function of the fading parameter for different values of the average power decay rate.

4. Conclusion The multitone DS-CDMA system and the orthogonal MC DS-CDMA system can be viewed as a member of the class of generalized MC DS-CDMA systems having arbitrary subcarrier spacing of k [23]. In this paper, the effect of the rate of average power decay on the BER performance of the multitone DS-CDMA system and the orthogonal MC DS-CDMA system is presented. The numerical results indicate that the rate of average power decay has an important effect on the BER performance comparisons between the multitone DS-CDMA system and the orthogonal MC DS-CDMA system. Also, our results which are realized for a low rate of average power decay show that the orthogonal MC DS-CDMA scheme starts to outperform the multitone DS-CDMA at different fading values for various SNR per bit. On the contrary of that observed for a low rate of average power decay, the results obtained for a high rate of average power decay indicate that the orthogonal MC DS-CDMA scheme begins to achieve better performance than the multitone DS-CDMA at the same fading value for both SNR per bit considered in this study.

Acknowledgements The authors would like to thank the anonymous reviewers for their valuable comments and suggestions, which provided valuable guidance as to how we could improve this paper. They would also like to thank Dr. Lie-Liang Yang for sharing his experience about understanding the Eqs. (11) and (12).

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]

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S. Sener et al. / Computers and Electrical Engineering 35 (2009) 1–8 Seher Sener received the B.S. and M.S. degrees in Electronics Engineering from Erciyes University, Kayseri, Turkey, in 2004 and 2006, respectively. Her fields of interest include wireless and mobile communications, multicarrier communication systems, multiuser detection, spread spectrum communications, and generalized multicarrier DS-CDMA system.

Ibrahim Develi received the B.S., M.S., and Ph.D. degrees in Electronics Engineering from Erciyes University, Turkey, in 1995, 1997, and 2003, respectively. From October 1995 to May 2003, he was a Research Assistant in the department of electrical and electronics engineering at the Erciyes University. Currently, he is an Assistant Professor at the same department. He teaches courses in wireless communications and his current research interests are in spread spectrum communications, multicarrier communication systems, multiuser detection, wireless networks, radio-over-fibre transmission, millimeter waves, multiple access interference rejection in DS-CDMA systems, and applications of artificial intelligence techniques to multiuser communication systems. Dr. Develi is an Associate Editor for the EURASIP Journal on Wireless Communications and Networking, as well as a member of the Editorial Board of International Journal of Mobile Communications.

Nurhan Karaboga received the B.S., M.S. and Ph.D. degrees in Electronics Engineering from Erciyes University, Turkey, in 1987, 1990 and 1995, respectively. From 1987 to 1995, she was a research assistant in the department of electrical and electronics engineering at the Erciyes University. Currently, she is an assistant professor at the same department. From 1992 to 1994 she also worked as an academic visitor in the University of Wales College of Cardiff, UK. Her current research interests include wireless communications, genetic algorithms, ant colony algorithms, simulated annealing algorithm, differential evolution algorithm, immune algorithm, and digital filter design for data communications.