Adaptive Parallel Interference Cancellation for Uplink MC-CDMA in Rayleigh Fading Channels

Xiaoyan Feng, Charalampos Tsimenidis, Bayan Sharif

School of Electrical, Electronic and Computer Engineering, Merz Court, University of Newcastle upon Tyne Newcastle upon Tyne, UK

E-mail: feng.xiaoyan@gmail.com

Abstract: In this paper, an adaptive parallel interference cancellation (PIC) receiver is introduced for asynchronous multicarrier code division multiple access based (MC-CDMA) communications systems. The multiple access interference (MAI) estimates are obtained using the bit estimates from the previous stage and the adaptive weights for the bit estimates. The adaptive weights are updated by minimizing the mean squared error between the received signal and its estimate based on the adaptation of the normalized least mean square (LMS) algorithm. The results from the simulations show that the performance of conventional PIC (CPIC) and adaptive PIC (APIC) can be different depending on the combining schemes used.

1. INTRODUCTION

The wideband nature of Direct Sequence CDMA (DS-CDMA) transmissions allows the receiver to resolve signals propagating through different paths, and gains multipath diversity to combat fading effects. A RAKE receiver can be used to enhance the system performance [1]. However, the goal of the future wireless communication systems is to achieve data rates as large as 100 Mbps by using a large bandwidth. With such a wide bandwidth, a transmitted signal experiences a broadband channel with very large multipath delay spread, causing very severe intersymbol interference (ISI). Although in principle this problem can be alleviated using multiuser detection (MUD) combined with the Rake receiver, it may still be difficult for DS-CDMA to keep the multiple-access interference (MAI) and ISI under a desired level. And the computational complexity for a RAKE receiver in DS-CDMA systems increases exponentially as the data transmission rates required for the wireless communication systems increase. Therefore, instead of only relying on increasingly complex algorithms, the combination of OFDM with CDMA, known as MC-CDMA [2]-[4], is introduced to solve the frequency selectivity problem. It has been shown in [5]-[7] that the MC-CDMA system exhibits better performance than the conventional DS-CDMA system in the broadband channel.

For uplink asynchronous transmission in the MC-CDMA systems, the transmitted signal from each user arrives at the base station through a different fading channel. In practical systems, it is difficult and expensive to maintain synchronization of all users. Asynchronous transmission

between users results in misalignment in the signal arriving times among different users. In this case, the orthogonality among different subcarriers and spreading codes of different users are destroyed, which results in very strong MAI among users [8]. Therefore, effective interference cancellation schemes [9] and MUD [10][11] need to be employed to improve the capacity of the MC-CDMA systems.

In this paper, the design of receivers for asynchronous MC-CDMA systems is concerned. Among the MUD schemes, the parallel interference cancellation (PIC) approach is attractive because of the potential capacity increases and the simplicity of its practical implementation. Some works [12][13] of PIC have been done in the quasi-synchronous uplink channel, in which the timing differences are small compared to the cyclic prefix, and thus the useful parts of the consecutive symbols of different users are not overlapping [14]. To further improve the performance, adaptive PIC (APIC) scheme is proposed. In each stage of the APIC receiver, MAI estimates are obtained using the bit estimates from the previous stage and the adaptive weights for the bit estimates. The adaptive weights are obtained by minimizing the Euclidean distance between the received signal and its estimate through the LMS algorithm [15]. The proposed APIC scheme is examined with the simple despreading and combining (DC) receiver suggested in [3][16]. It is assumed that the fading process is constant at least over one symbol interval and hence there is no intercarrier interference arising in the considered system.

The remainder of this paper is organized as follows. Section 2 introduces the system model. In Section 3, the receiver structure of the proposed APIC detector is described. In Section 4, the performance of the system is verified with computer simulations. Finally, Section 5 summarizes the paper with some concluding remarks.

2. SYSTEM DESCRIPTION

Suppose that there are K active users in an uplink, each of which employs N subcarriers and binary phase-shift keying (BPSK) modulation. The mth bit of the kth user )(mbk is

spread by user k’s spreading sequence { }Nnknc 1= in the

transmitter. In order to fully eliminate the ISI, a cyclic prefix (CP) of length longer than the multipath delay spread is inserted between two consecutive bits [17]. The transmitted

signal over a symbol block for the kth user, including the CP, is then given by

∑−

=

−=1

0

)(/2)()()(N

n

tTnjsknkkk

bemTtpcmbAts ψπ (1)

where kA is the signal amplitude, )(tp is the pulse-shaping function defined in ),[ bCP TT− with bT denoting the bit duration, CPT and CPbs TTT += are the CP interval and the MC-CDMA symbol duration. The function )(tψ is defined as

+<≤−<≤−−+

=bsss

sCPssb

TmTtmTmTtmTtTmTmTTt

t,

,)()(ψ (2)

A slowly varying frequency-selective Rayleigh fading channel is considered, which means that the channel parameters are unchanged over one bit duration bT . Since it is the uplink transmission, the signal from each different user has a distinct propagation channel. Thus, there is a set of random amplitudes and a set of random phases associated with each user. The channel model for the kth user during the mth bit is given by

∑=

−=L

lklklk ttth

1

)()( δβ (3)

where )(⋅δ is the Dirac delta function, lkt , is the lth path delay, and klβ is a complex-valued independent Gaussian random variable (r.v.) with zero mean. It is assumed that the multipath power is normalized to one such as

{ } 11

=∑=

∗L

lklklE ββ ( {}⋅E denotes expectation). Denoting the

channel gain for the nth subcarrier of the kth user as knh , the channel transfer function can be written as

1,,1,0,1

/2 −==∑=

− NnehL

l

Tntjklkn

bklπβ (4)

The received signal can be written as

)(

)()()(

)(/2

1

1

0

te

mTtphcmbAtr

kb tTnj

ks

K

k

N

nknknkk

η

τ

τψπ +×

−−=

−

=

−

=∑ ∑ (5)

where kτ is the kth user’s asynchronous transmission delay, and )(tη is a complex additive white Gaussian noise (AWGN) with zero mean and variance 2/0

2 N=ησ .

3. RECEIVER STRUCTURE

Fig. 1 shows the receive structure of the MC-CDMA system. As shown the figure, a fast Fourier transform (FFT) operation is applied to the received signal to obtain the transmitted signal on each subcarrier. The received signal on the ith subcarrier for the qth user after applying FFT is given by

∫++

+

−−−=qbs

qs

sqbTmT

mT

mTtTij

bqi dtetr

Tr

τ

τ

τπ )(/2)(1' (6)

Without loss of generality, it is assumed that the first user is the one of interest and the observation window is mth symbol duration. The delays of all the active users are ordered in the following manner: bK T<<<<≤ τττ …210 . Therefore, the received signal with the first user as reference after demodulation can be written as

∑−

=

=1

01''

N

iirr (7)

)(tr )(1 mb'r

11'r

12'r

Nr 1'

∑

Figure 1 - Receiver structure of MC-CDMA system Substituting (6) into (7) by setting 1=q produces

∑ ∫−

=

++

+

−−−=1

0

)(/21

1

1)(1'N

i

TmT

mT

mTtTij

b

bs

s

sb dtetrT

rτ

τ

τπ (8)

It is assumed that the transmission delay 1kd is smaller than the cyclic prefix. The discrete-sample of the received signal at the subcarrier n after demodulation can be written as

nkn

K

kkk

ndTnj

knkn

K

kkkn

HmbA

echmbAr kb

ζ

ζπ

+=

+=

∑

∑

=

−

=

1

/2

1

)(

)(' 1

(9)

where nζ is the noise term at the subcarrier n. knH is the element of the NK × channel matrix H given by

=

=

−

−

−−−

−−

−−−

−−−−

)1(10

)1(22120

111110

/2)1()1(

/211

/200

/2)1(2)1(2

/22121

/22020

)1(1)1(111111010

111

212121

NKKK

N

dTnjNKNK

dTnjKK

dTnjKK

dTnjNN

dTnjdTnjNN

HHH

HHHHHH

ehcehcehc

ehcehcehchchchc

KbKbKb

bbb

πππ

πππ

H

(10) The APIC detector is depicted in Fig. 2. From Fig. 2, the

initial estimates from the user detectors are used to regenerate the signal of the desired user at the receiver. Mathematically expressed as

knknkkn chbs ~ˆˆ = (11)

where 1/2~ kbdTnjknkn ecc π−= and { })(sgnˆ

kk zrealb = .

Here ∑−

=

=1

0

'N

nnknknk rcGz . knG is the equalisation parameter,

where kn

knkn h

hG

∗

= with the Equal Gain Combining (EGC)

scheme and ∗= knkn hG with the Maximal Ratio Combing (MRC) scheme.

The regenerated signal of user k using the estimated data

kb corresponds to

knknkn swr ˆˆ = (12)

nr

Ky

1yns1

Kns

'r

2yns2ˆ

nw1

nw2

Knw

'nr

ne

∑

∑

∑

Figure 2 - Structure of APIC detector for MC-CDMA system And these regenerated signals are then summed up to form the estimated signal

∑=

=K

kknknkknn chbwr

1

~ˆˆ (13)

To obtain the optimal weights, the normalized LMS algorithm was introduced in [15], which tries to minimize the Euclidean distance between the received signal 'nr and the estimated signal nr . The normalized LMS algorithm based on the MSE criteria can be expressed as follows

[ ]2min neEw

(14)

where nnn rre ˆ'−= is the estimation error. The weight vector nw are adjusted on chip basis within a bit period according to

n

n

nnn e21

ˆ

ˆ

s

sww

µ+=+ (15)

where µ is the step size. There are totally N iterations until the final weights 1−Nw are obtained. And at the end of the N iterations, the final weights 1−Nw are used to multiply the input signals ns over all subcarriers. Hence, the regenerated signal of all interfering users are removed from the desired user and the interference free signal for user 1 is given by

∑=

−=K

kknnn rry

21 ˆ' (16)

After projecting ny1 onto the orthogonal basis and despreading, the combining technique is employed and the signal output is hard-limited to obtain the final decision.

4. SIMULATION RESULTS

In this section, simulation results are presented. Since a proper CP is used, the subchannels are independently Rayleigh fading and frequency-non-selective. A uniform multipath profile is adopted. The spreading sequences employed are Gold codes of 63-chip length. Perfect power control is assumed. The terms conventional PIC (CPIC) and adaptive PIC (APIC) are used. To highlight the combining schemes used in the different stages, for both CPIC and APIC the name of the combining schemes are reported. For example, the notation APIC-EGC-MRC will refer to an APIC receiver using the EGC scheme at the 0th stage and the MRC scheme at the 1st stage.

Fig. 3 shows the bit error rate (BER) vs. 0NEb (average

Figure 3 - BER versus 0NEb for the conventional receiver using different combining schemes with the number of users K=10, 20 energy per information bit to the noise power spectral density at the receiver input) of the conventional receiver using different combining schemes for different user populations. As can be seen, the EGC scheme outperforms the MRC scheme when the number of users is equal to 10 and 20 users. For example, the EGC receiver requires approximately 4 dB less in 0NEb than the MRC receiver to achieve a BER of

2102 −× when the number of users is equal to 10. To investigate the effects of different combing schemes at

different stages on the performance of CPIC, results are given

in terms of BER versus 0/ NEb in Fig. 4 (a) and (b)

(a) 10 users.

(b) 20 users.

Figure 4 - BER versus 0NEb for 1-stage CPIC using different combining schemes (a) 10 users. (b) 20 users. for CPIC using different combining schemes and the number of users is equal to 10 and 20. Fig. 4 (a) shows that there is not much difference between different combining schemes used when the number of users equals to 10. However, for the case of 20 users the performance of CPIC is different depending on the combining schemes used. Among all the different combing schemes, the CPIC receiver has the best performance when the EGC scheme is applied at both stages. For example, the CPIC-EGC-EGC receiver requires approximately 5 dB less in 0NEb than the CPIC-EGC-MRC receiver to achieve a BER of 2102 −× when the number of users is equal to 20. In Fig. 5, the effects of different combing schemes at different stages on the performance of APIC receiver are also investigated. The results are similar to

the case of CPIC receiver. There is not much difference between different combining schemes used for the case of 10 users while the APIC-EGC-EGC receiver performs best among all the combinations for the case of 20 users. And a closer look reveals that both the CPIC-EGC-EGC receiver and the conventional EGC receiver are outperformed by the proposed APIC-EGC-EGC receiver with 20 users.

(a) 10 users

(b) 20 users

Figure 5 - BER versus 0NEb for 1-stage APIC using different combining schemes (a) 10 users. (b) 20 users.

Fig. 6 shows the performance comparison for various detectors. The step size is set to be 0.2. The proposed APIC receiver exhibits best performance among all types of detectors when the number of users is bigger than 13. For example, to maintain a BER of 0.01, the conventional and the CPIC receiver can accommodate 9 and 18 users respectively, while the APIC can support 25 users.

Figure 6 - Performance comparison of one-stage APIC, one-stage CPIC and conventional receiver with respect to the number of users ( 0NEb =12dB)

5. CONCLUSION

In this paper, the adaptive PIC is proposed for the asynchronous MC-CDMA systems operating over Rayleigh multipath fading channels. The quasi-synchronous channels are considered. That is the relative delays are smaller than the cyclic prefix, and thus the useful parts of the consecutive symbols of different users are not overlapping. Simulation results show that the performance of CPIC and APIC can be different depending on the combining schemes used. It is shown that the APIC receiver outperforms the conventional receiver. And compared with the CPIC, the APIC receiver can improve the performance in the middle to heavy load of networks. REFERENCES [1] J. G. Proakis, Digital Communications, New York: McGraw-Hill, 4th ed., 2001. [2] N. Yee, J. P. Linnartz, and G. Fettweis, “Multicarrier CDMA in indoor wireless radio,” in Proc. IEEE MILCOM’93, Boston, MA, Oct. 1993, pp. 52–56. [3] E. A. Sourour and M. Nakagawa, “Performance of orthogonal multicarrier CDMA in a multipath fading channel,” IEEE Trans. Commun., vol. 44, pp. 356–367, Mar. 1996. [4] F. Adachi, D. Garg, S. Takaoka, and K. Takeda, “Broadband CDMA techniques”, IEEE Wireless Commun., vol. 12, pp. 8 – 18, April 2005. [5] S. Hara and P. Ramjee, “Design and performance of multicarrier CDMA system in frequency-selective Rayleigh fading channels,” IEEE Trans. Veh. Technol., vol. 48, pp. 1584–1595, Sep. 1999.

[6] D. Carey, D. Roviras, and B. Senadji, “Comparison of multiple access interference in asynchronous MC-CDMA and DS-CDMA systems,” in Proc. IEEE Int. Sym. Signal Processing and Its Applications, July 2003, pp. 351 - 354. [7] C. W. You and D. S. Hong, “Multicarrier CDMA systems using time-domain and frequency-domain spreading codes,” IEEE Trans. Commun., vol. 51, pp. 17–21, Jan. 2003. [8] B. M. Popvic, “Spreading sequences for multicarrier CDMA systems,” IEEE Trans. Commun., vol. 47, June 1999. [9] D. J. Shyy and J. Dunyak, “Capacity enhancement of cdma networks using interference cancellation techniques”, IEEE Commun. Magazine, vol. 44, pp. 86 – 92, July 2006. [10] S. Verdu, Multiuser Detection, Cambridge University Press, 1998. [11] H. Cheng, S. C. Chan, “Robust multiuser detection for wireless MC-CDMA systems under narrowband interference”, in Proc. IEEE ISPACS 2005, 13-16 Dec. 2005, pp. 501 – 504. [12] C.-L Wang and C.-C Wu, “Improved partial parallel interference cancellation for MC-CDMA uplink systems,” in Proc. IEEE Globe Telecommun. (GLOBECOM ’04), vol.5, 29 Nov.-3 Dec. 2004, pp.2823 – 2827. [13] Z. Duan, T. Hidalgo Stitz, M. Valkama, and M. Renfors, “Modified PIC in MC-CDMA systems,” in Proc. IEEE Int. Symp. Control, Commun., Signal Processing, Hammamet, Tunisia, March 2004, pp. 795-798. [14] S. Tsumura and S. Hara, “Design and performance of quasi-synchronous multi-carrier CDMA system,” in Proc. IEEE Veh. Technol. Conf., Atlantic City, NJ, Oct. 2001, pp. 843-847. [15] G. Xue, J. Weng, T. Le-Ngoc and S. Tahar, “Adaptive multistage parallel interference cancellation for CDMA,” IEEE J. Select. Areas Commun., vol. 17, no. 10, pp.1815-1827, Oct. 1999. [16] S. Kondo and L. B. Milstein, “Performance of multicarrier DS CDMA systems,” IEEE Trans. Commun., vol. 44, pp. 238–246, Feb. 1996. [17] K. Ko, M. Park, D. Hong, “Performance analysis of asynchronous MC-CDMA systems with a guard period in the form of a cyclic prefix,” IEEE Trans. Commun., vol. 54, pp. 216 – 220, Feb. 2006