2005 IEEE International Symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications Proceedings

Analysis of Frequency Diversity in MC-CDMA Systemsunder Correlated Fading Channels

Kan Zheng, Lu Han, Wenbo WangWireless Signal Processing & Network Lab (WSPN)

Beijing University ofPosts and Telecommunications, Beijing, 100876, P. R. CEmail: zkan@buptnetedutcn

N/SF = P N/SF =PAbstractMC-CDMA can obtain a good frequency diversity effect Spreading Athrough spreading and despreading operation infrequency cX] c.R)1 CX] C,2] C,[2] c,[2] PJSFW C[SFIdomain. In this paper, the impact ofchannelparameters to (a)inherentfrequency diversity is analyzed atfirst. Then, three SF SFspreading methods to achieve the frequency diversity are Spreading B ____investigated Not onlyfrequency diversity but also multiple- -.r! 4 4[31 c.[2]Co23]c3.I] e[2J c,[3]user interference (MUI) are taken into account in our (b)analysis. The achievedfrequency diversity gains with dif-ferent spreading methods are also affected by the combin- Figure 1. Spreading methods In the frequency domaining schemes at the receivers when there are multiple usersin the systems. In this paper, we analyze and compare the system perform-

ance with several different spreading methods and lengthKeywords of spreading sequences. And the effects of MUI to fre-OFDM; MC-CDMA; frequency diversity; MUI quency diversity are also discussed. Ideal synchronization

and channel estimation in the downlink are assumed.I. INTRODUCTION'he amazing increase of Internet services and electrics The rest of this paper is organized as follows: Section IIcommercial is a strong demand for higher data rate com- gives the brief description of MC-CDMA systems withmunication services not only in fixed network but also in different spreading methods. The impact of channel to fre-the mobile communication systems. MC-CDMA, which is quency diversity is analyzed in Section III, and the fre-based on orthogonal frequency division multiplex- quency diversity with different spreading methods is inves-ing(OFDM), can not only solve the difficult multipath en- tigated in Section IV. The effect ofMUI is also included invironment problem but also have good frequency effi- this Section. Finally our conclusions are given in Section V.ciency and easy implementation[l]-[3]. II. SYSTEM MODELIn MC-CDMA systems, the original data stream is spread In MC-CDMA systems, the original signal of each user isby using a given spreading code, and then modulated to a spread by a special spreading code in frequency domain atdifferent sub-carrier with each chip, i.e. spreading in the the transmitter. In the downlink Walsh-Hadamnard codes arefrequency domain. Using such transmission scheme, MC- used for the frequency spreading to achieve the orthogonal-CDMA can achieve frequency Rake diversity effect. In ity among users. The binary information data sequence oforder to obtain good spectral efficiency, the spacing be- kth user is QPSK-modulated. And then the resulting sym-tween the subcarriers is kept as close as possible while bol sequence is SIP converted to P-NISF parallel se-maintaining the orthogonality between them. However, quences {ako[i], akl[i],- ., atp[J]}. Here Nis the number ofsuch close subcarrier spacing can't guarantee the frequency the subcarriers and SF is the value of the spreading factor,diversity conceived in [3] because the subcarrires that carry i.e., the length of the spreading sequence. Consequently, Pon the same information are correlated, not independent So is the number of symbols transmitted at the same time byhow much diversity gain can be achieved highly depends one user. Each branch of the parallel complex sequences ison the channel correlation properties. Then, the spreading copied into SF parallel sequences and is multiplied by amethods and the length of spreading sequence need to be corresponding chip of the special spreading sequence. Asselected carefully to exploit the frequency diversity order shown in Fig. 1 (a), in order to obtain the better frequencyinherent in the channel. On the other hand, orthogonality diversity effect, the interval of every chip of one spreadbetween different users will be destroyed by the transmis- sequence can be P subcarriers. And this spreading methodsion through the fading channels. Multiple user interfer- is called as Spreading A . Usually the data can also beence (MUT) will deteriorate the system performance when spread onto the continuous subcarriers by the chips of onemultiple active users. The more frequency diversity ob- spread sequence showed in Fig.1 (b), which is called astined, the more sensitivity the systems are to MUI. Spreading B. Then, the parallel data sequences are modu-Sponsored by China National 863 Pioject (2003AA12331004 and2004AA123160)

0-7803-9128-4/05/$20.00 C 2005 IEEE. 1054

lated by the inverse discrete Fourier transform (IDFT) and TABLE 1. System Parametersguard intervals are inserted between the OFDM symbols to Channel Model Jakes Modelavoid theISI caused by multipath fading. Finally the paral- Channel Parameters Type L r , rI'M

us uslel sequences are converted back into a serial data stream. A 0.8000 0.2687Thus, the transmitted signal of the kth user can be ex- B 6 1.0000 02862pressed as c 12 1.1000 02900

+co P-i SF-I D 24 0.2875 0.0725sk(t)= EZakP[i]ZCk[flpS (iT)eJ24fo+f(flP)]' (1) E 24 1.1500 0 2912

i=--6P=o An=o Carrier frequency f = 5GHz

(Pn+ p)Af'ifSpreadA Bandwidth 80MHzf(n,p) = '"'''(2) Mobile speed 60 km/h

* SF +n)O,f if SpreadFBOFDM Symbol Duration T,= (6.4 + 1.6)usn)Af', pf Spread B Number of Subcarriers 512(GI=128)

where Af =I (Ts'-A), TS + A =PT, C [n] is the Modulaion QPSKnth chip of the k-th user's spreading code and fo is the 1.00

0.95

lowest subcarrier frequency. ,Af' and A are the sym- 0o85bol duration at each subcarrier, the miniimum subcarrier 0.80I

E 0.75-separation and the guard interval(GI), respectively. p. (t) 0.707is the rectangular pulse response defined on the interval '.65 /> 060-

[0TS). E 0.55UJ0.50 -0--ChannelA

For downlink transmissions, since a tenninal receives its 0.45 || - ChannelBinterfering signal designated for other users (k=1,2,..,K-l) -040- 1

O Channel C

through the same channel as the desired signal, the user 0.30 / - Channel Eindex for the channel can be omitted. The signal from the 0.25th user is assumed the desired without the loss of general- 0.20. 10 1'

ity. The Rayleigh fading channel with L paths can be ex- Egenalue Indexpressed as

h(t;La)=E-1 (t)S(r - rS) (3) FIgur 2. Distribution of cumulated elgenvaluesh(t; vr) = h,, (t)8(r- - -r.) (3)_=o the decision variable. Without the loss of generality, the

decision variable for the 0th user can be written aswhere IiS(t) is the sth path gain which is independently SF-1complex Gaussian random process with zero mean and Do(iTs) = .G0(n)H,,p [iT']a,,p [i]c[n]variance cr, for different s, and Zr is the propagation de- K-i SF-i SF1 (5)lay for the sth path. +E ZG.(n)H,fp[iTs']ak,p[i]ck[n] +I Go (n)n(iT2)Transrnitted tirough the Rayleigh fading channel with ad- k-1 n-o n-0ditive white Gaussian noise (AWGN), the received signal Two different combining techniques are discussed: Maxi-can be written as mal Ratio Combining (MRC) and Minimum Mean Square

K I Error Combining (MMSEC). The gains are given by (6)r(t) = E f's(t- r)h(t; r)dr + n(t) and (7) respectively [2].

+aD P 1SF IK 1 R

Z ZdjHd.P(t)akp[i]ck[n]p(t iT')J2rfU0+f(np)k + n(t)(4) GDG/RC (n) = cD[n]H,p (6)i= <p=0 n=Ok=O GMS ( ) =c["]H; /[K | H 2 +°n] (7)

where K is the number of active users, H,p(t) represents the III-IMPACT OF CHANNEL FREQUENCY DIVERSITYcomplex envelop at the ](n,p)-th sub-channel. At the re- The st pa Ameer f R DImulaIo[ceiver, the inverse operation, which comprises S/P conver- The system parameters for our analysis and simulation [4]sion, removal of guard interval and DFT (or FFT) are per- are shown in Table 1. The effect of frequency diversityformed. After that, each received symbol of each subcarrier depends on frequency correlation of the subcarriers onis multiplied by the gain factor, which is the combined sig- which the same information is transmitted. The path delaynal of the corresponding chip of the spread sequence and of the channel is assumed to be uniform distributed overthe estimated channel gain associated with each subcarrier. [O,V,ma) and the delay profile assumed to be exponentialThey are then accumulated in the frequency domain to get

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delay, i.e. 0(r) = Ce r/s . The channel frequency cor-

FM~~~~~cnChannelA8relation matrix R'HH = E H }= p,}cabeex- 4 ChannelB15-J C:hannel Cpressed as Chnn Db1 g . > - ~~~~~~~~~~~~~~~~~~~~C;hannel E

pi 2E e-i .tnr E53)103=

Since the eigenvalue Aj of RH can represent the way cc

by which the power is shared and spread among the sub-carriers, their cumulated sumn is a good criterion to showthe power distribution among the subcaniers

P(i) - E2 (9) 2 4 8 16 2 64

P(i)= t;Spreading Factor

To highlight the different frequency diversity gain in the Figum 3. SNR Vs SFfor SU with FH at BER= 10different channel, the channels with different parametersare analyzed by mean of SVD. As shown in Fig.2, the cu-mulated eigenvalue sum in Channel A is increased very 25rapidly with the eigenvalue index, which means most of -0- Spread Atransmitted signal power concentrated on few subcarriers 20and not much frequency diversity gain can be achieved. On 15\the other hand, the cumulated eigenvalue sum in Channel \D or E becomes close to 1 when the eigenvalue index in- 10creases more slowly, and more frequency diversity gain isinherent. z

soIV. FREQUENCY DIVERSITY VS SPREADING g C

Single User (SU) MRCFrequency diversity order inherent in the channel can't be -10,exploited easily. It depends not only on the spreading 2 4 SeiFt 32 CA

methods but also on the length of spreading sequence. In Spreading Factor

order to fuirther exploit inherent high diversity available inChannel D and Channel E, a frequency hopping (FH) Figure 4. SNR Vs SFfor SU with FHlSpread AIB at BER=1O3scheme, which enables to map chips related to the same on it. The performance applying FH is only regarded ascopy of one symbol onto randomly spaced sub-carriers, is reference because FH scheme is lack of practicability.used together with Spreading A and Spreading B men- Then, the system performance with practical Spreading Ationed above. and Spreading B in Channel D have to be fiurther investi-Since MRC scheme is optimal for the single-user receiver, gated and shown in Fig.4. The performance applyingthe single-user systems with MRC, i.e. no MUI are consid- Spreading A is much better than that applying Spreading B,ered at first and. Fig.3 shows the system performance ap- and almost as same as that applying FH which can achieveplying FH spreading method with various spreading factors largest frequency diversity gain. The performance gainat target BER=l 03 under different channels. As spreading between Spreading A and Spreading B is increased slightlyfactor increases, the required mean SNR is decreased sig- after the spreading factor becomes larger than 16 since thenificantly. However, after spreading factor becomes larger frequency diversity has been close to its saturation point.than 32, the system perfonmance change slightly. It indi- Furthermore; the length of spreading factor won't be toocates that with spreading factor increasing, the system can large and usually is selected to be 16 or 32. Obviously, inachieve certain diversity, but the diversity will eventually order to make good use of frequency diversity, Spreadingsaturate depending on the channel envirouments. And with A will be a good choice when no MUI.the same spreading factor, the required SNR in Channel Dand Channel E is smallest, which is consistent with the fact Multi-User (MU)tShat Channel D and Chan^nel E have the highest frequency From the analysis and simulation results above, Sprealdingdiversity order. A seemns to be a good choice when single active user in the

Sinc thefreuenc diersiy o ChanelD ca be systems. However, in MC-CDMA systems, MUI usuallyacineve more easy, thveraalsisy follwewinnllDcabebae exists and should be considered when system design. More

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active users, more serious MUI is. So the system applyingSpreading A won't be always better than that applyingSpreading B. In the other words, the negative effect ofMUI will become more dominant with more active users.Multi-user interference (MUI) is taken into account with --- -- _.-.- /,the simulation of different number of active users at a fixed 0.01/SNR=8dB. The spreading factor of4, 8 or 16 is adopted in fthe systems respectively. On the other hand, the system Eperformance of multiple active users also highly depends *E.- -4+SpASF=4on the combining schemes at the receiver. I--(-SPM8dBSF=4Fig.5 shows the performance in term of BER versus the MRC 6-Sp,eadASF=18system load, in which MRC is applied. From the second SNR-8dB -C--Spfd B SF=16term of the equation (5), i.e. the multi-user interference, it 1E8(5~~~ i.e. thelt ~~~~1 2 4 816can be seen that the system will suffer from the less multi- Number of active users (K)user interference when the correlation of the subearriersrelated to the same copy of one symbol is higher if MRC is Fiqure 5. BER Vs K with Spread A/B (MRC)applied. The continuous subcarriers related to the samecopy of one symbol in the system applying Spreading B 01have relatively stronger correlation than the discontinuoussubcarriers in the system applying Spreading A. So the 0.01Aperformance of system applying Spreading B is less sensi- -tivity to MUI. If Spreading B is adopted, the BER per-

I Ei3formance is degraded slightly with the number of activeusers increases. On the other hand, the BER perforrnancewith Spreading A is deteriorated rapidly with more active 1I E-4 Ausers since it will introduce more multi-user interference m SpreadA SF=4than Spreading B. When spreading factor (SF) is small (4 -0 SpreadBSF=4or 8), the BER curves with Spreading A and Spreading B --A--SpeadB SFE8 MMSEC

--SpeedA SF=16 N 8dare crossed at the point with about less than half system -e-SpreadB SF=16 SNR = 8dBload. The BER performance with Spreading A is even 1E-6 , 2 4 8 16worse than that with Spreading B when full system load. Number of active users (K)Although the BER performance with Spreading A is muchbetter than that with Spreading B in single-user systems, it Figure 6. BER Vs Kwith Spread A/B (MMSEC)is deteriorated too rapidly and become worse than withSpreading B in the systems that have heavier load. If MUIis considered, Spreading A is no longer an appropriate pose of simplification and practicability, MRC withspreading method for the system with 1 Spreading B may be a good choice when system load is not

heavy. If more active users were, MMSEC with SpreadingNot only the noise power but also the multi-user interfer- A outperforms the others.ence is taken into account when MMSEC is applied at thereceiver. Since it can restore the orthogonality of the dif- REFERENCESferent users signals approximately, MMSEC shows its ro- [1] S. Abeta, and H. Atarashi, "Forward link capacity ofbustness to MUI. M'eanwhile, when Spreading A is applied coherent DS-CDMA and MC-CDMA broadbandin the system with MMSEC, frequency diversity can be packet wireless access in a multi-cell environment,"exploited well even in multi-user systems. Fig.6 shows the IEEE VTC2000-Fall, pp.2213-2218,Sept.2000,performance in term of BER versus the system load, in [2] S.Hara, R. Prasad, "Design and performance of multi-which MMSEC is applied. The BER performance with carrier CDMA System in frequency selective RayleighSpreading A is always better that that with Spreading B no fading channels," IEEE Trans. on Veh. Tech,, vol.48,matter how many active users is in the systems. No.5, pp.1584-1594,Sep.1999.

[3] N. Yee,, and J. P. Linnartz, "Multi-carrier CDMA inV.CONCLUSION indoor wireless radio networks" IBICE Trans. Coi-In this paper, three different spreading methods (Spreading mun.d . 900-904, July 1994.A Spreading B and FH) in MC-CDMA system are investi- n . 9 Ygated. Considering the practicahility of thie system, Spread- [4] N. Maeda, H.Atarashi,S.Abeta, " Pilot channel assiteding A is an appropriate spreadinlg method in a single user MMSE combining in forward link for broadbandcase. When the number of active users increases, te sys- OFCDM packet wireless access," IEICE Trans. Fun-tem performance will be deteriorated due to the inc}easing damentals ,vol.E85-A,No.7,pp.1635-1646,July 2002

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