Adaptive Spreading Code Assignment for Up-Link MC-CDMA∗

Hua Zhang∗

National Mobile Communications Research LaboratorySoutheast University, Nanjing, China

Ye (Geoffrey) LiSchool of Electrical and Computer Engineering

Georgia Institute of Technology, Atlanta, GA 30332-0250

Yi Yuan-WuOrange Labs, RESA/WIN

38-40, Rue du General Leclerc92794 Issy Moulineaux Cedex 9, France

Abstract— Multi-carrier (MC) code division multiple access(CDMA) is able to take the advantages of OFDM and CDMA andis a potential technique for future wireless communications. Foran uplink MC-CDMA system, the symbols of different users arespread in the frequency domain. However, the frequency-selectivefading of wireless channels destroys the othogonality of the spread-ing codes for different users and causes multiple access interfer-ence (MAI), especially for a network with full load. To reducethe impact of MAI, we adaptively assign spreading codes accord-ing to channel state information and MAI environments. Sinceit requires high computational complexity to find an optimal setof spreading codes for all active users, we develop several sim-plified approaches to search the suboptimal spreading code sets.It is demonstrated by the computer simulation that the adaptivespreading code assignment, even though suboptimal, can signifi-cantly improve the performance of MC-CDMA systems.

I. INTRODUCTION

Multi-carrier (MC) code division multiple access (CDMA)is a promising candidate for the future high-rate data transmis-sion. It combines OFDM and CDMA and takes their advan-tages. In an up-link MC-CDMA system, the symbols of dif-ferent users are spread by different spreading sequences/codesand transmitted from different mobile stations over the samefrequency band. At the receiver, all of the user symbols arede-spread and detected. To make a full use of frequency di-versity, each symbol is spread over the whole band. However,frequency-selective fading of wireless channels, which is inde-pendent for different users, destroys the orthogonality amongthe spreading sequences, and causes multiple access interfer-ence (MAI). The strong MAI degrades the performance of thedetector. Therefore, it is desirable to find ways to reduce theMAI.

The MAI in MC-CDMA systems depends both on the chan-nel fading and the selection of spreading sequences. Since the

—————————* The work was supported by Orange Labs.

wireless channels are time varying, a fixed assignment of thespreading sequences can not guarantee small MAI for all chan-nel and user scenario. Therefore, adaptively allocate the spread-ing sequences according to the channel variation could be aneffective method of reducing the MAI. The spreading code allo-cation has been studied in [2]-[6] for the downlink MC-CDMAsystem. In a downlink system, it is difficult for one user toknow the channel state information (CSI) of the other activeusers. Without the full CSI of all active users, it is impossibleto achieve satisfactory performance for any adaptive spreadingcode allocation scheme. However, for the uplink system, the re-ceiver has all active users’ CSI from the channel estimation. Asa result, the MAI caused by the independent user channels canbe explicitly calculated. Therefore, the algorithms developedfor the downlink system can not be directly applied to the up-link system. In [7], adaptive spreading code assignment for theuplink MC-CDMA system is studied to reduce the power con-sumption at the transmitter. Exploiting correlation of frequencyresponses of wireless channels, MAI-free spreading codes hasbeen developed in [8], which can be used in systems with a lim-ited number of active users and is not applicable to systems withfull load. In this paper, we investigate the adaptive spreadingcode assignment for uplink MC-CDMA systems and developseveral approaches to obtain the spreading code sets resultingless MAI. The developed approaches can significantly improvethe detection performance, especially when the system is withfull load.

The rest of the paper is organized as follows. In Section II,we introduce a basic up-link MC-CDMA system and demon-strate the impact of MAI. In Section III, we develop approachesto adaptively assign spreading codes to minimize MAI and thendemonstrate their performance improvement by simulation.

II. UP-LINK MC-CDMA SYSTEM

In this section, we first introduce a basic up-link MC-CDMAsystem, and then show how the MAI caused by frequency selec-

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978-1-4244-3435-0/09/$25.00 ©2009 IEEE

tivity of wireless channels degrades the detection performance.

A. A Basic Uplink MC-CDMA System

Spreading

lc i

De-spreading and detection

OFDMdemodulation

OFDMmodulation

Pilot insertion

kb in kd i

n ks in

kxn kb in

ˆ

(a) Transmitter for user k (mobile station)

(b) Receiver (base station)

kf in

Channel estimation kH i

nˆ

Fig. 1. An up-link MC-CDMA system.

Figure 1 shows an up-link MC-CDMA system. Denote{b(i)

n [k]}M−1i=0 the symbols to be transmitted by the i-th user at

the n-th block and {c(i)[l]}L−1l=0 the spreading sequence/code

corresponding to the i-th user. Without loss of generality, weassume {c(i)[l]}’s are real, with constant modulus, and orthog-onal for different i’s, that is,

L−1∑l=0

c(i)[l]c(m)[l] ={

L, if i = m,0, if i �= m,

,

andc(i)[l] ∈ {+1,−1},

where L is the spreading gain. The symbols to be transmittedis first spread by the user spreading sequence, then the chipsare transmitted through the equally spaced subcarriers over thewhole band. The spread signal can be written as

d(i)n [lM + m] = c(i)[l]b(i)

n [m], (1)

for l = 0, · · · , L− 1 and m = 0, · · · ,M − 1, where d(i)n [lM +

m] is the l-th chip that would be transmitted through the (lM +m)-th subcarrier. The spread signal is transformed into timedomain by the OFDM modulation and sent to the base station.

At the receiver, the signal is transformed from time to fre-quency domain by inverse discrete fourier transform (IDFT).The signal in the frequency domain can be expressed as 1

xn[k] =∑

i

H(i)n [k]s(i)

n [k] + Nn[k], (2)

where Nn[k] is additive white Gaussian noise (AWGN) at thek-th subcarrier, which is assumed to be with zero mean and

1We assume that all active users are synchronized in this paper.

variance σ2n, s

(i)n [k] is either spread data chip, d

(i)n [k], or train-

ing, and H(i)n [k] is the channel frequency response of the k-

th subcarrier of user i at the n-th OFDM block. The channelcan be obtained through channel estimation. The channel es-timation approaches have been widely addressed in the litera-ture. Therefore, we assume that the receiver has perfect CSIfor signal detection and spreading code assignment. To showthe impact of the MAI, we give the performance of minimummean square error (MMSE) successive interference cancela-tion (SIC) detector in our discussion since they provide a goodtrade-off between the performance and complexity [9]. In nextsubsection, we show that the MAI due to the frequency selec-tive fading will degrade the detection performance severely if afixed code assignment is used.

B. Multiple Access Interference

Inthis section, we show that the frequency-selectivity ofwireless channels causes severe MAI, especially for full loadedsystem. For simplicity, we drop the time index in the rest of theanalysis without any confusion. When a MC-CDMA system isworking in data transmission mode, the received signal at eachsubcarrier can be expressed as

xn[lM + m]=∑

i

H(i)[lM + m]c(i)[l]b(i)[m] + Nn[lM + m],

(3)for l = 0, · · ·L − 1 and m = 0, · · ·M − 1. Note that thechannel response H(i)[lM +m]’s are almost independent whenM is large enough. Usually when M is larger than the channelcoherent bandwidth, the channel responses corresponding to thechips of the same user code can be regarded to be independent.For the single user case, this system can achieve up to L orderfrequency diversity gain. When the number of users is large, forexample, in the full loaded case, the diversity gain is degradedby the MAI.

The mutual interference between users i and j is defined as

Iij [m]=

∣∣∣∣∣L−1∑l=0

H(i)[lM+m]c(i)[l]b(i)[m](H(j)[lM+m]c(j)[l]b(j)[m]

)∗∣∣∣∣∣

=

∣∣∣∣∣L−1∑l=0

H(i)[lM+m]H(j)∗[lM+m]c(i)(l)c(j)(l)

∣∣∣∣∣ , (4)

which depends on both the spreading codes and the frequencyresponses of the channels corresponding to user i and j. In thediscussion above, we have used the assumption that |b(i)[m]| =1 for convenience. If channels are flat fading, that is, H(i)[lM+m] = Hi and H(j)[lM + m] = Hj for l = 0, · · · , L − 1, thenIij [m] = 0. In general, Iij [m] �= 0. The power of the mutualinterference between i and j-th user is given by

σ2ij =

1M

M−1∑m=0

I2ij [m]

=

(L−1∑l=0

H(i)[lM+m]H(j)∗[lM+m]c(i)[l]c(j)[l]

)2. (5)

Then, the total power of MAI at user i is

σ2i =

∑j �=i

σ2ij , (6)

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and the overall power of MAI for all active users

ΓA =Nu−1∑i=0

σ2i = 2

Nu−1∑i=0

Nu−1∑j=0,i�=j

σ2ij . (7)

From the discussion above, MAI is determined by spread-ing codes and channels and increases with the number of activeusers. Even though wireless channels are determined by theenvironments, we can adjust spreading codes for mobile usersaccording to channels to reduce MAI.

Computer simulation is performed to show the impact ofMAI on the receiver. In our simulation, the subcarrier space(bandwidth) is Δf = 56.34 kHz and therefore the block lengthof OFDM is Ts = 1

Δf = 17.75 μs. There are K = 736 subcar-riers in one OFDM block. Consequently, the bandwidth of thesignal is B = 41.46 MHz. Each user will spread a symbol to16 subcarriers uniformly distributed over the whole frequencyband to obtain frequency diversity. Hadamard code is used asthe spreading code. As a results, each user will transmit 46QPSK symbols over an OFDM block and the system can holdup to 16 active users. Channel used in our simulation is BRAN-E model [10].

Figure 2 demonstrates the bit error rate (BER) of MMSE-SIC detectors. From the figure, BER increases with the numberof active users. The performance loss due to MAI is large, es-pecially for the system with full load (16 users). At 10−3 BER,the performance loss is about 6 dB. For the MMSE-SIC de-tector, the performance loss is negligible when the number ofactive users is increased from 1 to 8; however, the performanceloss increases from 2 dB to 6 dB when the number of usersis increased from 12 to 16. Therefore, it is strongly desiredto have techniques to reduce MAI in MC-CDMA systems forlarge users.

0 5 10 15 2010

−4

10−3

10−2

10−1

Eb/N

0 (dB)

BE

R

MMSE−SIC Detector

1 user2 users4 users8 users12 users16 users

Fig. 2. Performance degradation due to MAI for a MC-CDMA system withdifferent numbers of active users.

III. ADAPTIVE SPREADING CODE ASSIGNMENT

From the discussion above, the impact of MAI is significantfor a MC-CDMA system with a fixed spreading code assign-

ment. The power of MAI depends on the assignment of spread-ing codes for active users. To reduce MAI, we should find aproper spreading code for every active user so that the MAIunder a given CSI is minimized. In this section, we develop ap-proaches that adaptively assign the spreading codes accordingto channel condition to reduce MAI.

In a MC-CDMA system with adaptive assignment of spread-ing codes, the spreading code for each user will not be fixed.Instead, it changes according the instantaneous CSI. In up-linkMC-CDMA systems, the good assignment of spreading codesfor all active users is first searched at the receiver and then fedback to each active user (handset).

A. Chip-by-Chip Suboptimal Approach

In a traditional MC-CDMA system, spreading codes are usu-ally Walsh-Hardamard sequences or other codes with good cor-relation property that guarantee low correlation between users.In the discussed system, we allow the spreading sequence as-signed to users could be any binary sequence. In fact, the chan-nels corresponding to different user and different chip of thecode are almost independent. Then, any fixed spreading codehas similar performance statistically. Consequently, the codeset for each user has 2L sequences if the sequence length is L.Here, we do not put any restriction on the code assignment fordifferent users.

To find the optimal spreading code set for a MC-CDMA sys-tem with Nu active users, we have to search for 2LNu differentcombinations of 2L different sequences, which is with forbid-ding complexity. Therefore, we have to find a low complexapproach to search a spreading code set that may be subopti-mal.

If a spreading code can be arbitrary binary sequence of lengthL, the following chip-by-chip suboptimal approach (CCSA)can be used to find a good spreading code set. We initializethe assignment approach with an arbitrary code set. Then, up-date the spreading code one by one chip. Each step, we finda code for the new user so that it minimizes the MAI to all ofexisting users. However, each user has 2L choice of code. It re-quires too much complexity to find the best code for each user.CCSA finds the code for each user through trying each chip ofthe code. The details are given as follows.

Step 1: Set the initial spreading code assignment for all usersas

c(i)[l] = 1, l = 0, · · · , L−1, and i = 0, · · · , Nu−1. (8)

Step 2: Optimize spreading code for the i-th user, i =1, · · · , Nu − 1:

Step 2.i: Calculate σ2i (0), the overall MAI power be-

tween the previous i − 1 users and the i-th user.Step 2.ii: Optimize the k-th chip for the i-th user: De-

note{c(i)[l]

}L−1

l=0to be the current spreading code

for the i-th user and σ2i (k) to be the maximum mu-

tual interference between the previous i − 1 usersto the i-th user. Change the sign of c(i)[k] whilekeeping the rest chips the same and calculate thecorresponding overall interference, σ2

i (k).

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings

Step 2.iii: If σ2i (k) < σ2

i (k), then the new chip isc(i)[k] = −c(i)[k]; otherwise, c(i)[k] = c(i)[k]. Andsubstitute σ2

i (k) by σ2i (k).

Step 2.iv: Repeat Steps 2.i - 2.iii for k = 0, · · · , L− 1.Step 3: Repeating Step 2 for i = 1, · · · , Nu − 1.

In the above approach, we optimize the spreading code forone user by one user and one chip by one chip. Therefore, thefound spreading code set is local optimal. We can search thebetter code set by using the CCSA iteratively. For the iterativeCCSA, Steps 2 and 3 in the above procedure are repeated usingthe spreading codes obtained in the previous iteration and theoverall interference for the i-th user caused by all other Nu− 1users is used instead of the MAI caused by the previous i − 1users.

Though CCSA can achieve good performance, it require thereceiver to feed back the whole spreading sequence to the users.Therefore, it requires lots of feedback bandwidth. In the next,we give another approach that requires less feedback band-width.

B. Sequence-by-Sequence Suboptimal Approach

In the CCSA, the spreading code is selected from all possi-ble binary sequences of length L, which requires to feed backthe whole spreading code of L bits. To reduce the number offeedback bits, we introduce a sequence-by-sequence subopti-mal approach (SSSA).

In the SSSA, we first form a book of spreading codes thatcontains a subset of all binary sequences of length L and thenchoose spreading code for each user from the code book to

minimize the MAI. Denote{{xn[l]}L−1

l=0

}N−1

n=0as the book of

spreading codes. The SSSA is similar to the CCSA except thatthe code selection for the new user can not be performed chipby chip. Then, the code has to be selected from the whole codebook to minimize the MAI. The procedure of SSSA can be sum-marized as follows.

Step 1: Set the spreading code for the zeroth user:

c(0)[l] = x0[l], l = 0, · · · , L − 1. (9)

Step 2: Find the spreading code for the i-th user: Calculateσ2

i (n) for n = 0, · · · , N − 1, the maximum mutual inter-ference between the previous i− 1 users and the i-th userwhen it uses {xn[l]}L−1

l=0 as its spreading code. Then as-sign a spreading code that minimizes the maximum mu-tual interference to the i-th user. Let

ni = arg min0≤n≤N−1

σ2i (n),

then c(i)[l] = xni[l] for l = 0, · · · , L − 1.

Step 3: Repeat Step 2 for i = 1, · · · , Nu − 1.The approach described above is called SSSA-I. Another

slightly different approach, SSSA-II, will be obtained if σ2i (n)

in Step 2 is substituted by the total interference from the previ-ous i users to the i-th user when it uses {xn[l]}L−1

l=0 as a spread-ing code.

Similar to that of the CCSA, an iterative SSSA can be derivedbased on the SSSA. For the iterative SSSA, Step 2m and Step

3 in the above procedure are repeated, where Step 2m is themodified version of Step 2 and is expressed as

Step 2m: Find the spreading code for the i-th user: Calculateσ2

i (n) for the n = 0, · · · , N − 1, the maximum mutualinterference between the i-th user and the other Nu − 1users when i-th user employs {xn[l]}L−1

l=0 as its spread-ing code, the previous i−1 users use the spreading codesfound in this iteration, and the other Nu − i − 1 usersuse the spreading codes found in the previous iteration.Then assign a spreading code that minimizes the maxi-mum mutual interference to the i-th user. Let

ni = arg min0≤n≤N−1

σ2i (n),

then c(i)[l] = xni[l] for l = 0, · · · , L − 1.

Compared with CCSA, SSSA has higher complexity becauseit needs to calculate all possible MAIs caused by the cur-rent user using the code selected from the code book. How-ever, as we claimed before, SSSA requires less feedback bits( only log2 N ). The code book should be designed so that themaximum correlation between the codes is minimized. WhenN ≤ L, we can select any N orthogonal codes. When N > L,there is no regular way to find the code book. We can use ex-haustive search since the code book is designed off-line.

−5 0 5 10 15 2010

−4

10−3

10−2

10−1

Eb/N

0 (dB)

BE

R 16 users

Fixed16 codeset 64 codeset256 codesetCCSA

Fig. 3. Performance of SSSA with different sizes of code book.

IV. SIMULATION RESULTS

In this section, we demonstrate the performance of the pro-posed adaptive spreading code assignment through extensivesimulation.

The system model and parameters used in our simulation arethe same as in Section II-B. The channel is assumed to be blockfading channel. The spreading code assignment is performedevery fading block. Therefore, the rate of the reassignment ofthe spreading code depends on the time varying parameters ofthe channel (for example, the Doppler frequency). The spread-ing gain is 16 and 16 users are employed in the system. Foriterative CCSA and SSSA, we give the performance of 4 itera-tions because more iteration can not improve the performancetoo much in our simulation.

First, we show the BER performance of CCSA and SSSAwith various code book size in Figure 3. From the figure,

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings

0 5 10 15 20

10−4

10−3

10−2

10−1

Eb/N

0 (dB)

BE

R

16 users

FixedSSSA−ISSSA−IISSSA−II 4 itersCCSACCSA 4 iters

Fig. 4. Uncoded performance for adaptive spreading code assignment.

the performance of SSSA with code book size of 16 is goodenough. Therefore, in the rest of simulation, we give the per-formance of SSSA with code book size 16.

4 6 8 10 12 1410

−3

10−2

10−1

100

Eb/N

0 (dB)

FE

R

1/2 convolutional code 16 users

FixedSSSACCSASSSA 4 itersCCSA 4 iters

Fig. 5. Coded performance for 1/2 convolutional code.

Figures 4 gives the BER of the MMSE-SIC detector for thethe uplink MC-CDMA system. The performance for fixedspreading codes and adaptively assigned spreading codes us-ing CCSA and SSSA are compared. From the figure, the sys-tem with adaptively assigned codes has significant gain over theone with fixed spreading codes. At a BER of 10−3, the spread-ing codes obtained through SSSA has gain about 3 dB over thefixed codes. While the performance for CCSA has gain about4.5 dB over the fixed assignment. We also compare the per-formance of SSSA-I and SSSA-II. From the simulation results,SSSA-II is a little better than SSSA-I. Therefore, we give iter-ative SSSA-II in the following simulation. From the figure, theiterative CCSA has better performance gain than the iterativeSSSA over the non-iterative version, especially at low BER.

Since in most of the practical system, error correction codeis usually used to improve the reliability of the link, we alsogive the performance of the coded system. In the simulation,we group 8 OFDM blocks as one frame. A 1/2 convolutioncode with constraint length 7 and code polynomial [171,133] isused. To transmit higher data rate, the encoder output can bepunctured to obtain a 3/4 rate. Figure 5 gives the frame errorrate (FER) of the coded system. From the figure, a significantgain can be obtained for the adaptive spreading code assign-ment in the coded systems. For 3/4 code rate, there is about 4

4 6 8 10 12 1410

−3

10−2

10−1

100

Eb/N

0 (dB)

FE

R

3/4 convolutional code 16 users

FixedSSSACCSASSSA 4 itersCCSA 4 iters

Fig. 6. Coded performance for 1/2 convolutional code.

dB gain for iterative CCSA and 3 dB for iterative SSSA overthe fixed spreading code at a FER of 10−2. However, at the lowcode rate, the performance gain is reduced to 2 dB and 1.5 dB.And the performance of iterative approach has also a small gainover the non-iterative approach. However, at high code rate asin Figure 6, the performance gain for the CCSA over the SSSAis significant. Furthermore, the iterative approach achieve sat-isfactory performance gain over the non-iterative approach.

V. CONCLUSIONS

In this paper, we have introduced our work in adaptivespreading code assignment for uplink MC- CDMA systems anddeveloped several low-complexity sub-optimal spreading codeassignment approaches. We have demonstrated significant per-formance improvement of the developed approaches by exten-sive computer simulations. The proposed approach can be usedin future wireless communication systems.

REFERENCES

[1] S. Hara and R. Prasad, “Overview of multicarrier CDMA,” IEEE Com-munication Mag., vol. 35, pp. 126-133, 1997.

[2] Q. Shi and M. Latva-aho, “Simple spreading code allocation scheme fordownlink MC-CDMA,” IEEE Electronics Letters, vol. 38, pp. 807-809,July, 2002.

[3] T. O’Farrell “New signiture code sequence design techniques for CDMAsystems,” IEEE Electronics Letters, vol. 27, pp. 373-371, Feb. 1991.

[4] A. Mourad, A. Gueguen, and R. Pyndiah, “Impact of Spreading Se-quences on the Performance of the Forward Link MC-CDMA Systems,”IEEE ISSSAT 2004 pp. 683-687, Aug-Sept. 2004.

[5] D. Mottier and D. Castelain, “A Spreading Sequence Allocation Proce-dure for MC-CDMA Transmission Systems,” IEEE VTC 2000, vol. 3,pp.1270-1275, Sept. 2000.

[6] H. E. Ghazi, C. Garnier and Y. Delignon, “Efficient Spreading Code Al-location Strategy for a Downlink MC-CDMA System in a Time VaryingFrequency Selective Channel,” PIMRC’06, pp. 1-5, Sept. 2006.

[7] T. M. Lop,“Optimal Uplink Sequence Assignment for MulticarrierCDMA Systems in Rayleigh Fading Channels,” IEEE ICICS-FCM2003,pp. 636-640, Dec. 2003.

[8] S.-H. Tsai, Y.-P. Lin, and C.-C. Jay Kuo, “Design of MAI-free MC-CDMA systems over frequency-selective fading channels via codewordselection,” Proc. 2005 IEEE International Conf. Acoustics, Speech, andSignal Processing, March 2005,

[9] J. Andrews and T. Meng, “Optimum power control for successive interfer-ence cancellation with imperfect channel estimation,” IEEE Trans. Wire-less Commun., vol. 2, pp. 375-383, Mar. 2003.

[10] ETSI. Project Broasband Radio Access Networks (BRAN); HIPERLANType 2, Technical specification; Physical layer, Oct. 1999.

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings