A Cluster-Based MC-CDMA System for Up-Link Transmission

The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)

A CLUSTER-BASED MC-CDMA SYSTEM FOR UP-LINK TRANSMISSION A. Goupil, M. Colas, and G. Gelle D´eCom-CReSTIC — University of Reims Champagne-Ardenne Moulin de la Housse, 51687 REIMS CEDEX 2, FRANCE {alban.goupil, maxime.colas, guillaume.gelle}@univ-reims.fr A BSTRACT A new scheme of detection for multiple access channel is investigated, which consists in the combining of PIC-like detection and joint decoding of LDPC codes. The joint decoding is first studied through the use of LDPC codes over Galois extensions of binary field for the AWGN multiple access channel. Then, a hierarchical MC-CDMA system which uses both Parallel Interference Canceler and joint detection is implemented and simulations show that it can provide a substantial improvement without any complexity growth of the emitter in a MCCDMA like up-link framework. I.

I NTRODUCTION

Multi Carrier Code Division Multiple Access (MC-CDMA) has been received much attention these last few years in the context of 4G communication systems such Wireless broadband multimedia applications. MC-CDMA combines the main advantages of both techniques, i.e. high spectral efficiency, robustness to frequency selective channels, narrow band interference rejection and simple equalization and multiple access capability [1], [2]. However MC-CDMA is generally not used in up-link transmission due to the loss of orthogonality of the spreading sequence which greatly complicates the receiver design. That’s why other techniques such as Spread Spectrum Multi Carrier Multiple Access (SS-MC-MA) is preferred which combines MC-CDMA scheme for transmission and FDMA for user access [3]. However, using MC-CDMA for up-link transmissions provides some interesting challenges. In this paper we propose a new hierarchical MC-CDMA scheme which uses the error correcting codes to perform a better user’s detection into a subgroup of users called cluster, as well as error correction. So, the hierarchical MC-CDMA approach allows higher rate transmissions and mitigates the Multiple Access Interference (MAI) by the number of users in one cluster. This paper is organized as follows. In section II. we describe the proposed structure of the transmission system combining PIC-like detection and joint decoding of LDPC codes. In section III. the joint decoding is investigated into one cluster, using LDPC codes over Galois extension of binary field. The section IV. presents simulation results of the global hierarchical MC-CDMA system including the in-cluster joint-detection and Parallel Interference Cancellation steps. Finally some conclusions are drawn in section V.. II.

G LOBAL SYSTEM

Usually, multiple access in up-link transmissions presents some difficulties because each user’s signal is affected by a different c 1-4244-0330-8/06/$20.00 2006 IEEE

channel. So, the complexity of the base station receiver rapidly increases with the number of users. We focus in this paper on this problem and give it a solution thanks to the concept of clusters. A.

A cluster-based MC-CDMA hierarchical system

Ideally, an optimal solution to cancel the MAI can be done using joint detection receiver. However such an approach leads to high complexity receiver when the number of users increases but can be envisaged for a small number of users (about 2 or 3 users). The basic idea of a cluster-based MC-CDMA hierarchical system consists to combine the nearly-optimality of a joint-detection of a small subset of users, which we call thereafter a cluster, and a global detection based, as in MC-CDMA, on the spreading codes. Therefore, users in a same cluster share the same spreading code and different clusters have different spreading codes. The overall synopsis of the transmitter is given in the figure 1.

s1

s2

Symbol mapper

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MC-CDMA(c1 )

Symbol mapper

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MC-CDMA(c1 )

Cluster 1 h1

h2

noise

+ N

s

Symbol mapper

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+

FFT −∆

R

hN

Figure 1: Illustration of the users clustering. As we see in the figure 1, each user’s transmitter is composed of a bit/symbol converter followed by the encoder of the user’s error-correcting code and by a MC-CDMA modulator. This modulation depends on the spreading code ci . This code is shared in this case by the first and the second users. The modulated signals are sent through the channel, composed of each user’s channel hi . The receiver gets then a noised sum of all these signals. The idea behind the global detection using the concept of cluster and hierarchical receiver is roughly described by the figure 2. The receiver is now broken into two stages: the first considers only clusters’ signals and separate them thanks to the spreading codes. The second step concerns the users’ signals inside a given cluster where the error-correcting codes separate them. The overall is performed several time to improve the performances. As in the case of a classical MC-CDMA communication system, the received signal is first demodulated thanks to the

The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)

C.

Received signal Spreading code Cluster 1

Cluster 2

Cluster 3 Joint detection

User 1

User 2

User 3

User 4

User 5

User 6

Figure 2: Principle of the hierarchical MC-CDMA receiver. cyclic prefix removal and a FFT. Although the simple change on the spreading codes distribution on the clusters gives an opportunity to do hierarchical detection. This part of the detection could be performed thanks to the channel codes as it proposed in section III.. B.

Global detection

Equation (4) shows that the second step of the process could be done by a joint detection of users on a synchronous multiple access channel thanks to their error-correcting codes. So, it allows us to design an iterative two-step decoder including a Parallel Interference Canceler andwith a joint detection inside as described on figure 3. Demod(c1 )

Joint detection of cluster 1

Channel simulation

−

Demod(cN )

Joint detection of cluster N

Channel simulation

−

R

Channel model for in-cluster detection

The system uses an OFDM modulation with guard interval. We assume here that this guard interval is large enough to absorb the spreading and the delay of the channel. So after the demodulation, the signal becomes: X (1) R= Hk sk ck + B, k

where R is the signal vector, Hk is a diagonal matrix given by the channel of the user k whose symbol is sk and the spreading code ck . The additive noise B is supposed to be white and Gaussian distributed. The part of the cluster g in the signal R can be thereafter estimated through its spreading code cg . This signal rg can be decomposed as r g = cg H R (2) k k X g X X X g 0 X X Hp s + cp cgp Hpk sk + cp bp , = Nc p g 0 6=g k∈Gg0 p k∈Gg p {z } | | {z } | {z } Useful signal

MAI

Interference Canceler (PIC)

Figure 3: Per cluster MC-CDMA PIC Receiver. The first phase consists in using the spreading code of a cluster to obtain an estimation of the combined signal of the grouped users. Once this is done, a joint detection is used to discriminate the users inside a cluster. This discrimination of the users are done thanks to their channel code. To summarize, the overall reception is done by iteratively performing the following steps: 1. despread the cluster signal thanks to the spreading codes; 2. estimate the power of the total noise including MAI; 3. decode jointly the users thanks to the model (4) by using channel codes as explained in Section III.; 4. perform the interference cancellation for each cluster after re-spreading each user’s signal and after simulating the channel.

Noise

(3) where p corresponds to the carrier index, Nc is the number of carriers and Gg is the set of users in the cluster g. Note that the codes are assumed to be normalized such that P spreading k 2 |c | = 1. p p So assuming that the multiple access interference is a Gaussian noise, the g-th cluster signal can be modeled by X rg = hk sk + n with n ∼ N (0, σ 2 ), (4) k∈Gg

where hk is simply the average of the diagonal channel matrix Hk and σ 2 represents the total noise plus multiple access interference power and will be estimated between each PIC iteration. The synchronous expression of (4) is a consequence of the hypothesis made on the guard interval length. It would be possible to take into account a small asynchronous aspect but the receiver would be more complex. This aspect is out of the scope of the prospective work presented in this paper, so we suppose that (4) holds.

D.

Advantages of the proposed approach

The approach presented above has several advantages over the same scheme without the clusters: • the number of spreading sequences does not limit the number of users anymore. Indeed the product of the number of spreading sequences by the number of users by cluster is of interest. Then the approach of clusters permits to increase the number of users. However, the number of users is quite limited because of joint detection whose complexity growth exponentially with the size of the cluster; • this system does not modify the users part of the transmission, because the cluster aspect is not taken into account at the user level. So the clusterization becomes only a spreading code management problem; • all the resources (temporal, frequential, of spreading codes and of channel codes) are used in the detection process. So the performances expected should be better than a more classical receiver;

The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)

• by shortening the spreading sequences, the transmission rate of the system can be increased.

5. Go to 2 and repeat this process a fixed number of times.

π1

All these pros can be summarized by the flexibility the cluster approach gives through a small increase in complexity of the base-station. III.

Complete factor graph

In this section, we describe the factor graph [4] related to one cluster. The joint detection and decoding is performed using a belief propagation algorithm on a factor graph based on the combining of each user LDPC code. Theses codes are interfaced through new function nodes defined as state nodes and denoted by e in the synopsis. The figure 4 describes the 2-users case using GF(4) LDPC codes. The ri variable nodes represent the received noisy code bits. The scheduling of the messages exchanged in the graph is described hereafter: 1. The signal ri from the equivalent channel (5) as well as the prior information provided by the codes of the other users are used by the function node ei in order to compute the extrinsic information passed to the nodes bji . These nodes represent the i-th bit of the codeword of the user j; 2. After scrambling through a random interleaver σ, these informations are grouped (pairwise in GF(4)) in the dji function nodes to compute the GF(4) symbols likelihoods sji ; 3. These likelihoods are input to the Tanner graph of the LDPC code of the user j and an single belief propagation pass of this decoder is performed; 4. Finally, the extrinsic information issued from sji are demapped by the dji nodes and the resulting extrinsic bits informations are σ −1 -interleaved;

d11

d1n b12

b12n−1

b12n

b22n−1

b22n

e2

σ

b21

b22 d21

d2n

s21

s2n π2

• the factor graph is sparser than the equivalent binary codes;

A.

s1n

e1

r1

• the decoding algorithm is a belief propagation algorithm over the factor graph which is sparse. This could be done thanks to the Fourier transform over GF(2m ), which is performed in this case by a Fast Hadamard Transform;

• the LDPC over GF(2m ) are expected to outperform the binary equivalent codes because the local parity codes are decoded in a more efficiently manner.

s11

b11

I N - CLUSTER JOINT DETECTION USING LDPC CODES

Focus now on a single cluster. The user joint detection is performed thanks to the channel codes. We propose to use LDPC codes because they form a good code family with a simple decoding algorithm. In [6] we showed that LDPC Codes over non-binary field GF(2m ) provide numerous advantages such as:

c1m1

c11

• the global rate and load of the system can be easily adapted through the rate of the error correcting code of the users.

c2m2

c21

Figure 4: Factor graph of one Cluster in a two user case in GF(4) The interleavers σ are used in order the diffuse the bit information more widely and to break the dependencies between GF(2m ) symbols of the different users’ codewords. Note that only N − 1 interleavers are needed for N users in a cluster. B.

Some results of joint detection

We present here some simulation results of joint detection in one cluster. The simulations were done using a 2-users symmetric channel. So, the received signal can be written r = h1 s1 + h2 s2 + b,

(5)

where b denotes a white additive Gaussian noise with zero mean and variance σ 2 . The rate-compensated signal to noise ratio Eb /N0 is defined as: Eb h2 + h2 = 1 22 N0 2Rσ

(6)

where R is the global system rate, simply equal to the sum of the different user’s rate. Except for the binary case, all the LDPC codes we designed are regular (2, 4)-codes. In the binary case, we used the regular (3, 6)-codes which is well known to provide better performance. Consequently, the transmission rate was set to 1/2. We used codeword lengths equal to 1022 bits. Although they are very short in the LDPC code framework, this requirement is highly desirable in real time applications. The figure 5 illustrates the performance of the joint detection for different Galois Fields in term of average bit error rate

The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)

2·10−1

2·10−1

−1

10−1

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Figure 5: Joint detection for 2 users with equal power.

Figure 6: Joint detection for 3 users with equal power

(BER) versus Eb /N0 , for the (2 users/AWGN)-channel with exactly the same power. We notice that the non-binary codes exhibit better performances than the binary one and so validate the use of such codes in a joint-detection process with an extra gain of almost 4 dB compared to the binary code at BER = 10−3 . Contrary to known results in the single user case [5], the best code is not built in the higher Galois field, i.e. GF(32) in the simulation. Indeed, the performance loss which occurs when using codes in GF(8) and up, seems to indicate that no simple link exists between the detection performances and the Galois field order. Nevertheless, this assessment is also due to the use of short length codes which implies a dense factor graph and consequently a strongly sub-optimal decoding process. The figure 6 illustrates the performances of our system for 3 users and a total load of the system equal to 1.5 (3 users with a coding rate equal to 0.5). Here also, the BER results indicate that the GF(4)-codes exhibit the best performances. In this simulation, we have also introduced a special case in which the users are coded using different Galois fields (GF(2), GF(4), GF(8)). It appears that this does not improve the performances of the systems because of the permutation introduced in the factor graph as mentioned in the figure 4.

carrier. As this work is prospective, we consider a simple system with Hadamard spreading codes over a 2-carriers MCCDMA which is modeled by (1). Otherwise, the three scenarios are:

IV.

S2 Four users separated into two clusters of two users. Each user uses a binary (3,6)-regular LDPC code (rate = 0.5). S3 As in scenario S2 but the LDPC codes are (2,4)-regular LDPC codes defined over GF(4) (rate = 0.5). If the scenario uses a LDPC codes, the number of iterations of the procedure described in section A. is fixed to 10. Moreover, the PIC is performed 10 times. Figure 7 describes the average bit error rate versus the Eb /N0 . As above mentioned in the part III. the LDPC codes on GF(4) lead to the high performance and allow a gain of 5 dB compared to same approach using LDPC in GF(2) at BER = 10−3 . Moreover we can also noted that the Parallel Interference Canceler is more efficient with the LDPC in GF(4). Finally, the use of LDPC codes in GF(4) allows to • detect the users into a same cluster;

S IMULATION STUDY OF THE CLUSTER - BASED MC-CDMA SYSTEM

The simulation results of the global system described on the figure 3 are presented. As it is prospective work, we assume here a perfect knowledge of the user channels. Noise variance and time synchronization of the receiver are also assumed to be known. All the simulations were done using a user’s codewords length equal to 400 bits, which is quite short for LDPC codes. We present here the results for 2 clusters √ √ related to the spreading codes pair: [1, 1]/ 2 and [1, −1]/ 2. A.

S1 Two users without error-correction code (rate = 1). Each user is alone inside its cluster.

Hierarchical MC-CDMA versus MC-CDMA

We compare several scenarios using the preceding decoding scheme. In each case, the total transmission rate is 1 bit/sub-

• implement a forward error correction of the transmission errors. As a conclusion, the performance gain between the hierarchical MC-CDMA using LDPC in GF(4) and perfect CDMA for an Eb /N0 higher than 4 dB enables an improvement of the QoS even if the number of system users is doubled. However, whereas the global system load remains the same in this case, the rate of each user is divided by two. B.

Performances of Hierarchical MC-CDMA in the GF(4) case As the user detection is hierarchical, we are looking for a tight cooperation between the PIC and the joint detection. In the case of the scenario S3 (in GF(4)) we draw in Figure 8 the BER of

The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)

this difficulty, by creating clusters of users sharing the same spreading sequence. The first results indicate that the hierarchical approach is a promising one. Moreover the hierarchical MC-CDMA allows to construct systems with more flexibility having the possibility to control the performance/complexity trade-off.

GF(2) 10−1

10−2 BER

GF(4)

R EFERENCES 10−3

perfect CDMA without FEC

10−4

0

2

4 Eb /N0

6

8

Figure 7: Performance comparison for the three scenarios. each user in two sub-cases: when no PIC iteration is performed (in plain line in the figures) and when 10 PIC iterations are done (in dashed lines). Therefore, the figure 8 illustrates the effect of PIC detector for each user. Clearly, whereas the PIC based receiver increases the overall performance, the user BER for a given SNR are spread out when no PIC is used.

10−1

BER

10−3 10 PIC iteration 10−4

10−5 2

4

6

Eb /N0

Figure 8: PIC / Joint detection cooperation in scenario S3. In the scenario S3, the GF(4) based LDPC codes increases the first iteration gain of the PIC and concentrate the user BER of each user. In that way, each user have the same predictable QoS. V.

[3] Stefan Kaiser. Multi carrier CDMA mobile radio systems — analysis and optimization of detection, decoding, and channel estimation. Number 531 in 10. VDI-Verlag, D¨usseldorf, January 1998. [4] F. R. Kschischang, B. J. Frey, and H.-A. Loeglier, “Factor graphs and the sum-product algorithm,” IEEE Trans. Inform. Theory, vol. 47, no. 2, pp. 498–519, Feb. 2001.

[6] A. Goupil, M. Colas, D. Declercq and G. Gelle Multiple access receiver basec on hierarchical clusters/users detection using non-binary LDPC codes. In Proceedings of PacRim’05, Victoria, BC, Canada, August 2005.

No PIC

0

[2] L. Hanzo, M. Munster, B. J. Choi, and T. Keller. OFDM and MC-CDMA for broadband multi-user communications, wlans and Broadcasting. IEEE press. John Wiley and sons, 2003.

[5] D. Declercq, M. Colas, and G. Gelle. Regular GF(2q )LDPC modulations for higher order QAM-AWGN channels. In International Symposium on Information Theory and its applications ISITA, Parma, Italia, 2004.

GF(4), PIC it : 0 (normal), 10(dashed))

10−2

[1] S. Hara and R. Prasad. Overview of multi-carrier CDMA. IEEE Communication Magazine, 35(12):126–133, December 1997.

C ONCLUSION

We proposed a new receiver scheme for up-link MC-CDMA transmission. Usually the loss of orthogonality of the spreading sequences in the up-link case generally prevent the use of such modulation. Two facts leads to this loss: the channel’s spreading and the channel coefficients. The first is assumed absorbed by the guard interval, and this paper deals only with the latter asynchronousness cause. The presented approach circumvent