MULTI-USER DETECTION TECHNIQUES FOR POTENTIAL 3GPP ...

MULTI-USER DETECTION TECHNIQUES FOR POTENTIAL 3GPP LONG TERM EVOLUTION (LTE) SCHEMES

Qinghua Guo, Xiaojun Yuan and Li Ping Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR [email protected]

Abstract:

This paper is concerned with multi-user detection techniques for orthogonal frequency division multiplexing – interleave division multiple access (OFDM-IDMA) and IDMA with cyclic prefix (IDMACP). These two schemes have attractive features such as low-cost multi-user detection/equalization and flexible rate adaptation. We will show that significant performance improvement (i.e., the so-called multi-user gain) can be achieved by allowing concurrent multiple user transmission on common carries.

Key words:

Multi-carrier, Single-carrier, multi-user detection, IDMA, OFDM, FDE.

1.

INTRODUCTION

Multiple access interference (MAI) and inter-symbol interference (ISI) are major hazards in wireless communication systems. Conventional multi-user detection and time domain equalization techniques are very costly. It has been shown that ISI can be efficiently resolved by orthogonal frequency division multiplexing (OFDM) [1] and single carrier transmission with frequency domain equalization (SC-FDE) [8] techniques. OFDM has the advantage of allowing water-filling among frequency sub-carriers and SCFDE has the advantage of low peak-to-average-power-ratio. These two

 This work was supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region, China, under Project CityU 116706.

77 S. Plass et al. (eds.), Multi-Carrier Spread Spectrum 2007, 77–86. © 2007 Springer.

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techniques are currently considered for the 3rd Generation Partnership Project Long Term Evolution (3GPP LTE). In this paper, we examine multi-user transmission options for OFDM and SC-FDE. The interleave division multiple access (IDMA) [4] principle is combined with OFDM and SC-FDE respectively, resulting in the so-called OFDM-IDMA [2][3] and IDMA with cyclic prefix (IDMA-CP) schemes. In both schemes, we assume that the synchronization errors between users are within the range of CP extension so that it can be treated together with the multi-path delay spread of individual users. MAI and ISI in both schemes can be resolved efficiently using iterative frequency domain detection techniques. The related detection costs are very low. For both OFDM-IDMA and IDMA-CP receivers, the normalized cost (per user) is independent of simultaneous user number and path number. We will show that significant performance improvement (i.e., the so-called multi-user gain (MUG) [9][10]) can be achieved by allowing concurrent multi-user transmission on common carries, which is justified by both information theory study and simulation results. Notations: ENC, SP, DEC and DES denote encoder, spreader, decoder and de-spreader, respectively. 3 k denotes interleaver for user k and 3 k1 the corresponding de-interleaver. DFT and IDFT indicate the discrete Fourier transform and its inverse respectively. ACP denotes the operation of adding cyclic prefix and RCP removing cyclic prefix.

2.

MOTIVATION

Fig. 1 shows the required average transmitted sum power versus system sum rate for different multiple access schemes over quasi-static flat fading channels. From this figure, we can see that there are significant gaps between the theoretical limit and the required transmitted sum power of orthogonal frequency division multiple access (OFDMA) and conventional CDMA with single user detection. Comparing Fig. 1(a) with Fig. 1(b), we can also see that the gap increases with the number of simultaneous users. The theoretical limit shown in Fig. 1 can only be achieved by schemes with multi-user transmission and detection [9][10]. This advantage of multi-user systems is referred to as multi-user gain (MUG). Although only flat fading channels are considered in this figure, the trend is the same for frequency selective channels, which is demonstrated by the simulations in section 5. Note that Fig. 1 is for a single-cell environment. Since transmission power saving can lead to interference reduction, we expect that MUG can bring about significant improvement in multi-cell performance. Also, other considerations arise for a multi-cell environment. For example, the spreading

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gain of a CDMA type system can mitigate the worst case cross-cell interference, which can be beneficial to curb fluctuation in carrier to interference (C/I) ratio. This is partially the reason why CDMA is used in 3G systems. However, a detailed discussion on multi-cell scenario is beyond the scope of this paper. The above provides the motivation of work, i.e., how to realize MUG, which is the focus of the discussion below. 40 Average transmitted sum power (dB)

Average transmitted sum power (dB)

40

30

20

10

0

30

20

10

0 0

1

2

3

4

5

6

7

System sum rate R

(a) 2 simultaneous users

8

0

1

2

3

4

5

6

7

8

System sum rate R

(b) 4 simultaneous users

Figure 1. The average transmitted sum power versus system sum rate for different multiple access schemes in a single-cell environment. The users are uniformly distributed in a single hexagon cell. All the users have the same rate R/K (K denotes the user number). The channel effect includes path loss (fourth law), Rayleigh fading and lognormal fading (standard deviation = 8dB). The distance from the farthest corner of the cell to the base station is normalized to 1. Transmitters have the knowledge of channel information and an outage probability of 0.01 is allowed.

3.

OFDM-IDMA

The OFDM-IDMA system shown in Fig. 2 follows the principles proposed by Mahafeno, Langlais and Jego. Supposition coded modulation [5] is employed when high single user rate is required. The input data sequence dk for user k is encoded into a coded bit sequence ck1. Then, the coded bits are interleaved by a user-specific interleaver 3k, and mapped to a complex sequence {Xk(n)} by using quadrature-phase-shift-keying (QPSK). The sequence is modulated onto sub-carriers via IDFT before transmission. At receiver side, the received signals after OFDM demodulation are given by

1

In order to achieve high frequency diversity in an OFDM-IDMA system, a low-rate code is needed. A simple way to realize a low-rate code is to concatenate a common FEC code (e.g., rate-1/2 convolutional code) with a repetition code.

Q. Guo, X. Yuan and L. Ping

80 K

¦H

Y (n)

k

( n ) X k ( n )  Z ( n ), n

0,1,, N  1

(1)

k 1

where N is the number of sub-carriers and {Z(n)} are samples of a complex additive white Gaussian noise (AWGN) with zero mean and variance N0/2 per dimension. The coefficients {Hk(n)} are the DFT of the L channel taps {hk(l), l = 0, 1,…L-1} seen by user k. We focus on a particular bit carried by X kRe (n ) . Let H k (n ) H k (n ) e jT . Then (1) can be rewritten as Re  e  jT Y ( n )

H k ( n ) X kRe ( n )  [ kRe ( n ) ,

(2)

where [kRe (n) Re(e jT ¦mzk Hm (n) X m (n)  e jT Z (n)) represents the interference and noise components in Re( e  jT Y (n ) ) with respect to X kRe (n ) . From the central limit theorem, [kRe ( n ) can be approximated by a Gaussian random variable. ... dk

User k User k+1

dk+1

ENC ENC

ck ck+1

Πk Π k +1

Xk(n)

IDFT

ACP

IDFT

ACP

Elementary Y(n) signal DFT estimator (ESE)

RCP

Xk+1(n)

... ...

User k

User k+1

dˆk

dˆ k +1

DEC

DEC

Multiple access multipath channel

Π k−1 Πk Π k−1+1

...

Π k +1

 IDMA layer



OFDM layer

Figure 2. The transmitter/receiver structure for OFDM-IDMA.

The core of the OFDM-IDMA receiver shown in Fig. 2 consists of the following iteration process carried out by the elementary signal estimator (ESE) and a posteriori probability decoders (APP DECs). The discussion below is brief. The interesting readers may refer to [2][4] for details. The ESE Operations: The ESE computes the extrinsic log-likelihood ratio (LLR) about X kRe (n ) , n, k, given by



eESE XkRe (n)



ln

2 Hk (n) Pr(Re(e jTY (n)) | XkRe (n) 1) Re e jTY (n)  E [kRe (n) . (3) Pr(Re(e jTY (n)) | XkRe (n) 1) Var [kRe (n)











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The method for calculating E [kRe (n ) and Var [kRe (n ) can be found in [4]. The treatment for X kIm (n ) is similar. The DEC Operations: The extrinsic LLRs calculated by ESE are delivered to the DEC for APP soft output decoding. The outputs of DECs are then used to refine E [kRe (n ) and Var( [kRe ( n ) ) in the next iteration. OFDM-IDMA supports flexible allocation of resources among users. Suppose that a repetition code is employed for frequency diversity. High-rate transmission can be supported by the superposition coding techniques [5]. Superposition coding provides a convenient means for rate adaptation by assigning an appropriate number of code streams to each user. The adjustment step size can be made very fine by using low-rate repetition codes. This is useful for resource allocation as well as water-filling. For example, each user may superimpose a different number of code streams on different sub-carriers according to channel conditions. As a comparison, rate adaptation using conventional coded modulation schemes can be a difficult issue: a large collection of different encoders/decoders may be needed if we want a large adaptation range and/or a fine adjustment step size.

4.

IDMA-CP

Πk Π k +1

dˆ1

Π k−1 Πk

dˆk +1

Π k−1+1 Π k +1

Figure 3. Transmitter/receiver structure for IDMA-CP.

SC-FDE is an alternative technique to combat severe ISI in wireless communications [8]. The IDMA-CP scheme shown in Fig.3 is a multiple access technique based on iterative SC-FDE techniques [11]. The encoded bit stream ck is interleaved by a user-specific interleaver 3k, QPSK modulated and padded with cyclic prefix before transmission. Let N be the length of xk = {xk(n)} and Xk = {Xk(n)} be DFT of xk, i.e.,

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X k (n)

1 N

¦

N 1 m 0

xk ( m)e  j 2S mn / N , n = 0, 1, …, N-1

(4)

where j 1 . At the receiver side, CP is first removed. DFT is then applied to the received signal y, producing Y = {Y(n)} : K

Y ( n)

¦H

k

( n) X k ( n )  Z ( n ) ,

n = 0, 1, …, N-1.

(5)

k 1

Similar to (2), we rewrite (5) in a signal plus distortion form as

Y ( n) where [ k ( n )

H k (n) X k (n)  [ k (n) , n = 0, 1, …N-1

¦

mzk

(6)

H m ( n ) X m ( n )  Z ( n ) represents the signal plus noise

component. We again approximate [k(n) by a Gaussian random variable. Before going into the details in the detection algorithm, we first explain the computation of statistical parameters (i.e., means and variances) for the signals in Fig. 3. Let us treat the entries in xk as random variables and assume that their means E(xk) are given. Let F be the normalized DFT matrix with the (m, n)-th entry given by N1/2exp(j2Smn/N). Then the means of Xk = {Xk(n)} and Y = {Y(n)} can be computed as E  X k = FE  xk E Y

¦

K k 1

Hk E  Xk ,

(7a) (7b)

where Hk is a diagonal matrix, i.e., Hk = diag[Hk(0), …, Hk(N-1)]. We assume that all {xk(n)} have symmetric Gaussian distributions, i.e., their real and imaginary parts have the same variance. Furthermore, we assume these variances are the same and denoted by Var  xk (n) vxk , n and for a fixed k .

(8)

(We will come back to this assumption later when we discuss message converters.) With this assumption, the variances of {Xk(n)} are given by Var  X k (n) vxk , n and for a fixed k .

(9a)

The variance of Y(n) can be computed as Var Y ( n )

¦

K k 1

| H k ( n ) |2 Var  X k ( n )  N 0 .

(9b)

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Multi-user Detection Techniques

We are now ready to present the detection algorithm. Note that Xk(n) is not a binary variable. Instead, it can be approximated by a Gaussian random variable by applying the central limit theorem to (4). Therefore, MMSE estimation is used below to estimate Xk(n). This is the key difference between the detection algorithm in Section 3 and the one presented here. The MMSE Operations: Generate the MMSE estimate (characterized by the a posterior mean and variance) for Xk(n) [6] E

post

 X k (n)

E  X k (n) 

Var  X k (n) Hk* (n) Y (n)  E Y (n) Var(Y (n)) 2

Var

post

 Var  X (n) | H (n) |  X (n) Var  X (n)  Var Y (n)

2

k

k

k

k



(10a)



.

(10b)

IDFT is applied to transform the estimates of {Xk(n)} to those of { xk(n)}: E post  xk

Var where v xpost k

post

F H E post  X k ,

 xk ( n )

v

post xk

, n and for a fixed k

(11a) (11b)

N 1

(1/ N )¦ n 0 Var post  X k ( n ) . Due to the use of interleavers, we

will assume that the correlation among {Epost(xk(n))} can be ignored. The Message Conversion Operations: The kth message converter in Fig. 3 performs the following functions. x In the direction from the DEC to the MMSE estimator, it converts the DEC outputs in terms of LLR into the corresponding means {E(xk(n))} and variances {Var(xk(n))} [4]. As mentioned for (8), we assume that Var(xk(n)) are the same for a fixed k and different n. In practice, this is realized by approximating {Var(xk(n)),  n} using their average v xk .

x

In the direction from the MMSE estimator to the DEC, it converts the a posteriori means and variances of {xk(n)} to the extrinsic LLRs of { xkRe (n) } and { xkIm ( n ) } (assuming the a posteriori variances of xkRe (n) and xkIm ( n ) are the same) as [6] e  xkRe ( n )

§ Re  E post  xk ( n ) Re  E  xk ( n ) · ¸. 4¨  ¨ ¸ v xpost v x k k © ¹

Similarly, e( xkIm ( n )) can be obtained.

(12)

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The DEC Operations: The kth DEC performs soft output decoding based on inputs { e( xkRe ( n )) } and { e( xkIm ( n )) }. Its outputs are converted into means and variances by the kth message converter and used by the MMSE estimator as a priori information in the next iteration.

Similar to OFDM-IDMA, IDMA-CP can also be implemented based on superposition coding techniques for flexible resource allocation among users.

5.

SIMULATION RESULTS AND DISCUSSIONS

We first show that OFDM-IDMA and IDMA-CP have similar complexity as well as performance. For complexity analysis, the computational costs in all the operations (i. e., ESE, DEC, MMSE and message conversion) are independent of user number and path number. The total cost of DFT (using FFT) is O(NLog2N), or equivalently, O(Log2N) per bit. Also, the receiver cost increases linearly with iteration number. 1.E+00 OFDM-IDMA IDMA-CP S=8 S=16 S=32

1.E-01

BER

1.E-02

1.E-03

1.E-04

1.E-05 3

3.5

4

4.5

5

5.5

6

Eb/No (dB)

Figure 4. Performance comparison between OFDM-IDMA and IDMA-CP with different length of repetition code S. The information block length for both systems is 512. The system sum rate is 2. The number of iterations for both systems is 15.

Fig.4 shows the performance of OFDM-IDMA and IDMA-CP. The coding scheme for both systems is a rate-1/2 convolutional code (with generator (23, 35)8) followed by a length-S repetition code and QPSK modulation. The uncorrelated fading channel model [1] is used. The system sum rate is fixed to 2, so the number of simultaneous users is 2S. Overall, OFDM-IDMA and IDMA-CP can offer similar performance. There are some subtle differences. OFDM-IDMA performs slightly worse in the low BER range due to the frequency selectiveness among different

85

Multi-user Detection Techniques

OFDM sub-carriers, but the difference reduces when spreading length S increases. On the other hand, IDMA-CP performs slightly worse in the waterfall range, which may be caused by the approximation in (8). 1.E+00 OFDM-IDMA OFDMA 1.E-01

BER

1.E-02

1.E-03

1.E-04

1.E-05 12

14

16 18 20 Average transmitted power (dB)

22

24

Figure 5. Performance comparison between OFDM-IDMA and OFDMA with throughput 3. The number of iterations for both systems is 10. In OFDM-IDMA, the information block length for each code stream is 512 (i. e., 1024 coded bits after a rate-1/2 FEC coding). The total information block length for each user is (512×24)/K for both OFDM-IDMA (with 24/K code streams per user) and OFDMA.

Next, we examine MUG as discussed in Section 2. Fig. 5 shows the performance of the worst user (with the lowest power) in an OFDM-IDMA system (with superposition techniques [5]) using a rate-1/2 convolutional code (with generator (23, 35)8) followed by a length-8 repetition code and QPSK modulation. We fix the system sum rate R to 3, so 24 code streams are involved. We assume that all users have the same number of streams. Thus each user is assigned one stream when the number of users K = 24, and two streams when K = 12, etc. The channel conditions considered here are the same as those in Fig. 1 except that the effect of frequency selectiveness is added (The uncorrelated fading channel model [1] is used). The unequal power allocation approach follows from [4], and the channel matching strategy [4] are used based on the received power profile shown in table 1. For comparison, we also show the OFDMA performance (with the same throughput 3) based on a BICM scheme using 16-QAM modified set partitioning mapping [7]. It can be observed from Fig. 5 that the performance of OFDMA degrades with increasing K. (This performance loss is caused by the decrease of block length when K increases.) In contrast, the power efficiency of OFDM-IDMA improves as K increases due to MUG. We observe that, when K = 4, OFDM-IDMA can achieve about 4 dB gain compared with OFDMA. This

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agrees with the gap shown in Fig. 1(b). Clearly, the impact of MUG is significant. Similar gain can also be shown for IDMA-CP. Table 1 THE RECEIVED POWER PROFILE FOR AN OFDM-IDMA SYSTEM WITH THROUGHPUT 3

6.

Code stream number

13

2

2

7

Power level (dB)

0

3.1677

3.9596

5.5430

CONCLUSIONS

In this paper, we have outlined the basic principles of OFDM-IDMA and IDMA-CP for wireless communications and showed their merits including low-complexity MUD detection, flexible resource allocation among users. We also show their significant power efficiency improvement (MUG) compared with OFDMA. In conclusion, OFDM-IDMA and IDMA-CP offer two attractive options for future wireless communications.

REFERENCES [1] K. Fazel and S. Kaiser, Multi-Carrier and Spread Spectrum Systems. Chichester: John Wiley & Sons, 2003. [2] I. Mahafeno, C. Langlais, and C. Jego, “OFDM-IDMA versus IDMA with ISI cancellation for quasi-static Rayleigh fading multipath channels,” in Proc. 4th Int. Symp. on Turbo Codes & Related Topics, Munich, Germany, Apr. 3-7, 2006. [3] S. Zhou, Y. Li, M. Zhao, X. Xu, J. Wang, and Y. Yao, “Novel techniques to improve downlink multiple access capacity for beyond 3G, “ IEEE Commun. Mag., vol. 43, pp. 61-69, Jan. 2005. [4] L. Liu, J. Tong, and Li Ping, “Analysis and optimization of CDMA systems with chiplevel interleavers,” IEEE J. Select. Areas Commun., vol. 24, pp. 141-150, Jan. 2006. [5] J. Tong, Li Ping, and X. Ma, “Superposition coding with peak-power limitation,” in Proc. IEEE Int. Conf. on Commun. (ICC’06), Istanbul, Turkey, 11-15 June 2006. [6] Q. Guo, Li Ping, and H. Loeliger, “Turbo equalization based on factor graphs,” in Proc. IEEE Int. Symp. Inform. Theory (ISIT), pp.2021-2025, Australia, 4-9 Sept. 2005. [7] J. Tan and G. L. Stüber, “Analysis and design of symbol mappers for iteratively decoded BICM,” IEEE Trans. Wireless Commun., vol. 4, pp. 662-672, Mar. 2005. [8] D. Falconer, S. L. Ariyavisitakul, A. Benyamin-Seeyar and B. Eidson, “Frequency domain equalization for single-carrier broadband wireless systems,” IEEE Commun. Mag., pp. 58-66, April 2002. [9] P. Wang, J. Xiao, and Li Ping, “Comparison of orthogonal and non-orthogonal approaches to future wireless cellular systems,” IEEE Vehicular Technology Magazine, vol. 1, no. 3, pp. 4-11, Sept. 2006. [10] D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge: Cambridge University Press, 2005. [11] M. Tüchler, and J. Hagenauer, “Turbo equalization using frequency domain equalizers,” in Proc. Of Allerton Conference, Monticello, IL, USA, Oct. 2000.