Performance Evaluation of Iterative IDMA Receivers on Modulation ...

Short Paper Int. J. on Recent Trends in Engineering & Technology, Vol. 05, No. 02, Mar 2011

Performance Evaluation of Iterative IDMA Receivers on Modulation Schemes for Relay and Ad-Hoc Networks Kulbhushan Gupta1, C.K. Shukla2, Shashi Tiwari3 and M. Shukla4 Member IEEE 1, 2

Sam Higginbottom Institute of Agriculture Tech. & Sciences (Deemed University), Allahabad, India Email: [email protected], [email protected] 3, 4 Harcourt Butler Technological Institute, Kanpur, India Email: [email protected]

Abstract—In this paper, we have evaluated Bit Error Rate (BER) performance of interleave-division multiple-access (IDMA) systems with BPSK & QPSK modulation techniques when the system is subjected to Additive White Gaussian Noise (AWGN) in the channel. The BPSK and QPSK modulation techniques are already well trusted techniques with codedivision multiple-access (CDMA) systems however, IDMA scheme is referred as the extension of CDMA scheme. The simulation results demonstrate the superior performance of QPSK modulation in comparison to that of BPSK modulation method apart from the inherited advantage of better spectrum utilization. Thus, with the QPSK modulation exposes optimum and efficient data rate to mobile terminal for IDMA schemes. Index Terms— IDMA Systems, BPSK, QPSK, BER, Random Interleaver.

I. INTRODUCTION Interleave division multiple access (IDMA) has been identified as a most promising candidate in terms of multiple access technique in the context of cellular networks and selforganizing networks (e.g. ad-hoc networks).The increased demand for multimedia applications promotes the investigation on multiple access (MA) technologies that can support high date rates, various quality of services in future broadband wireless networks. Latest research investigations have revealed the interleave-division multiple access (IDMA) scheme as a potential solution to high data-rate/multi-rate applications over fading channels for fourth generation communication systems. Interference among users is inevitable in IDMA but can be suppressed by a low-cost iterative multi-user detection (MUD) procedure. Although IDMA was originally proposed for multiple access channels (MACs), similar principles have been studied for many other applications, e.g., broadcast systems, coded modulation, multiple antenna systems, relay and ad- hoc networks. Section II contains an introduction of the IDMA communication system. In section III, we have a brief look over importance of modulation techniques used for the purpose of performance evaluation of IDMA systems. Section IV presents computer simulations of IDMA systems with the intended modulation schemes with random interleavers and AWGN channel. Section V concludes the paper.

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II. IDMA MECHENISM WITH RANDOM INTERLEAVERS A. System Model Here, in this paper, an IDMA system with random interleaver has been considered for performance evaluation as shown in Figure 1, with K simultaneous users using a single path channel. The block C is constructed by serially concatenating a forward error correction (FEC) code and repletion code of length-sl. The forward error correction code used here is Memory-2 Rate-1/2 Convolutional coder. We call the elements in c k ‘chips’. The repetitive coding has been performed in order to spread the data related to various users. This repetitive coding is kept same for all the users however it may be taken as user specific too. But in case of user specific spreading, the receiver complexity increases very heavily. The upper part of Figure 1 demonstrates the transmitter structure of the IDMA scheme under consideration with K simultaneous users. The input data sequence d k of user-k is encoded based on a low-rate code C, generating a coded sequence. T

C k   ck (1), ck (2),.......c k ( j )........ck ( J )  …………(1)

where J is the frame length. The elements in ck are referred to as coded bits. Then ck is permutated

by

an

interleaver  k ,

hence,

T

producing Xk  xk (1), xk (2),.......xk ( j)........xk (J) . Following the CDMA convention, the element in xk will be denoted as “chips”. Users are solely distinguished by their interleavers, hence the name interleave division multiple access (IDMA) scheme [1]. The key principle of IDMA is that the interleavers  k  , opted for user separation, should be orthogonal for all the users. It is assumed that the interleavers are generated independently and randomly. The randomly generated interleavers disperse the coded sequences so that the adjacent chips are approximately uncorrelated, facilitating the simple chip-by-chip detection scheme as discussed below.

130 Electronic copy available at: http://ssrn.com/abstract=1955822

Short Paper Int. J. on Recent Trends in Engineering & Technology, Vol. 05, No. 02, Mar 2011  k ( j)  r ( j )  hk xk ( j) 



hk 'xk '( j )  n ( j)

k ' k

………. (5)

 k ( j ) is the distortion (including interference-plus-noise) in r  j  with respect to user-k. From the central limit theorem,

 k ( j ) can be approximated as a Gaussian variable, and r  j  can be characterized by a conditional Gaussian probability density function; Figure 1. IDMA transmitter and receiver structure

Adopting an iterative sub-optimal receiver structure, as demonstrated in figure 1, consisting of the primary signal estimator (PSE) and K single user a posteriori probability (APP) decoders (DECs), the data is iterated for pre-decided number iterations before finally taking hard decision on it. The multiple access and coding constraints are considered separately in the PSE and DECs. The outputs of the PSE and DECs are extrinsic log-likelihood ratios (LLRs) about

 x  j  defined below as; k

  r ( j )  (hk  E(k ( j)))  2  1 exp      2Var (k ( j)) 2Var (k ( j ))  

p(r( j) / xk ( j )  1) 

…..(6) where E (.) and Var (.) are the mean and variance functions, respectively. The following is a list of the PSE detection algorithm based on (3) ~ (5), assuming that the a priori statistics  E  x k  j   and V a r  x k  j   are available [1]. Based on [1], the algorithm for chip-by-chip detection will now be presented in next sub-section.

…….. (2) Those LLRs are further distinguished by subscripts, i.e.,

C. Algorithm for chip by chip Detection Step (i): Estimation of Interference Mean and Variance E r ( j)  

e PSE  x k ( j )  and e D EC  x k ( j )  , depending on whether they are generated by the PSE or DECs.

hk E  x k



 j  ,

…………..(7)

k

V a r r

 j   

2

hk V a r  x k

 j   

2

,

k

For the PSE section, y in (2) denotes the received channel output while for the DECs, y in (2) is formed by the deinterleaved version of the outputs of the primary signal estimator (PSE) block. A global turbo type iterative process is then applied to process the LLRs generated by the PSE and DECs blocks [1]. B. Basic Primary Signal Estimator (PSE) Assuming that the channel with no memory and after chip matched filtering, the received signal from K users can be written as; K

r ( j) 

h

k

x k ( j )  n ( j ), j=1,2,…..,J ... (3)

k 1

…(8)

E  k  j    E  r  j    hk E  x k  j   , ….. V a r  k

 j    V a r  r  j  

hk

2

Var xk

(9)

 j   . (10)

Step (ii): LLR Generation

ePSE  xk  j    2 hk .

r  j   E  k  j   Var  k  j  

. . . .. (11)

D. DEC Function The DECs in figure 1 carry out APP decoding using the output of the PSE as the input. With binary phase shift keying (BPSK) signaling, their output is the extrinsic log-likelihood

where hk is the channel coefficient for user-k and {n (j)} are

ratios (LLRs) e D E C ( x k ( j ) )  of xk ( j ) defined in (2), which

samples of an AWGN process with zero mean and variance,

are used to generate the following statistics,



2

 N 0 / 2 . Assuming that the channel coefficient {} are

known a priori at the receiver. Due to the use of random interleaver {}, the PSE operation can be carried out in a chipby-chip

S

e D E C ( x k ( ( j ))) 



e E SE ( x k ( ( j )))

j 1

.. ....(12)

manner, with only one sample r  j  used at a time.

r ( j )  hk x k ( j )   k ( j ) where,

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DOI: 01.IJRTET.05.02.162

…….. (4)

In the iterative process, PSE and DEC-k exchange the

extrinsic information about xk ( j ) . The CBC 131 Electronic copy available at: http://ssrn.com/abstract=1955822

Short Paper Int. J. on Recent Trends in Engineering & Technology, Vol. 05, No. 02, Mar 2011 been performed using MATLAB 7.9 under AWGN channel using random interleavers only.

detection for IDMA scheme can be concluded as follows,





(1) Primary signal estimator generates ePSE xk  j  by

IV. SIMULATION RESULTS

(2.4.6f) for decoder DEC-k.

At the transmitter side as in fig. 1 for BPSK by using random interleaver for different number of users i.e. 1, 4,8,16,32,48 without any coding scheme for spreader length 16 and number of blocks 20 ( each block contains 1024 bits) data is sent over AWGN channel. If we compare this with CDMA under same conditions, results are better as number of users is increased. Up to 8 users both gives satisfactorily results. And for more than 8 users un-coded IDMA gives much better results than CDMA. Simulation result is shown in fig 4 with 15 iterations at the receiver.

(2) DEC-k generates eDEC ( xk ( ( j ))) , which are used to update mean and variance of xk ( j ) . Under the assumption that { xk  j  } are independent, (7)(11) are a straightforward consequence of (3) and (4). The Step (ii), shown in algorithm, is obtained by evaluating (2) based on (6). Algorithm shown is an extremely simplified form for all spreading sequences to be length-1. The operations in (7) and (11), i.e., generating E(r(j))and Var(r(j)), are shared by all users, costing only three multiplications and two additions per coded bit per user. Overall, the PSE operations shown in step (i) and step (ii), cost only seven multiplications and five additions per coded bit per user, which is very modest [2]. Interestingly, the cost per information bit per user is independent of the number of users K. This is considerably lower than that of other alternatives. III.

MODULATION SCHEMES FOR IDMA SCHEME

One of the future requirements of wireless communication is to provide high data rate and high spectral efficiency with optimum BER at those channels which are subjected to Additive White Gaussian Noise (AWGN) .Modulation schemes that will be studied are BPSK and QPSK under Additive White Gaussian Noise (AWGN) channel. Such channel has two characteristics. The first is that the channel is linear, with a bandwidth that is wide enough to accommodate the transmission of signal with negligible or no distortion (white noise). The channel noise is the sample function of a zero-mean white Gaussian noise process and power spectral density No/2. As the IDMA scheme is referred as the extension of CDMA systems [9] and phase shift keying modulation schemes are well trusted with CDMA systems, the BPSK and QPSK schemes are extended to IDMA systems. Coherent M-ary PSK, which includes BPSQ & QPSK as special case with M=2 and M=4 respectively has been taken for simulation. In BPSK, the binary symbols 1&0 differ only in a relative phase shift of 180 degrees. Coherent BPSK system is therefore characterized by having a signal space that is one dimensional, with a signal constellation consisting of two message points. QPSK is bandwidthconserving modulation scheme. In QPSK as with BPSK, information carried by the transmitted signal is carried in the phase. It transmits 2 bits per symbol. In particular, the phase takes on one of four equally spaced values such as ð/ 4,3ð/4,5ð/4,7ð/4, where each value of phase corresponds to a unique pair of message bits. Accordingly, a QPSK signal has two-dimensional signal constellation and four message points, M=4, whose phase angles increase in counterclockwise direction and for a prescribed performance, QPSK uses channel bandwidth better than BPSK. The Bit Error Rate (BER) performance of QPSK& BPSK system has

Figure 4. Simulation of IDMA with no FEC coding and Random Interleaver

For the purpose of BER performance of other modulation schemes, the simulation has been performed on 15 iterations and 16 as spreadlenghs. The results have been taken for variation in data lengths. Figure 5 presents the results for IDMA scheme with four users for variation in user data lengths. While the figure 6 demonstrates the performance of IDMA systems for 8 users. The other parameters have been kept constant for the purpose of simulations. In figure 6 and 7, the simulation has been repeated for rate ½ covolutionally coded IDMA systems with other similar parameters. Comparing uncoded simulation graph in simulation figures 4 and 5, for BPSK &QPSK modulation schemes, it is observed that for four users, at Eb/No=2dB ,BER for QPSK is found to be 1.4x10- 2 whereas for BPSK, it becomes 6.6 x10- 2 thus BER improvement of 5.2 x10- 2 by using QPSK. Therefore, from uncoded simulation graphs, it is concluded that as Eb/No increases, reduction of BER in QPSK is more as compared to BPSK.

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Short Paper Int. J. on Recent Trends in Engineering & Technology, Vol. 05, No. 02, Mar 2011 To reduce the bit error rate the loss of information and signal fading should be minimized. Here we analyze two modulation techniques, BPSK &QPSK to reduce the error performance of the signal and compare which technique is better in the presence of AWGN channel. The performance of IDMA system in AWGN channel shows that QPSK has a better performance compared to that of BPSK. But for large no. of users (n>=32), the error performance is almost same for both modulation techniques and is constant for different values of Eb/No. However QPSK shows better performance for large no. of users (n>=32) with higher values of Eb/No. REFERENCES [1] Li ping, Lihai Liu, Keying Wu and W. K. Leung, “InterleaveDivision Multiple-Access,” IEEE Trans. Wireless Commun., vol. 5, pp. 938-947, April 2006. [2] M. Shukla, V.K. Srivastava, S. Tiwari “Interleave Division Multiple Access for Wireless Communication,” ‘International Conference on Next Generation Communication Systems: A Perspective’, “ICONGENCOM 06”, J.K. Institute, Allahabad, India, pp. 150-154, Dec 9-11, 2006. [3] M. Shukla, V.K. Srivastava, S. Tiwari “Analysis and Design of Tree Based Interleaver for Multiuser Receivers in IDMA Scheme,” 16th IEEE International Conference on Networks “ICON 2008”, Delhi, India, pp. 1-4, Dec. 13-14, 2008. [4] X. Wang and H. V. Poor, “Iterative (turbo) soft interference cancellation and decoding for coded CDMA,” IEEE Trans. Commun., vol. 47, pp. 1046–1061, July 1999. [5] R. H. Mahadevappa and J. G. Proakis, “Mitigating multiple access interference and intersymbol Interference in uncoded CDMA Systems with chip level interleaving,” IEEE Trans. Wireless Commun., vol. 1, pp. 781–792, Oct. 2002. [6] H. Wu, L.Ping and A. Perotti, “User-specific chip-level interleaver design for IDMA System,” IEEE Electronics Letters, Vol.42, No.4, (2006). [7] M. Shukla, V.K. Srivastava, S. Tiwari, “Analysis and Design of Optimum Interleaver for Iterative Receivers in IDMA Scheme,” Wiley Journal of Wireless Communication and Mobile Computing, Vol. 9, Issue 10, 2009, pp. 1312-1317. [8] M. Shukla, Aasheesh Shukla,, V.K. Srivastava, S. Tiwari “Different Designing Factors for IDMA Systems,” 1ST International Conference on Computer, Communication, and Control and Information Technology “C3 IT 2009” in Academy of Technology, Calcutta, India, pp. 748-756, Feb. 6-7, 2009. [9] L. Liu, W. K. Leung, and Li Ping, “Simple chip-by-chip multiuser detection for CDMA systems,” in Proc. IEEE VTC’2003Spring, Jeju,Korea, pp. 2157–2161, (2003).

Figure 5. Simulation of IDMA with no FEC coding and Random Interleaver for user=4

Figure 9. Simulation of IDMA with and without FEC coding and Random Interleaver

Similar conclusions have also been drawn with coded IDMA systems. In figure 9, the coded as well uncoded IDMA systems have been compared for performance. The coded IDMA system performs much better in comparison to uncoded IDMA systems. CONCLUSIONS In communication field the major challenge is to convey the information as efficiently as possible through limited bandwidth, though the some of information bits are lost in most cases and signal which is sent originally will face fading.

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