2010 2010International InternationalConference Conferenceon onComputational ComputationalIntelligence Intelligenceand andCommunication CommunicationNetworks Systems
Prime Number Based Interleaver for Multiuser Iterative IDMA Systems
Ruchir Gupta, B.K. Kanaujia
R.C.S. Chauhan, M. Shukla, Member IEEE
Department of Electronics & Communication Engineering Ambedkar Institute of Technology Delhi, India
[email protected]
Department of Electronics Engineering Harcourt Butler Technological Institute Kanpur, India
[email protected]
Abstract—In recently proposed multiple access techniques such as IDMA and OFDM-IDMA, the user separation is done by user specific interleavers in contrast to conventional CDMA scheme where user separation is assured with user-specific signature sequences. The user specific interleavers must demonstrate minimum probability of collision amongst each other in addition to other merits including minimal consumption of bandwidth, least hardware for their generation, and least memory requirement. Previously, random interleaver and other interleavers proposed by researchers is still leaving some space for further research leading to optimality of interleavers. In this paper, we propose a novel interleaver based on prime numbers for generation of user specific interleavers to remove the problem of high consumption of bandwidth. The simulation results demonstrate the optimal performance of prime interleaver (PI) apart from other merits in comparison to random and other interleavers.
each user. The system performance seriously degrades when the interleaving patterns are not orthogonal to each other i.e. the collision among the interleaving patterns is not minimum. These interleavers disperse the coded sequences so that the adjacent chips are approximately uncorrelated, which facilitates the simple chip-by-chip detection. In case of interleavers in IDMA systems, the parameters such as ease of generation, hardware required, bandwidth consumption during transmission, and memory requirement at transmitter and receiver end, may be vital parameters for generation of orthogonal interleavers. The greater the size of interleaver the more it consumes the memory and extra bandwidth for transmission, this becomes a greater problem when the number of users increase. In [2], random interleaver has been utilized in IDMA systems, while in [4], an efficient technique for interleaver generation in IDMA has been proposed in. The second section highlights the IDMA systems model. In third section, concepts of interleaving scheme along with various orthogonal interleavers are presented. In section 4, the proposed prime interleaver has been demonstrated while in section 5, the simulation results are demonstrated.
Keywords- prime numbers; computational complexity; interleaving; bandwidth requirement; memory requirement; orthogonality.
I.
INTRODUCTION
II.
By researchers, significant amount of research has been done in the field of wireless communication. The recently developed techniques including iterative multi user detection (MUD) techniques for suppressing multiple access interference (MAI) [1-2] has also drawn their attention. Interleave division multiple access (IDMA) and OFDM-IDMA are the two multiple access (MA) schemes that make use of the iterative MUD efficiently, [3]. In IDMA, interleavers are being employed as the only means of user separation while in CDMA the signature sequences were designed to be means of user separation as the spreader provides no coding gain [3]. With even random interleavers, the IDMA system performs similarly and even better than a comparable CDMA system [2]. IDMA outperforms CDMA in terms of better immunity to multiple access interference (MAI) and higher user count. IDMA also inherits the advantages of CDMA such as asynchronous transmission, diversity against fading and cross cell interference mitigation at a reduced cost of complexity [3] and high data rate. This chip by chip turbo type detection technique in IDMA also reduces the complexity of receiver multi use detector (MUD) as compared to that used in CDMA system [23].
In multipath channels, adjacent chips from each user interferes each other. In CDMA, the bits are spreaded and then passed with the same interleaver and transmitted consecutively, so the corresponding log-likelihood ratios (LLRs) are heavily correlated. In IDMA, however chip level interleaving is performed. After random chip level interleaving, the replicas are dispersed more randomly, so the corresponding LLRs become less correlated. In order to minimize the forward error correction (FEC) code rate IDMA transmitter is employed. The key principle of IDMA is that the interleavers {Пk} should be user-specific i.e. the cross correlation between specific interleavers must me minimum [7]. It is assumed that the interleavers are generated independently and randomly. These interleavers disperse the coded sequences so that the adjacent chips are approximately
The efficiency of IDMA system is dependent on the generation of various pseudo random interleaving patterns for 978-0-7695-4254-6/10 $26.00 © 2010 IEEE DOI 10.1109/CICN.2010.119
IDMA MECHENISM
IDMA does not involve signature sequences, which greatly simplifies the problem of computational complexity in the receiver. The major difference between IDMA and CDMA is regarding chip-level interleaving and bit level interleaving respectively. It can be analyzed that the performance advantage of IDMA increases with the number of users when compared to CDMA [1-2].
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uncorrelated, which facilitates the simple chip-by-chip detection scheme.
ζ k ( j ) = r ( j ) − hk x k ( j ) =
∑h
k' ≠k
k'
xk ' ( j ) + n ( j )
is the distortion in r( j) with respect to user-k. The output of ESE and DECOD-DESPREEADERs block is given as [2]
eESE ( xk ( j )) = 2 hk .
r ( j ) − E ( r ( j )) + hk E ( xk ( j )) 2
Var ( rj ) − hk Var ( xk ( j )) S
eDEC ( xk (π ( j ))) = ∑ eESE ( xk (π ( j ))) j =1
where
Figure 1. Iterative IDMA Transmitter and Receiver
III.
Fig. 1 presents the transmitter and receiver structure of the multiple access scheme under consideration with K simultaneous users. The input data sequence dk of user-k is encoded based on a low-rate code C, generating a coded sequence ck [ck(1), . . . , ck(j), . . . , ck(J)], where J the frame length. The elements in ck are referred to as coded bits. The coded bits are further spreaded over entire bandwidth with the help of spreader. The spreader may be counted to be common or user specific. In this case, we have considered the spreader to common to all the users. Then ck is permutated by an interleaver k, producing xk [xk(1), . . . , xk(j), . . . , xk(J)]. Following the CDMA convention, we call the elements in xk “chips”. Users are solely distinguished by their interleavers; hence the name interleave-division multiple-access (IDMA).The chip interleavers allow adopting a chip – by-chip estimation technique [2].
VARIOUS ORTHOGONAL INTERLEAVERS FOR IDMA SCHEME
The principle of traditional periodic interleaving scheme which is suitable to block codes can be expressed by interleaving the data of array I × n. Let the interleaving degree may be I for n bits. At the initial step, (I,n) linear block codes are arranged in rows in an array I × n. Now, we transmit the array column by column. At the receiver, the received data are rearranged in the same array column by column, then decoding it rank by rank. In theory, the user-specific interleavers are generated independently and randomly [2], known as random interleavers (RI). In this case, the base station (BS) has to employ a considerable amount of memory to store these interleavers at transmitter and receiver side, which may cause serious concern in case of large user count. Also, during the initial link settingup phase, there should be messages passing between the BS and mobile stations (MSs) to inform each other about user specific interleavers. Extra bandwidth resource will be consumed for this purpose if the interleavers used by the BS and MSs are long and randomly generated. In [5], master random interleaver or power interleaver generation method is presented to alleviate this concern. With this method, the interleaver assignment scheme is simplified and memory cost is greatly reduced without sacrificing performance, but the complexity for regeneration of interleavers and deinterleavers at the receiver side is major concern in case of higher user count [7] provided that enough memory space is not used to store all required interleavers.
At the receiver side, the outputs of the elementary signal estimator`s (ESE) and DECOD-DESPREEADERs are extrinsic log-likelihood ratios (LLRs) about {xk }defined as [2]
⎛ p ( y / xk ( j ) = +1) ⎞ e( xk ( j )) = log ⎜ ⎟ , ∀k , j. (1) ⎝ p ( y / xk ( j ) = −1) ⎠ These LLRs are further distinguished by the subscripts i.e.,
eSEB ( xk ( j )) and eDEC ( xk ( j )) , depending upon whether they are generated by ESE and DECOD-DESPREEADERs.
Researchers has proposed various other interleavers in [813][15][16]. PEG interleaver generation mechanisms [8] explain the selection of suitable orthogonal interleavers out of pre-generated random interleavers while other mechanisms including [9-13], [15-16] explain the independent generation of orthogonal interleavers which are losing their orthogonality in case of higher user count. In [7], tree base interleaver (TBI) generation scheme is presented which employs two master interleavers, which are randomly selected. User specific interleaver is designed using a combination of both master
Due to the use random interleavers {Π k}, the ESE operation can be carried out in a chip-by-chip manner, with only one sample r(j) used at a time. The received signal at the receiver is given as
r ( j ) = hk xk ( j ) + ζ k ( j )
j = 1,..., S
(2)
where
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The bandwidth required by the Prime Interleaver (PI) is smaller than other available interleavers as now only seed is to be transmitted, in addition to very small amount of memory required at the transmitter and receiver side as shown in table 1.
interleavers. The scheme is optimum in terms of bandwidth requirement and BER [14]; however, still there is space for development of other efficient interleavers for IDMA scheme. Here, in this paper, a new interleaver is proposed based on prime number which gives a novel user-specific interleaver generation mechanism with lesser time to get it generated and along with minimal consumption of bandwidth required during transmission well similar performance in terms of BER to that of random interleaver. IV.
TABLE I COMPARISON OF BANDWIDTH REQUIREMENT FOR TRANSMISSION OF THE INTERLEAVING MASK
User Count
MECHANISM OF PRIME INTERLEAVER
In IDMA, different users are assigned different interleavers which are weakly correlated. The computational complexity and memory requirement should be small for generation of interleavers. The Prime Interleaver is basically aimed to minimize the bandwidth and memory requirement that occur in other available interleavers with bit error rate (BER) performance comparable to random interleaver.
3===> (1+2p) mod n
.
2
1
30
30
2
1
62 126
62 126
2 2
1 1
Comparison Graph showing Bandwidth Requirement of 4 Interleavers
x 10
Bandwidh requirement of Random Interleaver Bandwidth requirement of Master Random Interleaver Bandwidth requirement of Tree Based Interleaver Bandwidth requirement of Prime Interleaver
4
3.5
3
2.5
2
1.5
1
0
0
10
20
30
40
50 60 User Number
70
80
90
100
Figure 2. Comparison of Bandwidth requirement of various interleavers
In master random interleaving scheme the computational complexity and transmitter and receiver end is quite high due to calculation of user-specific intereleaving masks. The prime interleaving scheme reduces the computational complexity that occurs in master random interleaving scheme; however, it is higher to that of tree based interleaving scheme due computation involved for calculation of user specific interleavers.
n===> (1+(n-1)p) mod n For Example if we have to interleave 8 bits such that {1, 2, 3, 4, 5, 6, 7, 8} and we wish to interleave these bits with seed 3 then the new location of bit will be as follows 1===> 1 2===> (1+1*3) mod 3===>4 3===> (1+2*3) mod 3===>7
V.
4===> (1+3*3) mod 3===>2
NUMERICAL RESULTS
For simplicity, IDMA system with BPSK signaling in AWGN channel for hk=1, ∀ k is assumed. Without loss of generality, a uniform repetition coding CREP {+1, -1, +1, -1, --------} is used with spread length sl =16, for all users. In figure 3, uncoded IDMA cases are considered, i.e., without any forward error correction (CFEC) coding while data length is taken to be 512. In figure 5, Memory-2 Rate-1/2 Convolutional code is used. The iteration at the receiver side is chosen to be 15 in each case.
5===> (1+4*3) mod 3===>5 6===> (1+5*3) mod 3===>8 7===> (1+6*3) mod 3===>3 8===> (1+7*3) mod 3===>6 6}.
14
1
0.5
4===> (1+3p) mod n
.
1
14
B an dw idt h R eq uirem ent of Int erleav er(N o.of bits requ ired/u s e r)
2===> (1+p) mod n
.
2
4.5
1===> 1
.
6
6
For understanding the mechanism of prime interleaver, let us consider a case of interleaving n bits with seed p. First, we consider a Gallois Field GF (n). Now, the bits are interleaved with a distance of seed over GF (n). In case, if {1, 2, 3, 5, 6, 7, 8… n} are consecutive bits to be interleaved with seed p then location of bits after interleaving will be as follows
.
6
5
In generation of prime interleaver we have used the prime numbers as seed of interleaver. Here, user-specific seeds are assigned to different users.
.
Tree Based Interleaver Generation 2
Prime Interleaver
2
Random Interleaver Generation 2
Now, the new order of bits will be {1, 4, 7, 2, 5, 8, 3, and
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CDMA under same conditions, results are better with IDMA scheme as number of users is increased [2].
From these figures, it is evident that the BER performances of IDMA scheme are similar for random and prime interleavers. But from figure 2, it is clear that, on the front of bandwidth consumption, the prime interleaver is outperforming the other interleavers because only the user specific prime numbers have to be sent along with data format during transmission.
In figure 4, the coded IDMA for 16 users have been presented along with results in uncoded as well coded IDMA environment. The result shows similar BER performances of prime interleavers to random interleavers in coded as well uncoded IDMA environments. The simulation results for coded IDMA systems outperform the uncoded IDMA systems when compared in terms of bit error rate (BER) performance. The prime interleaver is, however, performing similar to that of random interlevers.
0
10
-1
10
VI. B it E rror Rate
Prime Interleaver 1 user Random Interleaver 1 user Random Interleaver 4 users Prime Interleaver 4 users Random Interleaver 8 users Prime Interleaver 8 users Random Interleaver 16 users Prime Interleaver 16 users Prime Interleaver 24 users Random Interleaver 24 users Random Interleaver 32 users Prime Interleaver 32 users Random Interleaver48 users Prime Interleaver 48 users Random Interleaver 64 users Prime Interleaver 64 users
-3
10
-4
10
-5
10
-6
10
2
4
CONCLUSION
The proposed ‘Prime Interleaver’ is very easy to generate and is better than the random or any other interleavers in terms of bandwidth consumption problems. The Prime interleaver is better than master random interleaver in terms of computational complexity. With tree based interleaver, the proposed interleaver seems to be having little bit more complexity due to involvement of higher calculation for calculation of user-specific interleavers.
-2
10
6
8
10
12
14
The BER performance of all the interleavers including random interleaver and tree based interleaver is almost similar. However, entertaining the other issues including memory and bandwidth requirements, the proposed interleavers seems to be optimum and can take the place of the random or any other interleaver techniques without performance loss in IDMA systems.
16
Eb/No
Figure 3. Performance comparison of Prime Interleaver (PI) with Random Interleaver (RI) in uncoded IDMA systems
REFERENCES
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Prime Interleaver 16 users Coded Random Interleaver 16 users Coded Random Interleaver 16 users Uncoded Prime Interleaver 16 users Uncoded
-1
10
[1]
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B it E rror R ate
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10
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2
3
4
5
6
7 Eb/No
8
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Figure 4. Performance comparison of Prime Interleaver (PI) with Random Interleaver (RI) in Rate ½ Convolutionally coded IDMA systems
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