K. Kusume and G. Bauch, "Some Aspects of Interleave Division Multiplex Access in Ad Hoc Networks," in Proc. Int. Symp. on Turbo Codes & Related Topics in connection with Int. ITGConf. on Source and Channel Coding, (Munich, Germany), April 2006.

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Katsutoshi Kusume http://kusume.googlepages.com/

Some Aspects of Interleave Division Multiple Access in Ad Hoc Networks Katsutoshi Kusume and Gerhard Bauch DoCoMo Eurolabs, Landsbergerstr. 312, 80687 Munich Germany,{kusume,bauch}@docomolab-euro.com

Abstract We consider some aspects of interleave division multiple access (IDMA) in ad hoc networks. IDMA is a multiple access technique which relies on an iterative multiuser detection and it has a close relation to CDMA. Traditionally, the medium access control protocol sees the physical layer as a collision model, while in literature the potential of multiuser detection techniques in ad hoc networks has been discussed. Higher efficiency can be achieved if a certain amount of interference is allowed due to the multiuser detection. In this paper we propose a simple complexity reduction technique for IDMA and a design of multiple user-distinct interleavers. The complexity reduction technique is aimed to support a variety of receivers with different capabilities of handling interference. It allows to reduce the complexity significantly while graceful performance degradation can be realized. The proposed multiple interleavers are designed so as to minimize memory requirements and signaling overhead by deriving multiple interleavers from one common interleaver.

1

Introduction

CDMA is a strong candidate to achieve high spectral efficiency along with high power efficiency. In order to obtain the potential benefits from CDMA, iterative multiuser detection techniques based on the turbo principle have been intensively studied in the last years, e.g. [1]. Iterative multiuser detection techniques comprise a multiuser detector (MUD) and a bank of user-independent a posteriori probability (APP) decoders. Both MUD and APP decoder are soft-in softout (SISO) blocks which exchange soft information. Multiple access interference (MAI) as well as inter symbol interference (ISI) is iteratively mitigated. Interleave Division Multiple Access (IDMA) has a close relation to CDMA, but instead of using userdistinct spreading codes, a bandwidth expansion is fully exploited for coding resulting in a very low rate code, and users are separated only by user-distinct interleavers [2], [3]. The performance of IDMA is better than or as good as that of CDMA in various scenarios such as user-asynchronism, multipath channels, near-far effects, and highly user-loaded scenarios, as reported in [4]. The advantage of IDMA is its reasonably low complexity of MUD which can be much simpler than the state-of-the-art MUD technique for CDMA, e.g. the one proposed in [1]. This reduction of complexity allows to support a higher number of users. In this paper we consider some aspects of IDMA in ad hoc networks. Traditionally, the medium access control (MAC) protocol sees the physical layer as a collision model (e.g. [5]) and tries to avoid simultaneous transmissions. That leads to a low efficiency because a large area will be blocked, while in [6] the potential of multiuser detection techniques in such

a network is discussed. We propose in this paper a simple complexity reduction technique and a design of multiple user-distinct interleavers. If IDMA is used in ad hoc networks, not all receivers will probably afford the full complexity of MUD. Furthermore, not all signals, which are simultaneously transmitted, are necessary to be detected. Then, in addition to desired signals, only a few strong interferers may be important to be detected and canceled. In such scenarios, our strategy may be found useful since, as we will see, the complexity can be significantly reduced while achieving graceful performance degradation. It is known that the interleaver plays an important role in an iterative receiver. It has been noted in literature that performance of CDMA generally improves when each user interleaves a bit-stream after channel encoding using a user-specific interleaver [7]. As mentioned earlier, using user-specific interleavers is the only means for user separation in IDMA. To the authors’ knowledge, generally interleavers for such systems are randomly chosen and there are very few papers on design of multiple interleavers [7], [8], while there has been a relatively large number of research results on single interleaver design for turbo codes. Since we have ad hoc networks in mind, our goal is to minimize memory requirements and signaling overhead by deriving multiple interleavers from one common interleaver. Our proposal is based on a single interleaver, which is common for all users, and userspecific cyclic shifts in order to generate multiple interleavers. Although the design is empirical and no optimality is claimed, we will show that the performance is at least as good as completely randomly chosen interleavers.

k) CDMA c(n,m b (k ) Convolutional Πk

Symbol mapper

encoder

IDMA b (k ) Convolutional

k) c(n,m Rep.

encoder

un(k )

s (nk )

(k) ′

s (nk )

Πk

Symbol mapper

MUD

yj

)

− (m) k ) La ( c(n,m

for K users

)

(d)

Π−1 k Πk

k) ) La ( c(n,m

− (d) k ) Le ( c(n,m

)

APP decoder

Transmitter (m) k ) Le ( c(n,m

L( b (k ))

Receiver

Fig. 1. System model of CDMA and IDMA. Basic receiver structure is common for both schemes.

2

(k) ′

System Model

We consider CDMA and IDMA systems illustrated in Fig. 1. At the transmitter, information bits b(k) of user k, k = 1, . . . , K, are encoded by the rate Rc convolutional code. For CDMA, the coded bits are interleaved by the interleaver Πk , mapped on the complex (k) symbols sn which are elements of a QAM/PSK signal space constellation S where |S| = M , and then spread (k) (k) (k) by the spreading code un = [un,0 , . . . , un,Nu −1 ]T ∈ CNu where (·)T denotes transposition. For IDMA, the convolutionally coded bits are further encoded by the rate Rr simple repetition code. Then, the coded bits are interleaved by Πk and mapped on the complex symbols (k) (k) sn . For convenience, we denote by cn,m the coded bits before the interleaver for both CDMA and IDMA. In the following, we develop a linear equation system which is common for both CDMA and IDMA (see also [1], [4]). The channel is P modeled with the finite(k) νk length impulse response filter ℓ=0 g δ[j − ℓ] which Pνk ℓ (k) 2 has the normalized energy of ℓ=0 E[|gℓ | ] = 1. We denote by τk and νk , respectively, a user-specific delay and a memory of multipath channel of user k, then the total delay of user k becomes τk + νk which is normalized by a chip duration. Then, it is convenient to define the delays: Dc = maxk (τk + νk + 1) in chips and Ds = ⌈(Dc −1)/Nu ⌉+1 in symbols. ⌈·⌉ rounds the argument to the nearest integer towards infinity. Note that the symbol delay Ds is equal to the chip delay Dc for IDMA since there is no spreading after Πk . By (1) (K) denoting sn = [sn , . . . , sn ]T and the effective chan(1) (K) nel H n,ℓ = [hn,ℓ , . . . , hn,ℓ ] of dimension Nu × K, which is defined later, then the signal vector PDreceived s may be expressed as y n = ℓ=0 H n−ℓ,ℓ sn−ℓ + η n where η n is a vector of zero-mean complex Gaussian noise with a variance of N0 /2 per real dimension. The effective channel takes into account the channel and the spreading code. It is generally time-varying in case of CDMA since the spreading code usually depends on the symbol index n due to a scrambling (k) code. The effective channel hn,ℓ can be determined



= ak ui ∗ g (k) from the discrete convolution f (k) n ′ (k) (k) T T where g (k) = [0τk , g0 , . . . , gνk , 0T Dc −τk −νk −1 ] , (k) T

T un = [un , 0T and 0n denotes a zero Nu (Ds −1) ] vector of dimension n. The amplitude of user k is denoted by ak ∈ R which takes into account nearfar scenarios. Then, the effective channel is defined (k) (k) (k) as hn,ℓ = [fn,ℓNu +1 , . . . , fn,(ℓ+1)Nu ]T ∈ CNu . Now, we consider a sliding window for the detection of a symbol at time n. By defining the symbol vector T T T s = [sT of dimension n−Ds +1 , . . . , sn , . . . , sn+Ds −1 ] K(2Ds − 1) and the channel matrix   H n−Ds +1,Ds −1 · · · H n,0   .. .. .. H =  . . .

H n,Ds −1 · · · H n+Ds −1,0

of dimension Nu Ds × K(2Ds − 1), the received signal T T vector y = [y T can be concisely n , . . . , y n+Ds −1 ] expressed as y = Hs + η,

T T where η = [η T n , . . . , η n+Ds −1 ] . The MUDs of CDMA and IDMA compute the a posteriori log-likelihood ratio (L-values): (k)

L(m) (cn,m ) = log = log

P (c(k) n,m =+1|y) (k)

P (cn,m =−1|y) P (k) (k) + P (y|sn =si )P (sn =si ) s ∈Sm . P i (k) (k) − P (y|sn =si )P (sn =si ) s ∈S i

(1)

m

+ Sm

We denote by the set of all constellation points − si where its m-th bit is +1 and by Sm the set of all constellation points si where its m-th bits is −1. (k) The a priori probability of the symbol P (sn = si ) is computed from the a priori probabilities of the (k) code bits P (cn,m = ci,m ) which are assumed to be uncorrelated due to the interleaver. Thus, we compute P (s(k) n = si ) =

M Y

P (c(k) n,m = ci,m ),

(2)

m=1 (k)

where P (cn,m = ci,m ) is computed from the L-value sent from the decoder: 1 (m) (k) P (c(k) n,m = ci,m ) = (1 + ci,m tanh(La (cn,m )/2)), 2 (m)

(k)

and La (cn,m ) is initialized to 0 before the first (k) iteration. The computation of P (y|sn = si ) depends on particular schemes and will be explained in the next subsections. The decoder computes improved a posteriori L(k) values L(d) (cn,m ) about the code bits taking into account the code constraints. The decoding of the repetition code is to sum up every 1/Rr L-values [9]. The decoding of the convolutional code can be based on the BCJR algorithm [10], and in this paper we use its max-log approximation (Max-Log-MAP) which can be found, e.g. in [11]. In the following, the computation of the conditional (k) probability P (y|sn = si ) is briefly explained for CDMA and IDMA.

−1

In [1], iterative multiuser detection technique for CDMA based on the instantaneous minimum mean square error (MMSE) filter has been proposed. This technique is developed for BPSK modulation. We extend it for higher order modulation like QAM/PSK constellations. There are two steps to compute the (k) conditional probability P (y|sn = si ). The first step is the soft interference cancellation: ˜ y

(k)

= y − H(˜ s−

s˜(k) n eκ ),

(3)

T ˜ ˜T ˜T ˜ = [˜ where s sT n = n+Ds −1 ] , s n, . . . ,s n−Ds +1 , . . . , s (1) (K) T [˜ sn , . . . , s˜n ] , κ = (Ds − 1)K + k, and eκ denotes the κ-th column of identity matrix. The softsymbol estimates are computed from the a priori P (k) (k) (k) information: s˜n = E[sn ] = = si ∈S si P (sn (k) si ) where P (sn = si ) is computed from (2). By defining a covariance operator Cov(x, y) = E[xy H ] − (k) E[x]E[y H ], the auto-correlation of the symbol sn is (k) (k) (k) (k) 2 computed as ρn = Cov(sn , sn ) = E[|sn | ] − P (k) (k) (k) sn |2 where (·)H |˜ sn |2 = si ∈S |si |2 P (sn = si ) − |˜ denotes Hermitian transpose. Assuming uncorrelated symbols, the covariance matrix can be written as C = T T Cov(s, s) = diag([ρT n−Ds +1 , . . . , ρn , . . . , ρn+Ds −1 ]) (1) (K) T and ρn = [ρn , . . . , ρn ]. In the second step, we apply the MMSE filtering to the received sequence after the soft interference (k) H (k) (k) (k) ˜ cancellation: zn,si = wn,si y where zn,si is the output of the MMSE filter given the symbol si is trans(k) mitted. The MMSE weight vector is found as wn,si = (k) −1 (k) H ˜ (k) 2 (k) argminw E[|sn − w y | |sn = si ] = Rn,si r n,si where the correlation vector and the correlation matrix (k) ∗ (k) (k) y (k) sn |sn = si ] = can be computed as r n,si = E[˜ (k) ˜ (k)H |sn = si ] = y (k) y Heκ |si |2 and R(k) n,si = E[˜ (k) H H(C − (ρn − |si |2 )eκ eT κ )H + N0 I, respectively. (k) The output zn,si is approximated to be Gaussian dis(k) (k) (k) tributed with the mean µn,si = E[zn |sn = si ] = (k) H wn,si Heκ si and the variance (k) (k) H (k) (k) µn,si |2 |sn = si ] = wn,si r n,si

(k) 2 σn,si = (k) − |µn,si |2 .

(k) E[|zn



Then, we finally compute the conditional probability as (k)

P (y|sn = si )

(k)

(k)

≈ P (zn |sn  = si )  2 (k) −µ(k) |zn,s n,si | 1 i = . exp − (k) 2 (k) 2 πσn,si

σn,si

2.2 IDMA The multiuser detection technique for IDMA has been presented e.g, in [2]–[4] for BPSK symbols. We extend it for higher order modulation. The first step is the soft interference cancellation as for CDMA in (3). We apply the approximation to get the conditional probability: Q νk (k) (k) (k) P (y|sn = si )≈ ℓ=0 P (˜ yℓ+τk +1 |sn = si )  (k) (k) Pνk |˜yℓ+τ −gℓ si |2 k +1 , =α · exp − ℓ=0 (k) 2 σℓ

Πk



decoder of convolutional code

(d)

k) ) La ( c(n,m Πk DeMux

2.1 CDMA

+

Rep.

L(b(k ))

(d)

k) ) Le ( c(n,m

Fig. 2. Decoder of user k for IDMA. Decoding of convolutional code can be avoided for complexity reduction.

Q νk (k) 2 where the scalar α is defined as α = ℓ=0 1/(πσℓ ). The approximation is to compute the probability from the independent channel delay components, and the probability of each delay component is approximated to be Gaussian distributed with the (k) mean gℓ (channel tap coefficient) and the vari(k) 2

(k)

(k)

(k)

ance σℓ = Cov(˜ yℓ+τk +1 , y˜ℓ+τk +1 |sn = si ) = (k) (k) H T eℓ+τk +1 HCH eℓ+τ +1 − ρn |gℓ |2 + N0 .

3

Complexity Reduction Strategy

The complexity of the MUD for IDMA is relatively low as we saw in the previous section. The complexity of the decoder, on the other hand, can be quite high for a large number of users because of the K independent decoders. The decoding task for IDMA is two fold as shown in Fig. 2: decoding the repetition code and the convolutional code, where the former is far simpler than the latter. We propose to limit the exploitation of the decoding of convolutional code aiming at complexity reduction. If we do not decode the convolutional code, there will be still some improvements due to the decoding of the repetition code. In case of CDMA, however, no performance improvement can be obtained without decoding the convolutional code. In the following, we will show that our simple method is beneficial for IDMA in the two different switching strategies.

3.1 User-Wise Switching Strategy In ad hoc networks, not all network nodes are likely to afford the full complexity of the multiuser detection. Therefore, some form of complexity reduction should be considered. Here, we propose to decode the convolutional code for a limited number of users. Computer simulations are performed to evaluate our scheme. Nb = 128 information bits are encoded by the rate Rc = 1/2 memory 4 standard [23, 35]8 convolutional code. The trellis is terminated with 4 additional termination bits. For CDMA the code bits are interleaved by the random interleaver, mapped on the BPSK symbols, and then spread by the Nu = 4 spreading code that is constructed from the OVSF codes and the UMTS uplink long scrambling sequence as specified in [12]. For IDMA the convolutionally coded bits are further encoded by the rate Rr = 1/4 repetition code, interleaved, and then mapped on the BPSK symbols. Both schemes have the same bandwidth-efficiency.

0

0

10

10

−1

0

−1

10

−2

10

−1

10 IDMA CDMA

−2

10

−2

10

−3

single user bound

−3

10

10

−4

10

0

−6

single user bound

10

2

10

−5

2

4 6 8 Eb/N0 in dB

10

10

0

Nb=128 Nb=512

−6

Nb=1024

−7

4 6 8 Eb/N0 in dB

Nb=1024

10

Nb=4096 10

Fig. 3. BER performance of IDMA and CDMA on AWGN channel after 6 iterations.

Fig. 3 shows the performance of IDMA and CDMA on an AWGN channel where K = 4 equal-power users are asynchronous with τk = k − 1 user delays. The convolutional code is decoded for the first and the second users (left figure) and only for the first user (right figure). The BER performance of user 1 is plotted. It can be observed that IDMA performs better than CDMA due to the decoding of the repetition codes. The performance gap between IDMA and CDMA becomes larger by decreasing the number of users for which the convolutional code is decoded. We have also simulated for multipath channels and a near-far scenario since the power control would be difficult in ad hoc networks. A similar advantage of our strategy has been observed. The results are omitted due to space limitation. We conclude that the proposed scheme achieves graceful performance degradation while reducing the overall complexity. We note that, if the convolutional code is always decoded for all users, the performance of IDMA and CDMA is very similar as reported in [4].

3.2 Iteration-Wise Switching Strategy It is well known that the interleaver size must be large enough for the iterative processing to be effective while it is always limited in practice. Fig. 4 shows the BER performance of IDMA on an AWGN channel for different sizes of interleaver. The coding parameters are the same as in Fig. 3. The code bits are QPSK modulated. K = 8 users are synchronous. On the left figure the performance is plotted when the convolutional code is always decoded for all users. It can be seen that the performance improves as the frame size gets larger. It converges to the single user bound at Eb /N0 = 6 dB for Nb = 4096. Plotted on the right is the performance when only the repetition code is decoded in the first 4 iterations, then the convolutional code is also decoded in the rest of iterations in addition to the repetition code. Surprisingly, the performance already converges to the single user bound at Eb /N0 = 6 dB for Nb = 1024. The system is analyzed using extrinsic information transfer (EXIT) chart [13]. In our system, the horizontal

Nb=4096

−7

0

2 4 Eb/N0 in dB

6

10

0

2 4 Eb/N0 in dB

6

Fig. 4. BER performance of IDMA for different sizes of interleaver after 14 iterations. 0.5 trajectory with N b=1024

0.4

MUD K=8, QPSK gray mapping Eb/N0=6 dB

0.48

( c (k))) I ( c (k) , L(m) e

−5

10

−5

10

Nb=512

10 single user bound

first 4 itrs. w/o max−log MAP of convolutional code

−4

10

Nb=128

−5

10 −4

single user bound

−3

10

always with max−log MAP of convolutional code

−4

10

−3

10

−2

10

IDMA CDMA BER

BER of user 1

10

10

−1

10

0

10 max−log MAP decoding of convolutional code for user 1 only

max−log MAP decoding of convolutional code for user 1&2

0.3

0.47 0.46

0.2

0.45 0.97

0.98

1

Decoder rate 1/2 convolutional code with rate 1/4 repetition code Decoder rate 1/4 repetition code

0.1 0

0.99

0

0.2

0.4

0.6

0.8

( c (k))) I ( c (k) , L(d) e

1

Fig. 5. EXIT charts. Trajectories for Nb = 1024 are plotted for: (1) convolutional code is always decoded (solid line) and (2) convolutional code is decoded after initial 4 iterations (dashed line). (d)

axis is the mutual information I(c, Le (c)) at the input of the MUD, which is sent from the decoder. The (m) vertical axis is the mutual information I(c, Le (c)) at the output of the MUD, which is sent to the decoder as the input. Fig. 5 shows the EXIT charts. Trajectories for Nb = 1024 are plotted for two cases: (1) convolutional code is always decoded (solid line), and (2) the decoding of the convolutional code starts after the first 4 iterations (dashed line). We observe that the trajectories do not follow the prediction of EXIT curves after some iterations due to the limited interleaver size. However, in the latter case, the trajectory reaches the error free (d) point I(c, Le (c)) = 1 while it does not in the former case. We note that with a sufficiently large frame size the trajectory follows the prediction of EXIT curves in both cases. The trajectory for such a large block size, e.g. for Nb = 4096, is omitted due to space limitation. It should be also pointed out that, in the lower part of the EXIT charts in Fig. 5, the improvement is similar with/without the decoding of the convolutional code. Thus, it makes sense to decode only the repetition code (also reducing complexity) in initial few iterations. We observed that the number of initial iterations with the ‘repetition-code-only decoding’ does not influence the final performance as long as it is taken large enough.

0

0

10

10

−1

AWGN channel

10

Π Multipath channel

−1

10

Π

−2

10

random interleavers common random interleaver −3 10 user synchronous common random interleaver user asynchronous

BER

−3

10

−4

10

10

−7

10

10

0

−6

2

4 6 8 Eb/N0 in dB

10

0

2

4 6 8 Eb/N0 in dB

10

Fig. 6. BER performance of IDMA on AWGN channel after 6 iterations (left figure) and on multipath channel after 4 iterations (right figure).

4

(c)

Π

∆ k,1

(c)

∆ k,D

Fig. 7. (a) User delay as a means for user separation and (b) user cyclic shift, analogous to (a). (c) Generalization of interleaver generation by multiple cyclic shifts and a common interleaver.

−5

−6

(b) common interleaver and cyclic delay

(c) repeat (b) with multiple cyclic delays

−4

10 10

(c)

∆k

Πk

10

−5

Π

(a) common interleaver and user delay

−2

10

τk

Multiple Interleavers

IDMA requires user-specific interleaver. Each node, which applies multiuser detection, needs to know all interleavers that results in a significant signaling overhead in ad hoc networks. There have been very few studies on multiple interleavers. In [7], [8], the authors proposed empirical criteria of goodness of a set of interleavers for convolutionally coded CDMA systems. One of the criteria is to choose congruential interleavers (see [7]) for a given code having certain free distance such that the interleaved codes have good asymptotic distances. This approach requires an intensive search for a large number of users. Another criterion in [7] is ‘an iterative decoding suitability measure’ that takes into account correlations of L-values, but it is defined only for the case of two users. Moreover, no deterministic method to find good interleavers is provided.

4.1 Cyclically Shifted Multiple Interleavers Our approach is an empirical design based on some observations. We start with a question: what if only a single common interleaver is used for all users? To answer the question, we have performed computer simulations with parameters being the same as in Section 3.1. The left figure in Fig. 6 shows the BER performance of IDMA on an AWGN channel after 6 iterations. The coded bits are BPSK modulated. K = 4 users are either synchronous or asynchronous (τk = k − 1). In each scenario, the performance is plotted for two cases: (1) user-distinct multiple random interleavers and (2) single common random interleaver (same for all users). In the first case, since the performance is almost same for synchronous and asynchronous users, only one performance curve is plotted. It can be observed that the performance does not improve over iterations using a single common interleaver for all users in the user-synchronous case. However, the performance is as good as user-distinct multiple interleavers in the userasynchronous case with the user delays τk = k − 1.

The right figure in Fig. 6 shows the BER performance on a multipath channel after 4 iterations. The channel delay is νk = 7 for all K = 4 users. The channel taps are generated from zero mean Gaussian distribution with uniform power delay profile, i.e. E[|gk,ℓ |2 ] = 1/(νk + 1) = 1/8 and are constant over each frame. In contrast to the AWGN channel, the users are still separable using a single common interleaver in the user synchronous case. That is due to the multipath channels which are user-independent. However, we observe an error floor. We note that the performance improves with the user-distinct delays. We conclude that user-distinct delays can be helpful for user separation. That is because the interleaver cycle is shifted by a delay so that the deinterleaving of a certain user does not recover the original sequence order of other users. Thus, the users’ signals are effectively decorrelated. Our simple strategy to generate multiple interleavers is summarized in Fig. 7. The system with a common interleaver and a user delay is illustrated in Fig. 7(a). Instead of controlling the transmission delays of users, which would be difficult in ad hoc networks, we propose to exploit a cyclic shift as depicted in Fig. 7(b). However, as we observed in Fig. 6, only a single (cyclic) delay will be insufficient for a good user separation. Therefore, we propose to use multiple cyclic shifts with a common interleaver to construct multiple interleavers as shown in Fig. 7(c). The left figure in Fig. 8 shows the BER performance of IDMA on AWGN channel for 6 synchronous users. The coding parameters are the same as in Fig. 6. The code bits are QPSK modulated. The BER performance after 14 iterations is plotted for three cases: 1, 2 and 3 randomly chosen cyclic shifts are used to generate multiple interleavers with the common UMTS turbo interleaver in [14]. In principle, any interleaver can be used for the single common interleaver. The userspecific cyclic shifts are independently and randomly generated from a uniform distribution. The high error floors can be observed for one and two random cyclic shifts. With three random cyclic shifts, the error floor cannot be observed in the range of practical interests. The role of interleavers becomes more important for highly user-loaded scenarios since more iterations are necessary to mitigate the severe MAI. The right figure in Fig. 8 shows the BER performance of IDMA on an

0

0

10

10 one random cyclic shift two random cyclic shifts three random cyclic shifts random interleavers

−1

10

limited to the collision of the random seed to other ongoing transmissions, but the current interference level or the receiver’s capability of interference handling can be other possibilities.We note that the receiver, which makes the decision, is not only the desired receiver, but also nodes to which the prospective transmitter interferes. In this way, it is possible to support a variety of receivers with different capabilities.

K=110 users itr=5 −1

10

−2

10

−2

itr=30

10

itr=15

BER

BER

−3

10

−4

−3

10

10

−5

10

−6

10

single user bound

10

K=6 users

10

−4

single user bound

5

−5 random interleavers from one trubo interleaver

−7

10

0

−6

2

4 6 8 Eb/N0 in dB

10

10

5

6

7 8 9 Eb/N0 in dB

10

Fig. 8. BER performance of IDMA on AWGN for synchronous users. The left figure shows the performance for K = 6 users after 14 iterations where code bits are QPSK modulated. The right figure shows the performance for K = 110 users where Nb = 256 information bits are encoded only by the Rr = 1/64 repetition code and then BPSK modulated. Interleavers are generated from randomly chosen three cyclic shifts and the common UMTS turbo interleaver.

AWGN channel for 110 synchronous users. We encode Nb = 256 information bits by only the rate Rr = 1/64 repetition code. The coded bits are BPSK modulated. Note that this scenario corresponds to the number of users almost twice as large as the spreading code length in CDMA. Interleavers are generated from randomly chosen three cyclic shifts and the single common UMTS turbo interleaver. The performance is plotted after 5, 15 and 30 iterations and it is compared with the case of using completely randomly generated multiple interleavers. We see that our strategy works as good as the completely randomly generated interleavers. The proposed method requires little computational efforts to generate interleavers. Moreover, no additional storage is required to support multiple interleavers because they are derived from a single common interleaver. These are desired features in a practical system.

4.2 Information Exchange of Interleaver In ad hoc networks, it is difficult to manage multiple interleavers among transceivers due to the dynamic topology changes and the lack of a central control unit. Since each node needs to know the interleavers of the desired user and all interferers, a careful management of interleavers results in a large signaling overhead. Instead, we propose the following procedure. Each transmitter generates a random seed s and exchanges with a receiver a tuple (s, f, n) which determines a rule to generate interleavers where f and n denote an update frequency and the number of cyclic shifts, respectively. Each node randomly generates n cyclic shifts using the random seed s to compute the interleaver. The interleaver is frequently updated according to the frequency f , thus to decrease the probability of interleaver collision. Furthermore, we propose that the receiver decides whether the transmitter’s request should be accepted based on certain criteria. The criteria are not

Concluding Remarks

In this paper we proposed a simple complexity reduction technique for IDMA and a design of multiple userdistinct interleavers. We believe that these aspects are important to bring the potential of IDMA into ad hoc networks while keeping in mind that not all receivers are likely to afford the full complexity. There are still many aspects which need studies that include: synchronization of nodes to some extent, channel estimations, and a design of MAC protocol for network nodes with different capabilities of interference handling.

References [1] X. Wang and H. V. Poor, “Iterative (Turbo) soft interference cancellation and decoding for coded CDMA,” IEEE Trans. on Commun., vol. 47, no. 7, pp. 1046–1061, July 1999. [2] L. Ping, L. Liu, K. Y. Wu, and W. K. Leung, “Interleave-division multiple-access,” submitted to IEEE Tran. on Wireless Commun. [3] H. Schoeneich and P. A. Hoeher, “Adaptive interleave-division multiple access - a potential air interface for 4G bearer services and wireless LANs,” in IEEE and IFIP Int. Conf. on Wireless and Optical Commun. and Networks, June 2004, pp. 179–182. [4] K. Kusume and G. Bauch, “CDMA and IDMA: Iterative multiuser detections for near-far asynchronous communications,” in Proc. IEEE Int. Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC 2005), September 2005. [5] IEEE 802.11, “Part 11: Wireless LAN medium access control (MAC) and physical layer (PHY) specifications,” June 1997. [6] L. Tong, V. Naware, and P. Venkitasubramaniam, “Signal processing in random access,” IEEE Signal Processing Magazine, vol. 21, no. 5, pp. 29–39, September 2004. [7] A. Tarable, G. Montorsi, and S. Benedetto, “Analysis and design of interleavers for iterative multiuser receivers in coded CDMA systems,” IEEE Transactions on Information Theory, vol. 51, no. 5, pp. 1650–1666, May 2005. [8] S. Br¨uck, U. Sorger, S. Gligorevic, and N. Stolte, “Interleaving for outer convolutional codes in DS-CDMA systems,” IEEE Trans. on Commun., vol. 48, no. 7, pp. 1100–1107, July 2000. [9] D. Divsalar and F. Pollara, “Hybrid concatenated codes and iterative decoding,” California Institute of Technology, Pasadena, California, Tech. Rep. TDA Progress Report 42-130, 1997. [10] L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Trans. on Info. Theory, vol. 20, no. 2, pp. 284–287, March 1974. [11] P. Robertson, P. Hoeher, and E. Villebrun, “Optimal and suboptimal maximum a posteriori algorithms suitable for turbo decoding,” European Transactions on Telecommun. (ETT), vol. 8, no. 2, pp. 119–125, March 1997. [12] 3G TS 25.213, “3rd generation partnership project; technical specification group radio access network; spreading and modulation (FDD) (release 4),” June 2002. [13] S. ten Brink, “Convergence behavior of iteratively decoded parallel concatenated codes,” IEEE Trans. on Commun., vol. 49, no. 10, pp. 1727–1737, October 2001. [14] 3G TS 25.212, “3rd generation partnership project; technical specification group radio access network; multiplexing and channel coding (FDD) (release 1999),” March 2000.

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