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An Interleaver-based Asynchronous Cooperative Diversity Scheme for Wireless Relay Networks Zhaoxi Fang, Liangbin Li, Zongxin Wang Department of Communications Science and Engineering Fudan University Shanghai, P.R.China Email: [email protected], [email protected], [email protected] Abstract—Distributed space time coding can achieve full spatial diversity in wireless relay networks. However, it requires accurate symbol-level synchronization and priori coordination between cooperative relay terminals, which is difficult to implement in distributed networks. In this paper, we propose a novel scheme based on interleaving to achieve cooperative diversity in both synchronous and asynchronous networks with little protocol overhead. A low complexity iterative detection algorithm is also proposed to combine signals from different relays at the receiver. The simulation results demonstrate the comparable performance to space-time codes based cooperative schemes which require perfect synchronization and coordination.
I. INTRODUCTION It is generally acknowledged that MIMO technology is an important means to improve the performance in wireless systems through space time coding, and/or to increase data rate through spatial multiplexing. However, in a practical scenario, due to the size, cost or hardware complexity limitations, mobile terminals may not be able to support multiple transmit antennas. Recently, cooperative communication [1-4] is proposed to improve transmission reliability in fading channels by exploiting the broadcasting features of wireless channels, where mobile terminals share their antennas and resources to create a virtual array to achieve spatial diversity. In [2], the authors developed and analyzed several cooperative diversity protocols, namely, amplify-and-forward (AF), fixed decode-and-forward (FDF) and selection decodeand-forward (SDF). It was shown that except fixed decodeand-forward protocol, all the others can achieve full transmit diversity. A bandwidth efficient cooperative protocol was proposed in [3] by directly using the existing orthogonal spacetime block codes (OSTBC) [5]. In order to keep the orthogonality of the space time codes, perfect synchronization of various signals from different cooperative terminals (or relays) is required at the receiver. However, unlike conventional point-to-point MIMO systems where multiple transmit antennas are co-located at the same place, the terminals in a wireless relay network are geographically dispersed. As a result, the received signals at the destination terminal are asynchronous in nature. In such asynchronous networks, the orthogonality of space time codes is hard to maintain that a diversity loss is inevitable, thus giving birth to some recent works to explore cooperative diversity in asynchronous networks [6-7].
All of the previous space-time cooperative diversity protocols require a central control unit or prior coordination between the terminals. In a large-scale wireless network, the number of cooperative terminals is not fixed and is presumably unknown, making it essential for all the terminals, apart from the destination, to have the instantaneous knowledge of the other terminals in cooperation in order to select the corresponding space time code matrix. This causes a large protocol overhead. In [8], a novel multiple access scheme named as interleavedivision multiple-access (IDMA) was proposed. In IDMA, each user is assigned a unique interleaver to enable low complexity multiuser detection at the receiver. Inspired by IDMA, we propose a simple uncoordinated cooperation scheme based on interleaving, where each cooperating terminal simply interleaves the detected bits using a preallocated interleaver. Compared with the protocols proposed in [3, 4, 6, 7], the proposed scheme shares several advantages: 1.
The cooperating terminals are not required to know who their partners are.
2.
This protocol supports arbitrary number of cooperative terminals, whereas full rate full diversity orthogonal space time codes does not exist in most cases [5].
3.
The spatial diversity can be achieved through a low complexity symbol-by-symbol iterative detection algorithm at the receiver even if the received signal is asynchronous.
The remainder of this paper is organized as follows Section II describes the system and channel model. Section III presents the iterative multi-relay detection algorithm. Some numeric results are presented in Section IV. Finally, some concluding remarks are given in Section V. II.
SYSTEM MODEL
Considering a wireless communication system shown in Fig. 1 with M+2 terminals, where S is the source terminal, D is the destination terminal, and all the other M terminals Rm, m=1,2,…,M, serve as the potential relays. Similar to [2], a time division scheme is adopted. There are two phases during the cooperative communication: broadcasting phase and cooperative phase, each phase occupying one slot in transmission. In Phase one (broadcasting phase), terminal S broadcasts its information bits to the destination terminal D as
978-1-4244-2075-9/08/$25.00 ©2008 IEEE
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.
S
during phase two if FDIF protocol is adopted, i.e., Ra ={ Rm | m=1,2,…,M}, Ma=M.
D
On the other hand, if SDIF protocol is adopted, The relay Rm first performs CRC check to see if the whole frame has been received correctly. If so, the relay Rm then forwards the interleaved and re-modulated signal xm to the destination D as in the FDIF protocol. Otherwise, Rm will keep idle, i.e. doesn’t participate in the second phase. In this case, Ra = {Rm | bˆm (n) = b(n), ∀n} . Meanwhile, terminal S transmits xs again regardless of which protocol is adopted by the relay terminals. The signal received at terminal D in the cooperative phase can be expressed as
…
R1
RM Figure 1. A wireless relay network with M potential relays.
well as M other potential relays Rm, m=1,2,…,M. In the second phase (cooperative phase), relay Rm decides whether to forward the detected signal according to the adopted cooperative protocols, while terminal S continues its transmission and terminal D keeps receiving signal. In this paper, we will consider two interleaver-based cooperative communication protocols: fixed decode-interleave-andforward (FDIF) protocol and selection decode-interleave-andforward (SDIF) protocol. Since not all of the M relay terminals are active in cooperative phase, it is convenient to denote Ra as the set of the terminals being active in cooperative phase and Ma as the size of the set, Ma=|Ra|. In the broadcasting phase, terminal S transmits a modulated symbol sequence with length N, xs(n), n=0,1,...,N-1, containing information bits b(n), n=0,1,,…,Nb-1, and several cyclic redundancy check (CRC) bits, which helps to detect the signals received at the relays in SDIF protocol. Assuming the channels are flat fading and remain constant in the consecutive two slots, the received signal at terminal D in the broadcasting phase can be expressed as rd ,1 (n) = hsd xs (n) + η d ,1 (n)
(1)
¦
Rm ∈Ra
hmd xm (n − τ m ) + hsd xs (n − τ s ) + ηd ,2 (n)
(3)
where ηd ,2 (n) is the AWGN at destination D during phase two with the same statistical properties as ηd ,1 (n) , and τ S , τ m is the asynchronous delay for terminal S and terminal Rm , respectively. III. LOW COMPLEXITY ITERATIVE DETECTION Relying on (1), (3), a low complexity symbol-by-symbol iterative detection method can be applied at receiver to achieve cooperative diversity. Without loss of generality, we assume QPSK modulation and each modulated symbol can be expressed as x(n) ∈ {±1 ± j} , j = −1 . Note that destination terminal D processes signal received at two distinctive slots. Terminal D first extracts initial prior information of xs(n) from signal received at the first slot, then employs symbol-bysymbol iterative detection based on the signal received at the second slot, the detail algorithm is listed below: Initialization: The initial log likelihood ratio (LLR) information of xs can be derived according to the received signal rd,1 during the broadcasting phase:
and the signal at relay Rm , m=1,2,…,M, can be written as rm (n) = hsm xs (n) + ηm (n)
rd ,2 (n) =
(2)
where hij, i,j=s,d,1,2,…,M, are the channel coefficients between terminal i and j, which are Rayleigh distributed with mean-square Gij=E(|hij|2); ηd ,1 (n) and ηm (n) are the AWGN at destination D during phase one and at relay terminal m, respectively, both have zero mean and variance σ 2 per dimension. During the cooperative phase, terminal Rm first demodulates and decodes the received signal rm to get an estimate of the transmitted information bits: bˆm (n) , n=0,1,…,Nb-1. If FDIF protocol is used, the decoded bit stream is first interleaved by a random interleaver π m , then remodulated to produce symbol sequence xm(n), n=0,1,...,N-1. The relay terminal Rm will forward xm to the destination D without any CRC checking, i.e., the relay Rm is always active
L1 ( xsRe (n)) = 2 Re[hsd* rd ,1 (n)] σ 2 , ∀n L1 ( xsIm (n)) = 2 Im[hsd* rd ,1 (n)] σ 2 , ∀n.
(4)
L1(xs(n)) serves as the initial prior information for iterative detection at the cooperative phase, i.e, L1a ( xs (n)) = L1 ( xs (n)) , L1a ( x m (n)) = L1 ( x s (π m (n))) , ∀m, n
where the superscript 1 denotes the first iteration, the subscript 1 denotes the first slot, and π m (⋅) denotes the interleaving operation. The i-th iteration:
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.
Firstly, calculate the expectation and variance of xm(n) from the prior information Lia ( x m (n)) derived at the previous iteration:
Hence, the prior information for next iteration can be updated as Lia+1 (x s (n)) = Li (x s (n)) − Li2 (x s (n))
Re m
i a
E( x (n)) = tanh( L ( x (n)) / 2), ∀m, n E( xmIm (n)) = tanh( Lia ( xmIm (n)) / 2), ∀m, n Var( xmRe (n)) = 1− | E( xmRe (n)) |2 , ∀m, n
(5)
Var( xmIm (n )) = 1− | E( xmIm (n)) |2 , ∀m, n
where E(x) and Var(x) denotes the mean and variance of the variable x. The derivation of the mean and variance of xs(n) is similar. While detecting symbol xk(n), k=1,2,…,M, forwarded by the kth relay Rk , (3) can be rewritten as rd ,2 (n + τ k ) = hkd xk (n) + ξ k (n)
(6)
where ξ k (n) is the interference to xk (n) , Due to interleaving, ξk (n) is uncorrelated with xk (n) and can be assumed Gaussian distributed for large M according to the central limit theorem. ξ k (n) can be written as
ξk (n) = rd ,2 (n + τ k ) − hkd xk (n) =
¦
hmd xm (n + τ k − τ m )
Rm ∈Ra , Rm ≠ Rk
(7)
+ hsd xs (n + τ k − τ s ) +ηd ,2 (n + τ k ). The phase offset due to hkd in (6) can be cancelled out by *
multiplying both sides of (6) with hkd , thus the detection of the real part and imaginary part of xk ( n) can be treated separately as [8] 2
i 2
Re k
L ( x (n)) =
2 hkd (Re[ yk ,d (n)]-E[Re[hkd* ξ k (n)]]) * Var[Re[hkd ξ k (n)]] 2
Li2 ( xkIm (n)) =
2 hkd (Im[ yk , d (n)]-E[Im[hkd* ξ k (n)]])
(8)
Var[Im[hkd* ξ k (n)]]
* where yk , d (n) = hkd rd,2 (n + IJ k ) .
After de-interleaving, the LLRs derived from the signal forwarded by all the active relays and by the source terminal S during phase two are combined with the LLR derived from the signal transmitted at the first phase as
Li ( xs (n)) =
¦
Rm ∈ Ra
∀n
L (xm (n)) = L (x s (π m (n))) − L (xm (n)) ∀m, n. i +1 a
Re m
Li2 ( xm (π m−1 (n))) + Li2 ( xs (n)) + L1 ( xs (n)) (9)
i
i 2
(10)
Then go back to equation (5) for next iteration. A hard decision is made based on L(xs(n)) in the last iteration. This symbol by symbol iterative detection shares the advantage of low complexity [8], the cost per information symbol per iteration involved in (5) ~ (10) is proportional to the total number of active terminals, Ma. IV. SIMULATION RESULTS During simulation, the channels are assumed to be Rayleigh flat fading and to maintain unchanged in the consecutive two slots. The bit SNR in the simulation results is defined as Eb EG = s sd N0 β Kc N0
(11)
where Kc, Es and ȕ are denoted as the number of information bits represented by each modulation symbol, the energy of each modulation symbol and transmission rate, respectively. Specifically, ȕ=1 for direct transmission and ȕ=0.5 for interleaver-based cooperative transmission due to the fact that one data frame occupies two consecutive slots. Furthermore, we assume that the maximum asynchronous delay is LTs, where Ts is symbol duration, and the asynchronous delay for each terminal is uniformly generated from [0, LTs]. A random interleaver is employed in the protocol, with each frame containing 2048 QPSK symbols. The relative channel gain is defined as Bsm=Gsm/Gsd ˈBmd=Gmd/Gsd, m=1,2,…,M. In this simulation, we assume that relays Rm, m=1,2,…,M, are close to terminal S, Bmd = 1, m=1,2,…,M, and that the channel gains between the relays and the terminal S are equivalent, Bsm=Bˈ m= 1,2,…,M. We first consider the synchronous case, i.e., L=0. Fig. 2 illustrates the frame error rate (FER) performance when different cooperative diversity protocols are employed with one relay in the system. In Fig.2, B=inf. indicates that the channels between source terminal S and relays are error-free; hence no errors occur during phase one transmission. For comparison, Fig. 2 also includes the performance of direct transmission (labeled as ‘Direct Trans.’ in the figure) and that of the OSTBC based cooperative transmission[3] employing the Alamouti space time code[9] under B=inf. The iteration number is 2 for the proposed cooperative diversity scheme. It is shown in the figure that interleaver-based cooperative diversity protocols provide significant performance improvement to the direct transmission. Specifically, the transmission scheme employing SDIF protocol achieves the same diversity order as that using Alamouti space time code, while the performance of FDIF protocol is worse than that of SDIF. This is due to the fact that the relay will always forward
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.
the signals even if it fails to decode the received frame correctly in FDIF. It can be seen from Fig.2 that the diversity order of the fixed relaying protocol FDIF is 1 as the direct transmission scheme. The FER performance under the different number of relay terminals with synchronous receiving is shown in Fig. 3. The proposed Selection Decode-Interleave-and-Forward protocol is employed and the iteration number is six for M=3 and 8. Obviously, the achievable diversity order increments with the number of relays. Fig.4 demonstrates a comparison of the performances related to synchronous receiving and asynchronous receiving, both employing SDIF protocol and the relative channel gain is set to be B=10. It is shown that the FER performance of the asynchronous case is the same as that of synchronous receiving, indicating the effectiveness of the proposed interleaver-based cooperative diversity protocol. V.
Figure 2. Comparison among the systems employing various protocols with 1 relay and synchronous receiving.
CONCLUSION
A novel interleaver-based cooperative diversity protocol is introduced in this literature. Furthermore, a low complexity iterative symbol-by-symbol detection algorithm is proposed to combine signals from all active relays. In contrast to conventional space-time coded cooperative diversity protocol, the proposed scheme is more attractive for distributed implementation since the cooperating relays do not have to know which other relays are active, and full cooperative diversity is achievable in both synchronous and asynchronous networks. REFERENCES [1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
A. Nosratinia, T. E. Hunter, and A. Hedayat, "Cooperative Communication in Wireless Networks", IEEE Commun. Mag., vol.42, no.10, pp.74-80, Oct. 2004. J. N. Laneman, D. N. C. Tse, and G. W. Wornell, " Cooperative diversity in wireless networks : Efficient protocols and outage behavior," IEEE Trans. Inf. Theory, vol.50, no.12, pp.3062-3080, Dec. 2004. J. N. Laneman, and G. W. Wornell, " Distributed Space-Time-Coded Protocols for Exploiting Cooerative Diversiy in Wireless Networks," IEEE Trans. Inf. Theory, vo.49, no.10, pp.2415-2425, Oct 2004. G. Scutari, S. Barbarossa, " Distributed space-time coding for regenerative relay networks," IEEE Trans. Wireless Commun., vol.4, no.5, pp.2387-2399, Sept. 2005. V. Tarokh, H. Jafarkhani, and A. R. Calderbank, "Space-time block codes from orthogonal designs," IEEE Trans. Inform. Theory, vol.45, pp. 1456-1467, July 1999. S. Wei, D. Goeckel, and M.Valenti, “Asynchronous cooperative diversity,” in Proc. Conf. Inform. Sci. and Sys, Princeton, NJ, Mar. 1719, 2004. Y. Shang, X.-G. Xia, "Shift-Full-Rank Matrices and Applications in Space-Time Trellis Codes for Relay Networks With Asynchronous Cooperative Diversity," IEEE Trans. Inform. Theory, vol.52, no.7, pp.3153-3168, July 2006. L. Ping, L. Liu, K. Y. Wu, and W. K. Leung, "Interleave-Division Multiple-Access," IEEE Trans. Wireless Commun., vol.5, no.4, pp.938947, April 2006. S. M. Alamouti, “A Simple Transmitter Diversity Scheme for Wireless Communications,” IEEE J. Select. Areas Commun.,vol.16, pp.14511458, October 1998.
Figure 3. FER performance under different number of relays with synchronous receiving. SDIF protocol is employed.
Figure 4. Comparison with synchronous and asynchronous receiving with multiple relays. SDIF protocol is employed.
An Interleaver-based Asynchronous Cooperative Diversity Scheme for Wireless Relay Networks Zhaoxi Fang, Liangbin Li, Zongxin Wang Department of Communications Science and Engineering Fudan University Shanghai, P.R.China Email: [email protected], [email protected], [email protected] Abstract—Distributed space time coding can achieve full spatial diversity in wireless relay networks. However, it requires accurate symbol-level synchronization and priori coordination between cooperative relay terminals, which is difficult to implement in distributed networks. In this paper, we propose a novel scheme based on interleaving to achieve cooperative diversity in both synchronous and asynchronous networks with little protocol overhead. A low complexity iterative detection algorithm is also proposed to combine signals from different relays at the receiver. The simulation results demonstrate the comparable performance to space-time codes based cooperative schemes which require perfect synchronization and coordination.
I. INTRODUCTION It is generally acknowledged that MIMO technology is an important means to improve the performance in wireless systems through space time coding, and/or to increase data rate through spatial multiplexing. However, in a practical scenario, due to the size, cost or hardware complexity limitations, mobile terminals may not be able to support multiple transmit antennas. Recently, cooperative communication [1-4] is proposed to improve transmission reliability in fading channels by exploiting the broadcasting features of wireless channels, where mobile terminals share their antennas and resources to create a virtual array to achieve spatial diversity. In [2], the authors developed and analyzed several cooperative diversity protocols, namely, amplify-and-forward (AF), fixed decode-and-forward (FDF) and selection decodeand-forward (SDF). It was shown that except fixed decodeand-forward protocol, all the others can achieve full transmit diversity. A bandwidth efficient cooperative protocol was proposed in [3] by directly using the existing orthogonal spacetime block codes (OSTBC) [5]. In order to keep the orthogonality of the space time codes, perfect synchronization of various signals from different cooperative terminals (or relays) is required at the receiver. However, unlike conventional point-to-point MIMO systems where multiple transmit antennas are co-located at the same place, the terminals in a wireless relay network are geographically dispersed. As a result, the received signals at the destination terminal are asynchronous in nature. In such asynchronous networks, the orthogonality of space time codes is hard to maintain that a diversity loss is inevitable, thus giving birth to some recent works to explore cooperative diversity in asynchronous networks [6-7].
All of the previous space-time cooperative diversity protocols require a central control unit or prior coordination between the terminals. In a large-scale wireless network, the number of cooperative terminals is not fixed and is presumably unknown, making it essential for all the terminals, apart from the destination, to have the instantaneous knowledge of the other terminals in cooperation in order to select the corresponding space time code matrix. This causes a large protocol overhead. In [8], a novel multiple access scheme named as interleavedivision multiple-access (IDMA) was proposed. In IDMA, each user is assigned a unique interleaver to enable low complexity multiuser detection at the receiver. Inspired by IDMA, we propose a simple uncoordinated cooperation scheme based on interleaving, where each cooperating terminal simply interleaves the detected bits using a preallocated interleaver. Compared with the protocols proposed in [3, 4, 6, 7], the proposed scheme shares several advantages: 1.
The cooperating terminals are not required to know who their partners are.
2.
This protocol supports arbitrary number of cooperative terminals, whereas full rate full diversity orthogonal space time codes does not exist in most cases [5].
3.
The spatial diversity can be achieved through a low complexity symbol-by-symbol iterative detection algorithm at the receiver even if the received signal is asynchronous.
The remainder of this paper is organized as follows Section II describes the system and channel model. Section III presents the iterative multi-relay detection algorithm. Some numeric results are presented in Section IV. Finally, some concluding remarks are given in Section V. II.
SYSTEM MODEL
Considering a wireless communication system shown in Fig. 1 with M+2 terminals, where S is the source terminal, D is the destination terminal, and all the other M terminals Rm, m=1,2,…,M, serve as the potential relays. Similar to [2], a time division scheme is adopted. There are two phases during the cooperative communication: broadcasting phase and cooperative phase, each phase occupying one slot in transmission. In Phase one (broadcasting phase), terminal S broadcasts its information bits to the destination terminal D as
978-1-4244-2075-9/08/$25.00 ©2008 IEEE
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.
S
during phase two if FDIF protocol is adopted, i.e., Ra ={ Rm | m=1,2,…,M}, Ma=M.
D
On the other hand, if SDIF protocol is adopted, The relay Rm first performs CRC check to see if the whole frame has been received correctly. If so, the relay Rm then forwards the interleaved and re-modulated signal xm to the destination D as in the FDIF protocol. Otherwise, Rm will keep idle, i.e. doesn’t participate in the second phase. In this case, Ra = {Rm | bˆm (n) = b(n), ∀n} . Meanwhile, terminal S transmits xs again regardless of which protocol is adopted by the relay terminals. The signal received at terminal D in the cooperative phase can be expressed as
…
R1
RM Figure 1. A wireless relay network with M potential relays.
well as M other potential relays Rm, m=1,2,…,M. In the second phase (cooperative phase), relay Rm decides whether to forward the detected signal according to the adopted cooperative protocols, while terminal S continues its transmission and terminal D keeps receiving signal. In this paper, we will consider two interleaver-based cooperative communication protocols: fixed decode-interleave-andforward (FDIF) protocol and selection decode-interleave-andforward (SDIF) protocol. Since not all of the M relay terminals are active in cooperative phase, it is convenient to denote Ra as the set of the terminals being active in cooperative phase and Ma as the size of the set, Ma=|Ra|. In the broadcasting phase, terminal S transmits a modulated symbol sequence with length N, xs(n), n=0,1,...,N-1, containing information bits b(n), n=0,1,,…,Nb-1, and several cyclic redundancy check (CRC) bits, which helps to detect the signals received at the relays in SDIF protocol. Assuming the channels are flat fading and remain constant in the consecutive two slots, the received signal at terminal D in the broadcasting phase can be expressed as rd ,1 (n) = hsd xs (n) + η d ,1 (n)
(1)
¦
Rm ∈Ra
hmd xm (n − τ m ) + hsd xs (n − τ s ) + ηd ,2 (n)
(3)
where ηd ,2 (n) is the AWGN at destination D during phase two with the same statistical properties as ηd ,1 (n) , and τ S , τ m is the asynchronous delay for terminal S and terminal Rm , respectively. III. LOW COMPLEXITY ITERATIVE DETECTION Relying on (1), (3), a low complexity symbol-by-symbol iterative detection method can be applied at receiver to achieve cooperative diversity. Without loss of generality, we assume QPSK modulation and each modulated symbol can be expressed as x(n) ∈ {±1 ± j} , j = −1 . Note that destination terminal D processes signal received at two distinctive slots. Terminal D first extracts initial prior information of xs(n) from signal received at the first slot, then employs symbol-bysymbol iterative detection based on the signal received at the second slot, the detail algorithm is listed below: Initialization: The initial log likelihood ratio (LLR) information of xs can be derived according to the received signal rd,1 during the broadcasting phase:
and the signal at relay Rm , m=1,2,…,M, can be written as rm (n) = hsm xs (n) + ηm (n)
rd ,2 (n) =
(2)
where hij, i,j=s,d,1,2,…,M, are the channel coefficients between terminal i and j, which are Rayleigh distributed with mean-square Gij=E(|hij|2); ηd ,1 (n) and ηm (n) are the AWGN at destination D during phase one and at relay terminal m, respectively, both have zero mean and variance σ 2 per dimension. During the cooperative phase, terminal Rm first demodulates and decodes the received signal rm to get an estimate of the transmitted information bits: bˆm (n) , n=0,1,…,Nb-1. If FDIF protocol is used, the decoded bit stream is first interleaved by a random interleaver π m , then remodulated to produce symbol sequence xm(n), n=0,1,...,N-1. The relay terminal Rm will forward xm to the destination D without any CRC checking, i.e., the relay Rm is always active
L1 ( xsRe (n)) = 2 Re[hsd* rd ,1 (n)] σ 2 , ∀n L1 ( xsIm (n)) = 2 Im[hsd* rd ,1 (n)] σ 2 , ∀n.
(4)
L1(xs(n)) serves as the initial prior information for iterative detection at the cooperative phase, i.e, L1a ( xs (n)) = L1 ( xs (n)) , L1a ( x m (n)) = L1 ( x s (π m (n))) , ∀m, n
where the superscript 1 denotes the first iteration, the subscript 1 denotes the first slot, and π m (⋅) denotes the interleaving operation. The i-th iteration:
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.
Firstly, calculate the expectation and variance of xm(n) from the prior information Lia ( x m (n)) derived at the previous iteration:
Hence, the prior information for next iteration can be updated as Lia+1 (x s (n)) = Li (x s (n)) − Li2 (x s (n))
Re m
i a
E( x (n)) = tanh( L ( x (n)) / 2), ∀m, n E( xmIm (n)) = tanh( Lia ( xmIm (n)) / 2), ∀m, n Var( xmRe (n)) = 1− | E( xmRe (n)) |2 , ∀m, n
(5)
Var( xmIm (n )) = 1− | E( xmIm (n)) |2 , ∀m, n
where E(x) and Var(x) denotes the mean and variance of the variable x. The derivation of the mean and variance of xs(n) is similar. While detecting symbol xk(n), k=1,2,…,M, forwarded by the kth relay Rk , (3) can be rewritten as rd ,2 (n + τ k ) = hkd xk (n) + ξ k (n)
(6)
where ξ k (n) is the interference to xk (n) , Due to interleaving, ξk (n) is uncorrelated with xk (n) and can be assumed Gaussian distributed for large M according to the central limit theorem. ξ k (n) can be written as
ξk (n) = rd ,2 (n + τ k ) − hkd xk (n) =
¦
hmd xm (n + τ k − τ m )
Rm ∈Ra , Rm ≠ Rk
(7)
+ hsd xs (n + τ k − τ s ) +ηd ,2 (n + τ k ). The phase offset due to hkd in (6) can be cancelled out by *
multiplying both sides of (6) with hkd , thus the detection of the real part and imaginary part of xk ( n) can be treated separately as [8] 2
i 2
Re k
L ( x (n)) =
2 hkd (Re[ yk ,d (n)]-E[Re[hkd* ξ k (n)]]) * Var[Re[hkd ξ k (n)]] 2
Li2 ( xkIm (n)) =
2 hkd (Im[ yk , d (n)]-E[Im[hkd* ξ k (n)]])
(8)
Var[Im[hkd* ξ k (n)]]
* where yk , d (n) = hkd rd,2 (n + IJ k ) .
After de-interleaving, the LLRs derived from the signal forwarded by all the active relays and by the source terminal S during phase two are combined with the LLR derived from the signal transmitted at the first phase as
Li ( xs (n)) =
¦
Rm ∈ Ra
∀n
L (xm (n)) = L (x s (π m (n))) − L (xm (n)) ∀m, n. i +1 a
Re m
Li2 ( xm (π m−1 (n))) + Li2 ( xs (n)) + L1 ( xs (n)) (9)
i
i 2
(10)
Then go back to equation (5) for next iteration. A hard decision is made based on L(xs(n)) in the last iteration. This symbol by symbol iterative detection shares the advantage of low complexity [8], the cost per information symbol per iteration involved in (5) ~ (10) is proportional to the total number of active terminals, Ma. IV. SIMULATION RESULTS During simulation, the channels are assumed to be Rayleigh flat fading and to maintain unchanged in the consecutive two slots. The bit SNR in the simulation results is defined as Eb EG = s sd N0 β Kc N0
(11)
where Kc, Es and ȕ are denoted as the number of information bits represented by each modulation symbol, the energy of each modulation symbol and transmission rate, respectively. Specifically, ȕ=1 for direct transmission and ȕ=0.5 for interleaver-based cooperative transmission due to the fact that one data frame occupies two consecutive slots. Furthermore, we assume that the maximum asynchronous delay is LTs, where Ts is symbol duration, and the asynchronous delay for each terminal is uniformly generated from [0, LTs]. A random interleaver is employed in the protocol, with each frame containing 2048 QPSK symbols. The relative channel gain is defined as Bsm=Gsm/Gsd ˈBmd=Gmd/Gsd, m=1,2,…,M. In this simulation, we assume that relays Rm, m=1,2,…,M, are close to terminal S, Bmd = 1, m=1,2,…,M, and that the channel gains between the relays and the terminal S are equivalent, Bsm=Bˈ m= 1,2,…,M. We first consider the synchronous case, i.e., L=0. Fig. 2 illustrates the frame error rate (FER) performance when different cooperative diversity protocols are employed with one relay in the system. In Fig.2, B=inf. indicates that the channels between source terminal S and relays are error-free; hence no errors occur during phase one transmission. For comparison, Fig. 2 also includes the performance of direct transmission (labeled as ‘Direct Trans.’ in the figure) and that of the OSTBC based cooperative transmission[3] employing the Alamouti space time code[9] under B=inf. The iteration number is 2 for the proposed cooperative diversity scheme. It is shown in the figure that interleaver-based cooperative diversity protocols provide significant performance improvement to the direct transmission. Specifically, the transmission scheme employing SDIF protocol achieves the same diversity order as that using Alamouti space time code, while the performance of FDIF protocol is worse than that of SDIF. This is due to the fact that the relay will always forward
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.
the signals even if it fails to decode the received frame correctly in FDIF. It can be seen from Fig.2 that the diversity order of the fixed relaying protocol FDIF is 1 as the direct transmission scheme. The FER performance under the different number of relay terminals with synchronous receiving is shown in Fig. 3. The proposed Selection Decode-Interleave-and-Forward protocol is employed and the iteration number is six for M=3 and 8. Obviously, the achievable diversity order increments with the number of relays. Fig.4 demonstrates a comparison of the performances related to synchronous receiving and asynchronous receiving, both employing SDIF protocol and the relative channel gain is set to be B=10. It is shown that the FER performance of the asynchronous case is the same as that of synchronous receiving, indicating the effectiveness of the proposed interleaver-based cooperative diversity protocol. V.
Figure 2. Comparison among the systems employing various protocols with 1 relay and synchronous receiving.
CONCLUSION
A novel interleaver-based cooperative diversity protocol is introduced in this literature. Furthermore, a low complexity iterative symbol-by-symbol detection algorithm is proposed to combine signals from all active relays. In contrast to conventional space-time coded cooperative diversity protocol, the proposed scheme is more attractive for distributed implementation since the cooperating relays do not have to know which other relays are active, and full cooperative diversity is achievable in both synchronous and asynchronous networks. REFERENCES [1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
A. Nosratinia, T. E. Hunter, and A. Hedayat, "Cooperative Communication in Wireless Networks", IEEE Commun. Mag., vol.42, no.10, pp.74-80, Oct. 2004. J. N. Laneman, D. N. C. Tse, and G. W. Wornell, " Cooperative diversity in wireless networks : Efficient protocols and outage behavior," IEEE Trans. Inf. Theory, vol.50, no.12, pp.3062-3080, Dec. 2004. J. N. Laneman, and G. W. Wornell, " Distributed Space-Time-Coded Protocols for Exploiting Cooerative Diversiy in Wireless Networks," IEEE Trans. Inf. Theory, vo.49, no.10, pp.2415-2425, Oct 2004. G. Scutari, S. Barbarossa, " Distributed space-time coding for regenerative relay networks," IEEE Trans. Wireless Commun., vol.4, no.5, pp.2387-2399, Sept. 2005. V. Tarokh, H. Jafarkhani, and A. R. Calderbank, "Space-time block codes from orthogonal designs," IEEE Trans. Inform. Theory, vol.45, pp. 1456-1467, July 1999. S. Wei, D. Goeckel, and M.Valenti, “Asynchronous cooperative diversity,” in Proc. Conf. Inform. Sci. and Sys, Princeton, NJ, Mar. 1719, 2004. Y. Shang, X.-G. Xia, "Shift-Full-Rank Matrices and Applications in Space-Time Trellis Codes for Relay Networks With Asynchronous Cooperative Diversity," IEEE Trans. Inform. Theory, vol.52, no.7, pp.3153-3168, July 2006. L. Ping, L. Liu, K. Y. Wu, and W. K. Leung, "Interleave-Division Multiple-Access," IEEE Trans. Wireless Commun., vol.5, no.4, pp.938947, April 2006. S. M. Alamouti, “A Simple Transmitter Diversity Scheme for Wireless Communications,” IEEE J. Select. Areas Commun.,vol.16, pp.14511458, October 1998.
Figure 3. FER performance under different number of relays with synchronous receiving. SDIF protocol is employed.
Figure 4. Comparison with synchronous and asynchronous receiving with multiple relays. SDIF protocol is employed.
