An Opportunistic Network-Coded Cooperative Uplink Transmission Scheme For Wireless MultiRelay Networks Jian Wang, Kui Xu, Lianguo Wu, Youyun Xu College of Communications Engineering, PLA University of Science and Technology Nanjing 210007, China Email:
[email protected],
[email protected],
[email protected],
[email protected] Abstract—In this paper, a feedback-based opportunistic network-coded cooperative scheme is proposed to be combined with cooperative communication in wireless uplink multi-relay networks. Different from previous network-coded schemes that conduct network coding all the time, we propose a scheme that conducts network coding and direct transmission alternately according to the quality of the channels. The outage probability is analyzed theoretically and the approximate expression of outage probability is derived. Compared with the previous schemes, the proposed scheme achieves a performance gain in terms of outage probability. The validity of the proposed scheme is verified by theoretical analysis and simulation results. Keywords-Cooperative Communication; Multi-relay; Opportunistic Network Coding; Feedback-based; Outage Probability
I.
INTRODUCTION
The cooperative communication has emerged as a promising approach to provide diversity in combating multipath fading and is widely used in many communication scenarios, such as wireless sensor networks and cellular system [1]. Tremendous research interest have been inspired by the benefits of cooperative communication that could achieve diversity without facing the restriction in MIMO [2]. One of the shortage of cooperative communication, however, lies in its unquenchable needs for extra resources, which reduce spectral efficiency. One way to deal with this problem is to apply network coding. Network coding has emerged as a promising technique that is well known for its excellent performance in enhancing throughput [3,14-16]. It was first introduced by R. Ahlswede et al in [3], to be applied in computer networks. Soon it was introduced to wireless ad hoc networks in [4], called physical-layer network coding (PNC). It has been shown that PNC could theoretically achieve 100% improvement in physical-layer throughput over the traditional multi-hop transmission scheduling scheme. Another way to leverage network coding in wireless networks is to encourage a terminal to forward a mixture of different messages, and the destination tries to decode the superposed message with network-level
information, and extracts the message it needs, which is called analog network coding (ANC) [5]. Applying network coding in wireless networks with cooperative communication could achieve diversity gain [6]. [7] proposes a novel network coding approach to cooperative diversity that makes efficient use of available resources. However, network coding may not always be helpful [8]. Actually, there is situation that network coding does harm to the performance of cooperative communication. As a result, it is of great importance to use opportunistic network coding [9]. When no opportunity for network coding exists at an intermediate node, it is beneficial to send an uncoded packet [10]. But when there is a future chance for network coding, whether to wait for the chance is a question. To answer this question，a stochastic dynamic program with the objective of minimizing the long-run average cost per unit time is formulated in [11]. Recently, a network-coded scheme combined with cooperative diversity is proposed in [12], achieving better performance in terms of outage probability as well as ergodic capacity. This work is soon extended to an opportunistic network-coded cooperative scheme in [13] achieving better performance in outage behavior as well as throughput. However, [13] only considers the moderate-tohigh signal-to-noise ratio (SNR) regime and it assumes that relays could always decode superposed packets from users, which is impossible for low SNR. Motivated by the above observation, a feedback-based opportunistic network-coded cooperative scheme is proposed in this paper, and we study the outage behavior of the proposed scheme. Compared with direct transmission and the scheme proposed in [12], the proposed scheme achieves a performance gain in terms of outage probability. The rest of this paper is organized as follows: Section II describes a uplink multi-relay system with two users. The proposed feedback-based opportunistic network-coded cooperative scheme is given in section III. Section IV analyzes the outage performance of the proposed scheme. Numerical simulation comparison is given in Section V. Finally, conclusions are provided in Section VI.
978-1-4799-0308-5/13/$31.00 © 2013 IEEE
Fig 1.
System model where two users communicate with a base station with the help from L relays.
II.
DESCRIPTION OF SYSTEM MODEL
Consider a uplink transmission scenario where two users, i.e., U i (1 ≤ i ≤ 2) , are communicating with a base station D with the help form L relays, i.e., Ri (1 ≤ i ≤ L) , as shown in Fig.1. When users transmit packets, denoted as s1 (by U1 ) and s2 ( by U 2 ) to the base station, according to the nature of wireless transmission, all relays can overheard the packets, and are willing to help transmit packets to the base station to enhance redundancy on the purpose of gaining better performance. The half-duplex model is expected for relays in this paper, that means all relays couldn’t transmit and receive at the same time. It is assumed that all channels here undergo identically independent quasi-static frequency-flat Rayleigh fading and remain unchanged during a system period, with variance denoted as λ . Time is divided into time slots, and during one time slot, only one packet could be sent by a user or a relay. A system period is no more than two time slots, i.e., the first time slot and a may be unnecessary second time slot.
III.
Feedback-based Opportunistic Network Coding Protocol
In this section, we discuss feedback-based opportunistic network coding, which means that whether we decide to adopt network coding is based on the quality of the channels. Feedback message sent out by the base station at the end of each time slot is vital in the proposed protocol, for it tells users and relays whether to send a new packet or repeat a certain packet for decoding. By using feedback message, it just looks like that the base station is selecting packets from users and relays. To be specific, we divide the protocol into two stages, i.e., initialization stage and feedback-based cooperative stage as shown in Fig.2. A. Initialization During the initialization stage, each terminal has access to its local channel state information(CSI) by using training sequence. Actually, the time needed in the initialization stage is quite short compared with the duration of packets transmission, so it can be ignored. In this paper, we assume
Fig 2.
Diagram for the description of the proposed beedback-based opportunistic network coding protocol with two users
that the base station knows the exact CSI of all user–station, relay–station links, and to fit the needs of the strategy, all user–relay links are also assumed known at the base station. B. Feedback-based Cooperative During this stage, the base station decides whether the two users transmit simultaneously or transmit by turns according to the quality of links that are assumed known. And the base station also decides whether relays would do help to enhance the performance. With the already known CSI, the base station knows exactly whether it could decode a packet successfully. For the base station, to decode superposed packet from the two users is to save time resources. Accordingly, it broadcasts the first feedback message, which we call the start message, to tell the two users whether to transmit packets or not in the first time slot of a period according to the capacity of the channels between users and the base station. The uplink broadcast process is actually a two-user multiple-access model. And its channel capacity region can be given as follows
( ) = log (1 + ρ h ) = log (1 + ρ ( h + h ))
C1D = log 2 1 + ρ h1 D
2
(1a)
C2 D
2
(1b)
CtotD
2
2D
2
2
1D
2
2D
(1c)
where CiD ( i ∈ {1, 2} ) denotes the single-user capacity of U i , CtotD denotes the multi-access capacity of U 1 and U 2 . hiD ( i ∈ {1, 2} ) denotes the channel between Ui and D, and ρ denotes the transmit SNR. In this paper, we assume all users and relays’ transmission power are the same, and noise is treated as AWGN with same variance, thus the transmit SNR are all the same for users and relays. For simplicity, a symmetric system is considered here, both users as well as relays share the same target rate, denoted as r. According to the relationship between C iD ( i ∈ {1, 2} ) and r. We divide the scheme into five cases for better discussion.
Case 1: Here, C1D ≥ r , C2 D ≥ r and CtotD ≥ 2r , that means the mixture of packets from the two users could be decoded successfully simultaneously. To make full use of the channels, the base station sent the start message to inform the two users to transmit packets in the first time slot. Then two packets would be successfully decoded, a system period is over. Case 2: Here, C1D ≥ r , C2 D ≥ r but CtotD < 2r , that means each packet could be decoded successfully if transmitted separately but couldn’t when transmitted simultaneously. In this case, direct transmission scheme is conducted that the two users take turns to transmit their packets, to make sure that packets from the two users are decoded successfully. Case 3: In this case, we have C1D < r and C2 D ≥ r. That means only s2 could be decoded when transmitted separately. Here the base station makes two users send their packets simultaneously. According to the nature of wireless transmission, all of the relays overheard the superposed packet. As long as there is one relay that could decode s1 successfully, it could offer help in the second time slot. To be specific, the base station knows whether a relay could decode s1 , since the CSI is assumed known at the base station. Then, it selects a relay with the best relay–station link, and compares the link with U1 ' s user–station link, picks up the one with better link quality, denotes it as RC 3 . RC 3 transmits s1 in the second time slot, and the system period is over after that. Here we briefly analysis the outage behavior under the condition of case 3. There are three situations that both s1 and s2 could be decoded successfully. First, s2 is decoded in the first time slot and extracted from the superposed packet, then maximum ratio combination (MRC) could be applied for the two time slots’ observation to decode s1 ; second, s2 couldn’t be decoded in the first time slot, thus MRC is directly applied on s1 , after decoding s1 successfully, s2 is then decoded since C2 D ≥ r ; third, the average rates satisfy channel capacity region. We will give the expression in Section IV. Case 4: Here, we have C1D ≥ r , C2 D < r. And it’s just the reverse of case 3. Similarly, the base station selects a RC 4 that could decode s2 with best link quality to the base station, and makes RC 4 transmits s2 in the second time slot. Case 5: We have C1D < r and C2 D < r . The base station makes two users transmit their packets simultaneously, and selects a relay with best link quality to the base station that could decode both s1 and s2 , denoted as RC 5 . In the second time slot, RC 5 transmits a perturbed mixture of the two users’ messages 2
sRC 5 = ∑ γ RC 5 ,i si k =1
(2)
where γ RC 5 ,i is the weighting factor. The choice of the weighting factor γ RC 5 ,i is devised to satisfy (3) ΓH Γ = 1 T where Γ = [γ RC 5 ,1 , γ RC 5 ,2 ] , which ensures that the signal combination strategy proposed in (2) will be constrained.
When the base station receives the superposed packet, it checks whether it could decode both s1 and s2 by applying successive decoding and interference cancellation, if not, just treats the two observations acquired in the two time slots as two linear equations, where the two packets are treated as unknown variables, and such linear equations are solvable.
IV.
PERFORMANCE ANALYSIS
In this section, the system outage probability will be studied. The outage probability measures the robustness performance a system can achieve, and provides a performance evaluation for the proposed feedback-based opportunistic network coding protocol. A. Preliminary Analysis In order to analyze the outage performance of the proposed protocol, we first analyze some probability of different events. a) The probability for a certain relay，such as R1 , to successfully decode a certain packet , such as s1 sent by U1 , and both of the packets from the two uses respectively, denoted as Pdecode1 and Pdecode respectively. They are given by (4) and (5). Pdecode1 = Pr ⎡⎣ C1R1 ≥ r ∩ C2 R1 ≥ r ∩ CtotR1 ≥ 2r
(
)
(
)
∪ C3 R1 ≥ r ∩ C2 R1 < r ⎤⎦
(
= ( 2r − 1)
2
(4)
)
ρλ + 1 − 2- r e
(
−
2
2r
−1
ρλ
+ 2- r e
Pdecode = Pr C1R1 ≥ r ∩ C2 R1 ≥ r ∩ CtotR1 ≥ 2r =
(( 2
r
− 1)
2
)
ρλ + 1 − 2− r e
−
2
2r
−
r
2 −1
)
−1
ρλ
ρλ
(5)
where Pr ( ⋅) denotes the probability of an event, and C1R1 C2 R1
) ( log (1 + ρ h )
log 2 1 + ρ h1R1
2
(6a)
2
(6b)
2 R1
2
(
2
C3 R1
log 2 1 + ρ h1R1
CtotR1
log 2 1 + ρ h1R1
( (
(ρ h
2
2 R1
2
+ h2 R1
2
))
+1
))
(6c) (6d)
where hkR1 ( k ∈ {0,1} ) denotes the channel between U k and R1 . b) The probability of exsiting K relays that could successfully decodes one certain packet, such as, s1 from U1 , and both packets from the two uses respectively, denoted as Pr ( N1 = K ) and Pr ( N = K ) , where N1 denotes the number of relays that could decode s1 and N denotes the number of relays that could decode both s1 and s2 . They are given by (7) and (8). ⎛L⎞ L−K Pr ( N 1 = K ) = ⎜ ⎟ Pdecode1 K (1 − Pdecode1 ) ⎝K ⎠
(7)
{ ( (
3 = 1 − Pr ⎡ log 2 1 + ρ h2 D Pout ⎢⎣
( ( { (
⎡ ∪ ⎢ log 2 1 + ρ h1D ⎢⎣
2
(
= 1 − Pr log 2 1 + ρ hRC 3 D
{ ( (
2
2
2
))
2
RC 3 D
2
(
1 + ρ h1 D
)≥ r )
1 + ρ h1 D
2
2
) ) ≥ r ∩ log (1 + ρ h 2
) ) ≥ r ∩ log (1 + ρ h 2
2 RC 3 D
2 RC 3 D
2
+ ρ h1D
⎛⎛ 2 ⎞ ≥ r ∩ log 2 ⎜ ⎜ 1 + ρ ∑ hmD ⎟ 1 + ρ hRC 3 D ⎜ m ={1,2} ⎠ ⎝⎝
PΔ 1
− Pr log 2 1 + ρ h2 D
2
2
1D
+ hRC 3 D
3 Pout ≈ 1 − Pr ⎡ log 2 1 + ρ h2 D ⎢⎣
( (
(1 + ρ h ) ) ) ≥ r ∩ log (1 + ρ h
2
+ ρ h1 D
+ ρ h1 D
2
2
) ≥ r ⎤⎥⎦ ∪ ⎡⎢⎣log (1 + ρ h ⎤⎫ ) ⎟⎟⎠⎞ ≥ r ⎥⎥⎦ ⎪⎭⎪⎬
2
) ≥ r ⎤⎥⎦ ∪ ⎡⎢⎣ log (1 + ρ h 2
) ≥ r ∩ log (1 + ρ h 2
2
RC 3 D
2
2 RC 3 D
2 RC 3 D
) ≥ r ⎤⎥⎦
) ≥ r ⎤⎥⎦}
(14)
(15)
) < r}
PΔ 2
⎡ ⎛⎛ ⎞ ⎞ 5 = 1 − Pr ⎣⎡ log 2 (1 + 0.5 ρ | hRD |2 ) ≥ r ∩ log 2 (1 + ρ | hRD |2 ) ≥ 2r ⎦⎤ ∪ ⎢ log 2 ⎜ ⎜ 1 + ρ ∑ | hmD |2 ⎟ (1 + ρ | hRD |2 ) ⎟ ≥ 4 r Pout ⎜ ⎟ m ={1,2} ⎢⎣ ⎠ ⎝⎝ ⎠
{
(
)
(
)
}
PΔ 2 =
∑P
(22)
∩ log 2 1 + ρ (| h1D |2 +0.5 | hRD |2 ) ≥ r ∩ log 2 1 + ρ (| h2 D |2 +0.5 | hRD |2 ) ≥ r ⎤ ⎦ ⎛L⎞ L−K Pr ( N = K ) = ⎜ ⎟ Pdecode K (1 − Pdecode ) ⎝K ⎠
(8)
c) The probability for the base station to successfully decode a certain packet, such as, s1 from U 1 or a relay, denoted as Psuc . It is given by (9).
(
)
Psuc = Pr r ≤ log 2 (1 + ρ | hD |2 ) = e
2r −1 − ρλ
(9)
where hD denotes the channel between the base station and the certain user or relay. B. Outage Probability First, the definition of the system outage is given here. Definition 1: During a transmission period , outage occurs when the base station does not successfully decode the packets from the two users. On the basic of the discussion in the former section, we can denote the system outage probability applying complete probability formula, i.e., 1 2 3 4 5 (10) Pout = Pout P1 + Pout P2 + Pout P3 + Pout P4 + Pout P5 where Pi (1 ≤ i ≤ 5 ) denotes the probability of case i , and i denotes the outage probability under the condition of Pout case i . For case 1 and case 2, it’s easy to find 1 (11) Pout =0 (12)
2 Pout =0 For case 3,
P3 = Pr ( C1D ≤ r ≤ C2 D ) = Psuc (1 − Psuc )
(13)
The outage probability in case 3 is given by (14). The exact 3 solution of the Pout can be difficult to find, and we note that its approximation is given by (15). The components PΔ1 and PΔ 2 in (15) can be given by (16) and (17). L
PΔ1 = 1 − ∑ (1 − Psuc ) P ( N1 = k ) k =0
k
(16)
L
k =0
Δ3
P ( N1 = k )
(17)
where PΔ 3 is given by (18). PΔ 3 =
(1 − Psuc )
k −1
2r
2 r ( 2 r −1) ⎞ ⎛ − ⎜ 1 − e λρ ⎟ ⎜ ⎟ ⎝ ⎠
( 2r − i )( 2r −1) ⎞ ⎛ − ( −1) ⎛ k ⎞ 1 i ⎜ 2 λρ ⎟ − ⎜ ⎟ ( Psuc ) ⎜ 1 − e r ⎟ (1 − Psuc ) ∑ i=0 2 − i ⎝ i ⎠ ⎝ ⎠
(18)
i
k
For case 4, due to the symmetry, we have P4 = P3 as well as 4 3 Pout = Pout For case 5,
P5 = Pr ( C1D ≤ r ∩ C2D ≤ r ) = (1 − Psuc )
(19) (20) 2
(21)
Under the condition of case 5, we find that it is optimal to ensure γ RC 5 ,1 = γ RC 5 ,2 = 1 2 , then the outage probability in 5 case 5 can be given by (22). The exact solution of the Pout can be difficult to find, and we note that its approximation is
{ (
5 Pout = 1 − Pr log 2 1 + 0.5 ρ hRD
(
2
∩ log 2 1 + ρ hRD
) ≥ 2 r}
2
)≥r
(23)
k
2 −1 ⎞ ⎛ − = ∑ ⎜ 1 − e ρλ ⎟ Pr ( N = k ) ⎟ k =0 ⎜ ⎝ ⎠ 2R
L
V.
SIMULATION RESULTS
In this section, we provide numerical simulations to verify the validity of the proposed feedback-based opportunistic network-coded cooperative scheme. The target data rate is set as r = 4 bits/Hz/s , and the variance of the channels is set as λ = 1. The performance of the proposed
Fig 3.
Comparison of outage probability versus ρ for different schemes with different numbers of L
scheme is to be compared with two existing transmission scheme, i.e., the direct transmission scheme, and the network-coded cooperative sheme, i.e., nc-co scheme, proposed in [12]. The outage probability versus ρ comparison of the three schemes is shown in Fig.3 with different numbers of relays, i.e., L=1 and L=2. From the Fig.3, we find that the proposed feedback-based opportunistic network-coded cooperative scheme achieves a significant performance gain with a fixed number of relays both for L=1 and L=2, compared with the direct transmission as well as nc-co scheme. The main reason for this lies in the way of decoding packets at the base station. In this paper, we comprehensive consider the chance for the base station to decode packets, for example, in case 3 and case 4, since only one packet is sent to the base station at the second time slot, maximum ratio combining could be conducted at the base station to decode the packet sent in the second time slot and also the successive decoding and interference cancellation based approachs is applied in the first time slot at the base station for all cases. In Fig.4, we compare the outage probability versus L of the three scheme with different ρ, i.e., ρ = 25 dB and ρ = 30 dB. For different ρ , the proposed feedback-based opportunistic network-coded cooperative scheme achieves a significant performance gain to co-nc scheme in [12] in terms of outage probability. We also find that the slope of the proposed scheme is larger than co-nc scheme for both ρ = 25 dB and ρ = 30 dB. That means with the increasing of L, the performance gain achieved by the proposed scheme becomes larger. VI.
CONCLUSION
In this paper, we propose a feedback-based opportunistic network coding scheme for a L-relay uplink transmission system with two users. Compared with direct transmission and previous network-coded cooperative scheme proposed in [12] in terms of outage probability, the proposed scheme
Fig 4.
Comparison of outage probability versus L for different schemes with different ρ
achieves better outage performance with the inceasing of the number of relays. Both theoretical analysis and simulations confirm the effectiveness of the proposed scheme. Due to space limitation, the study of a system with M users is left as a future direction. ACKNOWLEDGMENT This work was supported by the Jiangsu Province National Science Foundation under Grant (BK2011002), Jiangsu Province Natural Science Foundation for Young Scholar under Grant (BK2012055), National Natural Science Foundation of China (No. 61371123) and National Natural Science Foundation of China for Young Scholar (No. 61301165). REFERENCES [1] A. Sendonaris, E. Erkip, and B. Aazhang, "User cooperation diversity. Part I. System description," Communications, IEEE Transactions on, vol. 51, pp. 1927-1938, 2003. [2] A. Nosratinia, T. E. Hunter, and A. Hedayat, "Cooperative communication in wireless networks," Communications Magazine, IEEE, vol. 42, pp. 74-80, 2004. [3] R. Ahlswede, C. Ning, S. Y. R. Li, and R. W. Yeung, "Network information flow," Information Theory, IEEE Transactions on, vol. 46, pp. 1204-1216, 2000. [4] S. Zhang, S. C. Liew, and P. P. Lam, "Hot topic: physical-layer network coding," in Proceedings of the 12th annual international conference on Mobile computing and networking, 2006, pp. 358-365. [5] S. Katti, S. Gollakota, and D. Katabi, "Embracing wireless interference: analog network coding," in ACM SIGCOMM Computer Communication Review, 2007, pp. 397-408. [6] Y. Chen, S. Kishore, and J. Li, "Wireless diversity through network coding," in Wireless Communications and Networking Conference, 2006. WCNC 2006. IEEE, 2006, pp. 1681-1686. [7] L. Xiao, T. Fuja, J. Kliewer, and D. Costello, "A network coding approach to cooperative diversity," Information Theory, IEEE Transactions on, vol. 53, pp. 3714-3722, 2007. [8] S. Sharma, Y. Shi, J. Liu, Y. Hou, S. Kompella, and S. F. Midkiff, "Network coding in cooperative communications: friend or foe?," Mobile Computing, IEEE Transactions on, vol. 11, pp. 1073-1085, 2012. [9] W. Chen, K. B. Letaief, and Z. Cao, "Opportunistic network coding for wireless networks," in Communications, 2007. ICC'07. IEEE International Conference on, 2007, pp. 4634-4639.
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