Relay Assignment Schemes for Multiuser DF-AF Cooperative Wireless ...
Relay Assignment Schemes for Multiuser DF-AF Cooperative Wireless Networks Juhyun Lee and Jae Hong Lee Department of Electrical Engineering and INMC Seoul National University Seoul 151-744, Korea E-mail : {ljh1112, jhlee}@snu.ac.kr Abstract—In this paper, a multiuser DF-AF cooperative wireless network is considered. When a user is assigned to another user by a base station, the user relays the received signal from another user by using either the DF or the AF protocol. We consider two types of feedbacks: full feedback and limited feedback. For full feedback cases, three relay assignment schemes are considered. The relay assignment scheme with limited feedback is also considered to reduce the signaling overhead caused by full feedback. The simulation results show that in full feedback case, the worst user outage probability of the min-max assignment scheme is much lower than that of the greedy assignment scheme. It is also shown that the average outage probability of the optimal assignment scheme with three feedback bits is slightly lower than that of the greedy assignment scheme. Index terms — Relay assignment, multiuser, DF-AF protocol, outage probability.
I. I NTRODUCTION Cooperative communication has been studied to mitigate the performance degradation caused by multipath fading in wireless networks [1]-[4]. In cooperative communication, one or more users and relays share their resources to form a virtual multiple input multiple output (MIMO) antenna array without deploying multiple antennas at the each of users and relays [5]. Cooperative communication achieves spatial diversity, so that the spectral efficiency and reliability of the network is improved [6]. A decode-and-forward (DF) protocol and an amplify-and-forward (AF) protocol are well-known cooperative communication protocols [7]. In [8], the DF-AF protocol is investigated to provide better performance than DF and AF protocols. In a multiuser cooperative system, all users are not simultaneously involved in every cooperative communication, so that relay assignment schemes are needed [9], [10]. In [11], a relay assignment scheme based on a list of users is developed. In this scheme, each user makes a list of users with the average inter-user channel SNR higher than a given threshold and a base station assigns a user to another user by using this list. In [12], a distributed relay assignment scheme is considered to reduce feedback and overhead compared to other relay assignment scheme. Most of previous works consider a multiuser cooperative wireless network where the user and its own relay help each other for cooperative communication. However, this network does not gives the best performance
and it does not provide cooperative communication for an odd number of users. In [13], the relay assignment scheme is developed for multiuser cooperative wireless networks, where a user does not need to help its own relay for cooperative communication. However, the DF protocol is only investigated in this network and various relay assignment schemes are not considered. In this paper, we investigate a multiuser cooperative network, where a user does not need to help its own relay for cooperative communication. When a user is assigned to another user by a base station, the user relays the received signal from another user by using either the DF or the AF protocol. The outage probability is approximated for relay assignment schemes. We consider two types of feedbacks: full feedback and limited feedback. For full feedback case, three relay assignment schemes are considered. The limited feedback scheme is also considered to reduce the signaling overhead caused by full feedback. The rest of this paper is organized as follows. Section II provides a system model and the outage probability of the DF-AF protocol. In Section III, relay assignment schemes for cooperative communication are presented. Section IV presents simulation results of the relay assignment schemes. Section V concludes this paper. II. S YSTEM M ODEL AND THE O UTAGE P ROBABILITY A. System Model Consider a multiuser cooperative wireless network which consists of a base station and K users. Suppose that each user has a single antenna and transmits a signal through an orthogonal channel. Assume that the channel between any two nodes is a quasi-static flat fading channel. Also assume that all users transmit signals with equal power. In this network, the base station assigns users to other users for relaying. For simplicity, assume that each user is assigned to at most one user. For the relay assignment, each user sends inter-user average channel state information (CSI) to the base station. Since this average CSI is based on the geographical information, it changes slowly compared to instantaneous CSI so that the signaling overhead caused by feedback can be reduced. The signal transmission of the i-th user, Ui , is performed in two phases. In the first phase, Ui broadcasts its own signal
to the base station and other users. In the second phase, when Ui is assigned to the j-th user, Uj , Ui relays the signal of Uj to the base station. When Ui is not assigned to any other user, Ui retransmits its own signal transmitted in the first phase. After each user transmits a signal in the second phase, the base station combines the received signals using maximal ratio combining (MRC). The user relays the received signal to the base station with DF-AF protocol [8]. In the DF-AF protocol, the relay decodes and forwards the received signal to the base station if the instantaneous channel coefficient from the source to the relay is larger than a given threshold. If the channel coefficient is smaller than the threshold, the relay amplifies and forwards the signal to the base station. Let hi,j and hi,D denote the channel coefficients from Ui to Uj and from Ui to the base station, D, respectively. When Ui broadcasts its own signal, the received signals at Uj and D in the first phase are given by √ yi,j,1 = P hi,j xi + ni,j (1) √ (2) yi,D,1 = P hi,D xi + ni,D , respectively, where P is the transmit power of a user in each phase, xi is the transmitted signal from Ui , and ni,j and ni,D are zero-mean complex additive white Gaussian noises with variance N0 of channels from Ui to Uj and from Ui to D, respectively. In the second phase, Ui selects either noncooperative mode or cooperative mode according to the result of the assignment at the base station. In the non-cooperative mode, Ui retransmits its own signal. Then, the received signal at D is given by √ yi,D,2 = P hi,D xi + ni,D . (3) In the cooperative mode, a user relays the received signal with either the DF or AF protocol according to the inter-user channel coefficients. Suppose that Ui is assigned to Uk . When 2R |hk,i |2 ≥ ∆ = N0 (2P −1) , Ui relays the received signal with the DF protocol. Then, the received signal at D is given by √ yi,D,2 = P hi,D x ˆk + ni,D (4) where x ˆk is the decoded signal of xk . When |hk,i |2 < ∆, Ui relays the received signal with the AF protocol. Then the received signal at D is given by √ yi,D,2 = P hi,D βk,i yk,i,1 + ni,D (5) p where βk,i = 1/ P |hk,i |2 + N0 . B. Outage Probability for Multiuser DF-AF Cooperative Wireless Networks Assume that hi,j and hi,D are zero-mean complex Gaussian 2 2 random variables with variance σi,j and σi,D , respectively. When Ui retransmits its own signal, the outage probability for the i-th user is given by à ! ¸ · ∆ ∆ 2 out = 1 − exp − 2 Pi,i = Pr |hi,D | < . (6) 2 2σi,D
When Uj relays the received signal from Ui , the outage probability for the i-th user is given by [8] h i 2 out Pi,j = Pr |hi,j | < ∆ ¯ h i ¯ 2 2 × Pr |hi,D | + a < ∆ ¯ |hi,j | < ∆ h i h i 2 2 2 + Pr |hi,j | ≥ ∆ Pr |hi,D | + |hj,D | < ∆ (7) where a = |hi,j |2 |hj,D |2 /(|hi,j |2 + |hj,D |2 + N0 /P ). 2 In (7), Pr[ |hi,j |2 < ∆ ] = 1 − exp(− ¯∆/σi,j ). Assume 2 2 2 σi,D 6= σj,D then Pr[|hi,D | + a < ∆ ¯|hi,j |2 < ∆ ] and Pr[|hi,D |2 + |hj,D |2 < ∆] are given by (8) and (9), respectively, at the top of the next page. ¯ When 0 < x0 < 1, Pr[a < ∆ (1 − x0 ) ¯|hi,j |2 < ∆ ] ≈ 1 − x0 for high SNR [8]. Then, (8) becomes ¯ h i ¯ 2 2 Pr |hi,D | + a < ∆ ¯ |hi,j | < ∆ à ! Z 1 ∆ ∆ x0 0 ≈ (1 − x ) exp − 2 dx0 2 σ σ 0 i,D i,D à à !! 2 σi,D ∆ =1− 1 − exp − 2 . (10) ∆ σi,D Putting (9) and (10) into (7), we obtain à ! !! à à 2 2 σi,D σi,D ∆ ∆ out Pi,j ≈ 1 − + exp − 2 + exp − 2 ∆ ∆ σi,D σi,j à ! à ¡ ¢ ! 2 2 2 2 σi,D σi,j + σi,D ∆ σi,D − exp − + 2 − σ2 2 σ2 σi,D ∆ σi,j j,D i,D ! à ¡ ¢ 2 2 2 + σj,D ∆ σj,D σi,j + 2 exp − . 2 2 σ2 σi,D − σj,D σi,j j,D III. R ELAY A SSIGNMENT S CHEMES BASED ON THE O UTAGE P ROBABILITY In this section, relay assignment schemes based on the outage probability are considered for cooperative communication. Assume that each user knows exact inter-user average CSI for all users. For relay assignment, this CSI is fed back to the base station. There are two types of feedbacks for relay assignment: full feedback and limited feedback [14]. In the full feedback, each user sends a infinite number of feedback bits to the base station. In the limited feedback, each user sends only a few number of feedback bits to the base station. A. Full Feedback For full feedback case, we consider three relay assignment schemes: optimal assignment, greedy assignment, and minmax assignment. 1) Optimal Assignment Scheme In the optimal assignment scheme, the base station assigns a user to another user by exhaustive search to minimize the outage probability. We consider two minimization problems
à ! ¯ h i x ¯ 2 Pr a < ∆ − x ¯|hi,j | < ∆ exp − 2 dx 2 σi,D 0 σi,D à ! ¯ h i ∆ x0 ∆ 2 0 ¯ Pr a < ∆ (1 − x ) ¯|hi,j | < ∆ exp − 2 dx0 2 σi,D σi,D
¯ i Z ¯ 2 |hi,D | + a < ∆ ¯ |hi,j | < ∆ =
h
2
Pr Z
1
= 0
h i 2 2 Pr |hi,D | + |hj,D | < ∆ = 1 −
∆
1
1 2 2 σj,D − σi,D
for the outage probability: minimization problem for the average outage probability and that for the worst user outage probability. The minimization problem for the average outage probability is formulated as min
{ρi,j }
K X K X
out ρi,j Pi,j
(11)
i=1 j=1
subject to: ρi,j ∈ {0, 1} , ∀i, j K X
(12a)
ρi,j = 1, ∀i
(12b)
ρi,j = 1, ∀j
(12c)
j=1 K X i=1
where ρi,j is the relay assignment indicator variable. When ρi,j = 1, Uj is assigned to Ui . When ρi,j = 0, Uj is not assigned to Ui . By solving this minimization problem, the performance for total network is improved. However, the performance of each user cannot be guaranteed. The minimization problem for the worst user outage probability is formulated as min
K X
max
{ρi,j } i∈{1,2,··· ,K}
(
Ã
2 σj,D
∆ exp − 2 σj,D
!
Ã
−
2 σi,D
∆ exp − 2 σi,D
(8)
!) (9)
To minimize the average outage probability while reducing computational complexity, the greedy assignment scheme is considered. This scheme is based on the greedy matching in [9]. In greedy matching, the base station randomly selects a free user and then matches the free user with another user in order that the sum of the outage probability for two users is minimized. This process continues until all users are matched. In greedy assignment scheme, the base station randomly selects a free user and then assigns another user to the free user in order that the outage probability for the free user is minimized. This process continues until there are no free user. As the base station searches only possibilities of relay assignment corresponding to the randomly selected user, the computational complexity of the greedy assignment scheme is lower than that of the optimal assignment scheme. 3) Min-max Assignment Scheme We consider the min-max assignment scheme to minimize the worst user outage probability while reducing the computational complexity [13]. The algorithm of the min-max assignment scheme is as follows: out , ∀i, j. i) Initialize ρi,j = 0, Zi,j = Pi,j
ii) Find a user pair (i, j) such that out ρi,j Pi,j
(13) (i∗ , j ∗ ) = arg max Zi,j .
j=1
(15)
i,j
subject to: ρi,j ∈ {0, 1} , ∀i, j K X
(14a)
ρi,j = 1, ∀i
(14b)
ρi,j = 1, ∀j.
(14c)
j=1 K X i=1
The performance of the worst user is improved by solving this minimization problem. However, the total system performance cannot be guaranteed. (11) and (13) can be solved by exhaustive search for all possibilities of ρi,j . However, the complexity of exhaustive search becomes very high when the number of users is large. 2) Greedy Assignment Scheme
Set Zi∗ ,j ∗ = 0. iii) Check if there is the possibility of relay assignment when Uj ∗ is not assigned to Ui∗ . If no relay assignment exists, set ρi∗ ,j ∗ = 1, Zi,j ∗ = 0, ∀i, Zi∗ ,j = 0, ∀j. iv) Go to step ii) until Zi,j = 0, ∀i, j. As the maximum value of Zi,j is removed in step ii), the min-max assignment scheme provides the low outage probability for the worst user. The complexity of the minmax assignment scheme is lower than that of the optimal assignment scheme but higher than the complexity of the greedy assignment scheme. The reason is that the possibility of relay assignment is checked in step iii).
0 0
10
Outage probability
Outage probability
10
-1
10
-2
10
-1
10
-2
10
Min-max, full feedback
DF-AF, approximation
Greedy, full feedback
DF-AF, simulation
-3
10
Optimal, full feedback
No cooperation
Random
DF -3
10 0
5
10
15
20
25
30
35
40
45
0
5
10
15
SNR (dB)
20
25
30
35
40
45
SNR (dB)
Fig. 1. Average outage probability for the optimal assignment with full feedback.
Fig. 3. Worst user outage probability for various relay assignment schemes.
0
10 0
Outage probability
Outage probability
10
-1
10
-2
10
-1
10
-2
10
Optimal, limited feedback, Optimal, limited feedback,
Min-max, full feedback
10
Greedy, full feedback
-3
10
Optimal, limited feedback,
-3
N N N
=1 =2 =3
Optimal, full feedback
Optimal, full feedback
Greedy, full feedback
Random
0 0
5
10
15
20
25
30
35
40
45
5
10
15
20
25
30
35
40
45
SNR (dB)
SNR (dB)
Fig. 2.
Average outage probability for various relay assignment schemes.
B. Limited Feedback The relay assignment scheme with limited feedback is considered to reduce the overhead caused by full feedback. In this relay assignment scheme, each user sends only a few bits for the inter-user average CSI to the base station. The base station evaluates the outage probabilities for all users by using the feedback information and assigns relays to users. As this relay assignment is also based on the outage probability, all relay assignment schemes with full feedback can be used. IV. S IMULATION R ESULTS Consider the multiuser system for the number of users K = 16. Suppose that the users are distributed in the circle with a radius 200m centered at the base station. Suppose that the
Fig. 4. Average outage probability for the optimal assignment with various feedback.
transmit data rate, R, is 1bps/Hz and the path loss exponent is 3. For comparison, the random assignment scheme is considered. As users are randomly assigned to other users in the random assignment scheme, the complexity of this relay assignment scheme is significantly reduced compared to that of the optimal assignment scheme. However, we can expect that the random assignment scheme gives worse performance than any other relay assignment scheme with full feedback, since the feedback information is not used. Fig. 1 shows the average outage probability for optimal assignment with full feedback. The outage probability for a non-cooperative network and that for a DF cooperative network are plotted for comparison. It is shown that the DFAF protocol gives better performance than the DF protocol and
the no cooperation. It is also shown that the outage probability of the DF-AF protocol by approximation is similar to that by simulation. Thus, this outage probability can be used for relay assignment schemes. Fig. 2 shows the average outage probability for various relay assignment schemes. It is shown that the average outage probability of the greedy assignment scheme is slightly lower than that of the min-max assignment scheme. Although the performance gap between greedy assignment scheme and minmax assignment scheme is negligible, the complexity of the greedy assignment scheme is lower than that of the min-max assignment scheme. Fig. 3 shows the worst user outage probability for various relay assignment schemes. It is shown that the worst user outage probability of the min-max assignment scheme and that of the optimal assignment scheme are identical. Note that the computational complexity of the former is lower than that of the latter. It is also shown that the worst user outage probability of the greedy assignment scheme is slightly lower than that of the random assignment scheme. Fig. 4 shows the average outage probability for the optimal assignment for the number of feedback bits N = 1, 2, 3. Also, the outage probabilities of the greedy assignment scheme and optimal assignment scheme with full feedback are plotted for comparison. It is shown that the average outage probability of the optimal assignment scheme with N = 3 is slightly lower than that of the greedy assignment scheme with full feedback. It means that when the optimal assignment scheme is used, only three feedback bits are needed to achieve better performance than the greedy assignment scheme. V. C ONCLUSIONS In this paper, we consider the multiuser DF-AF cooperative network. The outage probability of the DF-AF protocol is approximated for relay assignment schemes based on the outage probability. We consider two types of feedbacks: full feedback and limited feedback. To minimize either the average outage probability or the worst user outage probability, we examine relay assignment schemes with full feedback. The relay assignment scheme with limited feedback is also considered to reduce the overhead caused by full feedback. Simulation results show that in full feedback case, the worst user outage probability of the min-max assignment scheme is much lower than that of the greedy assignment scheme. It is also shown that the average outage probability of the optimal assignment scheme with three feedback bits is is slightly lower than that of the greedy assignment scheme with full feedback. ACKNOWLEDGMENT This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MEST) (No. 2011-0017437). R EFERENCES [1] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversityPart I: System description,” IEEE Trans. Commun., vol. 51, no. 11, pp. 1927-1938, Nov. 2003.
[2] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversityPart II: Implementation aspects and performance analysis,” IEEE Trans. Commun., vol. 51, no. 11, pp. 1939-1948, Nov. 2003. [3] A. Stefanov and E. Erkip, “Cooperative coding for wireless networks,” IEEE Trans. Commun., vol. 52, no. 9, pp. 1470-1476, Sept. 2004. [4] T.E. Hunter, S. Sanayei, and Aria Nosratinia, “Outage analysis of coded cooperation,” IEEE Trans. Inform. Theory, vol. 52, no. 2, pp. 375-391, Feb. 2006. [5] J. N. Laneman and G. W. Wornell, “Distributed space-time-coded protocols for exploiting cooperative diversity in wireless networks,” IEEE Trans. Inform. Theory, vol. 49, no. 19, pp. 2415-2425, Oct. 2003. [6] 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. [7] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Trans. Inform. Theory, vol. 50, no. 12, pp. 3062-3080, Dec. 2004. [8] W. Su and X. Liu, “On optimum selection relaying protocols in cooperative wireless networks,” IEEE Trans. Commun., vol. 58, no. 1, pp. 52-57, Jan. 2010. [9] J. N. Laneman, “Cooperative diversity in wireless networks: Algorithms and architectures,” Ph.D. dissertation, MIT, Cambridge, MA, 2002. [10] A. Nosratinia and T. E. Hunter, “Grouping and partner selection in cooperative wireless networks,” J. Sel. Areas Commun., vol. 25, no. 2, pp. 369-378, Feb. 2007. [11] Y. S. Jung and J. H. Lee, “Partner assignment algorithm for cooperative diversity in mobile communication systems,” in Proc. IEEE VTC 2006Spring, Melbourne, Australia, May 2006. [12] Y. Yang, H. Hu, J. Xu, and G. Mao, “Relay technologies for WiMAX and LTE-advanced mobile systems,” IEEE Commun. Mag., vol. 47, no. 10, pp. 100-105, Oct. 2009. [13] J. Shi, G. Yu, Z. Zhang, Y. Chen, and P. Qiu, “Partial channel state information based cooperative relaying and partner selection,” in Proc. IEEE WCNC 2007, Kowloon, Hong Kong, Mar. 2007. [14] S. Ren and K. B. Letaief, “Cooperative networks with limited feedback,” in Proc. IEEE GLOBECOM 2008, New Orleans, LA, Nov. 2008.
I. I NTRODUCTION Cooperative communication has been studied to mitigate the performance degradation caused by multipath fading in wireless networks [1]-[4]. In cooperative communication, one or more users and relays share their resources to form a virtual multiple input multiple output (MIMO) antenna array without deploying multiple antennas at the each of users and relays [5]. Cooperative communication achieves spatial diversity, so that the spectral efficiency and reliability of the network is improved [6]. A decode-and-forward (DF) protocol and an amplify-and-forward (AF) protocol are well-known cooperative communication protocols [7]. In [8], the DF-AF protocol is investigated to provide better performance than DF and AF protocols. In a multiuser cooperative system, all users are not simultaneously involved in every cooperative communication, so that relay assignment schemes are needed [9], [10]. In [11], a relay assignment scheme based on a list of users is developed. In this scheme, each user makes a list of users with the average inter-user channel SNR higher than a given threshold and a base station assigns a user to another user by using this list. In [12], a distributed relay assignment scheme is considered to reduce feedback and overhead compared to other relay assignment scheme. Most of previous works consider a multiuser cooperative wireless network where the user and its own relay help each other for cooperative communication. However, this network does not gives the best performance
and it does not provide cooperative communication for an odd number of users. In [13], the relay assignment scheme is developed for multiuser cooperative wireless networks, where a user does not need to help its own relay for cooperative communication. However, the DF protocol is only investigated in this network and various relay assignment schemes are not considered. In this paper, we investigate a multiuser cooperative network, where a user does not need to help its own relay for cooperative communication. When a user is assigned to another user by a base station, the user relays the received signal from another user by using either the DF or the AF protocol. The outage probability is approximated for relay assignment schemes. We consider two types of feedbacks: full feedback and limited feedback. For full feedback case, three relay assignment schemes are considered. The limited feedback scheme is also considered to reduce the signaling overhead caused by full feedback. The rest of this paper is organized as follows. Section II provides a system model and the outage probability of the DF-AF protocol. In Section III, relay assignment schemes for cooperative communication are presented. Section IV presents simulation results of the relay assignment schemes. Section V concludes this paper. II. S YSTEM M ODEL AND THE O UTAGE P ROBABILITY A. System Model Consider a multiuser cooperative wireless network which consists of a base station and K users. Suppose that each user has a single antenna and transmits a signal through an orthogonal channel. Assume that the channel between any two nodes is a quasi-static flat fading channel. Also assume that all users transmit signals with equal power. In this network, the base station assigns users to other users for relaying. For simplicity, assume that each user is assigned to at most one user. For the relay assignment, each user sends inter-user average channel state information (CSI) to the base station. Since this average CSI is based on the geographical information, it changes slowly compared to instantaneous CSI so that the signaling overhead caused by feedback can be reduced. The signal transmission of the i-th user, Ui , is performed in two phases. In the first phase, Ui broadcasts its own signal
to the base station and other users. In the second phase, when Ui is assigned to the j-th user, Uj , Ui relays the signal of Uj to the base station. When Ui is not assigned to any other user, Ui retransmits its own signal transmitted in the first phase. After each user transmits a signal in the second phase, the base station combines the received signals using maximal ratio combining (MRC). The user relays the received signal to the base station with DF-AF protocol [8]. In the DF-AF protocol, the relay decodes and forwards the received signal to the base station if the instantaneous channel coefficient from the source to the relay is larger than a given threshold. If the channel coefficient is smaller than the threshold, the relay amplifies and forwards the signal to the base station. Let hi,j and hi,D denote the channel coefficients from Ui to Uj and from Ui to the base station, D, respectively. When Ui broadcasts its own signal, the received signals at Uj and D in the first phase are given by √ yi,j,1 = P hi,j xi + ni,j (1) √ (2) yi,D,1 = P hi,D xi + ni,D , respectively, where P is the transmit power of a user in each phase, xi is the transmitted signal from Ui , and ni,j and ni,D are zero-mean complex additive white Gaussian noises with variance N0 of channels from Ui to Uj and from Ui to D, respectively. In the second phase, Ui selects either noncooperative mode or cooperative mode according to the result of the assignment at the base station. In the non-cooperative mode, Ui retransmits its own signal. Then, the received signal at D is given by √ yi,D,2 = P hi,D xi + ni,D . (3) In the cooperative mode, a user relays the received signal with either the DF or AF protocol according to the inter-user channel coefficients. Suppose that Ui is assigned to Uk . When 2R |hk,i |2 ≥ ∆ = N0 (2P −1) , Ui relays the received signal with the DF protocol. Then, the received signal at D is given by √ yi,D,2 = P hi,D x ˆk + ni,D (4) where x ˆk is the decoded signal of xk . When |hk,i |2 < ∆, Ui relays the received signal with the AF protocol. Then the received signal at D is given by √ yi,D,2 = P hi,D βk,i yk,i,1 + ni,D (5) p where βk,i = 1/ P |hk,i |2 + N0 . B. Outage Probability for Multiuser DF-AF Cooperative Wireless Networks Assume that hi,j and hi,D are zero-mean complex Gaussian 2 2 random variables with variance σi,j and σi,D , respectively. When Ui retransmits its own signal, the outage probability for the i-th user is given by à ! ¸ · ∆ ∆ 2 out = 1 − exp − 2 Pi,i = Pr |hi,D | < . (6) 2 2σi,D
When Uj relays the received signal from Ui , the outage probability for the i-th user is given by [8] h i 2 out Pi,j = Pr |hi,j | < ∆ ¯ h i ¯ 2 2 × Pr |hi,D | + a < ∆ ¯ |hi,j | < ∆ h i h i 2 2 2 + Pr |hi,j | ≥ ∆ Pr |hi,D | + |hj,D | < ∆ (7) where a = |hi,j |2 |hj,D |2 /(|hi,j |2 + |hj,D |2 + N0 /P ). 2 In (7), Pr[ |hi,j |2 < ∆ ] = 1 − exp(− ¯∆/σi,j ). Assume 2 2 2 σi,D 6= σj,D then Pr[|hi,D | + a < ∆ ¯|hi,j |2 < ∆ ] and Pr[|hi,D |2 + |hj,D |2 < ∆] are given by (8) and (9), respectively, at the top of the next page. ¯ When 0 < x0 < 1, Pr[a < ∆ (1 − x0 ) ¯|hi,j |2 < ∆ ] ≈ 1 − x0 for high SNR [8]. Then, (8) becomes ¯ h i ¯ 2 2 Pr |hi,D | + a < ∆ ¯ |hi,j | < ∆ à ! Z 1 ∆ ∆ x0 0 ≈ (1 − x ) exp − 2 dx0 2 σ σ 0 i,D i,D à à !! 2 σi,D ∆ =1− 1 − exp − 2 . (10) ∆ σi,D Putting (9) and (10) into (7), we obtain à ! !! à à 2 2 σi,D σi,D ∆ ∆ out Pi,j ≈ 1 − + exp − 2 + exp − 2 ∆ ∆ σi,D σi,j à ! à ¡ ¢ ! 2 2 2 2 σi,D σi,j + σi,D ∆ σi,D − exp − + 2 − σ2 2 σ2 σi,D ∆ σi,j j,D i,D ! à ¡ ¢ 2 2 2 + σj,D ∆ σj,D σi,j + 2 exp − . 2 2 σ2 σi,D − σj,D σi,j j,D III. R ELAY A SSIGNMENT S CHEMES BASED ON THE O UTAGE P ROBABILITY In this section, relay assignment schemes based on the outage probability are considered for cooperative communication. Assume that each user knows exact inter-user average CSI for all users. For relay assignment, this CSI is fed back to the base station. There are two types of feedbacks for relay assignment: full feedback and limited feedback [14]. In the full feedback, each user sends a infinite number of feedback bits to the base station. In the limited feedback, each user sends only a few number of feedback bits to the base station. A. Full Feedback For full feedback case, we consider three relay assignment schemes: optimal assignment, greedy assignment, and minmax assignment. 1) Optimal Assignment Scheme In the optimal assignment scheme, the base station assigns a user to another user by exhaustive search to minimize the outage probability. We consider two minimization problems
à ! ¯ h i x ¯ 2 Pr a < ∆ − x ¯|hi,j | < ∆ exp − 2 dx 2 σi,D 0 σi,D à ! ¯ h i ∆ x0 ∆ 2 0 ¯ Pr a < ∆ (1 − x ) ¯|hi,j | < ∆ exp − 2 dx0 2 σi,D σi,D
¯ i Z ¯ 2 |hi,D | + a < ∆ ¯ |hi,j | < ∆ =
h
2
Pr Z
1
= 0
h i 2 2 Pr |hi,D | + |hj,D | < ∆ = 1 −
∆
1
1 2 2 σj,D − σi,D
for the outage probability: minimization problem for the average outage probability and that for the worst user outage probability. The minimization problem for the average outage probability is formulated as min
{ρi,j }
K X K X
out ρi,j Pi,j
(11)
i=1 j=1
subject to: ρi,j ∈ {0, 1} , ∀i, j K X
(12a)
ρi,j = 1, ∀i
(12b)
ρi,j = 1, ∀j
(12c)
j=1 K X i=1
where ρi,j is the relay assignment indicator variable. When ρi,j = 1, Uj is assigned to Ui . When ρi,j = 0, Uj is not assigned to Ui . By solving this minimization problem, the performance for total network is improved. However, the performance of each user cannot be guaranteed. The minimization problem for the worst user outage probability is formulated as min
K X
max
{ρi,j } i∈{1,2,··· ,K}
(
Ã
2 σj,D
∆ exp − 2 σj,D
!
Ã
−
2 σi,D
∆ exp − 2 σi,D
(8)
!) (9)
To minimize the average outage probability while reducing computational complexity, the greedy assignment scheme is considered. This scheme is based on the greedy matching in [9]. In greedy matching, the base station randomly selects a free user and then matches the free user with another user in order that the sum of the outage probability for two users is minimized. This process continues until all users are matched. In greedy assignment scheme, the base station randomly selects a free user and then assigns another user to the free user in order that the outage probability for the free user is minimized. This process continues until there are no free user. As the base station searches only possibilities of relay assignment corresponding to the randomly selected user, the computational complexity of the greedy assignment scheme is lower than that of the optimal assignment scheme. 3) Min-max Assignment Scheme We consider the min-max assignment scheme to minimize the worst user outage probability while reducing the computational complexity [13]. The algorithm of the min-max assignment scheme is as follows: out , ∀i, j. i) Initialize ρi,j = 0, Zi,j = Pi,j
ii) Find a user pair (i, j) such that out ρi,j Pi,j
(13) (i∗ , j ∗ ) = arg max Zi,j .
j=1
(15)
i,j
subject to: ρi,j ∈ {0, 1} , ∀i, j K X
(14a)
ρi,j = 1, ∀i
(14b)
ρi,j = 1, ∀j.
(14c)
j=1 K X i=1
The performance of the worst user is improved by solving this minimization problem. However, the total system performance cannot be guaranteed. (11) and (13) can be solved by exhaustive search for all possibilities of ρi,j . However, the complexity of exhaustive search becomes very high when the number of users is large. 2) Greedy Assignment Scheme
Set Zi∗ ,j ∗ = 0. iii) Check if there is the possibility of relay assignment when Uj ∗ is not assigned to Ui∗ . If no relay assignment exists, set ρi∗ ,j ∗ = 1, Zi,j ∗ = 0, ∀i, Zi∗ ,j = 0, ∀j. iv) Go to step ii) until Zi,j = 0, ∀i, j. As the maximum value of Zi,j is removed in step ii), the min-max assignment scheme provides the low outage probability for the worst user. The complexity of the minmax assignment scheme is lower than that of the optimal assignment scheme but higher than the complexity of the greedy assignment scheme. The reason is that the possibility of relay assignment is checked in step iii).
0 0
10
Outage probability
Outage probability
10
-1
10
-2
10
-1
10
-2
10
Min-max, full feedback
DF-AF, approximation
Greedy, full feedback
DF-AF, simulation
-3
10
Optimal, full feedback
No cooperation
Random
DF -3
10 0
5
10
15
20
25
30
35
40
45
0
5
10
15
SNR (dB)
20
25
30
35
40
45
SNR (dB)
Fig. 1. Average outage probability for the optimal assignment with full feedback.
Fig. 3. Worst user outage probability for various relay assignment schemes.
0
10 0
Outage probability
Outage probability
10
-1
10
-2
10
-1
10
-2
10
Optimal, limited feedback, Optimal, limited feedback,
Min-max, full feedback
10
Greedy, full feedback
-3
10
Optimal, limited feedback,
-3
N N N
=1 =2 =3
Optimal, full feedback
Optimal, full feedback
Greedy, full feedback
Random
0 0
5
10
15
20
25
30
35
40
45
5
10
15
20
25
30
35
40
45
SNR (dB)
SNR (dB)
Fig. 2.
Average outage probability for various relay assignment schemes.
B. Limited Feedback The relay assignment scheme with limited feedback is considered to reduce the overhead caused by full feedback. In this relay assignment scheme, each user sends only a few bits for the inter-user average CSI to the base station. The base station evaluates the outage probabilities for all users by using the feedback information and assigns relays to users. As this relay assignment is also based on the outage probability, all relay assignment schemes with full feedback can be used. IV. S IMULATION R ESULTS Consider the multiuser system for the number of users K = 16. Suppose that the users are distributed in the circle with a radius 200m centered at the base station. Suppose that the
Fig. 4. Average outage probability for the optimal assignment with various feedback.
transmit data rate, R, is 1bps/Hz and the path loss exponent is 3. For comparison, the random assignment scheme is considered. As users are randomly assigned to other users in the random assignment scheme, the complexity of this relay assignment scheme is significantly reduced compared to that of the optimal assignment scheme. However, we can expect that the random assignment scheme gives worse performance than any other relay assignment scheme with full feedback, since the feedback information is not used. Fig. 1 shows the average outage probability for optimal assignment with full feedback. The outage probability for a non-cooperative network and that for a DF cooperative network are plotted for comparison. It is shown that the DFAF protocol gives better performance than the DF protocol and
the no cooperation. It is also shown that the outage probability of the DF-AF protocol by approximation is similar to that by simulation. Thus, this outage probability can be used for relay assignment schemes. Fig. 2 shows the average outage probability for various relay assignment schemes. It is shown that the average outage probability of the greedy assignment scheme is slightly lower than that of the min-max assignment scheme. Although the performance gap between greedy assignment scheme and minmax assignment scheme is negligible, the complexity of the greedy assignment scheme is lower than that of the min-max assignment scheme. Fig. 3 shows the worst user outage probability for various relay assignment schemes. It is shown that the worst user outage probability of the min-max assignment scheme and that of the optimal assignment scheme are identical. Note that the computational complexity of the former is lower than that of the latter. It is also shown that the worst user outage probability of the greedy assignment scheme is slightly lower than that of the random assignment scheme. Fig. 4 shows the average outage probability for the optimal assignment for the number of feedback bits N = 1, 2, 3. Also, the outage probabilities of the greedy assignment scheme and optimal assignment scheme with full feedback are plotted for comparison. It is shown that the average outage probability of the optimal assignment scheme with N = 3 is slightly lower than that of the greedy assignment scheme with full feedback. It means that when the optimal assignment scheme is used, only three feedback bits are needed to achieve better performance than the greedy assignment scheme. V. C ONCLUSIONS In this paper, we consider the multiuser DF-AF cooperative network. The outage probability of the DF-AF protocol is approximated for relay assignment schemes based on the outage probability. We consider two types of feedbacks: full feedback and limited feedback. To minimize either the average outage probability or the worst user outage probability, we examine relay assignment schemes with full feedback. The relay assignment scheme with limited feedback is also considered to reduce the overhead caused by full feedback. Simulation results show that in full feedback case, the worst user outage probability of the min-max assignment scheme is much lower than that of the greedy assignment scheme. It is also shown that the average outage probability of the optimal assignment scheme with three feedback bits is is slightly lower than that of the greedy assignment scheme with full feedback. ACKNOWLEDGMENT This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MEST) (No. 2011-0017437). R EFERENCES [1] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversityPart I: System description,” IEEE Trans. Commun., vol. 51, no. 11, pp. 1927-1938, Nov. 2003.
[2] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversityPart II: Implementation aspects and performance analysis,” IEEE Trans. Commun., vol. 51, no. 11, pp. 1939-1948, Nov. 2003. [3] A. Stefanov and E. Erkip, “Cooperative coding for wireless networks,” IEEE Trans. Commun., vol. 52, no. 9, pp. 1470-1476, Sept. 2004. [4] T.E. Hunter, S. Sanayei, and Aria Nosratinia, “Outage analysis of coded cooperation,” IEEE Trans. Inform. Theory, vol. 52, no. 2, pp. 375-391, Feb. 2006. [5] J. N. Laneman and G. W. Wornell, “Distributed space-time-coded protocols for exploiting cooperative diversity in wireless networks,” IEEE Trans. Inform. Theory, vol. 49, no. 19, pp. 2415-2425, Oct. 2003. [6] 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. [7] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Trans. Inform. Theory, vol. 50, no. 12, pp. 3062-3080, Dec. 2004. [8] W. Su and X. Liu, “On optimum selection relaying protocols in cooperative wireless networks,” IEEE Trans. Commun., vol. 58, no. 1, pp. 52-57, Jan. 2010. [9] J. N. Laneman, “Cooperative diversity in wireless networks: Algorithms and architectures,” Ph.D. dissertation, MIT, Cambridge, MA, 2002. [10] A. Nosratinia and T. E. Hunter, “Grouping and partner selection in cooperative wireless networks,” J. Sel. Areas Commun., vol. 25, no. 2, pp. 369-378, Feb. 2007. [11] Y. S. Jung and J. H. Lee, “Partner assignment algorithm for cooperative diversity in mobile communication systems,” in Proc. IEEE VTC 2006Spring, Melbourne, Australia, May 2006. [12] Y. Yang, H. Hu, J. Xu, and G. Mao, “Relay technologies for WiMAX and LTE-advanced mobile systems,” IEEE Commun. Mag., vol. 47, no. 10, pp. 100-105, Oct. 2009. [13] J. Shi, G. Yu, Z. Zhang, Y. Chen, and P. Qiu, “Partial channel state information based cooperative relaying and partner selection,” in Proc. IEEE WCNC 2007, Kowloon, Hong Kong, Mar. 2007. [14] S. Ren and K. B. Letaief, “Cooperative networks with limited feedback,” in Proc. IEEE GLOBECOM 2008, New Orleans, LA, Nov. 2008.
