Outage Probability of Alamouti based Cooperative Communications with Multiple Relay Nodes using Network Coding

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1 Outage Probability of Alaouti based Cooperative Counications with Multiple Relay Nodes using Network Coding Gordhan Das Menghwar and Christoph F. Mecklenbräuker 2 Inforation Technology Centre Sindh Agriculture University, Tandoja, Pakistan Telephone: Fax: Eail: gordhan das@hotail.co 2 Institute of Counications and Radio Frequency Engineering Vienna University of Technology, Vienna, Austria Telephone: Fax: Eail: cf@nt.tuwien.ac.at Abstract In this paper, we extend our proposed schee of cooperative counications based on Alaouti schee which was aided by a single relay node to forward network coded bits to the destination. In this work, instead of a single relay node, we consider ultiple relays forwarding network coded bits, of the inforation received fro the cooperating users, to the destination. With analytical results on the outage probability, we show that the cooperative diversity gain of the proposed schee increases linearly with, the nuber of relay nodes assisting cooperating users by forwarding network coded bits of their inforation to the destination. I. INTRODUCTION Due to the proising gains offered by cooperative counications and the relay channel, the standard bodies for future generation wireless counications, like LTE-Advanced [] and IEEE802.6j [2][3], have shown great interest in cooperative transission and in the use of a fixed relay node [4] in the network. With cooperative transission between the base stations, it is planned to reduce the interference effects especially for the edge users [5][6]. In this way, the edge users are intended to not only have higher throughput but increased reliability as well. In the sae way, the use of a relay node is also proposed to offer higher data rates and to cover the coverage holes for the users at the cell boundary [3]. On the other hand, in user cooperation or cooperative counications setup, users in coon vicinity share their resources to achieve the sae goal like the diversity gain and the iproved throughput. Cooperative counications is a way of transission where the users help each other for reliable recovery of their essages at the destination [7][8][9]. Based on the fact that the future generation wireless systes are expected to have fixed relay node installed in the network, we proposed a schee which cobines the concept of cooperative counications, which does not require any dedicated terinal, and the use of a fixed relay node in the network [0][][2]. To ipleent that schee, we used two cooperating users using space-tie coding based Alaouti schee and a fixed relay node forwarding network coded bits to the destination. Network coding is an idea based on ixing the data at the interediate nodes when travelling fro source to the destination [3]. In a wireless network, like ad hoc or cellular systes, the available free users can also be considered as fixed relay nodes. In particular, in [2], we investigated the proposed schee using outage probability as a perforance easure. It was shown that with this cobination of cooperative counications and fixed relay node, we can outperfor cooperation using Alaouti schee only. While our previous work was based on the availability of a single relay node, in this paper, we extend the nuber of available relay nodes assisting the cooperating users. As a perforance analysis for slow fading channel, we derive the resulting outage probability of the proposed schee. The results indicate that there is a linear increase in the diversity order of the schee with every increase of the relay node. The rest of the paper is structured as follows. Section II describes our syste odel. Section III gives the perforance analysis of the schee. In Section III-A, we give the utual inforation and in Section III-B the resulting outage probability of the proposed schee is derived. The results are presented and discussed in Section IV. Finally, Section V draws the conclusion of our paper. II. SYSTEM MODEL We consider a cellular network with two cooperating users u and u 2, single base station, and ultiple relays or free users in their vicinity, as shown in Fig.. Since

2 In our schee, in addition to the cooperating users and the destination, we also introduce ultiple relay nodes in the network, as shown in Fig. 3. a) First Phase Fig.. Cooperative counications setup exploiting the availability ultiple dedicated relay nodes our schee builds upon cooperative counications using Alaouti schee [4], first we briefly go through this schee and then discuss our investigated strategy. Fig. 2 shows cooperative counications setup showing two users using space-tie coding based Alaouti schee. Transission of the essage is assued to take place in two phases. In the first phase, each of the user, in turn, transits Fig. 2. a) First Phase b) Second Phase Space-tie Cooperative counications using Alaouti schee its own essage s and s 2, respectively, to the destination, as depicted in Fig. 2a). This essage, along with the intended destination which is base station in our case, is also received at each other s receivers. In the next phase, both of the users, act as a relay node for each other. And following Alaouti schee, send s 2 and s, respectively, to the destination, as illustrated in Fig. 2b). The sign of represents the coplex conjugate operation. As a result, the destination receives two copies of the sae essage transitted fro the transitting users. These two copies of the essage, based on the channel condition, are received at the destination fro two independently fading paths and offer diversity order of two. b) Second Phase Fig. 3. Space-Tie Cooperative counications using Alaouti schee with network coding Again the transission of the essage is accoplished in two phases. During first phase, the cooperating users transit s and s 2, respectively to the destination. This tie due to the presence of ultiple relays in the vicinity of the transitting users, the essages are also received at these relay nodes. This is shown in Fig. 3a). Later in the next phase, the cooperating users transit s 2 and s, respectively to the destination. In the sae phase, all of the relay nodes decode the essages received fro the cooperating users and forward network coded bits of those decoded essages to the destination, as illustrated in Fig. 3b). To avoid the interference, the obile station users and all of the relay nodes jointly are assigned orthogonal channels. Although this orthogonality can equally be achieved by using different tie, frequency or code, as is done in today s cellular networks, we focus here only on tie based orthogonality. Table I shows the operational details of our proposed schee. r j represents the j th relay node, where j =, 2,...,. For instance, the first row of Table I indicates that TABLE I THE OPERATIONAL DETAILS OF THE SCHEME Tie Slot Transitting Node Transitted Message Receiving Node u s u 2, BS, r,... r 2 u 2 s 2 u, BS, r,... r 3 u s 2 BS 4 u 2 s BS 5 r,...r s s 2 BS during first tie slot user u transits s and user u 2, base

3 station BS), and all of the relay nodes receive this essage. Likewise in the next tie slot, user u 2 transits s 2 ; this tie user u, BS, and the relay nodes act as receiving nodes for this essage. Finally, in the fifth tie slot, all of the relay nodes transit network coded bits of the inforation received fro the cooperating users to the destination. Sybol of is used to show Ex-OR operation to ipleent the idea of network coding. We consider slow fading channel and the fading coefficients are odeled as zero ean coplex Gaussian rando variables with zero ean and σ 2 variance. In addition to that, additive white Gaussian noise AWGN) with zero ean and unit variance is assued at each receiver, i.e., at the receivers of the cooperating obile station users and at the destination. Both of the cooperating users and all of the relay nodes coply with a power restriction of P i. Furtherore, perfect channel state inforation is assued at the receiving end, but not at the transitters. Signal-to-noise ratio SNR) is defined as where γ h i,j 2, ) γ i N o. III. PERFORMANCE ANALYSIS In this section, we analytically evaluate the perforance of our proposed schee, i.e., cooperative counications using Alaouti schee with network coding when ultiple nubers of relay nodes are present in the network. As entioned before, these relay nodes forward network coded bits, of the essages received fro the cooperating users, to the destination. For perforance evaluation purpose, first we evaluate the analytical expression for the utual inforation between the cooperating user u i and the destination. Later on the basis of utual inforation, we derive the outage probability for the investigated schee. A. Mutual Inforation For siplicity, we assue that the channel between the cooperating users and fro the cooperating users to the relay nodes are error free. Based on this assuption, the utual inforation, for the schee with two cooperating users using space-tie codes and ultiple relays forwarding network coded bits to the destination, can be written as I = 2 5 log + γ 2 h i,0 2) + 2 +γ 5 log h r,0 2). 2) h i,0 and h r,0 shows the channel gain fro i th cooperating user and r th relay channel, respectively, to the destination. Here, the first of the two constituent ters is due to the Alaouti schee [5], and the second ter is due to network coded bits, forwarded fro the relay nodes to the destination [6]. The factor 2 5, in front of the utual inforation, indicates that five tie slots are used by two cooperating users to transit their essages to the destination. Here four tie slots are used when cooperating users use space-tie codes and additional one tie slot is used by the relay nodes which forward network coded bits to the destination. As described in Table I, all of the relay nodes are considered to transit siultaneously. B. Outage Probability As we know the axiu transfer rate is dependent on the utual inforation between input and output [7]. Mutual inforation expression 2) indicates the fact that the achieved rate is dependent on the channel gain, which is considered to follow Rayleigh distribution and is a rando variable. Following [8], we define the outage probability to be the probability when the channel cannot eet certain rate requireent R, deanded by soe particular application, like video or soe ultiedia application. Matheatically it can be written as [9][20] P [R] =P [I < R]. 3) With the help of 2) and 3), we derive the outage probability of the proposed schee as follows: P [R] =P [I < R] [ 2 5 log + γ h i,0 2) log + γ h r,0 2) ] <R [ 2 5 log + γ 2 [ + γ [ h i,0 2) + γ h r,0 2 + γ 2 h r, h r,0 2) ] <R h i,0 2 + γ2 h i,0 2 2 h r,0 2 < 2 5 R] 2 h i,0 2 + γ 2 h i,0 2 h r,0 2 < R γ Let h r,0 2 = x, 2 h i,0 2 = y, and R γ = ɛ. ] Logarthi with base 2 are considered throughout this paper.

4 Then [ P [R] =P x + 2 y + ] 2 γxy < ɛ [ y 2 + ) ] 2 γx <ɛ x [ y< ɛ x ] γ x ɛ [y < ɛ x ] γ x x P X x) dx where and = ɛ 0 [ expgh)] P X x) dx 4) g = λ ɛ x ) γ x, ɛ x ) h = +λ γ x. The second last line of the equation 4) is due to the law of total probability theore; and the last equation is obtained by using the cuulative distribution function cdf) for the su of two exponential rando variables, represented by y. A general for of cdf for the su of k exponential rando variables is given by [2] k F x) = exp λx) k=0 λx) k. 5) k! P X x) represents the probability distribution function pdf) for the su of independent exponential rando variables and is given by [2] P X x) = { λ )! λx) exp λx) for x>0 0 for x 0 where λ> 0 represents the paraeter of the exponential distribution. IV. RESULTS AND DISCUSSION In Figure 4, we show the outage probability results, based on the expression 4), evaluated at different values of SNR 2. Without loss of generality, λ is taken to be, and the required spectral efficiency R, is fixed at b/s/hz. As depicted, the relative diversity gains offered by non-cooperative transission and the cooperative counications using Alaouti schee are also shown. The diversity order of a particular schee can be seen as the slope of the outage probability curve [22]. With this definition, we can see that the non-cooperative counications and cooperative counication using Alaouti schee offer diversity order of one and two, respectively. On the other hand, the diversity gain offered by cooperative counications using 2 In the figure, the nuerals =, 2, 5, 7) show the nuber of relay nodes used to forward network coded bit to the destination. 6) P[R] Non Cooperation Coop. Alaouti Coop. Alaouti + NWC Coop. Alaouti + NWC 2 Coop. Alaouti + NWC 5 Coop. Alaouti + NWC SNR db) Fig. 4. Outage probability for cooperative counications using Alaouti schee with network coding aided by, 2, 5, and 7 relay nodes in coparison with the outage probability for direct transission and cooperative counication using Alaouti schee without network coding. The required spectral efficiency R is set to b/s/hz. Alaouti schee with network coding aided by relay nodes is of the order of +2. In the figure, we have shown the outage probability curves for =2, 5, and 7 which happens to be of the order of 4, 7, and 9, respectively. Furtherore, in the Figure 4, it is easy to see, with the help of the slope of outage probability curves, that there is a linear increase in the diversity order with every increase of the relay node. V. CONCLUSION We extended our work on cooperative counications using Alaouti schee aided by a single relay to ultiple relay nodes. As a perforance easure, we used outage probability of the schee. The derived results indicate that the achieved diversity gain outperfors the diversity gain achieved with cooperative counications using Alaouti schee only. Furtherore, this gain increases linearly with the nuber of relay nodes, assisting the cooperating users by sending the network coded bits of their essages to the destination. REFERENCES [] 3GPP TR V.2., Further advanceents for EUTRA: Physical layer aspects, Tech. Spec.n Group Radio Access Network, June [2] I. P802.6j/D9, Draft aendent to IEEE standard for local and etropolitan area network part 6: Air interface for fixed and obile broadband wireless access systes: Multihop relay specification, Feb [3] Y. Yang, H. Hu, J. Xu, and G. Mao, Relay technologies for WiMAX and LTE-Advanced obile systes, IEEE Counications Magazine, vol. 47, no. 0, pp , October [4] T. Cover and A. E. Gaal, Capacity theores for the relay channel, IEEE Trans. Infor. Theory, vol. IT-25, no. 5, pp , Sep 979. [5] S. Parkvall and D. Astely, The evolution of LTE towards IMT- Advanced, Journal of Counications, vol. 4, no. 3, pp , April 2009.

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