Network coding on cooperative relay networks

Viet Nam National University, Ha Noi University of Engineering and Technology Lam Sinh Cong Network Coding On Cooperative Relay Networks Master Thesis Ha Noi - 2012 Viet Nam National University, Ha Noi University of Engineering and Technology Lam Sinh Cong Network Coding On Cooperative Relay Networks Branch: Electronics and Telecommunications Technology Major: Electronics Engineering Code: 60 52 70 Master Thesis Supervisor: Dr Nguyen Quoc Tuan Ha Noi-2012 LỜI CAM ĐOAN Tôi xin cam đoan luận văn kết nghiên cứu tôi, không chép Nội dung luận văn có tham khảo sử dụng tài liệu, thông tin đăng tải hội nghị, tạp chí, trang web theo danh mục tài liệu tham khảo luận văn Tác giả luận văn Lâm Sinh Công Acknowledgements I am heartily thankful to my supervisor, Dr Nguyen Quoc Tuan, whose encouragement, guidance and support from the initial to the final level enabled me to develop an understanding of the subject My grateful thanks also go to Professor Dinh Thong Nguyen form University of Technology Sydney, Australia, my former colleagues from Department of Telecommunication Systems, Faculty of Electronics and Telecommunication, UET-VNU,H whose help, guidance helped me in all the time of research for and writing of this thesis I also want to thank Project 39/2012/HD/NDT granted by the Ministry of Science and Technology of Vietnam for the support for my researches I would also like to thank my family for the support they provided me through my entire life and in particular ii Contents Abstract 1 Introduction 1.1 1.2 1.3 Introduction to cooperative relay networks 1.1.1 The relay protocols 1.1.2 Advantages of Cooperative Diversity Relaying Networks Introduction to Network Coding 1.2.1 Non-Binary and Binary Network Coding 1.2.2 Advantages of Network Coding 1.2.3 Weaknesses of Network Coding 11 Cooperative Diversity Relaying Networks using network coding 13 System models 15 2.1 Traditional Relay Multiple-Wireless Networks 16 2.2 Single Relay Networks using Network Coding 20 2.3 Multiple-Relay Networks using Network Coding 22 Outage Probability Calculations 24 3.1 Mutual Information 24 3.2 Outage Probability Definition 25 3.3 Outage Probability of Multiple-Relay Networks 27 3.3.1 Traditional Decode-and-Forward relaying 27 3.3.2 Selection Decode-and-Forward relaying 29 3.4 Outage Probability of Single Relay Networks using Network coding 32 3.5 Outage Probability of Multiple-Relay Networks using Network Coding 36 Conclusions and Future Works 42 iii Bibliography 43 iv List of Figures 1.1 Frequency Diversity 1.2 Space Diversity 1.3 Cooperative relay network 1.4 An example of Network Coding 1.5 An example of Non-linear Network Coding 1.6 An example of linear Network Coding 1.7 The butterfly network 10 1.8 The weakness of Network Coding 12 2.1 A traditional single relay network 19 2.2 A traditional multiple-relay network 19 2.3 Network coding in single relay network 20 2.4 Multiple-relay network using network coding 22 3.1 The direct link between the input and the output 25 3.2 Outage probability of a direct link 27 3.3 Outage Probability of fixed and selection DF relay 32 3.4 The degraded system model of a single relay network based on NC 34 3.5 The degraded system model of a single relay network based on NC 35 3.6 Outage probability of the single relay network with and without network coding 36 3.7 Link s1 r1 is in outage 39 3.8 Outage probability of relay networks with different scenarios 41 v Abstract In communication, Cooperative Diversity Relaying refers to devices communicating with one another with the help of relays in order to increase the performance of the network However, in one timeslot, the relay only transmits the signal of one source Therefore, Network Coding is introduced to improve the throughput of the network Combining Cooperative Relay Network and Network Coding should be studied to achieve significant benefits and overcome some weakness In this thesis, we consider the effect of Network Coding on Cooperative Relay Network We propose to use Selection Decode-and-Forward instead of Traditional Decode-and-Forward protocol at the relay We also use the instantaneous channel gains to calculate the outage probability of the proposal system model The rest of the thesis is organized as follows In Chapter II, the system model of a multiple-relay network is described The outage probability is calculated in Chapter III Finally, the conclusions and the future works are drawn in Section IV Chapter Introduction 1.1 Introduction to cooperative relay networks The sharp increase in the number of mobile subscribers which needs large bandwidth for multimedia applications anywhere and anytime requires the network service providers to optimize and develop the current technologies in order to ensure that the Quality of Services (QoS) is always satisfied Diversity scheme are used to improve the reliability of a message signal by transmitting multiple version of the same signal over different communication channels Because of time-varying channel conditions, the diversity plays an important role in combating fading and co-channel interference Diversity techniques are divided into the following types: time diversity, frequency diversity, space diversity, polarization diversity, muiltiuser diversity! [1] • Time diversity: The transmitter sends the same data at different time instants or a redundant error correcting code is added into the messages before transmitting Repetition coding is one of the most popular types of time diversity • Frequency diversity: The signal transmitted by using different frequency channels on a single antenna At the destination, it requires the number of receivers as the number of frequencies used at the transmitter It therefore requires more spectrum usage Transmitter Transmitted signal antenna Receiver Recovered signal antenna Transmitter Receiver Figure 1.1: Frequency Diversity • Spatial diversity The signal is transmitted over different path by using several antennas at the transmitter in order to allow multiusers to share a spectrum and avoid co-channel interference Figure 1.2: Space Diversity • Polarization diversity: The same messages are transmitted and received by using antennas with different polarization A diversity combining technique designed to combine the multiple received signals at the destination is used in this case −1 10 −2 10 −3 Outage Probability 10 −4 10 Fixed Decode−and−Forward Relay Selection Decode−and−Forward Relay −5 10 −6 10 −7 10 0.005 0.01 0.015 0.02 0.025 µth 0.03 0.035 0.04 0.045 0.05 Figure 3.3: Outage Probability of fixed and selection DF relay 3.4 Outage Probability of Single Relay Networks using Network coding Considering the scenarios in Fig 2.3 and the fixed Decode-and-Forward protocol is used at the relay, we denote the outage probability of the uplink BERs of the two end-nodes to the destination as p1 and p2 , respectively and the uplink BERs of the relay in the network coding scenario as pr Then, the probability of system outage can be expressed as follows [23] p1 = ps1 d ps2 d (1 − prd ) + ps1 d prd (1 − ps2 d ) + prd ps2 d (1 − ps1 d ) + prd ps1 d ps2 d = ps1 d ps2 d + prd (ps1 d + ps2 d − 2ps1 d ps2 d ) 32 (3.20) In equation (3.20), the first term represents the link s1 d and the link s2 d being in outage and the link rd is not, the second term represents the link s1 d and the link rd being in outage and the link s2 d is not and the third term represents the link s2 d and the link rd being in outage and the link s1 d is not, and the final term is the case in which link s1 d, s2 d and rd are all in outage : In the Rayleigh fading environment, (3.20) is expressed as follows pout f ixed−DF (µth ) =Fs1 d (µth )Fs2 d (µth ) + Frd (µth ) {Fs1 d (µth ) + Fs2 d (µth ) − 2Fs1 d (µth )Fs2 d (µth )} (3.21) However, (3.20) is obtained in [23] by assuming the links between the sources and the relays are error-free and the authors not specify to the protocol used at the relay This assumption is not practical In our model, we not assume that these links are error-free, and we will analyze the outage probability based on the protocol of the relay Now, we analyze all events which cause system outage • Link s1 r is in outage, then the source s1 repeats transmitting its signal to D The system model in Figure 2.3 is degraded to the one which is depicted in Figure 3.4 Therefore, the outage probability of this degraded model is given by: p1 (µth ) =P (|hs1 r |2 < µth )P (2|hs1 d |2 < àth ) (3.22) ã Link s1 r and s2 r are free of errors It means that the relay decodes fully the sources’ messages, and then combine them into a unique signal before 33 S1 x1 hs1d hrd R hs2 r S2 x2 D hs2d x2 Figure 3.4: The degraded system model of a single relay network based on NC sending it to the destination The system is in outage if both link s1 d and s2 d are in failure The outage probability in this case is expressed as follows: p2 (µth ) =P (|hs1 r |2 > µth )P (|hs1 d |2 < µth ) P (|hs2 r |2 > µth ) P (|hs2 d |2 < µth ) + P (|hs2 d |2 > µth )P (|hrd |2 < µth ) (3.23) • Link s1 r is free of error, link s2 r is in outage, then the source s2 repeats transmitting its signal to D In this case, the relay only sends the signal of the source s1 The system model in this case is as shown in 3.5 Therefore, the outage probability in this case is given by: p3 (µth ) =P (|hs1 r |2 > µth )P (|hrd |2 + |Ps1 d |2 < µth )P (|hs2 r |2 < µth ) (3.24) out Finally, the outage probability of the system is PSDF (µth ) is calculated as 34 S1 x1 hs1r hs1d hrd R x1 D hs2d x2 S2 Figure 3.5: The degraded system model of a single relay network based on NC follow: out PSDF (µth ) = p1 (µth ) + p2 (µth ) + p3 (µth ) (3.25) In which µth is the threshold which can be calculated from equation (3.6) In a Rayleigh fading environment, by using 3.9, we have:     p1 (µth ) = Fs1 r (µth )Fs1 d ( µ2th )        p2 (µth ) = (1 − Fs1 r (µth ))Fs1 d (µth )           p3 (µth ) (3.26) (1 − Fs2 r (µth ))(Fs2 d (µth ) + (1 − Fs2 d (µth ))Frd (µth )) = 1−Fs1 r µsr −µs1 d (µrd Frd (µth ) − µs1 d Fs1 d (µth ))Fs2 r (µth ) Fig 3.6 compares outage probability of the system model with and without It is clear that in case of traditional relay network, there is no relationship between the detection probability of source s1 and source s2 Exactly, it only depends on links s1 r1 , r1 d and s1 d But if network coding is applied, relays transmit the combined signals of s1 and s2 So, the probability of s1 also 35 −1 10 −2 Outage Probability 10 −3 10 Traditional Multiple−Relay Wireless Network Only direct link Single Relay Network using Network Coding −4 10 −5 10 0.01 0.02 0.03 0.04 0.05 µth 0.06 0.07 0.08 0.09 0.1 Figure 3.6: Outage probability of the single relay network with and without network coding depends on the state of link s2 d This is the cause which makes the system worse So that, increasing the number of relay is very necessary to increase the robustness of the network 3.5 Outage Probability of Multiple-Relay Networks using Network Coding Recall that, the total SNR of the MRC output at destination is equal the sum of SNR transmitted from relay R1 and relay R2 γRD = γr1 d + γr2 d 36 or |hRD |2 = |hr1 d |2 + |hr2 d |2 Because |hr1 d |2 and |hr2 d |2 are exponentially distributed, the probability density function and cumulative distribution function of |hrd |2 respectively are: fRD (µ) = µr1 d − µr2d e −µ µr d −e −µ µr d and FRD (µ) = µr1 d − µr2 d µr1 d (1 − e −µ µr d ) − µr2 d (1 − e −µ µr d ) Because of −µ −µ Fr1 d (µ) = µr1 d (1 − e µr1 d ) and Fr2 d (µ) = µr2 d (1 − e µr2 d ) then FRD (µ) = {µr1 d Fr1 d (µ) − µr2 d Fr2 d (µ)} µr1 d − µr2 d By using the Taylor-Maclaurin approximation e−x = − x +     FRD (µ)     Fr1 d (µ)       Fr2 d (µ) = µ2 2µr1 d µr2 d = µth µr1 d = µth µr2 d x2 2, we have (3.27) Therefore FRD (µth ) = 0.5Fr1 d (µth )Fr2 d (µth ) (3.28) The outage probability of the source S1 is obtain by calculating the probability of all events in the source-to-relay links which make the destination 37 unable to decode the x1 messages from S1 • All source-relay links are free of error It means that r1 and r2 can decode the received messages successfully, then the message x1 ⊕ x2 is carried on both link r1 d and r2 d The signals at the destination are: x1 , x2 and x1 ⊕ x2 The destination is unable to decode x1 if link s1 is in outage and at least one of two links s2 d and RD is in outage The probability of this event is given by: P1co = Ps1 d (PRD + (1 − PRD )Ps2 d ) (3.29) Then, P1co (µth ) = Fs1 d (µth )(FRD (µth ) + (1 − FRD (µth ))Fs2 d (µth )) (3.30) In which, FRD is calculated by using equation 3.28 • Link s1 r1 is in outage and others are free of errors The relay R1 only decode fully the message of S2 In this case, an MRC is used to combine the signals transmitted on r1 d and s2 d, so that the destination receives x1 from S1 , x2 from MRC and x1 ⊕ x2 from S2 Therefore, an outage event occurs only when the direct link between the source S1 and the destination D is in failure, and either the receiver is unable recover x1 ⊕ x2 or x2 Notice that x2 is transmitted by using Selection Decode-and-Forward relay R1 then the probability the terminal node can not decode x2 is given 38 S1 h s1d x1 R1 h r1 d x2 x1  x2 R2 S2 hs2r2 x2 D h r2 d hs2d Figure 3.7: Link s1 r1 is in outage by using (3.19) µth )Fs2r1 (µth ) − Fs2r1 (µth ) {µs2d Fs2d (µth ) − µr1d Fr1d (µth )} + µs2d − µr1d co Fs2r1s (µth ) = Fs2d ( (3.31) The probability of this event is expressed as below P2co = ps1 r1 ps1 d {(1 − pr2 d )ps2 r1 s + pr2 d } (3.32) Then, P2co (µth ) = Fs1 r1 (µth )Fs1 d (µth ){(1 − Fr2 d (µth ))Fs2 r1 s (µth ) + Fr2 d (µth )} (3.33) • Link s1 r2 is in outage and others are in good It is easy to show that the outage probability in this case is express as 39 below P3co (µth ) = Fs1 r2 (µth )Fs1 d (µth ){(1 − Fr1 d (µth ))Fs2 r2 s (µth ) + Fr1 d (àth )} (3.34) ã Both s1 r1 and s1 r2 are in outage In this case, x2 is only carried on link s1 d, therefore probability of x1 not being recovered is: P4co (µth ) = Fs1 r1 (µth )Fs1 r2 (µth )Fs1 d ( µth ) (3.35) It is not difficult to see that in cases in which there are more than sourcerelay links or source s2 −ri (i = 1, 2) links are in errors, the outage probabilities are infinitesimal numbers (in the order of P or P ), so we can ignore these cases Thus, the outage probability of the source S1 of this model under a Rayleigh Fading environment is obtained by: P co (µth ) = P1co (µth ) + P2co (µth ) + P3co (µth ) + P4co (µth ) (3.36) Fig 3.8 indicates that the performance of the system model based on network coding with multiple-relay is better than others This can be explained as follows: • Using MRC at the destination to combine the signals from R1 and R2 into a better channel makes the transmission between the relays and destination become more reliability Thus, this system model will be more stable than an other which only uses one relay • In multiple-relay networks, there is no interaction between source i and 40 −1 10 Traditional Multiple−Relay Wireless Network Single Relay Network using Network Coding Multiple−Relay Network using Network Coding −2 Outage Probability 10 −3 10 −4 10 −5 10 0.01 0.02 0.03 0.04 0.05 µth 0.06 0.07 0.08 0.09 0.1 Figure 3.8: Outage probability of relay networks with different scenarios relay j (i, j = 1, and i j) and between the relay R1 and the relay R2 It means that x1 is only transmitted by the source S1 on s1 d and R1 on r1 d link While, in multiple-relay networks using network coding, x1 is carried on link s1 d, r1 d and r2 d 41 Conclusions and Future Works In this thesis, we consider the effects of network coding on cooperative relay networks Instead of using traditional DF relaying, propose to use selection DF relaying which is designed to overcome the weaknesses of DF relaying By using the instantaneous channel gains, we calculate exactly the outage probabilities of systems models, i.e relaying networks with and without network coding, under a Rayleigh fading environment Comparing between the system models that only use one relay, we see that the robustness of the networks will be reduced when network coding is applied However, when we increase the number of the relays (using relays), the performance of network may be increase strongly, even it is better than the case in which network coding is not used Therefore, it may be said that in some cases, network coding also improves the robustness of the network Our proposed system model may be sub-optimal, but it has achieved what we expected For future works, we see that if all outage probabilities of all links are the same, and equal to pe , equation (3.25) and (3.36) become, respectively out PSDF (µth ) = 1.5p2e co and PSDF (µth ) = 3p2e (3.37) By using equation (1.2), the diversity orders of these system models are equal to It means that when using XOR operator, the diversity gain does not in42 crease So that, it is said sub-optimal [24] In future work, we will concentrate on improving the diversity gain of non-binary system model by constructing a polynomial code [8] We also pay attention to non-binary network coding, and analyzing the throughput of both binary and non-binary network coding 43 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