The Pennsylvania State University the Graduate School

The Pennsylvania State University The Graduate School OUTAGE PROBABILITY AND TRANSMITTER POWER ALLOCATION FOR NC-BASED COOPERATIVE NETWORKS OVER NAKAGAMI-M FADING CHANNEL A Thesis in Electrical Engineering by Yi-Lin Sung c 2014 Yi-Lin Sung Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science May 2014 The thesis of Yi-Lin Sung was reviewed and approved∗ by the following: Sedig S. Agili Associate Professor, Department Head of Electrical Engineering Program Coordinator, Master of Science in Electrical Engineering Thesis Co-Advisor Aldo W. Morales Professor of Electrical Engineering Thesis Co-Advisor Robert Gray Associate Professor of Electrical Engineering ∗Signatures are on file in the Graduate School. Abstract In previous work, we proposed a modified network coding (NC) cooperation system based on complementary code (CC)-code division multiple access (CDMA) technique. This technique not only consumes fewer time slots in either synchronous or asynchronous transmission but also alleviates multi-path interference. In that system, a multiplier is used at the base station where the received signal is multiplied with redundant signals coming from the relays, rather than performing a binary sum operation in the media access control (MAC) layer, which is normally used in traditional network coding. In this thesis, a further investigation is car- ried out in the proposed system in terms of outage probability and transmitter power allocation. Outage probability was obtained by setting some conditions on a modified mutual information equation. In addition, using the max-min opti- mization method, the optimal power allocation was obtained. Simulation results show that the proposed NC-based cooperative system reduces the overall system outage probability and provides a better transmitter power allocation as compared to the traditional cooperative communication system. These results are obtained by using a Nakagami-m fading channel. Index Terms{Bit error rate, network coding, complementary code-code division multiple access (CC-CDMA), cooperative, relay, diversity, outage probability, capacity, optimal power. iii Table of Contents List of Figures vii List of Tables x List of Abbreviations and Symbols xi Acknowledgments xv Chapter 1 Introduction 1 1.1 Introduction . 1 1.2 Outage performance . 1 1.2.1 Outage probability . 1 1.2.2 Optimal power allocation . 2 1.2.3 System outage probability introduction . 2 1.3 The system framework . 2 1.3.1 Cooperation . 3 1.3.2 Network coding . 4 1.3.3 Multiplier . 4 1.4 Benefits of the proposed system . 5 1.4.1 TDMA . 6 1.4.2 CDMA . 6 1.4.3 Spectrum efficiency . 7 1.4.4 Benefits of complementary codes . 7 Chapter 2 Error rate probability 10 2.1 System model . 10 iv 2.1.1 Signals received at relay nodes . 11 2.1.2 Signals received at the destination . 14 2.2 DIVERSITY ANALYSIS . 15 2.2.1 Sub-optimal weights . 17 2.2.2 Probability of error at destination . 18 2.3 Numerical analyses . 20 2.3.1 NC-based cooperative by using a multiplier . 20 2.3.2 Multiplier network coding vs. ML distributed phase steering 21 2.3.3 Multiplier network coding vs. Network-Coded Cooperative Diversity (NCCD) . 23 2.3.4 Multiplier network coding vs. ML detection network coding 23 2.4 Summary of the advantages of using a multiplier network coding . 24 Chapter 3 Outage probability 31 3.1 Outage probability . 31 3.2 Numerical analyses . 37 3.2.1 Outage probability for NC-based cooperative by using a multiplier . 37 3.2.2 Multiplier network coding vs. Two users cooperative network coding . 37 3.2.3 Multiplier network coding vs. Network-coding-based hybrid AF and DF system . 38 3.2.4 Multiplier network coding vs. Distributed orthogonal Space- Time block codes . 38 3.3 Summary of the advantages of using a CC-CDMA cooperative network coding . 40 Chapter 4 Optimal power allocation 53 4.1 Optimal power allocation . 53 4.1.1 Standard max-min problem . 53 4.1.2 Lagrangian problem . 56 4.2 Summary of the advantages of using optimal power allocation . 58 4.3 Numerical analyses . 59 Chapter 5 Conclusions 71 5.1 Conclusions . 71 5.2 Future work . 72 v Appendix A Received signal at relay rj or destination d 73 Appendix B Received noise at relay rj or destination d 76 Appendix C Maximum output SNR analysis 78 Appendix D Error probability closed form solution for a special case and diversity gain analysis 82 Bibliography 86 vi List of Figures 1.1 Traditional cooperative communication scheme. Mobile user 2 con- veys user 1's signal to the base station because of its better communication channel quality. 3 1.2 An example of a network-coding-based cooperative communication with two mobile users, one relay station, and a receiver. 4 1.3 Comparison between the traditional XOR operation and a multiplier using BPSK signals. 5 2.1 Source t1 transmitter block diagram. 10 2.2 Transmitter-to-relay proposed method using CC-CDMA. 11 2.3 Received signals at the base station. Note that the boxed part of this block diagram will be depicted in detail in Fig. 2.4. 15 2.4 Detail diagram of the shaded area in Fig. 2.3 at the destination for DF case.y ~t2;d is multiplied byy ~r1;d in order to be a redundant signal for diversity achievement withy ~t1;d. 16 2.5 A general case of a NC-based cooperative communication system with K sources and Z relays. 20 2.6 Error probability when changing mt1 value with 1, 2, and 3, under the conditions of setting mt2 = 1, mr1 = 1. 25 2.7 Error probability when changing mt1 value with 1, 2, and 3, under the conditions of setting mt2 = 1, mr1 = 1, mr2 = 1. 26 2.8 Error probability when changing mt1 value with 1, 2, and 3, under the conditions of setting mt2 = 1, mr1 = 1, mr2 = 1, mr3 = 1. 27 2.9 Error probability when changing mt1 value with 1, 2, and 3, under the conditions of setting mt2 = 1, mr1 = 1, mr2 = 1, mr3 = 1, mr4 =1.................................. 28 2.10 Error probability when fixing all mti and mrj values with 1, under the conditions of changing the number of relays. 29 2.11 BPSK error probability performance. 30 vii 3.1 Illustration of a cooperative relay network with N parallel potential relays [35]. 32 3.2 General case: K source nodes with Z relay nodes. Users in this case cannot be relay. 33 3.3 Outage probability vs. SNR with R = 0:5 bit/sec/Hz, while the Gamma distribution with parameters α = m, β = Ω=m. 40 3.4 Outage probability vs. SNR with R = 1 bit/sec/Hz, while the Gamma distribution with parameters α = m, β = Ω=m. 41 3.5 Outage probability vs. SNR with R = 0:5 and R = 1 bit/sec/Hz, while the Gamma distribution with parameters α = m, β = Ω=m. 42 3.6 Outage probability vs. SNR with R = 0:5 and R = 1 bit/sec/Hz, while the Gamma distribution with parameters α = m, β = Ω=m. 43 3.7 Outage probability vs. SNR with R = 0:5 and R = 1 bit/sec/Hz, while the Gamma distribution with parameters α = m, β = Ω=m. 44 3.8 Outage probability vs. SNR with R = 0:5 and R = 1 bit/sec/Hz, while the Gamma distribution with parameters α = m, β = Ω=m. 45 3.9 Outage probability vs. SNR with R = 0:5 and R = 1 bit/sec/Hz, while the Gamma distribution with parameters α = m, β = Ω=m. 46 3.10 Outage probability vs. SNR with R = 0:5 and R = 1 bit/sec/Hz, while the Gamma distribution with parameters α = m, β = Ω=m. 47 3.11 Outage probability vs. SNR with R = 0:5 and R = 1 bit/sec/Hz, while the Gamma distribution with parameters α = m, β = Ω=m. 48 3.12 Outage probability vs. SNR with R = 0:5 and R = 1 bit/sec/Hz, while the Gamma distribution with parameters α = m, β = Ω=m. 49 3.13 Outage probability vs. SNR with R = 0:5 and R = 1 bit/sec/Hz, while the Gamma distribution with parameters α = m, β = Ω=m. 50 3.14 Outage probability vs. SNR with R = 0:5 and R = 1 bit/sec/Hz, while the Gamma distribution with parameters α = m, β = Ω=m. 51 3.15 Outage probability comparisons. 52 4.1 Two phases of DF cooperative strategy. 54 4.2 Illustration of water filling for power allocation case. 57 4.3 Optimal power vs. equal power with R = 0:5 bit/sec/Hz, while the Gamma distribution with parameters α = m, β = Ω=m. 59 4.4 Optimal power vs. equal power with R = 1 bit/sec/Hz, while the Gamma distribution with parameters α = m, β = Ω=m. 60 4.5 Optimal power vs. equal power with R = 0:5 and R = 1 bit/sec/Hz, while the Gamma distribution with parameters α = m, β = Ω=m. 61 4.6 Optimal power vs. equal power with R = 0:5 and R = 1 bit/sec/Hz, while the Gamma distribution with parameters α = m, β = Ω=m. 62 viii 4.7 Optimal power vs. equal power with R = 0:5 and R = 1 bit/sec/Hz, while the Gamma distribution with parameters α = m, β = Ω=m. 63 4.8 Optimal power vs. equal power with R = 0:5 and R = 1 bit/sec/Hz, while the Gamma distribution with parameters α = m, β = Ω=m.

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