Resource Allocation in OFDM Based Wireless Relay Networks ...

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2.3 Resource Allocation Schemes In order to relate the sub-carrier pair (k, j) to a specific user, we further define the binary variable τ m,(k,j) ∈ {0, 1}, such that ⎧ ⎨ 1, if sub-carrier pair (k, j) is allocated to the m-th user, τ m,(k,j) = ⎩ 0, otherwise. (2.6) With the above definition, the overall system throughput can be expressed as M∑ K∑ K∑ C = π k,j τ m,(k,j) r m,(k,j) , (2.7) m=1 k=1 j=1 and will be used as our main objective function throughout the chapter. 2.3 Resource Allocation Schemes Our target is to jointly optimize the sub-carrier allocation, sub-carrier pairing, and the power allocation such that the end-to-end system throughput is maximized under individual power constraints of MUs and RS. 2.3.1 Problem Formulation Mathematically, we need to optimize over the variables π = {π k,j }, τ = {τ m,(k,j) }, p = {p m,k } and q = {q j } for all m = {1, ..., M}, k = {1, ..., K}, j = {1, ..., K}. Let P m and Q be the total powers of the m-th MU and RS, respectively. The 21
2.3 Resource Allocation Schemes optimization can be formulated as max π,τ ,p,q s.t. C (2.8) K∑ K∑ π k,j = 1, ∀j, π k,j = 1, ∀k, k=1 j=1 M∑ τ m,(k,j) = 1, ∀(k, j), m=1 K∑ k=1 j=1 K∑ π k,j τ m,(k,j) p m,k ≤ P m , ∀m, K∑ q j ≤ Q, j=1 p m,k ≥ 0, q j ≥ 0, ∀m, k, j. The first and the second constraints come from the the fact that each sub-carrier on the first hop can be coupled with one and only one sub-carrier in the second hop and vice verse. The third constraint guarantees the exclusive allocation of the sub-carrier pair (k, j) to one user only. However more than one sub-carrier pairs can be allocated to a particular user. Other constraints represent individual power constraint at each node. Unfortunately, problem (2.8) involves a mixed binary integer programming [34] which is in general difficult to solve. Thanks to [35], the duality gap of (2.8) is proved to be asymptotically zero if the number of sub-carriers (K) is sufficiently large, and a rigorous investigation can be found in [36]. Thus we can solve the dual problem instead of the original problem. The dual function of (2.8) can be defined as [13] D (ν, λ) = max π,τ ,p,q s.t. L (p, q, π, τ , ν, λ) (2.9) K∑ π k,j = 1, ∀j, K∑ π k,j = 1, ∀k, M∑ τ m,(k,j) = 1, ∀(k, j), k=1 j=1 m=1 22
Page 1 and 2: Resource Allocation in OFDM Based W
Page 3 and 4: Dedications: To my family
Page 5 and 6: Acknowledgment I am greatly thankfu
Page 7 and 8: Contents 2.3.3 Proposed Low-Complex
Page 9 and 10: Abstract The combination of relay t
Page 11 and 12: List of Tables 3.1 Complexity compa
Page 13 and 14: List of Figures 4.1 System model fo
Page 15 and 16: List of Acronyms IEEE MU RS AWGN OW
Page 17 and 18: 1.1 Overview of Relay Networks wire
Page 19 and 20: 1.2 Overview of OFDM Figure 1.2: Th
Page 21 and 22: 1.3 Basics of the Optimization Theo
Page 23 and 24: 1.3 Basics of the Optimization Theo
Page 25 and 26: 1.4 Resource Allocation Problem is
Page 27 and 28: 1.5 Contribution and Organization o
Page 29 and 30: 1.5 Contribution and Organization o
Page 31 and 32: 2.1 Introduction allocated to a nod
Page 33 and 34: 2.1 Introduction The main contribut
Page 35: 2.2 System Model where h m,k denote
Page 39 and 40: 2.3 Resource Allocation Schemes ( )
Page 41 and 42: 2.3 Resource Allocation Schemes and
Page 43 and 44: 2.3 Resource Allocation Schemes tha
Page 45 and 46: 2.3 Resource Allocation Schemes 2.3
Page 47 and 48: 2.4 Generalization to Multiple Rela
Page 49 and 50: 2.4 Generalization to Multiple Rela
Page 51 and 52: 2.5 Simulation Results • OptSol/J
Page 53 and 54: 2.5 Simulation Results 0.9 0.85 0.8
Page 55 and 56: 2.6 Summary 2.6 2.4 2.2 2 Rate (bit
Page 57 and 58: 2.6 Summary 2.4 2.2 2 1.8 N=4 N=3 N
Page 59 and 60: 3.1 Introduction A new technology c
Page 61 and 62: 3.1 Introduction • Broadcast Phas
Page 63 and 64: 3.2 System Model MU MU 3 8 A 1 2 7
Page 65 and 66: 3.4 Joint Resource Allocation Schem
Page 67 and 68: 3.4 Joint Resource Allocation Schem
Page 69 and 70: 3.5 Step-Wise Low-Complexity Resour
Page 71 and 72: 3.6 Simulation Results and SNR B m,
Page 73 and 74: 3.6 Simulation Results 3 2.5 2 Uppe
Page 75 and 76: 3.7 Summary 1.8 1.6 1.4 JntOpt SubO
Page 77 and 78: 4.1 Introduction • Non-orthogonal
Page 79 and 80: 4.3 Cooperative Non-Orthogonal Tran
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4.4 Optimization under Orthogonal T
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4.4 Optimization under Orthogonal T
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4.5 Simulations Then, the over all
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4.5 Simulations 40 30 20 Sum−ρ S
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4.6 Summary 0.9 0.8 0.7 JPSC Pow EP
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Chapter 5 Lifetime Maximization in
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5.1 Introduction Figure 5.2: Linear
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5.2 System Model antenna that canno
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5.4 Lifetime Maximization Scheme 5.
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5.4 Lifetime Maximization Scheme wh
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5.5 Simulation Results 150 OPT−SO
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5.6 Summary Lifetime (S) 150 100 50
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Chapter 6 Resource Allocation in Co
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7. Conclusions were considered for
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Bibliography [12] A. Peled, and A.
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Bibliography [36] Z. Luo and S. Zha
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Bibliography [61] D. H. N. Nguyen,
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Bibliography [84] A. Goldsmith, S.
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Bibliography [105] Y. Li, W. Wang,
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Appendix A Derivations of Closed-Fo
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B. Derivations of the Optimal Power
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