Resource Allocation in OFDM Based Wireless Relay Networks ...

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4.3 Cooperative Non-Orthogonal Transmission Subcarrier Pairing under Fixed Power Allocation We define a K × K matrix Γ, where the (k, j)-th entry is ) [Γ] (k,j) = 1 N∑ (1 2 log 2 p k |h n,k | 2 ρ j |g n,j | 2 + p k |h n,k | 2 σr 2 + ρ j |g n,j | 2 σd 2 + . σ2 rσd 2 n=1 Our aim is to maximize the overall throughput such that a particular sub-carrier at hop-1 is paired with one and only one sub-carrier over hop-2. The different steps of algorithm are 1: Choose the optimal pairing (k ∗ , j ∗ ) such that (k ∗ , j ∗ ) = max([Γ] (k,j) ), ∀(k, j), where [Γ] (k,j) denote the (k, j)-th entry in Γ, 2: Remove the k ∗ -th row and j ∗ -th column from Γ. 3: Repeat step-1 and step-2 until we get the complete optimum pairing set π ∗ . Power Refinement Under Fixed Pairing To obtain a more close performance to the joint resource allocation scheme, we re-compute the power allocation for the obtained sub-carrier pairing in step 2. Assume that the sub-carrier k is paired with the sub-carrier m(k), where m is the mapping function. The problem in (4.18) becomes where D (µ, λ) = max p,ρ K∑ ( ) 1 2 log 2 (1 + SNR k ) − µp k − λρ j + µP S + λP R , (4.27) k=1 SNR k = N∑ n=1 a n,k p k b n,m(k) ρ m(k) a n,k p k + b n,j ρ m(k) + 1 . (4.28) The problem (4.27) can be decomposed into K sub-problems, each being similar to (4.19), and the solution for per sub-carrier problem follows the same steps in (4.19) to (4.23). Finally, the dual variables can be found from sub-gradient method. 71
4.4 Optimization under Orthogonal Transmission 4.3.3 Complexity Analysis In subsection 4.3.1, we decompose the power allocation problem into K 2 sub-problems. The complexity of solving each sub-problem is O(I(I ′ + I ′′ )), where I ′ is the number of iterations required for the convergence of fixed point algorithm in (4.23), I ′′ is the number of iterations for finding p k by gradient descent method, and I denotes the number of iterations for alternate optimization over p k and ρ j . Further the complexity of obtaining sub-carrier pairing through Hungarian algorithm is O(K 3 ). If the objective of dual function is minimized in M iterations, the total computational complexity of our proposed algorithm becomes O(MK 2 (II ′ + II ′′ + K)). On the other hand, in suboptimal algorithm the complexity of finding sub-carrier pairing is O(K), and the power allocation in step 3 requires a complexity of O(KĪ(Ī′ +Ī′′ )), where Ī′ , Ī′′ and Ī are the number of iterations similar to I′ , I ′′ and I, respectively. If the sub-gradient algorithm converges in ¯M iterations, the total complexity involves in step 1 to step 3 in subsection 4.3.2 is O( ¯MK(II ′ + II ′′ + 1)). Without loss of generality, we can consider ¯M, Ī, Ī′ , and Ī′′ are close to M, I, I ′ , and I ′′ , respectively due to the similarity between the algorithms. Then the overall complexity of the proposed suboptimal algorithm is much less than O(MK 2 (II ′ + II ′′ + K)), the complexity of the joint resource allocation scheme. 4.4 Optimization under Orthogonal Transmission In this section, an orthogonal transmission through time division is assumed where each node transmits in a preassigned time slot. The transmission from the source to the destination takes N + 1 time slots such that the source node transmits in the first time slot and then each RS transmits in subsequent time slots. The destination node combines the signals from all the relays through maximum ratio combining (MRC). Based on the proposed protocol, the received SNR at the destination is given 72
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Resource Allocation in OFDM Based W
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Dedications: To my family
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Acknowledgment I am greatly thankfu
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Contents 2.3.3 Proposed Low-Complex
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Abstract The combination of relay t
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List of Tables 3.1 Complexity compa
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List of Figures 4.1 System model fo
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List of Acronyms IEEE MU RS AWGN OW
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1.1 Overview of Relay Networks wire
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1.2 Overview of OFDM Figure 1.2: Th
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1.3 Basics of the Optimization Theo
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1.3 Basics of the Optimization Theo
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1.4 Resource Allocation Problem is
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1.5 Contribution and Organization o
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1.5 Contribution and Organization o
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2.1 Introduction allocated to a nod
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2.1 Introduction The main contribut
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Page 55 and 56: 2.6 Summary 2.6 2.4 2.2 2 Rate (bit
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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
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Page 91 and 92: 4.5 Simulations Then, the over all
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Page 99 and 100: 5.1 Introduction Figure 5.2: Linear
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Page 109 and 110: 5.6 Summary Lifetime (S) 150 100 50
Page 111 and 112: Chapter 6 Resource Allocation in Co
Page 113 and 114: 7. Conclusions were considered for
Page 115 and 116: Bibliography [12] A. Peled, and A.
Page 117 and 118: Bibliography [36] Z. Luo and S. Zha
Page 119 and 120: Bibliography [61] D. H. N. Nguyen,
Page 121 and 122: Bibliography [84] A. Goldsmith, S.
Page 123 and 124: Bibliography [105] Y. Li, W. Wang,
Page 125 and 126: Appendix A Derivations of Closed-Fo
Page 127: B. Derivations of the Optimal Power
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