Resource Allocation in OFDM Based Wireless Relay Networks ...

More documents

Recommendations

Info

2.5 Simulation Results 2.4.2 Suboptimal Algorithm To reduce the computational complexity, we extend the suboptimal algorithm in Section 2.3.3 to the multi-relay case. The idea is to allocate sub-carriers among RSs over the second hop in a similar fashion as for the MUs over the first hop. We only illustrate the difference from the Section 2.3.3 here: 1) Select K best sub-carriers at hop-1, such that each sub-carrier is allocated to a unique MU that has the best channel gain for this particular sub-carrier. 2) Select K best sub-carriers at hop-2, where each sub-carrier is allocated to a unique RS that has the best channel gain for this sub-carrier. 3) Sort the K selected sub-carriers from step 1 and the K selected sub-carriers from step 2, respectively. Then pair them according to their magnitude. 4) For the sub-carrier allocation and pairing found in previous three step, find the power allocation following the same way in (2.46) and (2.47). The algorithm requires a total complexity of O(K(I ′′′ + M + N + 2)), where I ′′′ denote the number of iterations required for sub gradient updates. 2.5 Simulation Results In this section, we provide numerical examples to evaluate the performance of our proposed algorithms. The frequency domain channels are generated using i.i.d Rayleigh distributed time domain taps. A flat fading channel condition is assumed for each sub-carrier. We choose K = 32 and assign the same total power to all MUs and RSs. The figure of the merit is taken as the per tone rate, i.e., sum rate divided by K and is obtained from the average of 10000 different channel realizations.. Moreover, the rates are obtained from the actual rate expression (2.7) while the solutions are computed from the high SNR approximation. The following algorithms are compared 35
2.5 Simulation Results • OptSol/JntSol: OptSol is the joint optimal solution proposed in subsection 2.3.2 and JntSol denote the joint optimal solution proposed in subsection 2.4.1. • SubOpt: The suboptimal solution presented in subsection 2.3.3 or subsection 2.4.2. • EP-ECarr: A solution without optimization where equal amount of sub-carriers are allocated among users and the available power is equally divided among the allocated sub-carriers • EP-RndCarr: In this case each user is randomly assigned an amount of sub-carriers and equal power distribution among the allocated sub-carriers is assumed. We first present numerical results for uplink transmission with single relay capability. The noise variances are set as σm,k 2 = σ2 j , ∀ m, k, j. The performance throughput of four different methods versus SNR for a system with M = 10 users are shown in the Fig. 2.3. We also display the objective of the dual problem at the solution points in the same figure. We first observe that the duality gap between the dual objective and OptSol is close to zero at all SNR region, which demonstrate the optimality of the proposed algorithm. This is consistent with the result presented from [35]. Moreover, it can be seen that OptSol exhibits best performance at all SNR values, e.g., it yields 1.1 dB and 2.6 dB gains over EP-ECarr and EP-RndCarr solutions, respectively, at the rate equal to 1 bits/s/Hz. In comparison, the rate loss of the proposed suboptimal solution is only 0.3 dB but it requires much less computational complexity. Next we examine the performance of the end-to-end rate versus the number of MUs for a single relay system. The corresponding curves at SNR= 10 dB are shown in Fig. 2.4. It can be seen that OptSol always yields the best performance, while a significant gain over EP-ECarr and EP-RndCarr is observed when the number of the users increases. This is basically due to two facts: i) the performance loss without optimization will become significant; ii) no multi-user diversity is exploited. 36
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 and 36: 2.2 System Model where h m,k denote
Page 37 and 38: 2.3 Resource Allocation Schemes opt
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: 2.4 Generalization to Multiple Rela
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
Page 87 and 88: 4.4 Optimization under Orthogonal T
Page 89 and 90: 4.4 Optimization under Orthogonal T
Page 91 and 92: 4.5 Simulations Then, the over all
Page 93 and 94: 4.5 Simulations 40 30 20 Sum−ρ S
Page 95 and 96: 4.6 Summary 0.9 0.8 0.7 JPSC Pow EP
Page 97 and 98: Chapter 5 Lifetime Maximization in
Page 99 and 100: 5.1 Introduction Figure 5.2: Linear
Page 101 and 102:
5.2 System Model antenna that canno
Page 103 and 104:
5.4 Lifetime Maximization Scheme 5.
Page 105 and 106:
5.4 Lifetime Maximization Scheme wh
Page 107 and 108:
5.5 Simulation Results 150 OPT−SO
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
show all

Resource Allocation in OFDM Based Wireless Relay Networks ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?