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Distributed Power Control and Spectrum Sharing in Wireless Networks

Explore optimizing power control and spectrum sharing in wireless networks to enhance performance by handling interference. Understand interference constraints, standard interference functions, and achieve rate optimality through distributed power allocation. Look into spectrum sharing with uneven power allocation for improved rate region. Dive into non-cooperative scenarios and Gaussian interference games for competitive equilibrium. Study iterative water-filling, Nash equilibrium, and repeated games for efficient resource allocation. Examine performance optimization and cognitive radio applications.

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Distributed Power Control and Spectrum Sharing in Wireless Networks

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  1. Distributed Power Control and Spectrum Sharing in Wireless Networks ECE559VV – Fall07 Course Project Presented by Guanfeng Liang

  2. Outline • Background • Power control • Spectrum sharing • Conclusion

  3. Background • Interference is the key factor that limits the performance of wireless networks • To handle interference, can optimize by means of • Frequency allocation: • Power control: • Or, jointly - spectrum sharing: f f f

  4. Power Control • N users, M base stations, single channel, uplink • Pj - transmit power of user j • hkj - gain from user j to BS k • zk – variance of independent noise at BS k

  5. General Interference Constraints • Fixed Assignment: BS aj is assigned to user j • Minimum Power Assignment: each user is assigned to the BS that maximizes its SIR • Limited Diversity: BS’s in Kj are assigned to user j

  6. Standard Interference function • Definition: Interference function I(p)is standard if for all p≥0, the following properties are satisfied. • Positivity - I(p) ≥0 • Monotonicity - If p ≥ p’, then I(p)≥I(p’). • Scalability – For all a>1, aI(p)>I(ap). • IFA, IMPA, ILD are standard. • For standard interference functions, minimized total power can be achieved by updating p(t+1)=I(p(t)) in a distributed fashion, asynchronously. (Yates’95)

  7. Spectrum Sharing Power is uniformly allocated across bandwidth W Transmission rate is not considered What should we do if power is allowed to be allocated unevenly? Can “rate” optimality be achieved in a distributed manner?

  8. Settings • M fixed 1-to-1 user-BS assignments • Noise profile at each BS: Ni(f) • Random Gaussian codebooks – interference looks like Gaussian noise

  9. Rate Region • Rate Region • Pareto Optimal Point

  10. Optimization Problem • Global utility optimization maximization • U(R1,…,RM) reflects the fairness issue • Sum rate: Usum (R1,…,RM) = R1+…+RM • Proportional fairness: UPF (R1,…,RM) = log(R1)+…+log(RM) • In general, U is component-wise monotonically increasing => optimal allocation must occur on the boundary R*

  11. Examples

  12. Infinite Dimension • Theorem 1: Any point in the achievable rate region R can be obtained with M power allocations that are piecewise constant in the intervals [0,w1), [w1,w2),…,[w2M-1,W], for some choice of {wi}i=1.2M-1. • Theorem 2:Let (R1,…,RM) be a Pareto efficient rate vector achieved with power allocations {pi(f)}i=1,…,M. If hi,jhj,i>hi,ihj,j then pi(f)pj(f)=0 for all f [0,W].

  13. Non-Cooperative Scenarios • Non-convex capacity expression -> rate region not easy to compute • Another approach: view the interference channel as a non-cooperative game among the competing users-> competitive optimal • Assumptions: • Selfish users • user i tries to maximize Ui(Ri) -> maximize Ri

  14. Gaussian Interference Game(GIG) • Each user tries to maximize its own rate, assuming other users’ power allocation are known. • Well-known Water-filling power allocation

  15. Iterative Water-filling (Yu’02)

  16. Equilibrium • Theorem 3:Under a mild condition, the GIG has a competitive equilibrium. The equilibrium is unique, and it can be reached by iterative water-filling. • Nash Equilibrium

  17. Is the Equilibrium Optimal? • NO! • Example: • h1,1=h2,2=1, h1,2=h2,1=1/4, W=1, N1=N2=1, P1=P2=P • Water-filling -> flat power allocation: • Orthogonal power allocation

  18. Repeated Game • Utility of user i : • Decision made based on complete history • Advantage: much richer set of N.E., hence have more flexibility in obtaining a fair and efficient resource allocation

  19. Equilibriums of a Repeated Game • Fact: frequency-flat power allocations is a N.E. of the repeated game with AWGN. • Theorem 4:The rate RiFS achieved by frequency-flat power spread is the reservation utility of player i in the GIG. • Result: If the desired operating point (R1,…,RM) is component-wise greater than (R1FS,…,RMFS), there is no performance loss due to lack of cooperation. (Tse’07)

  20. Results

  21. Summary • Performance optimization of wireless networks • 1-D: power = power control • Distributed power control with constant power allocation • 2-D: power + frequency = spectrum sharing • One shot GIG – iterative water-filling • Repeated game • 3-D: power + frequency + time • Cognitive radio

  22. Thank you and Questions?

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