1. Cross-Layer Design for Lifetime Maximization in Interference-Limited Wireless Sensor Networks Ritesh Madan, Shuguang Cui, Sanjay Lall, and Andrea Goldsmith 讲解：韩冬雪 指导教师：张瑞华副教授

2. An intial version of this paper was presented at IEEE INFOCOM in March 2005. R. Madan and A. J. Goldsmith are with the Department of Electrical Engineering, Stanford University

3. 1. 论文背景简介 2. 系统模型定义 3. 迭代的逼近算法 4. 算法结果比较 5. 总结和今后工作

4. 1. 论文背景简介 We consider the joint optimal design of the physical, medium access control (MAC), and routing layers to maximize the lifetime of energy-constrained wireless sensor networks. The focus of this paper is on the computation of optimal transmission powers, rates, and link schedule that maximize the network lifetime

5. For energy-constrained wireless networks, we can increase the network lifetime by using transmission schemes that have the following characteristics  Multihop routing  Load Balancing  Interference mitigation  Frequency reuse

6. 2. 系统模型定义 Then the network lifetime The maximum rate per unit bandwidth that can be supported over a link with the power consumption in the power amplifier circuit is given by (1+α)P.

7. 参数定义 1. G = (V,L) 有向图； A=A + -A - 2. N ： the number of time slots L n ： the set of links scheduled during time slot n

8. 3. p l n ， r l n the transmission power and rate per unit bandwidth, ver link l and slot n. 4. E v : initial amount of energy at node v. p ct, p cr :the power consumption of the transmitter and the receiver circuits at a node

9. 5. s v :the rate at which information is generated at node v. 6. :the link gain matrix of the network G lk : the power gain from the transmitter of link k to the receiver of link l.

10. We have the following constraints. 1. Flow Conservation 2. Rate Constraints 3. Energy Conservation 4. Range Constraints

11. Then, the problem of maximizing the network lifetime can be written as the following optimization problem. Variables: T net, r l n,p l n

12. q = 1/T net Variables: q,r l n,p l n

13. Optimal TDMA Schemes Variables: q, x l, n l

14. The function is convex over x,y ≥ 0, for β ≥ 0 Hence, it is easy to see that the above problem is a mixed integer-convex problem. It can be solved using branch and bound methods

15. 3. 迭代的逼近算法 TECHNICAL APPROACH FOR INTERFERENCE- LIMITED NETWORKS we allow mutually interfering links to be scheduled to transmit in the same time slot. we will use an iterative approach.During each iteration, we compute the rates and powers for a given link schedule, and then adapt the link schedule to the computed rates and powers. For a fixed link schedule (i.e. fixed L n,n = 1,...,N), we approximate the rate constraint as a convex constraint;

16. variables : q, r l n,Q l n

17. the function is convex in r n,Q n It become a general convex optimization problem.

18. Algorithm 1. Find an initial suboptimal, feasible schedule. 2. Solve problem(2) to find an optimal routing flow and transmission powers during each slot for the approximate rate constrant. If the problem is infeasible, quit. 3. Remove l from L n if where >1 is a constant close to 1 4. Find

19. Add to If the resulting schedule is one that was used in a previous iteration, quit 5. Check if ， for all l ∈ L n and n = 1,...,N is feasible. If yes, go to (2), else quit to prevent an infinite loop. there are 2 NL different link schedules ， the algorithm will terminate in at most 2 NL steps. However, since the solution computed at each step is feasible, we can terminate the algorithm as soon as we have a competitive solution.

21. 4. 算法结果比较 We will compare the performance of our algorithm with that of transmission schemes with specific scheduling at the MAC layer, outlined below 1. Uniform TDMA 2. Optimal TDMA 3. Spatially periodic time sharing ： a link schedule with T time slots ， In each time slot every Tth link is activated ， every link is activated once in every T slots. Thus if there are N links, in the first slot, links 1,T +1,2T +1,….. are activated, while in the second slot, links 2,T + 2,2T + 2,... are activated, and so on.

22. A. String Topology s 2,...,s 9 = 0 ；

24. B. Linear Topology s 1,...,s 9 = 0.1 nats/Hz/s

26. C. Rhombus Topology a) All sources on ： for s i = 0.4 nats/Hz/s,i = 1,2,3,4 b) Source 2 off: s 2 = 0,s i = 0.4nats/Hz/s,i=2,3,4

29. 5. 总结和今后工作 The algorithm computes competitive solutions that increase network lifetime for wireless networks with high bandwidth efficiency the suboptimality of the solution can be traded off with the required computational power 今后工作： 仿真， convex optimization problem 改进算法 将本算法思想扩展到更普遍的网络中

30. 谢谢！