Cross layer design is wireless multi-hop network 歐永俊 20090611

Outline Introduction Problem formulation System Model Simulation Reference 20090611

Introduction The overall communication network is modeled by a generalized network utility maximization problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems. Vertical decomposition into functional modules such as congestion control, routing, scheduling and power control. Horizontal decomposition into distributed computation. the master problem sets the price for the resources to each subproblem, which has to decide the amount of resources to be used depending on the price. 20090611

Introduction Primal problem: Dual problem: dual decomposition the problem has a coupling constraint such that, when relaxed, the optimization problem decouples into several subproblems 20090611

Introduction Dual problem: Primal problem: dual decomposition 20090611

Problem formulation In traditional framework, each link provides a fixed coding and modulation scheme in the physical layer, and that each user’s utility is only a function of local source rate. In many practical systems, utility for each user depends on both transmission rate and signal quality A higher throughput can be obtained on a link at the expense of lower decoding reliability, which in turn lowers the end-to-end signal quality for sources traversing the link and reduces users’ utilities, thus leading to an intrinsic tradeoff between rate and reliability the Pareto optimal tradeoff curves between rate and reliability. 20090611

System Model End-to-end reliability constraint is the end-to-end error probability is the error probability of source s at link l is the code rate of source s at link l is an increasing convex function reflecting the rate-reliability trade-off is the set of links used by source s 20090611

System Model Capacity constraint is the information data rate of source s is the transmission data rate of source s at link l is the set of sources using link l is the capacity of link l We assumes 20090611

System Model maximize subject to source problems link problems : “congestion price”, the price per unit rate to use link l : “reliability price”, the price per unit reliability that the source s must pay to the network : with an interpretation of “end-to-end congestion price” on source s : with an interpretation of “aggregate reliability price” paid by sources using link l 20090611

System Model at each source s The Lagrange dual function is maximize subject to separable parallel on each link l maximize subject to The dual problem is minimize subject to 20090611

System Model Local information exchange 20090611

System Model Note that when each link can provide different reliabilities(code rates) for the incoming traffic of different sources, such as there exist two class of users (primary users and secondary users),the problem becomes a GP. By change of variables , decomposition method still applies. maximize subject to posynomials 20090611

Simulation a linear topology consisting of four links and eight users accounts for scalarization ,changes form 0 to 1 in step size 0.1 20090611

Simulation a=0 a=1 Figure 1. rate reliability trade-off among users, each source has same code rate for a link 20090611

Simulation a=0 a=1 Figure 2. rate reliability trade-off among users, each source can have different code rate for a link 20090611

Reference [1] Lee, J.-W.; Mung Chiang; Calderbank, A.R., "Price-based distributed algorithms for rate-reliability tradeoff in network utility maximization," Selected Areas in Communications, IEEE Journal on , vol.24, no.5, pp. 962-976, May 2006 [2] M. Chiang “Balancing transport and physical layer in wireless multihop networks: Jointly optimal congestion control and power control,” IEEE J. Sel. Areas Commun., vol. 23, pp. 104, Jan. 2005. [3] Mung Chiang; Low, S.H.; Calderbank, A.R.; Doyle, J.C., "Layering as Optimization Decomposition: A Mathematical Theory of Network Architectures," Proceedings of the IEEE , vol.95, no.1, pp.255-312, Jan. 2007 [4] Palomar, D.P.; Mung Chiang, "A tutorial on decomposition methods for network utility maximization," Selected Areas in Communications, IEEE Journal on , vol.24, no.8, pp.1439-1451, Aug. 2006 [5] Lee Jang-Won; Tang Ao; Huang Jianwei; Mung Chiang; Robert, A., "Reverse-Engineering MAC: A Non-Cooperative Game Model," Selected Areas in Communications, IEEE Journal on , vol.25, no.6, pp.1135-1147, August 2007 [6] Jang-Won Lee; Mung Chiang; Calderbank, A.R., "Utility-Optimal Random-Access Control," Wireless Communications, IEEE Transactions on , vol.6, no.7, pp.2741-2751, July 2007 [7] Jang-Won Lee; Chiang, M.; Calderbank, R.A., "Jointly optimal congestion and contention control based on network utility maximization," Communications Letters, IEEE , vol.10, no.3, pp. 216-218, Mar 2006 20090611