Introduction Model Decentralized mechanism Conclusion A Game-Theoretic Approach to Decentralized Optimal Power Allocation for Cellular Networks Shruti Sharma Ph.D. candidate, Electrical Engineering and Computer Science and Demos Teneketzis Electrical Engineering and Computer Science University of Michigan, Ann Arbor GameComm 2008, October 20, Athens, Greece Shrutivandana Sharma University of Michigan, Ann Arbor 1 / 34
Introduction Model Decentralized mechanism Conclusion Outline Introduction 1 Cellular network model 2 Power allocation problem Decentralized mechanism 3 Solution approach: Implementation theory framework A decentralized mechanism for power allocation Results Conclusion 4 Shrutivandana Sharma University of Michigan, Ann Arbor 2 / 34
Introduction Model Decentralized mechanism Conclusion Overview Set-up Power allocation in cellular uplink and downlink networks Decentralized and asymmetric information Competitive/selfish/strategic users with no prior beliefs on other users’ information or strategies Our work Design of a decentralized power allocation mechanism that, preserves private information of the users makes the users willingly participate in the mechanism is budget balanced obtains optimal centralized allocations at all Nash equilibria Shrutivandana Sharma University of Michigan, Ann Arbor 3 / 34
Introduction Model Decentralized mechanism Conclusion Literature survey Uplink power control User utility formulation: Ji, Huang (98); Famolari, Mandayam, Shah (99). Pricing (single cell): Alpcan, Basar, Srikant, Altman (02); Saraydar, Mandayam, Goodman (02). Pricing (Multi-cell networks): Saraydar, Mandayam, Goodman (01). Pricing (Interfernce Temperature Constraint): Huang, Berry, Honig. Equilibrium analysis: Do not achieve globally optimum allocation Downlink power control Common knowledge utilities: Liu, Honig, Jordan (00); Zhou, Honig, Jordan (01). Partial cooperation between base station and mobiles: Lee, Mazumdar, Shroff. Common knowledge/cooperation assumed to obtain optimum allocation Shrutivandana Sharma University of Michigan, Ann Arbor 4 / 34
Introduction Model Decentralized mechanism Conclusion Contribution Developed decentralized power allocation mechanism for cellular networks that, preserves private information of the users makes the users willingly participate in the mechanism obtains optimal centralized allocations at all Nash equilibria balances the flow of money in the system Presented a method to characterize all Nash equilibria for a given system wide objective, and a given decentralized allocation mechanism Shrutivandana Sharma University of Michigan, Ann Arbor 5 / 34
Introduction Model Decentralized mechanism Conclusion Power allocation problem The uplink model Shrutivandana Sharma University of Michigan, Ann Arbor 6 / 34
Introduction Model Decentralized mechanism Conclusion Power allocation problem The uplink model One base station (BS) Shrutivandana Sharma University of Michigan, Ann Arbor 7 / 34
Introduction Model Decentralized mechanism Conclusion Power allocation problem The uplink model One base station (BS) N mobile users Shrutivandana Sharma University of Michigan, Ann Arbor 8 / 34
Introduction Model Decentralized mechanism Conclusion Power allocation problem The uplink model One base station (BS) N mobile users Transmission power of user i : p i Shrutivandana Sharma University of Michigan, Ann Arbor 9 / 34
Introduction Model Decentralized mechanism Conclusion Power allocation problem The uplink model One base station (BS) N mobile users Transmission power of user i : p i Channel gain from i to BS: h i 0 Received power at BS: p r i = p i h i 0 Shrutivandana Sharma University of Michigan, Ann Arbor 10 / 34
Introduction Model Decentralized mechanism Conclusion Power allocation problem The uplink model One base station (BS) N mobile users Transmission power of user i : p i Channel gain from i to BS: h i 0 Received power at BS: p r i = p i h i 0 Signature codes not orthogonal Causes interference Quality of Service (QoS) depends on: ( p r 1 , . . . , p r i , . . . , p r N ) Shrutivandana Sharma University of Michigan, Ann Arbor 11 / 34
Introduction Model Decentralized mechanism Conclusion Power allocation problem The uplink model One base station (BS) N mobile users Transmission power of user i : p i Channel gain from i to BS: h i 0 Received power at BS: p r i = p i h i 0 Signature codes not orthogonal Causes interference Quality of Service (QoS) depends on: ( p r 1 , . . . , p r i , . . . , p r N ) Multi User Detector (MUD) decoders Shrutivandana Sharma University of Michigan, Ann Arbor 12 / 34
Introduction Model Decentralized mechanism Conclusion Power allocation problem The uplink model One base station (BS) N mobile users Transmission power of user i : p i Channel gain from i to BS: h i 0 Received power at BS: p r i = p i h i 0 Signature codes not orthogonal Causes interference Quality of Service (QoS) depends on: ( p r 1 , . . . , p r i , . . . , p r N ) Multi User Detector (MUD) decoders Tax paid by i : t i ( >, <, =) 0 Shrutivandana Sharma University of Michigan, Ann Arbor 13 / 34
Introduction Model Decentralized mechanism Conclusion Power allocation problem The uplink model One base station (BS) N mobile users Transmission power of user i : p i Channel gain from i to BS: h i 0 Received power at BS: p r i = p i h i 0 Signature codes not orthogonal Causes interference Quality of Service (QoS) depends on: ( p r 1 , . . . , p r i , . . . , p r N ) Multi User Detector (MUD) decoders Tax paid by i : t i ( >, <, =) 0 All users are self utility maximizers / behave strategically. Shrutivandana Sharma University of Michigan, Ann Arbor 14 / 34
Introduction Model Decentralized mechanism Conclusion Power allocation problem Information available to the users Private information of user i : Maximum transmission power of i : P max i Channel gain from i to BS: h i 0 Utility of user i : u A i ( t i , p r ) � 1 − I S i ( p r ) � = − t i + u i ( p r ) − I S i ( p r ) − tax paid + QoS received := { p r | p r i ∈ [ 0 , P max h i 0 ]; p r S i j ∈ R + , i j � = i } u i is concave in p r . (Sharma, Teneketzis (07)) Shrutivandana Sharma University of Michigan, Ann Arbor 15 / 34
Introduction Model Decentralized mechanism Conclusion Power allocation problem Information available to the users Common knowledge: Number of users N System is static Channels gains are fixed Users’ utilities are fixed Shrutivandana Sharma University of Michigan, Ann Arbor 16 / 34
Introduction Model Decentralized mechanism Conclusion Power allocation problem The centralized power allocation problem Problem ( P C ) N � u A i ( t i , p r ) max ( t , p r ) i = 1 N � s.t. t i = 0 i = 1 N � u i ( p r ) equivalently, max ( t , p r ) ∈ S U i = 1 N { ( t , p r ) | � t i = 0 , t ∈ R N , p r i ∈ [ 0 , P max where S U = ] h i 0 } i i = 1 ( P C ) obtains an allocation that is balanced in money transfers and maximizes the sum of utilities of all the users. Solution of Problem ( P C ) = Ideal allocation Shrutivandana Sharma University of Michigan, Ann Arbor 17 / 34
Introduction Model Decentralized mechanism Conclusion Power allocation problem How to obtain centralized solution Characteristics of the uplink model Decentralized information: Nobody has complete system information. Strategic users: The users are selfish. Solution approach: Implementation theory Provides guidelines for: how the users should “ communicate ” with the BS, and how “ the information communicated by the users should be used by the BS to determine allocations ” so as to induce the selfish users to communicate information that results in optimal centralized allocations. Reference: Implementation theory – Maskin (1985), Jackson (2001), Palfrey (2002), Stoenescu and Teneketzis (2005) Shrutivandana Sharma University of Michigan, Ann Arbor 18 / 34
Introduction Model Decentralized mechanism Conclusion Solution approach Game form Results The uplink problem in implementation theory framework Shrutivandana Sharma University of Michigan, Ann Arbor 19 / 34
Introduction Model Decentralized mechanism Conclusion Solution approach Game form Results The uplink problem in implementation theory framework Shrutivandana Sharma University of Michigan, Ann Arbor 20 / 34
Introduction Model Decentralized mechanism Conclusion Solution approach Game form Results The uplink problem in implementation theory framework Shrutivandana Sharma University of Michigan, Ann Arbor 21 / 34
Introduction Model Decentralized mechanism Conclusion Solution approach Game form Results The uplink problem in implementation theory framework Shrutivandana Sharma University of Michigan, Ann Arbor 22 / 34
Introduction Model Decentralized mechanism Conclusion Solution approach Game form Results The uplink problem in implementation theory framework Shrutivandana Sharma University of Michigan, Ann Arbor 23 / 34
Introduction Model Decentralized mechanism Conclusion Solution approach Game form Results The uplink problem in implementation theory framework Decentralized mechanism – Game form: ( M , f ) Shrutivandana Sharma University of Michigan, Ann Arbor 24 / 34
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