Duality Gap Estimation and Polynomial Time Approximation for Optimal Spectrum Management
Consider a communication system whereby multiple users share a common frequency band and must choose their transmit power spectra jointly in response to physical channel conditions including the effects of interference. The goal of the users is to maximize a system-wide utility function (e.g., weigh...
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| Veröffentlicht in: | IEEE transactions on signal processing 2009-07, Vol.57 (7), p.2675-2689 |
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| creator | LUO, Zhi-Quan SHUZHONG ZHANG |
| description | Consider a communication system whereby multiple users share a common frequency band and must choose their transmit power spectra jointly in response to physical channel conditions including the effects of interference. The goal of the users is to maximize a system-wide utility function (e.g., weighted sum-rate of all users), subject to individual power constraints. A popular approach to solve the discretized version of this nonconvex problem is by Lagrangian dual relaxation. Unfortunately the discretized spectrum management problem is NP-hard and its Lagrangian dual is in general not equivalent to the primal formulation due to a positive duality gap. In this paper, we use a convexity result of Lyapunov to estimate the size of duality gap for the discretized spectrum management problem and show that the duality gap vanishes asymptotically at the rate O (1/radic N ), where N is the size of the uniform discretization of the shared spectrum. If the channels are frequency flat, the duality gap estimate improves to O (1/ N ) . Moreover, when restricted to the FDMA spectrum sharing strategies, we show that the Lagrangian dual relaxation, combined with a linear programming scheme, can generate an epsiv -optimal solution for the continuous formulation of the spectrum management problem in polynomial time for any epsiv > 0 . |
| doi_str_mv | 10.1109/TSP.2009.2016871 |
| format | Article |
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The goal of the users is to maximize a system-wide utility function (e.g., weighted sum-rate of all users), subject to individual power constraints. A popular approach to solve the discretized version of this nonconvex problem is by Lagrangian dual relaxation. Unfortunately the discretized spectrum management problem is NP-hard and its Lagrangian dual is in general not equivalent to the primal formulation due to a positive duality gap. In this paper, we use a convexity result of Lyapunov to estimate the size of duality gap for the discretized spectrum management problem and show that the duality gap vanishes asymptotically at the rate O (1/radic N ), where N is the size of the uniform discretization of the shared spectrum. If the channels are frequency flat, the duality gap estimate improves to O (1/ N ) . 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The goal of the users is to maximize a system-wide utility function (e.g., weighted sum-rate of all users), subject to individual power constraints. A popular approach to solve the discretized version of this nonconvex problem is by Lagrangian dual relaxation. Unfortunately the discretized spectrum management problem is NP-hard and its Lagrangian dual is in general not equivalent to the primal formulation due to a positive duality gap. In this paper, we use a convexity result of Lyapunov to estimate the size of duality gap for the discretized spectrum management problem and show that the duality gap vanishes asymptotically at the rate O (1/radic N ), where N is the size of the uniform discretization of the shared spectrum. If the channels are frequency flat, the duality gap estimate improves to O (1/ N ) . 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The goal of the users is to maximize a system-wide utility function (e.g., weighted sum-rate of all users), subject to individual power constraints. A popular approach to solve the discretized version of this nonconvex problem is by Lagrangian dual relaxation. Unfortunately the discretized spectrum management problem is NP-hard and its Lagrangian dual is in general not equivalent to the primal formulation due to a positive duality gap. In this paper, we use a convexity result of Lyapunov to estimate the size of duality gap for the discretized spectrum management problem and show that the duality gap vanishes asymptotically at the rate O (1/radic N ), where N is the size of the uniform discretization of the shared spectrum. If the channels are frequency flat, the duality gap estimate improves to O (1/ N ) . 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| subjects | Algorithms Applied sciences Asymptotic properties Channels Cognitive radio Communication systems complexity Crosstalk Discretization DSL duality epsilon -approximation Estimates Exact sciences and technology Formulations Frequency domain analysis Frequency estimation Information, signal and communications theory Interference Lagrangian functions Management Mathematical analysis Miscellaneous Operations research Polynomials Radio spectrum management Signal processing spectrum management Studies sum-rate maximization System performance Telecommunications and information theory |
| title | Duality Gap Estimation and Polynomial Time Approximation for Optimal Spectrum Management |
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