Low-complexity near-optimal spectrum balancing for digital subscriber lines

Lui, Raymond; Yu, Wei

doi:10.1109/icc.2005.1494679

Cited by 68 publications

(37 citation statements)

References 6 publications

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Section: Existing Workmentioning

confidence: 99%

“…Several algorithms were proposed to compute a Nash equilibrium solution (Iterative Waterfilling method (IWFA) [8], [24]) or globally optimal power allocations (dual decomposition method [6], [14], [23]). However, IWFA is known to perform poorly when the interference is strong, while the dual decomposition algorithm is only known to deliver a dual optimal solution [6], [11], [14], [23] rather than the actual optimal transmit power spectra (i.e., primal optimal solution). Moreover, the existing analysis of these algorithms is quite unsatisfactory: the convergence of IWFA to a Nash equilibrium solution is established only when channels satisfy certain restrictive diagonal dominance conditions [15], [22], [24], while the dual decomposition algorithm can fail to converge to a feasible spectrum sharing solution.…”

Section: Existing Workmentioning

confidence: 99%

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Duality Gap Estimation and Polynomial Time Approximation for Optimal Spectrum Management

Luo

Zhang

2009

IEEE Trans. Signal Process.

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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/ √ 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 -optimal solution for the continuous formulation of the spectrum management problem in polynomial time for any > 0.

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Section: Existing Workmentioning

confidence: 99%

Section: Existing Workmentioning

confidence: 99%

Duality Gap Estimation and Polynomial Time Approximation for Optimal Spectrum Management

Luo

Zhang

2009

IEEE Trans. Signal Process.

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“…The reason is the per-tone exhaustive search which still has exponential complexity in the number of users: O(B N ). In [13] [14] an iterative procedure is used to make this complexity linear. However, optimality cannot be guaranteed.…”

Section: Spectrum Management: On/off Power Loadingmentioning

confidence: 99%

Joint spectrum management and constrained partial crosstalk cancellation in a multi-user xDSL environment

et al. 2007

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“…Furthermore, they rigorously established the zero-duality gap result of Yu and Lui for the continuous formulation when the interference channels are frequency selective. The asymptotic strong zero duality result of [19,20] suggests that the Lagrangian dual decomposition approach ( [4,17,29]) may be a viable way to reach approximate optimality for finely discretized spectrum management problems. In fact, when restricted to the FDMA policy, they showed that the Lagrangian dual relaxation, combined with a linear programming scheme, could generate an -optimal solution for the continuous formulation of the spectrum management problem in polynomial time for any fixed > 0.…”

mentioning

confidence: 99%

“…From the optimization perspective, the problem solution can be formulated either as a noncooperative Nash game ( [7,28,25,18]); or as a cooperative utility maximization problem ( [3,30]). Several algorithms were proposed to compute a Nash equilibrium solution (Iterative Waterfilling method (IWFA) [7,28]); or globally optimal power allocations (Dual decomposition method ( [4,17,29]) for the cooperative game. Due to the problems nonconvex nature, these algorithms either lack global convergence or may converge to a poor spectrum sharing strategy.…”

mentioning

confidence: 99%

Competitive Communication Spectrum Economy and Equilibrium

2013

J. Oper. Res. Soc. China

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Consider a competitive "spectrum economy" in communication system where multiple users share a common frequency band and each of them, equipped with an endowed "monetary" budget, will "purchase" its own transmit power spectra (taking others as given) in maximizing its Shannon utility or pay-off function that includes the effects of interference and subjects to its budget constraint. A market equilibrium is a price spectra and a frequency power allocation that independently and simultaneously maximizes each user's utility. Furthermore, under an equilibrium the market clears, meaning that the total power demand equals the power supply for every user and every frequency. We prove that such an equilibrium always exists for a discretized version of the problem, and, under a weak-interference condition or the Frequency Division Multiple Access (FMDA) policy, the equilibrium can be computed in polynomial time.This model may lead to an efficient decentralized method for spectrum allocation management and optimization in achieving both higher social utilization and better individual satisfaction.Furthermore, we consider a trading market among individual users to exchange their endowed power spectra under a price mechanism, and show that the market price equilibrium also exists and it may lead to a more socially desired spectrum allocation.

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Low-complexity near-optimal spectrum balancing for digital subscriber lines

Cited by 68 publications

References 6 publications

Duality Gap Estimation and Polynomial Time Approximation for Optimal Spectrum Management

Duality Gap Estimation and Polynomial Time Approximation for Optimal Spectrum Management

Joint spectrum management and constrained partial crosstalk cancellation in a multi-user xDSL environment

Competitive Communication Spectrum Economy and Equilibrium

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