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This paper investigates the optimization of margins in digital subscriber lines employing level-2 dynamic spectrum management, where lines are jointly optimized with an emphasis on their stability, throughput-guarantee, and politeness. A new definition of noise margin and the concept of probability of outage are introduced, which allow for an easier formulation of the problems of joint margin and spectra optimization of the lines taking into account their stabilities. The solutions to the highly-coupled optimization problems are simplified using noise margins instead of signal-to-interference-and-noise-ratio margins.
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