Robust Chebyshev FIR Equalization

Mutapcic, Almir; Kim, Seung-Jean; Boyd, Stephen

doi:10.1109/glocom.2007.582

Cited by 7 publications

(4 citation statements)

References 32 publications

(33 reference statements)

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“…Overall, the frequency response of the channel-equalizer cascade is C(ω)E(ω), and the aim is to design the equalizer E so as to make C(ω)E(ω) as similar as possible to a desired frequency response that incorporates the idea that the equalized channel should introduce little distortion. In line with [41], the desired frequency response we consider is e −iDω , the frequency response of a pure delay of D time steps. As for the cost function, a grid ω k = k 100 π, k = 0, ±1, .…”

Section: Problem Formulation In a Digital Communication System A Simentioning

confidence: 99%

Scenario Min-Max Optimization and the Risk of Empirical Costs

2015

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We consider convex optimization problems in the presence of stochastic uncertainty. The min-max sample-based solution is the solution obtained by minimizing the max of the cost functions corresponding to a finite sample of the uncertainty parameter. The empirical costs are instead the cost values that the solution incurs for the various parameter realizations that have been sampled. Our goal is to evaluate the risks associated with the empirical costs, where the risk associated with a cost is the probability that the cost is exceeded when a new realization of the uncertainty parameter is seen. This task is accomplished without resorting to uncertainty realizations other than those used in optimization. The theoretical result proved in this paper is that these risks form a random vector whose probability distribution is an ordered Dirichlet distribution, irrespective of the probability measure of the stochastic uncertainty parameter. This result provides a distribution-free characterization of the risks associated with the empirical costs that can be used in a variety of application problems.

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Section: Problem Formulation In a Digital Communication System A Simentioning

confidence: 99%

Scenario Min-Max Optimization and the Risk of Empirical Costs

2015

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“…For more recent contribution see e.g. [14] and the references therein. In the robust approach, the designer wants to be robust with respect to all the possible uncertainty instances δ ∈ ∆, where ∆ is a suitably modeled set.…”

Section: A the Equalization Problemmentioning

confidence: 98%

Empirical cost distribution: A scenario approach to the construction of probability boxes with application to channel equalization

Carè

Garatti

Campi

2014

2014 European Control Conference (ECC)

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Based on recent results on randomized min-max convex problems, we present a technique for building probability boxes that envelop the probability distribution of the costs incurred by a sample-based solution. The proposed technique is data-based in that the probability boxes are built based on the same data that are used to obtain the solution. The construction is distribution-free, and no specific assumption is made about the probability distribution of the data. For concreteness, the proposed technique is presented on a channel equalization problem where a finite-impulse response equalizer is designed to minimize distortion. The presence of uncertainty affecting the channel is described by a sample of uncertainty instances, and the equalizer is chosen according to a min-max logic over this sample. A probability box, built according to the proposed technique, characterizes the performance of this equalizer when it is applied to other uncertain channel instances than those seen in the sample.

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“…robust feedback controller synthesis, as in Campi et al (2009b), one can takex corresponding to zero control. Similarly, a suitablex can be easily determined in applications as IPMs (Interval Predictor Models), see Campi et al (2009a), and robust Chebyshev FIR equalization, see Mutapcic et al (2007). In other more general contexts, one can resort to sequential randomized algorithms, see e.g.…”

Section: New Idea Behind Fastmentioning

confidence: 99%