156 research outputs found
Game theoretic aspects of distributed spectral coordination with application to DSL networks
In this paper we use game theoretic techniques to study the value of
cooperation in distributed spectrum management problems. We show that the
celebrated iterative water-filling algorithm is subject to the prisoner's
dilemma and therefore can lead to severe degradation of the achievable rate
region in an interference channel environment. We also provide thorough
analysis of a simple two bands near-far situation where we are able to provide
closed form tight bounds on the rate region of both fixed margin iterative
water filling (FM-IWF) and dynamic frequency division multiplexing (DFDM)
methods. This is the only case where such analytic expressions are known and
all previous studies included only simulated results of the rate region. We
then propose an alternative algorithm that alleviates some of the drawbacks of
the IWF algorithm in near-far scenarios relevant to DSL access networks. We
also provide experimental analysis based on measured DSL channels of both
algorithms as well as the centralized optimum spectrum management
Finite sample performance of linear least squares estimators under sub-Gaussian martingale difference noise
Linear Least Squares is a very well known technique for parameter estimation,
which is used even when sub-optimal, because of its very low computational
requirements and the fact that exact knowledge of the noise statistics is not
required. Surprisingly, bounding the probability of large errors with finitely
many samples has been left open, especially when dealing with correlated noise
with unknown covariance. In this paper we analyze the finite sample performance
of the linear least squares estimator under sub-Gaussian martingale difference
noise. In order to analyze this important question we used concentration of
measure bounds. When applying these bounds we obtained tight bounds on the tail
of the estimator's distribution. We show the fast exponential convergence of
the number of samples required to ensure a given accuracy with high
probability. We provide probability tail bounds on the estimation error's norm.
Our analysis method is simple and uses simple type bounds on the
estimation error. The tightness of the bounds is tested through simulation. The
proposed bounds make it possible to predict the number of samples required for
least squares estimation even when least squares is sub-optimal and used for
computational simplicity. The finite sample analysis of least squares models
with this general noise model is novel
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