Browsing by Subject "Random fields"

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Open Access
Optimal representation of non-stationary random fields with finite numbers of samples: A linear MMSE framework
(Elsevier, 2013) Özçelikkale, A.; Özaktaş, Haldun M.
In this article we consider the representation of a finite-energy non-stationary random field with a finite number of samples. We pose the problem as an optimal sampling problem where we seek the optimal sampling interval under the mean-square error criterion, for a given number of samples. We investigate the optimum sampling rates and the resulting trade-offs between the number of samples and the representation error. In our numerical experiments, we consider a parametric non-stationary field model, the Gaussian-Schell model, and present sampling schemes for varying noise levels and for sources with varying numbers of degrees of freedom. We discuss the dependence of the optimum sampling interval on the problem parameters. We also study the sensitivity of the error to the chosen sampling interval.
Open Access
Unitary precoding and basis dependency of MMSE performance for gaussian erasure channels
(IEEE, 2014) Özçelikkale, A.; Yüksel S.; Özaktaş, Haldun M.
We consider the transmission of a Gaussian vector source over a multidimensional Gaussian channel where a random or a fixed subset of the channel outputs are erased. Within the setup where the only encoding operation allowed is a linear unitary transformation on the source, we investigate the minimum mean-square error (MMSE) performance, both in average, and also in terms of guarantees that hold with high probability as a function of the system parameters. Under the performance criterion of average MMSE, necessary conditions that should be satisfied by the optimal unitary encoders are established and explicit solutions for a class of settings are presented. For random sampling of signals that have a low number of degrees of freedom, we present MMSE bounds that hold with high probability. Our results illustrate how the spread of the eigenvalue distribution and the unitary transformation contribute to these performance guarantees. The performance of the discrete Fourier transform (DFT) is also investigated. As a benchmark, we investigate the equidistant sampling of circularly wide-sense stationary signals, and present the explicit error expression that quantifies the effects of the sampling rate and the eigenvalue distribution of the covariance matrix of the signal. These findings may be useful in understanding the geometric dependence of signal uncertainty in a stochastic process. In particular, unlike information theoretic measures such as entropy, we highlight the basis dependence of uncertainty in a signal with another perspective. The unitary encoding space restriction exhibits the most and least favorable signal bases for estimation. © 2014 IEEE.