Browsing by Author "Singer, A. C."

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Open Access
Chapter 11 - Parametric estimation
(Academic Press, 2023-06-30) Corey, R. M.; Kozat, Süleyman Serdar; Singer, A. C.; Diniz, P. S. R.
An important engineering concept is that of modeling signals and systems in a manner that enables their study, analysis, and control. We seek models that are relatively easy to compute or estimate, yet at the same time provide insight into the salient characteristics of the signals or systems under study. One way to control the complexity of such models is through the use of parametric models. These are models that explicitly depend on a fixed number of parameters. In this chapter, we explore parametric models for signals and systems with a focus on the estimation of these model parameters under a variety of scenarios. Under statistical and deterministic formulations, we begin with models that are linear in their parameters and study both the batch and recursive formulations of these problems. We next apply these methods to problems in spectrum estimation, prediction, and filtering. Nonlinear modeling, universal methods, and order estimation are advanced topics that are also considered.
Open Access
Linear MMSE-optimal turbo equalization using context trees
(IEEE, 2013) Kim, K.; Kalantarova, N.; Kozat, S. S.; Singer, A. C.
Formulations of the turbo equalization approach to iterative equalization and decoding vary greatly when channel knowledge is either partially or completely unknown. Maximum aposteriori probability (MAP) and minimum mean-square error (MMSE) approaches leverage channel knowledge to make explicit use of soft information (priors over the transmitted data bits) in a manner that is distinctly nonlinear, appearing either in a trellis formulation (MAP) or inside an inverted matrix (MMSE). To date, nearly all adaptive turbo equalization methods either estimate the channel or use a direct adaptation equalizer in which estimates of the transmitted data are formed from an expressly linear function of the received data and soft information, with this latter formulation being most common. We study a class of direct adaptation turbo equalizers that are both adaptive and nonlinear functions of the soft information from the decoder. We introduce piecewise linear models based on context trees that can adaptively approximate the nonlinear dependence of the equalizer on the soft information such that it can choose both the partition regions as well as the locally linear equalizer coefficients in each region independently, with computational complexity that remains of the order of a traditional direct adaptive linear equalizer. This approach is guaranteed to asymptotically achieve the performance of the best piecewise linear equalizer, and we quantify the MSE performance of the resulting algorithm and the convergence of its MSE to that of the linear minimum MSE estimator as the depth of the context tree and the data length increase.
Open Access
Low Complexity Turbo Equalization: A Clustering Approach
(IEEE, 2014) Kim, K.; Choi, J. W.; Kozat, S. S.; Singer, A. C.
We introduce a low complexity approach to iterative equalization and decoding, or 'turbo equalization', which uses clustered models to better match the nonlinear relationship that exists between likelihood information from a channel decoder and the symbol estimates that arise in soft-input channel equalization. The introduced clustered turbo equalizer uses piecewise linear models to capture the nonlinear dependency of the linear minimum mean square error (MMSE) symbol estimate on the symbol likelihoods produced by the channel decoder and maintains a computational complexity that is only linear in the channel memory. By partitioning the space of likelihood information from the decoder based on either hard or soft clustering and using locally-linear adaptive equalizers within each clustered region, the performance gap between the linear MMSE turbo equalizers and low-complexity least mean square (LMS)-based linear turbo equalizers can be narrowed. © 2014 IEEE.
Open Access
Tracking the best level set in a level-crossing analog-to-digital converter
(Elsevier, 2013) Kozat, S. S.; Guan, K. M.; Singer, A. C.
In this paper, we investigate level-crossing (LC) analog-to-digital converters (ADC)s in a competitive algorithm framework. In particular, we study how the level sets of an LC ADC should be selected in order to track the dynamical changes in the analog signal for effective sampling. We introduce a sequential LC sampling algorithm asymptotically achieving the performance of the best LC sampling method which can choose both its LC sampling levels (from a large class of possible level sets) and the intervals (from the continuum of all possible intervals) that these levels are used based on observing the whole analog signal in hindsight. The results we introduce are guaranteed to hold in an individual signal manner without any stochastic assumptions on the underlying signal.