A general family of tracking algorithms for linear regression models is studied. It includes the familiar LMS (gradient approach), RLS (recursive least squares) and KF (Kalman filter) based estimators. The exact expressions for the quality of the obtained estimates are complicated. Approximate, and easy-to-use, expressions for the covariance matrix of the parameter tracking error are developed. These are applicable over whole time interval, including the transient and the approximation error can be explicitly calculated. I. Introduction Tracking is the key factor in adaptive algorithms of all kinds. We shall in this contribution study the special case where the underlying model is a linear regression, i.e., the observations are related by y k = ' ø k ` k + v k ; k 0: (1) Here y k is an observation made at time k, and ' k is a d- dimensional vector, that is known at time k, v k represents a disturbance and the parameter vector ` k describes how the components of ' k relate to the ...

. In a recent work [7], some general results on exponential stability of random linear equations are established, which can be appled directly to the performance analysis of a wide class of adaptive algorithms including the basic LMS ones, without requiring stationarity, independency and boundedness assumptions of the system signals. The main purpose of this paper is to provide further results on exponential stability of the LMS algorithms, in particular, to Supported by the National Natural Science Foundation of China y Supported by the Swedish Research Council for Engineering Sciences (TFR) z Supported by the National Natural Science Foundation of China provide a necessary and sufficient condition for such a stability in the case of possibly unbounded and non-OE-mixing signals. The results of this paper can be applied to a fairely large class of signals including those generated from, e.g., a Gaussian process via a stable linear filter. As an application, several refined and...

Abstract — The predominate traffic patterns in a wireless sensor network are many-to-one and one-to-many communication. Hence, the performance of wireless sensor networks is characterized by the rate at which data can be disseminated from or aggregated to a data sink. In this paper, we consider the data aggregation problem. We demonstrate that a data aggregation rate of � ( log n n) is optimal and that this rate can be achieved in wireless sensor networks using a generalization of cooperative beamforming called cooperative time-reversal communication.

piecewise-linear stochastic regression model useful for modeling conditionally normal response time-series data. However, in many applications, the response variable is conditionally non-normal, e.g. Poisson or binomially distributed. We generalize the open-loop Threshold Model by introducing the Generalized Threshold Model (GTM). Specifically, it is assumed that the conditional probability distribution of the response variable belongs to the exponential family, and the conditional mean response is linked to some piecewise-linear stochastic regression function. We introduce a likelihood-based estimation scheme for the GTM, and the consistency and limiting distribution of the maximum likelihood estimator are derived. A simulation study is conducted to illustrate the asymptotic results.

overall system performance is investigated by computing the theoretic outage rates achievable over the composite radio channels induced by the different transmission strategies. In particular, the analysis points out that a convenient exploitation of the available diversity branches leads to lower outage probabilities and, consequently, to higher outage rates. Incidentally, the ergodic capacity limit for the considered diversity schemes remains equal to the single transmit antenna case. On the other hand, transmit diversity reduces the statistical dispersion of the mutual information about its mean. As a result, the optimal selection of the delay for both LDD and CDD is addressed. Nevertheless, in many cases of interest the failure probability is the same with either SD, LDD or CDD. It is also mentioned that SD and TSTD are equivalent if the propagation medium is sufficiently slow time-varying, while SD outperforms TSTD over highly time-selective radio channels.

Mean and variance of the channel mutual information for OFDM (Orthogonal frequency division multiplexing) systems areinvestigated. Ontheonehand,theergodiccapacitydoesnot dependonthechannelpowerdelayprofilebutonthesignal-tonoise ratio only. On the other hand, exact and approximated expressions for the variance of the mutual information emphasize the key role played by multipath (frequency) diversity on the second-order statistical characterization of the system performance limits. Finally, the suitability of a Gaussian approximation for the distribution of the channel mutual information isstudied through thecomputation ofsystem outage rates. I

Building on the work of McLeish (1977) and Withers (1981), we derive central limit theorems for double arrays of heterogeneous, near epoch dependent functions of q- and o-mixing processes. The sequences may exhibit trending moments, and we do not impose asymptotic covariance stationarity requirements. The multivariate CLT accom- modates multiple time series with elements trending at different rates. The assumptions are straightforward to verify.

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The goal of this paper is to describe the application of quasilikelihood estimating equations for spatially correlated binary data. In this paper, a logistic function is used to model the marginal probability of binary responses in terms of parameters of interest. With mild assumptions on the correlations, the Leonov–Shiryaev formula combined with a comparison of characteristic functions can be used to establish asymptotic normality for linear combinations of the binary responses. The consistency and asymptotic normality for quasilikelihood estimates can then be derived. By modeling spatial correlation with a variogram, we apply these asymptotic results to test independence of two spatially correlated binary outcomes and illustrate the concepts with a well-known example based on data from Lansing Woods. The comparison of generalized estimating equations and the proposed approach is also discussed.