In this paper, a 60-GHz channel model that incorporates the presence of human activity, and which is an extension of the standard channel model proposed by the IEEE 802.15.3c group, is presented. In the presence of human activity, various measurement results show that the attenuation due to human blockage can be 20 dB or more, and thus is non-negligible. Various measurement results in the literature are used to determine the distribution of the shadowing attenuation caused by human blockage. A multiuser single-carrier system with a single receiver is considered, and system performance in the presence of blockage because of human activity is evaluated. Numerical results show that the 60-GHz system can incur a large degradation in bit error rate due to human blockage.

The effects of channel estimation errors on the performance of a system employing Tomlinson-Harashima precoding and the QR decomposition, operating over multiple antenna frequency-flat fading channels with decentralized receivers, is evaluated. The QR decomposition of the channel matrix is employed to arrive at an equivalent channel where successive interference cancellation at the transmitter can be used to remove the effect of the multiuser interference. However, in the case of imperfect channel estimation, it is not possible to remove the effect of the multiuser interference due to a mismatch between the precoder and the channel. Consequently, it is necessary to include the estimation error in deriving the probability of symbol error. We also provide simulations to corroborate the analytical results.

The estimation of bounded multivariate fields from 1-bit quantized and dithered noisy observations is considered. We consider two models for random sensor deployment based on regular Monte Carlo (simple random sampling) and stratified sampling. We propose linear estimators, and for both sensors deployment methods we establish exact expressions for the bias and variance of the estimates (including integrated mean-square errors). We show in particular that estimates of the field on the basis of stratified sensor locations always outperform estimates based on regular Monte Carlo sensor locations. For both estimation schemes, we also establish central limit theorems which can be used to compute the probability of events involving the estimates including confidence intervals.

We consider the estimation of the Fourier transform of continuous-time signals from a finite set N of discrete-time nonuniform observations. We introduce a class of antithetical stratified random sampling schemes and we obtain the performance of the corresponding estimates. For functions f(t) with two continuous derivatives, we show that the rate of mean square convergence is l/N5, which is considerably faster that the rate of l/N3for stratified sampling and the rate of l/N for standard Monte Carlo integration. In addition, we establish joint asymptotic normality for the real and imaginary parts of the estimate. The theoretical results are illustrated by examples for lowpass and highpass signals.

For delay-tolerant data applications in a wireless system, using average throughput as a quality of service (QoS) measure results in more efficient resources allocation strategies compared to using instantaneous signal to interference and noise ratio (SINR). By adapting both power and rate in a multiuser multi-antenna system based on the channel conditions, the overall power consumption can be greatly reduced. In this paper, we establish a general framework for optimal power and rate allocation when there is an average throughput constraint for each user. A key feature of the framework is that it allows consideration and evaluation of a wide range of practical receiver structures. The structural results show that the range of optimal rate and power allocation policy can be specified by a set of optimization problems over vectors, one for each fading state. The rate constraints are taken care by a rate weight vector μ, which can be tracked by a stochastic approximation algorithm. The performances of different receiver structures are compared numerically.

In this paper, we design jointly optimum transmitter and receiver beamforming structures in correlated MIMO Rayleigh fading channels with noisy channel estimates, and evaluate their performance through a closed-form expression for the probability of error. At the receiver, an estimate of the channel is obtained based on the transmitted pilot symbols. The knowledge of the estimate is then made available to the transmitter through a feedback channel. It is assumed that spatial correlation exists, either at the transmitter or at the receiver. A new exact closed-form expression for the probability of error is derived and the joint effects of diversity order and channel estimation accuracy on system performance are analyzed.

Motivated by applications in sensor networks and communications, we consider multivariate signal parameter estimation when only dithered 1-bit quantized samples are available. The observation noise is taken to be a stationary, strongly mixing process, which covers a wide range of processes including autoregressive moving average (ARMA) models. The noise is allowed to be Gaussian or to have a heavy-tail (with possibly infinite variance). An estimate of the signal parameters is proposed and is shown to be weakly consistent. Joint asymptotic normality of the parameters estimate is also established and the asymptotic mean and covariance matrices are identified.

The performance of a pre-Bell Laboratories Layered Space-Time Architecture (BLAST)-decision feedback equalization (DFE) technique with Tomlinson-Harashima precoding and decentralized receivers, operating over multiple-input single-output (MISO) frequency-selective fading channels, is evaluated. First, we derive the probability of symbol error for Tomlinson-Harashima precoding operating over single-input single-output channels with intersymbol interference. We then generalize this result to MISO frequency-selective fading channels with decentralized receivers by using the QR decomposition technique. The effect of optimal ordering of the decentralized receivers, which minimizes the total transmit energy, is investigated. We obtain a closed-form expression for the probability density function of the squared diagonal elements of the upper right triangular matrix belonging to the optimal QR decomposition when two transmit antennas and two receivers are used. We also provide simulations to corroborate the analytical results.

The performance of multicode direct-sequence spread-spectrum multiple-input multiple-output (MIMO) systems in the presence of frequency-selective fading is evaluated. We derive the asymptotic distribution of the multiple-antenna interference when the processing gain is sufficiently large. The probability of error is derived for the conventional RAKE receiver, and its performance is compared for various system configurations. We consider system tradeoffs for both fixed rate and fixed diversity. For a fixed total data rate, we demonstrate the advantage of decreasing the number of transmit antennas while increasing the number of codes, and for a fixed total diversity order, we demonstrate the advantage of decreasing the number of RAKE taps while increasing the number of receive antennas.

The focus of this paper is on the performance of orthogonal frequency division multiplexing (OFDM) signals in mobile radio applications, such as 802.11a and digital video broadcasting (DVB) systems, e.g., DVB-CS2. The paper considers the evaluation of the error probability of an OFDM system transmitting over channels characterized by frequency selectivity and Rayleigh fading. The time variations of the channel during one OFDM symbol interval destroy the orthogonality of the different subcarriers and generate power leakage among the subcarriers, known as inter-carrier interference (ICI). For conventional modulation methods such as phase-shift keying (PSK) and quadrature-amplitude modulation (QAM), the bivariate probability density function (pdf) of the ICI is shown to be a weighted Gaussian mixture. The large computational complexity involved in using the weighted Gaussian mixture pdf to evaluate the error probability serves as the motivation for developing a two-dimensional Gram-Charlier representation for the bivariate pdf of the ICI. It is demonstrated that its truncated version of order 4 or 6 provides a very good approximation in the evaluation of the error probability for PSK and QAM in the presence of ICI. Based on Jakes' model for the Doppler effects, and an exponential multipath intensity profile, numerical results for the error probability are illustrated for several mobile speeds.

We consider the problem of interference suppression in a multipath DS-CDMA downlink using a general RAKE receiver structure with M fingers and arbitrary finger delays. Utilizing asymptotically optimal sampling design theory, a new design approach that optimizes the receiver performance over the finger delays is proposed. It provides a set of delays which are asymptotically optimal for large M, and sheds light on the behavior of various finger placements' performance, as the number of fingers increases, and on the effect of the smoothness of the underlying chip pulse. Numerical results show that for certain Rayleigh fading channels and several chip pulses, the proposed finger placement is superior to the chip periodically-spaced finger placement.

The ability of impulse radio to resolve a large number of multipaths in a dense frequency selective channel suggests only a marginal improvement in performance by the use of multiple antennas from a diversity perspective. Furthermore, the small size of UWB receivers for in-home or sensor networking would result in a very high correlation among antenna elements, reducing even more the exploitable diversity. Therefore, we concentrate on the use of multiple antennas for interference suppression. Specifically, we investigate the performance of a quadrature receiver for impulse radio systems with multiple receive antennas and minimum-mean-square-error beamforming to combat interference

We derive the precise asymptote of the pairwise error probability for high signal-to-noise ratio (SNR) and apply it to obtain new results concerning transmit beamforming and selective Rake receivers. For downlink beamforming (with N transmit antennas and independently identically distributed (i.i.d.) Rayleigh fading) based on quantized feedback from the mobile, we show that at least /spl lceil/log/sub 2/(N)/spl rceil/ bits of feedback (per coherence time) is required to obtain full diversity, and among all beamforming schemes using /spl lceil/log/sub 2/(N)/spl rceil/ bits of feedback, selection diversity is optimal. We give the exact expression for the SNR loss of selection diversity with respect to ideal beamforming based on perfect knowledge of fading coefficients. Further, we study selective Rake receivers for independent arbitrary fading distribution and arbitrary power delay profile (PDP). In particular, we show that the SNR loss of the SRake receiver with respect to the all-Rake receiver does not depend on the PDP, and we also propose a transformation to adapt the expressions known for the symbol error probability for the case of i.i.d. Rayleigh fading to the general case.

We study the global convergence of the stochastic gradient constant modulus algorithm (CMA) in the absence of channel noise as well as in the presence of channel noise. The case of fractionally spaced equalizer and/or multiple antenna at the receiver is considered. For the noiseless case, we show that with proper initialization, and with small step size, the algorithm converges to a zero-forcing filter with probability close to one. In the presence of channel noise such as additive Gaussian noise, we prove that the algorithm diverges almost surely on the infinite-time horizon. However, under suitable conditions, the algorithm visits a small neighborhood of the Wiener filters a large number of times before ultimately diverging.

We consider the estimation of the multivariate probability density function f(x/sub 1/,...,x/sub p/) of X/sub 1/,...,X/sub p/ of a stationary positively or negatively associated (PA or NA) random process {X/sub i/}/sub i=1//sup /spl infin// from noisy observations. Both ordinary smooth and super smooth noise are considered. Quadratic mean and asymptotic normality results are established.

For the least mean square (LMS) algorithm, we analyze the correlation matrix of the filter coefficient estimation error and the signal estimation error in the transient phase as well as in steady state. We establish the convergence of the second-order statistics as the number of iterations increases, and we derive the exact asymptotic expressions for the mean square errors. In particular, the result for the excess signal estimation error gives conditions under which the LMS algorithm outperforms the Wiener filter with the same number of taps. We also analyze a new measure of transient speed. We do not assume a linear regression model: the desired signal and the data process are allowed to be nonlinearly related. The data is assumed to be an instantaneous transformation of a stationary Markov process satisfying certain ergodic conditions.

We consider the nonparametric estimation of multivariate regression functions and their derivatives for a regression model with long-range dependent errors. We adopt a local linear fitting approach and establish strong consistency and rates for the estimators of the regression function and its derivatives. The rates of convergence depend on the amount of smoothing relative to the strength of the long-range dependence (LRD) resulting in distinct rates for small and large bandwidths. Moreover, the conditions determining this dichotomy are different for the estimates of the regression function than for the estimates of its derivatives.

We consider the problem of optimal FIR linear and regression filters for jointly stationary symmetric alpha stable processes with index alpha greater than one. We then consider the signed-error and sign-sign adaptive filtering algorithms and provide various convergence results for the signal and tap weights estimation errors.

Let (Y,X)={Y(t),X(t),-/spl infin/<t</spl infin/} be real-valued continuous-time jointly stationary processes and let (t/sub j/) be a renewal point processes on (0,/spl infin/), with a finite mean rate, independent of (Y,X). We consider the estimation of regression function r(x/sub 0/, x/sub 1/,...,x/sub m-1/; /spl tau//sub 1/,...,/spl tau//sub m/) of /spl psi/(Y(/spl tau//sub m/)) given (X(0)=x/sub 0/, X(/spl tau//sub 1/)=x/sub 1/,...,X(/spl tau//sub m-1/)=/sub x-1/) for arbitrary lags 0</spl tau//sub 1/<...< /spl tau//sub m/ on the basis of the discrete-time observations {Y(t/sub j/),X(t/sub j/),t/sub j/)/sub j=1//sup n/. We estimate the regression function and all its partial derivatives up to a total order p/spl ges/1 using high-order local polynomial fitting. We establish the weak consistency of such estimates along with rates of convergence. We also establish the joint asymptotic normality of the estimates for the regression function and all its partial derivatives up to a total order p/spl ges/1 and provide explicit expressions for the bias and covariance matrix (of the asymptotically normal distribution).

We consider the problem of one-step-ahead prediction of a real-valued, stationary, strongly mixing random process (Xi)/sub i=-/spl infin///sup /spl infin//. The best mean-square predictor of X/sub 0/ is its conditional mean given the entire infinite past (X/sub i/)/sub i=-/spl infin///sup -1/. Given a sequence of observations X/sub 1/, X/sub 2/, X/sub N/, we propose estimators for the conditional mean based on sequences of parametric models of increasing memory and of increasing dimension, for example, neural networks and Legendre polynomials. The proposed estimators select both the model memory and the model dimension, in a data-driven fashion, by minimizing certain complexity regularized least squares criteria. When the underlying predictor function has a finite memory, we establish that the proposed estimators are memory-universal: the proposed estimators, which do not know the true memory, deliver the same statistical performance (rates of integrated mean-squared error) as that delivered by estimators that know the true memory. Furthermore, when the underlying predictor function does not have a finite memory, we establish that the estimator based on Legendre polynomials is consistent.

We consider the interpolation and prediction of continuous-time second-order random processes from a finite number of randomly sampled observations using Lagrange polynomial estimators. The sampling process (t/sub 1/) is a general stationary point process on the real line. We establish upper bounds on the mean-square interpolation and prediction errors and determine their dependence on the mean sampling rate /spl beta/ and on the number of samples used. Comparisons with the Wiener-Hopf estimator are given.

Given N i.i.d. observations {Xi}Ni=1 taking values in a compact subset of Rd, such that p* denotes their common probability density function, we estimate p* from an exponential family of densities based on single hidden layer sigmoidal networks using a certain minimum complexity density estimation scheme. Assuming that p* possesses a certain exponential representation, we establish a rate of convergence, independent of the dimension d, for the expected Hellinger distance between the proposed minimum complexity density estimator and the true underlying density p*.

The minimum complexity regression estimation framework (Barron, 1991; Barron and Cover, 1991 and Rissanen, 1989) is a general data-driven methodology for estimating a regression function from a given list of parametric models using independent and identically distributed (i.i.d.) observations. We extend Barron's regression estimation framework to m-dependent observations and to strongly mixing observations. In particular, we propose abstract minimum complexity regression estimators for dependent observations, which may be adapted to a particular list of parametric models, and establish upper bounds on the statistical risks of the proposed estimators in terms of certain deterministic indices of resolvability. Assuming that the regression function satisfies a certain Fourier-transform-type representation, we examine minimum complexity regression estimators adapted to a list of parametric models based on neural networks and by using the upper bounds for the abstract estimators, we establish rates of convergence for the statistical risks of these estimators. Also, as a key tool, we extend the classical Bernstein inequality from i.i.d. random variables to m-dependent processes and to strongly mixing processes.

We consider the problem of intercepting a direct sequence spread spectrum waveform which is embedded in both narrowband interference and additive white Gaussian noise. The receiver we analyze is a broadband radiometer which has been enhanced in the following manner. Prior to entering the square-law device in the radiometer, the received waveform is passed through a transform domain processor which serves as a notch filter to null out the narrowband interference before it can contribute unwanted energy to the output of the radiometer. A central-limit theorem is established for the receiver's output which forms the basis for analyzing the performance of the receiver. For various combinations of system parameters, numerical results are presented in the form of receiver operating characteristics.>

We consider the convergence analysis of the sign algorithm for adaptive filtering when the input processes are uncorrelated and Gaussian and a fixed step size /spl mu/>0 is used. Exact recursive equations for the covariance matrix of the deviation error are established for any step size /spl mu/>0. Asymptotic time-averaged convergence for the mean-absolute deviation error, mean-square deviation error, and for the signal mean-square estimation error are established. These results are shown to hold for arbitrary step size /spl mu/>0.>

The multiresolution decomposition of deterministic and random signals and the resulting approximation at increasingly finer resolution is examined. Specifically, an nth-order expansion is developed for the error in the wavelet approximation at resolution 2/sup -l/ of deterministic and random signals. The deterministic signals are assumed to have n continuous derivatives, while the random signals are only assumed to have a correlation function with continuous nth-order derivatives off the diagonal-a very mild assumption. For deterministic signals square integrable over the entire real line, for stationary random signals over finite intervals, and for nonstationary random signals with finite mean energy over the entire real line, the smoothness of the scale function can be matched with the signal smoothness to substantially improve the quality of the approximation. In sharp contrast, this is feasible only in special cases for nonstationary random signals over finite intervals and for deterministic signals which are only locally square integrable.>

Design and performance analyses of a fast frequency-hopped (FFH) spread spectrum communication system employing differential binary phase shift keying (DBPSK) modulation and differentially coherent demodulation are presented. The receiver utilizes a hop timing tracking loop to lock the hop clock. Through this tracking loop, the differentially coherent demodulation of an FFH signal is made possible. The authors present the system model of an FFH/DBPSK system. A digital, full-time early-late gate timing error estimator is investigated. The tracking loop is shown to be a Markov chain, and various performance characteristics of the tracking loop are studied.>

The purpose of the paper is to present the design and performance analysis of a fast frequency-hopped (FFH) spread spectrum communication system employing differential binary phase-shifted-keying (DBPSK) modulation and differentially coherent demodulation. The receiver utilizes a hop time tracking loop to "lock" the hop clock. The authors present an analysis of the average bit error probability of the overall system when it is operating in additive white Gaussian noise plus partial-band noise jamming. The effect of channel phase distortion is also studied.>

The wavelet transform of random processes with wide-sense stationary increments is shown to be a wide-sense stationary process whose correlation function and spectral distribution are determined. The second-order properties of the coefficients in the wavelet orthonormal series expansion of such processes is obtained. Applications to the spectral analysis and to the synthesis of fractional Brownian motion are given.>

The almost sure convergence properties of autoregressive spectral estimates from noisy observations are derived. Sharp rates of almost sure convergence are established for the estimates of the autoregressive parameters, innovation variance, and spectral density function of the signal process. The distributions of the signal and noise processes are arbitrary.>

The kernel-type estimation of the joint probability density functions of stationary random processes from noisy observations is considered. Precise asymptotic expressions and bounds on the mean-square estimation error are established, along with rates of mean-square convergence, for processes satisfying a variety of mixing conditions. The dependence of the convergence rates on the joint density of the noise process is studied.>

Flicker noise is a random process observed in a variety of contexts, including current fluctuations in metal film and semiconductor devices, loudness fluctuations in speech and music, and neurological patterns. The quadratic-mean convergence of appropriate estimates of the Allan variance for flicker noise is established when the latter is modeled as a stochastic process with stationary increments. A precise asymptotic expression of the mean-square error is given along with the rate of convergence.>

The L/sub 1/ and L/sub 2/ strong consistency of recursive kernel density estimators is established for mixing and ergodic stationary processes. Sharp rates of almost sure convergence are obtained in the L/sub 2/ case for mixing processes. In addition, the concept and properties of Hilbert space-valued mixingales are developed, and strong laws of large numbers are given.>

The convergence properties of constrained adaptive filtering algorithms are established. The constraint is in the form of a bounded set in which the filter's coefficients must lie. A recursive procedure that converges to the deterministic solution of the constrained linear mean-square estimation problem is obtained, using an appropriate contraction mapping. The recursion is used to derive the adaptive algorithm for the filter coefficients. Bounds on the mean-square error of the coefficients. Bounds on the mean-square error of the estimates of the filter coefficients and on the excess error of the input signal estimate are derived for processes that are either strong mixing or asymptotically uncorrelated. The algorithms use a moving window of size n on the data from one adaptation step to the next. However, tighter bounds can be obtained when a skipped sampling mechanism is used.>

The asymptotic performance of linear predictors of continuous-time stationary processes is studied from observations at n sampling instants on a fixed observation interval. Both optimal and simpler choices of predictor coefficients are considered, using uniform sampling as well as nonuniform sampling tailored to the statistics of the process under prediction. The focus is on stationary processes with rational spectral densities and the asymptotic performance for cases with and without a quadratic-mean derivatives is obtained. The analytical results are supplemented by numerical examples depicting small- and large-sample-size performance.>

The convergence properties of an adaptive linear mean-square estimator that uses a modified LMS algorithm are established for generally dependent processes. Bounds on the mean-square error of the estimates of the filter coefficients and on the excess error of the estimate of the signal are derived for input processes which are either strong mixing or asymptotically uncorrelated. It is shown that the mean-square deviation is bounded by a constant multiple of the adaptation step size and that the same holds for the excess error of the signal estimation. The present findings extend earlier results in the literature obtained for independent and M-dependent input data.>

In this paper, the worst-case power spectral density of a narrow-band Gaussian jammer operating in a direct sequence (DS) spread-spectrum system employing an interference-rejection filter is derived under a joint power and bandwidth constraint on the jammer. The effectiveness of the suppression filter under these conditions is examined and average probability of error results for the system's performance are presented.

A decentralized multiple access system in whichm \geq 2collided users employ a random access protocol is considered. Maximum entropy considerations are used to select the appropriate timeout distribution under various moment constraints. This analysis extends and corrects an earlier result form = 2.

Recursive estimation of the univariate probability density functionf(x)for stationary processes\{X_{j}\}is considered. Quadratic-mean convergence and asymptotic normality for density estimatorsf_{n}(x)are established for strong mixing and for asymptotically uncorrelated processes\{X_{j}\}. Recent results for nonrecursive density estimators are extended to the recursive case.

The performance of PN spread-spectrum communication systems in the presence of narrow-band interference is studied when linear interpolation filters are employed for the estimation and subsequent suppression of the interference. Closed-form analytical expressions for the system's performance are established for a broad class of interference processes. The advantages of linear interpolation filters over predictive filters with identical number of taps are examined analytically and some unexpected results are obtained. The analytical results are illustrated by examples.

Closed-form analytical expressions for the suppression of narrow-band interference in PN spread-spectrum digital communication systems are established. Exact and approximate results are presented for a broad class of interference processes.

Sampling designs for the detection of sure signals in Gaussian noise are considered. Both deterministic and random sampling schemes, using optimal and nonoptimal detectors, are presented and their performance is studied. The analytical results are supplemented by comparison of performance for small and large Sample size for some representative processes including the Gauss-Markov and Wiener processes.

For broad classes of deterministic and random sampling schemes\{t_{k}\}we establish the consistency and asymptotic expressions for the bias and covariance of discrete-time estimatesf̂_{n}(x)for the marginal probability density functionf(x)of continuous-time processesX(t). The effect of the sampling scheme and the sampling rate on the performance of the estimates is studied. The results are established for continuous-time processesX(t)satisfying various asymptotic independence-uncorrelatedness conditions.

Bounds are derived for the truncation error of the cardinal sampling expansion for a large class of band-limited deterministic and random signals. These bounds extend and improve upon the bounds available in the literature.

The reconstruction of a continuous-time signals(t)from the sign of its (deliberately) contaminated samples is considered. Sequential, generally nonlinear estimates ofs(t)are established and their performance is studied; error bounds and convergence rates are derived. The signals(t)need not be band-limited. The convergence rates obtained here are faster than those obtained previously for nonsequential estimates. The degradation in the reconstruction of the signal, due to transmission over a noisy channel, is also investigated, and bounds on the additional error are obtained.

A signal cannot in general be reconstructed from its sign, i.e., from its hard-limited version. However, by the deliberate addition of noise to samples of the signal prior to hard limiting, it is shown that the signal can be estimated consistently from its hard-limited noisy samples as the sampling rate tends to infinity. In fact, such estimates are shown to converge with probability one to the signal and to be asymptotically normal. Although the estimates are in general nonlinear, they can be made linear by a proper choice of the noise distribution. These rather unexpected results hold for all bounded and uniformly continuous signals. In addition to the hard-limiter, such results are also established for certain monotonic and nonmonotonic nonlinearities.

A nonrandom and unknown signals(t), in additive Gaussian noise with mean zero and known covariance function, is passed through a known memoryless nonlinearityf(x). The identification of the signal from the distributions or moments of the output process is considered. Arbitrary signals can be identified for monotonic and for certain odd, not necessarily monotonic, nonlinearities; these include hard limiters, quantizers, and infinite-interval windows. Arbitrary signals can be identified up to a global sign for two distinct classes of even nonlinearities; these include full-wave even\nuth-law devices and symmetric-interval windows.

The problem of reconstructing the varianceR(0)of a zero-mean stationary Gaussian process passed through a memoryless nonlinearityf(x)is considered whenfand the first two moments of the output

The problem of reconstructing the normalized covariance functionR(t)of a zero-mean stationary Gaussian process observed through a zero-memory nonlinearityf(x)is considered, when the nonlinearity and the correlation function or the second-order distribution of the output process are known. Three kinds of results are established. (i) Arbitrary covariances can be reconstructed for certain nonlinearities, including monotonicf, appropriate interval windows, and certain quite generalf. (ii) Certain covariances can be reconstructed for arbitrary nonlinearities: included here are positive covariances(\geq 0), covariances with rational spectral densities, and bandlimited covariances. (iii) Certain covariances, satisfying rather weak conditions, that can easily be checked in terms of the output correlation function, can be reconstructed for certain nonlinearities that include symmetric as well as nonsymmetricf.

A class of spectral estimates of continuous-time stationary stochastic processesX(t)from a finite number of observations\{X(t_{n})\}^{N}_{n}=ltaken at Poisson sampling instants\{t_{n}\}is considered. The asymptotic bias and covariance of the estimates are derived, and the influence of the spectral windows and the sampling rate on the performance of the estimates is discussed. The estimates are shown to be consistent under mild smoothness conditions on the spectral density. Comparison is made with a related class of spectral estimates suggested in [15] where the number of observations is {\em random}. It is shown that the periodograms of the two classes have distinct statistics.

A new concept of alias-free sampling of continuous-time processesX = \{ X(t), -\infty < t \infty \}is introduced. The new concept is shown to be distinct from the traditional concept [1]-[3]. various criteria for a given sampling scheme\{t_{n}\}to be alias-free in the new sense are developed. The relationship of the new definition to the question of estimating the spectral density function\Phi(\lambda)of the continuous-time processXfrom its samples\{X(t_{t})\}is discussed.

The problem of distortionless demodulation of a narrow-band single-sideband angle modulated signal is considered. The receiver uses a standard angle detector followed by a low-pass filter. The class of modulating signals is Zakai's class of band-limited functions and processes. It is shown that the demodulation of these baseband signals is distortionless under an appropriate boundedness constraint on the signals.

This paper presents a new estimation scheme for the spectral density function of a stationary time series from observations taken at discrete instants of time. The sampling instants are determined by a Poisson point process on the positive real line. Under weak smoothness conditions on the spectral density, asymptotic expressions for the bias and Variance are derived, and it is shown that the estimate is mean-square consistent for all positive values of the average sampling rate. The new estimate compares favorably with the classical continuous-time spectral estimates.

The analysis of the performance of a delta modulator with a Wiener process input is considered. The mean and the variance of the steady-state squared error are derived. In addition, the mean of the steady-state error of order four is calculated. It is shown that the behavior of all these moments as functions of the step size Δ and the sampling intervalTis similar: for each fixed Δ, the moments are monotonically increasing inT. More important, for each fixedT, there exists an optimal step size Δoptwhich minimizes each of these moments. It is shown that Δoptis a multiple ofT^{1/2}and that the corresponding minimum value of the moments is a multiple of eitherTor T2, depending on the order of the moment.

A classical result in signal theory is the completeness of the exponentials\{ e^{-\mu_n x} \}inL_2, the so-called Szasz's theorem. This paper generalizes Szasz's theorem by constructing broad classes of functionsg(x)such that the set of functions\{g(\mu_n x)\}is complete inL_2. Application to the problem of alias-free sampling of stochastic processes is considered.

This paper deals with the problem of recovering a band-limited process after it has been distorted by an instantaneous non-linearity and subsequently band-limited. Several uniqueness theorems for the input-output relationships are derived. In contrast with the deterministic case, no requirement that the nonlinearity be monotonic is made here. An iterative procedure for the recovery of the input is presented. Applications to two-level quantizers are considered, and a new result on the determination of a band-limited Gaussian process from its zero crossings is obtained.

This paper presents a general approach to the derivation of series expansions of second-order wide-sense stationary mean-square continuous random process valid over an infinite-time interval. The coefficients of the expansion are orthogonal and convergence is in the mean-square sense. The method of derivation is based on the integral representation of such processes. It covers both the periodic and the aperiodic cases. A constructive procedure is presented to obtain an explicit expansion for a given spectral distribution.