The design of a detection system in which sensors are randomly located to detect a low-power signal emitter in a random location tends to be difficult because the measurements are conditionally dependent in general and the alternative hypothesis is composite. It is shown that there are conditions that allow a system designer to deal with these problems by assuming a least favorable distribution for the emitter location that not only makes the alternative hypothesis simple and ensures a detection performance, but also causes the measurements to become conditionally i.i.d., making models more amenable for analysis. Since a design based on a least favorable distribution may be considered too conservative, this paper proposes the use of a most favorable distribution for the emitter location and uses the theory of asymptotic relative efficiency (ARE) to evaluate how conservative the design based on a least favorable distribution is. It is further shown that, if the system designer can place sensors in an enlarged deployment region, then there are situations in which the design based on a least favorable distribution becomes less and less conservative as the dimensions of the region of interest increase.

Wireless sensor networks are considered in which sensors convey binary decisions over fading channels to a common fusion center. The fusion center first takes each received signal and makes an estimate of the transmitted bit. The average of the estimated bits is compared to a threshold to make a global decision. Exponential error bounds are derived that allow one to trade off signal-to-noise ratio versus the number of sensors to achieve desired average error levels. An attractive feature of the bounds is that they do not require exact knowledge of the wireless channel statistics; approximations are sufficient.

The problem of choosing among candidate wireless sensor networks (WSNs) that send data to a fusion center to detect a binary phenomenon in nature is considered. Viewing the system as a communication channel in which nature is the transmitter and the fusion center is the receiver, it is intuitive to prefer the system that provides the highest mutual information between the phenomenon and the received signal at the fusion center. This paper reviews existing literature on this criterion and provides complementary results showing that, under a Bayesian framework, a WSN that provides equal or higher mutual information than other WSNs results in equal or better detection performance only in very restrictive settings. This paper also presents a bound on the detection performance of a WSN having the highest mutual information, and it is shown that the bound becomes tight as the mutual information approaches its maximum. Similar conclusions are obtained in the Neyman-Pearson framework.

This is a paper on modulation theory that addresses joint analog precoder and equalizer design for multichannel data transmission over the frequency-selective additive Gaussian noise (AGN) channel. The design goal is to maximize mutual information rate, minimize the mean square error, or minimize the bit error rate subject to a transmit power constraint. We assume a continuous channel model with precoder transmissions for m subchannels that lie in an n-dimensional linear subspace of L2(R). m and n are design parameters. We first design the subspace according to the channel characteristics, and then design the precoders as functions in this subspace. After the design of the optimal precoder and equalizer, we explore the geometry of these designs. We show that all of these precoder and equalizer designs are, in fact, decompositions of a virtual two- channel problem into a system of canonical coordinates, wherein variables in the canonical message channel are correlated only pairwise with corresponding variables in the canonical measurement channel. This finding clarifies the geometry of precoder and equalizer designs and illustrates that they decompose the two-channel communication problem into what might be called the Shannon channel.

In wireless communication systems, it is well known that the moments of the instantaneous signal-to-noise ratio (SNR) determine various performance measures. In the case of the IEEE 802.15.3a ultra-wideband (UWB) channel model, these performance measures have usually been estimated via simulation. However, there has recently been considerable progress in the theoretical analysis of this model by treating it as a two-dimensional Poisson cluster process. This theoretical framework is exploited in this paper to obtain formulas for the characteristic function of the SNR for both maximum-likelihood receivers and maximal ratio combining receivers. It is shown that several performance measures can be computed either in closed form or numerically. Closed-form expressions for the average SNR, amount of fading (AF), and higher-order statistics of the SNR are derived, and the outage probability is computed numerically without simulation.

When multipath arrival times and gains are specified by the IEEE 802.15.3a ultra-wideband (UWB) channel model, formulas are derived for the characteristic function of the sum of gains arriving in a given time window. These formulas are first used to determine structural properties of the corresponding distributions and densities. The formulas are then used to compute the distribution and density functions by numerically inverting the characteristic function. For small time windows, the densities of the path-gain sums are bimodal and therefore highly non-Gaussian

A recent study shows that the existing first-order canonical timing model is not sufficient to represent the dependency of the gate/wire delay on the processing and operational variations when these variations become more and more significant. Due to nonlinear mapping from variation sources to the gate/wire delay, the distribution of the delay will no longer be Gaussian even if variation sources are normally distributed. A novel “quadratic timing model” is proposed to capture the nonlinearity of the dependency of gate/wire delays and arrival times on the variation sources. Systematic methodology is also developed to evaluate the correlation and distribution of the quadratic timing model. Based on these, a statistical static timing analysis algorithm that retains the complete correlation information during timing analysis and has linear computation complexity with respect to both the circuit size and the number of variation sources is proposed. Tested on the ISCAS circuits, the proposed algorithm shows significant accuracy improvement over the existing first-order algorithm with a small amount of computational cost.

Recent study shows that the existing first order canonical timing model is not sufficient to represent the dependency of the gate delay on the variation sources when processing and operational variations become more and more significant. Due to the nonlinearity of the mapping from variation sources to the gate/wire delay, the distribution of the delay is no longer Gaussian even if the variation sources are normally distributed. Anovelquadratic timing model is proposed to capture the non-linearity of the dependency of gate/wire delays and arrival times on the variation sources. Systematic methodology is also developed to evaluate the correlation and distribution of the quadratic timing model. Based on these, a novel statistical timing analysis algorithm is propose which retains the complete correlation information during timing analysis and has the same computation complexity as the algorithm based on the canonical timing model. Tested on the ISCAS circuits, the proposed algorithm shows 10 × accuracy improvement over the existing first order algorithm while no significant extra runtime is needed.

It is frequently claimed in the literature that long-range dependence has equivalent formulations in the time domain and the frequency domain. Although many researchers understand that this is only "operationally true," i.e., it holds in cases of interest, many state this equivalence as a mathematical theorem. In particular, it is claimed as a theorem in the literature that if a covariance function decays like one over a fractional power of n, then the corresponding power spectral density tends to infinity at the origin. It is shown here that the power spectral density need not exist. Conversely, if the power spectral density exists and tends to infinity at the origin, it is shown here that the covariance may not have the claimed decay. To conclude, a new theorem is proved that gives sufficient conditions on the power spectral density to guarantee that a process is asymptotically second-order self-similar (ASOSS). This result is used to provide a counterexample to the claim in the literature that asymptotic second-order self-similarity implies long-range dependence

The detection of constrained subspace signals in additive infinite-dimensional interference and noise is motivated by consideration of multipath-Doppler channels subject to interference from partially overlapping frequency bands of other sources. Since the interference lies in an infinite-dimensional subspace, the standard method of projecting onto the subspace containing the signal plus interference does not yield a finite-dimensional detection problem. However, an alternative approach may be used to extract the appropriate finite-dimensional problem. Moreover, an energy constraint may be imposed on the desired signal. The generalized likelihood-ratio receiver for this problem is obtained, and expressions for its average probability of error are given.

In this paper, several methods for estimating long-range dependence parameters have been proposed. By far, the wavelet method is the most widely used. When a process is assumed to be second-order self-similar, a new method was introduced that uses the structure of the covariance function to estimate the Hurst parameter. The method was shown to be much faster and yield smaller confidence intervals than the wavelet method. The case was consider in this paper when the process is assumed to be fractional ARIMA and show that the new method still processes the aforementioned qualities.

We present a new method to estimate the Hurst parameter of the increment process in network traffic-a process that is assumed to be self-similar. The confidence intervals and biasedness are obtained for the estimates using the new method. This new method is then applied to pseudo-random data and to real traffic data. We compare the performance of the new method to that of the widely-used wavelet method, and demonstrate that the former is much faster and produces much smaller confidence intervals of the Hurst parameter estimate. We believe that the new method can be used as an on-line estimation tool for H and thus be exploited in the new TCP algorithms that exploit the known self-similar and long-range dependent nature of network traffic.

Nonparametric estimation of interaction functions for two-type pairwise interaction point processes is addressed. Such a problem is known to be challenging due to the intractable normalizing constant present in the density function. It is shown that the means of the marked interpoint distance functions embedded in the two-type pairwise interaction point process converge to the means of an inhomogeneous Poisson process. This suggests a simple and effective nonparametric estimation method. An example is presented to illustrate the efficacy of our method. Our results can be generalized to multitype point processes in a straightforward manner, although the notation is more involved.

The natural models of multi-access communication and modern radar and sonar systems involve infinite-dimensional waveform spaces. A common problem in these systems is the detection of subspace signals measured in the presence of subspace interference and broadband noise. By and large, the existing theory for such problems has been developed for finite-dimensional measurement spaces rather than the infinite-dimensional waveform spaces needed here. In this paper the log of the generalized likelihood ratio detector for the waveform problem is derived and is shown to have a certain chi-squared distribution, depending on the hypothesis.

The sufficient statistic for performing the likelihood ratio test for pairwise interaction point processes is well-known; however, the evaluation of its performance is a very difficult problem. It is shown that the distribution of the sufficient statistic can be approximated by the distribution of a Poisson-driven shot-noise random variable, which can be readily computed.

The performance of the likelihood ratio test is considered for a many-point interaction point process featuring a reduced number of isolated points. Limit theorems are proved that establish the Poissonian asymptotic distribution of the log-likelihood function for point processes with the isolated-point-penalization joint probability density function. The asymptotic distribution is used to approximate the detection probability associated with the likelihood ratio test. The approximation is compared to empirical results generated using Markov-chain Monte Carlo simulation. The reported results provide an efficient alternative method to simulation in assessing the performance of hypothesis testing for the point-process model considered.

A method that does not use numerical integration is presented for approximating the cumulative distribution of integer-valued random variables from their characteristic functions. Bounds on the approximation error are also given. The method is then used to compute photomultiplier counting distributions.

The performance of neural networks for which weights and signals are modeled by shot-noise processes is considered. Examples of such networks are optical neural networks and biological systems. We develop a theory that facilitates the computation of the average probability of error in binary-input/binary-output multistage and recurrent networks. We express the probability of error in terms of two key parameters: the computing-noise parameter and the weight-recording-noise parameter. The former is the average number of particles per clock cycle per signal and it represents noise due to the particle nature of the signal. The latter represents noise in the weight-recording process and is the average number of particles per weight. For a fixed computing-noise parameter, the probability of error decreases with the increase in the recording-noise parameter and saturates at a level limited by the computing-noise parameter. A similar behavior is observed when the role of the two parameters is interchanged. As both parameters increase, the probability of error decreases to zero exponentially fast at a rate that is determined using large deviations. We show that the performance can be optimized by a selective choice of the nonlinearity threshold levels. For recurrent networks, as the number of iterations increases, the probability of error increases initially and then saturates at a level determined by the stationary distribution of a Markov chain.

Bit-error rates are computed for an on-off keying optical communication system using avalanche photodiodes (APDs). We use a model for the APD that includes dead space and the finite response time. Dead space is the minimum distance that a newly generated carrier must travel in order to acquire sufficient energy to become capable of causing an impact ionization in the multiplication region of the APD. The detector's finite impulse response and its randomness are important for high data-rate systems. Using an exact analysis, we show that the presence of dead space enhances the performance at relatively low data rates. Using a Gaussian approximation technique with the exact mean and variance, we demonstrate that dead space degrades the performance at-high data rates since it is responsible for longer tails in the impulse response function of the APD, which in turn increases the effect of intersymbol interference.>

The random-code capacity region of a multiple-access arbitrarily varying channel subject to both state and input constraints is determined. Consideration of a simple erasure channel shows that the capacity region is not convex in general.>

Image detection under low-light-level conditions is treated as a hypothesis-testing problem in which the observations are modeled as a shot-noise process. Since computing the likelihood ratio for shot-noise processes is not feasible, the use of a one-dimensional test statistic obtained by filtering and sampling the observations is proposed. The filter is chosen to maximize a generalized signal-to-noise ratio. The likelihood ratio for the one-dimensional test statistic is evaluated numerically by inverting the corresponding characteristic function under each hypothesis.

An algorithm is developed for the design of a nonlinear, n-sensor, distributed estimation system subject to communication and computation constraints. The algorithm uses only bivariate probability distributions and yields locally optimal estimators that satisfy the required system constraints. It is shown that the algorithm is a generalization of the classical Lloyd-Max results.>

The discrete additive multiple-access arbitrarily varying channel (AVC) with two senders and one receiver is considered. Necessary and sufficient conditions are given for its deterministic-code average-probability-of-error capacity region under a state constraint to have a nonempty interior. In the case that no state constraint is present, the capacity region is characterized exactly. In the case of the noiseless mod-2 adder AVC using state constraint function l(s)=s and subject to a state constraint L less than or equal to 0.13616917, the capacity region is shown to be a 45-degree triangle whose legs have length 1-h(L), where h denotes the binary entropy function.>

A discrete multiple-access arbitrarily varying channel with two transmitters and one receiver is considered. It has recently been shown that if such a channel is symmetrizable, then the capacity region has an empty interior. It is shown that if the channel is subject to a suitable state constraint, then the capacity region can contain certain open rectangles and thereby possess a nonempty interior, even if the channel is symmetrizable. A new weak converse under a state constraint is also proved. These results are then used to establish the capacity region of the two-user adder channel under state constraint 1/2.>

A method that allows one to decide whether or not the capacity region of a multiple-access arbitrarily varying channel (AVC) has a nonempty interior is discussed. Using the method of types and an approach different from J.H. Jahn (ibid. vol.27, no.3, p.212-226, 1981) this problem is partially solved. The notion of symmetrizability for the two-user AVC as an extension of the same notion for the single-user AVC is considered. It is shown that if a multiple-access AVC is symmetrizable, then its capacity region has an empty interior. For the two-user AVC, this means that at least one (and perhaps both) users cannot reliably transmit information across the channel. More importantly, it is shown that if the channel is suitably nonsymmetrizable, then the capacity region has a nonempty interior, and both users can reliably transmit information across the channel. The proofs rely heavily on a complicated decoding rule. Conditions under which simpler multiple-message decoding techniques might suffice are therefore examined. In particular, conditions under which the universal maximal mutual information decoding rule will be effective are given.>

The work of Sohie and Maracas (ibid., vol.86, no.12, p.1616-18, Dec. 1988) concerned the representation of a decaying time function by a weighted sum of exponentials. It is shown that the problem can be solved in greater generality and in a more straightforward manner by using classical vector-space methods. The classical vector-space analysis is specialized to a particular function space containing the exponential transients.>