There has been much recent interest in damped sinusoidal models, probably as a result of their relevance to magnetic resonance imaging. In [1], a model which allowed the sinusoid to decay to 0 was examined, and a Fourier coefficient estimation procedure was proposed. [2] noted that in order for any asymptotic theory to be available, the decay should not be allowed to complete, and examined the asymptotic behavior of a Fourier coefficient procedure based on this assumption, for which the asymptotic behavior ofnonlinear least squares estimators had already been derived in [3]. In this paper, we consider the problem of estimating the frequency and damping factor when the frequency is so low that only a finite number of periods appear in the data. Additionally, we consider a Fourier technique for estimating the damping factor in a noisy real exponential.

In [1], Lomb developed a nonlinear regression approach to estimating the frequency of a noisy sinusoid when the measurement times were not equispaced, and a method for correcting the times so that the resulting regression sum of squares appeared very similar to the usual periodogram. Scargle [2] suggested that the usual periodogram be discarded, and replaced by the new version, which has become known as the Lomb-Scargle periodogram. In this paper, we extend Lomb's development to include a `DC' term. We show why it is important to include this term, especially when the times are irregular or the frequency low.

Sensor networks are a branch of distributed ad hoc networks with a broad range of applications in surveillance and environment monitoring. In these networks, message exchanges are carried out in a multi-hop manner. Due to resource constraints, security professionals often use lightweight protocols, which do not provide adequate security. Even in the absence of constraints, designing a foolproof set of protocols and codes is almost impossible. This leaves the door open to the worms that take advantage of the vulnerabilities to propagate via exploiting the multi-hop message exchange mechanism. This issue has drawn the attention of security researchers recently. In this paper, we investigate the propagation pattern of information in wireless sensor networks based on an extended theory of epidemiology. We develop a geographical susceptible-infective model for this purpose and analytically derive the dynamics of information propagation. Compared with the previous models, ours is more realistic and is distinguished by two key factors that had been neglected before: 1) the proposed model does not purely rely on epidemic theory but rather binds it with geometrical and spatial constraints of real-world sensor networks and 2) it extends to also model the spread dynamics of conflicting information (e.g., a worm and its patch). We do extensive simulations to show the accuracy of our model and compare it with the previous ones. The findings show the common intuition that the infection source is the best location to start patching from, which is not necessarily right. We show that this depends on many factors, including the time it takes for the patch to be developed, worm/patch characteristics as well as the shape of the network.

The problem of estimating the period of a point process from observations that are both sparse and noisy is considered. By sparse it is meant that only a potentially small unknown subset of the process is observed. By noisy it is meant that the subset that is observed, is observed with error, or noise. Existing accurate algorithms for estimating the period require O(N2) operations where is the number of observations. By quantizing the observations we produce an estimator that requires only O(N log N) operations by use of the chirp z-transform or the fast Fourier transform. The quantization has the adverse effect of decreasing the accuracy of the estimator. This is investigated by Monte-Carlo simulation. The simulations indicate that significant computational savings are possible with negligible loss in statistical accuracy.

In many network applications, the nature of traffic is of burst type. Often, the transient response of network to such traffics is the result of a series of interdependant events whose occurrence prediction is not a trivial task. The previous efforts in IEEE 802.15.4 networks often followed top-down approaches to model those sequences of events, i.e., through making top-view models of the whole network, they tried to track the transient response of network to burst packet arrivals. The problem with such approaches was that they were unable to give station-level views of network response and were usually complex. In this paper, we propose a non-stationary analytical model for the IEEE 802.15.4 slotted CSMA/CA medium access control (MAC) protocol under burst traffic arrival assumption and without the optional acknowledgements. We develop a station-level stochastic time-domain method from which the network-level metrics are extracted. Our bottom-up approach makes finding station-level details such as delay, collision and failure distributions possible. Moreover, network-level metrics like the average packet loss or transmission success rate can be extracted from the model. Compared to the previous models, our model is proven to be of lower memory and computational complexity order and also supports contention window sizes of greater than one. We have carried out extensive and comparative simulations to show the high accuracy of our model.

We consider least squares estimators of carrier phase and amplitude from a noisy communications signal. We focus on signaling constellations that have symbols evenly distributed on the complex unit circle, i.e., M-ary phase shift keying. We show, under reasonably mild conditions on the distribution of the noise, that the least squares estimator of carrier phase is strongly consistent and asymptotically normally distributed. However, the amplitude estimator is not consistent, but converges to a positive real number that is a function of the true carrier amplitude, the noise distribution and the size of the constellation. The results of Monte Carlo simulations are provided and these corroborate the theoretical results.

Estimating the coefficients of a noisy polynomial phase signal is important in many fields including radar, biology and radio communications. One approach to estimation attempts to perform polynomial regression on the phase of the signal. This is complicated by the fact that the phase is wrapped modulo 2π and therefore must be unwrapped before the regression can be performed. A recent approach suggested by the authors is to perform the unwrapping in a least squares manner. It was shown by Monte Carlo simulation that this produces a remarkably accurate estimator. In this paper we describe the asymptotic properties of this estimator, showing that it is strongly consistent and deriving its central limit theorem. We hypothesise that the estimator produces very near maximum likelihood performance.

Broadcasting a request or challenge is a classic method of collecting local information in distributed wireless networks. Neighbor discovery is known to be a fundamental element in ad hoc and sensor networks topology formation, which takes advantage of such methods. Most of the current neighbor discovery protocols rely on a challenge or request broadcast by the discovering node called “Hello.” Hello flooding attack was specifically designed to exploit the broadcasting nature of these protocols in order to convince a large group of nodes that the sender is their neighbor by using very high transmission power. Several studies have been done to mitigate the effectiveness of the flooding threats but little effort has been made in modeling and analyzing this problem. Arguing that random channel access protocols must be inevitably employed in neighbor discovery, we propose an analytical approach for stochastic modeling of the challenge-broadcasting scenarios in networks using slotted carrier sense multiple access with collision avoidance (CSMA/CA) protocols. We model the nonstationary channel right after issuance of the request by a recursive method and then put forward an approach to find the broadcaster's approximate payoff. The model also supports the cases where the broadcaster is a malicious node with an abnormally high transmission and reception range, which is found in severe flooding attacks. We investigate the applications of the model in finding the optimal attack range for the flooding adversaries and deriving a flood-resilient medium access control (MAC) protocol design framework to increase the security of challenge-response protocols. The latter one is especially relevant to mobile networks as it provides a low-cost solution. This paper describes the detailed analysis of the proposed theoretical framework as well as the comprehensive evaluations that have been carried out via simulations.

In many areas of signal processing, the phases of complex-valued random variables are used to estimate system parameters, the magnitudes being discarded. In this paper, we consider the implications of doing this: the loss of statistical information and subsequent increase in asymptotic variance. Two particular cases, those of estimating the phase of the mean of a complex distribution, and estimating the frequency of a complex sinusoid in white noise, are considered. The estimators are motivated by estimation under von Mises distributional assumptions. The asymptotic distributional properties are obtained under general assumptions, and are tested using a small number of simulations.

It has been well known for at least twenty years that computing the maximizer of the periodogram, in order to estimate the unknown frequency in a noisy sinusoid, is problematic. In particular, because the periodogram is highly nonlinear, a grid size of order o (T-1) is needed to find the maximizer reliably, where T is the sample size, and that Newton's method may fail to find the zero of the first derivative of the periodogram closest to the maximizer of the periodogram calculated, for example, using the FFT. In this paper, we show that Newton's method does, in fact, work if it is applied to an appropriately chosen monotonic function of the periodogram.

The latticeAn*is an important lattice because of its covering properties in low dimensions. Clarkson described an algorithm to compute the nearest lattice point inAn*that requiresO(nlogn) arithmetic operations. In this correspondence, we describe a new algorithm. While the complexity is stillO(nlogn), it is significantly simpler to describe and verify. In practice, we find that the new algorithm also runs faster.

The maximizer of the periodogram of a sinusoid in additive noise is known to have optimal asymptotic properties even when the noise is neither Gaussian nor white. The effect of tapering or windowing on the accuracy of the estimator does not appear to have been considered previously. In this paper, we present the asymptotic theory for the maximizer of windowed periodograms of Hamming and Hanning-type. We also introduce and analyse two closed-form frequency estimators constructed from three Fourier coefficients of a Hanning-tapered process

In low signal to noise regimes long time sequences are generally needed to estimate and track the frequency of a sinusoid accurately. In this paper, we propose and analyse techniques which use only the complex Fourier coefficients from fixed length time samples. The tracking technique is constructed under Markovian assumptions on the true frequency. The techniques are illustrated with Markovian and Doppler examples.>