Detection Of Deterministic Signals Research Articles

Performance of XOR Rule for Decentralized Detection of Deterministic Signals in Bivariate Gaussian Noise

In this paper, we consider the performance of exclusive-OR (XOR) rule in detecting the presence or absence of a deterministic signal in bivariate Gaussian noise. Signals, when present at the two sensors, are assumed unequal, whereas the noise components have identical marginal distribution but are correlated. The sensors send their one-bit quantized data to a fusion center, which then employs the XOR rule to arrive at the final decision. Here we prove that, in the limit as the correlation coefficient <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula> approaches 1, the optimum fusion rule for both parallel and tandem topologies is XOR with identical, alternating partitions (XORAP) of the observations at the sensors. We further quantify the asymptotic decrease of the Bayes error of XORAP towards zero as a constant multiplied by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sqrt {1-r}$ </tex-math></inline-formula> , as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula> approaches 1. When compared to the asymptotic Bayes error of CLRT, which decreases to zero exponentially fast, as a function of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1/(1-r)$ </tex-math></inline-formula> , the Bayes error of XORAP decreases to zero much slower.

Optimal Precoding Design and Power Allocation for Decentralized Detection of Deterministic Signals

We consider a decentralized detection problem in a power-constrained wireless sensor networks (WSNs), in which a number of sensor nodes collaborate to detect the presence of a deterministic vector signal. The signal to be detected is assumed known \emph{a priori}. Given a constraint on the total amount of transmit power, we investigate the optimal linear precoding design for each sensor node. More specifically, in order to achieve the best detection performance, shall sensor nodes transmit their raw data to the fusion center (FC), or transmit compressed versions of their original data? The optimal power allocation among sensors is studied as well. Also, assuming a fixed total transmit power, we examine how the detection performance behaves with the number of sensors in the network. A new concept "detection outage" is proposed to quantify the reliability of the overall detection system. Finally, decentralized detection with unknown signals is studied. Numerical results are conducted to corroborate our theoretical analysis and to illustrate the performance of the proposed algorithm.

Design and performance analysis of a signal detector based on suprathreshold stochastic resonance

This paper presents the design and performance analysis of a detector based on suprathreshold stochastic resonance (SSR) for the detection of deterministic signals in heavy-tailed non-Gaussian noise. The detector consists of a matched filter preceded by an SSR system which acts as a preprocessor. The SSR system is composed of an array of 2-level quantizers with independent and identically distributed (i.i.d) noise added to the input of each quantizer. The standard deviation σ of quantizer noise is chosen to maximize the detection probability for a given false alarm probability. In the case of a weak signal, the optimum σ also minimizes the mean-square difference between the output of the quantizer array and the output of the nonlinear transformation of the locally optimum detector. The optimum σ depends only on the probability density functions (pdfs) of input noise and quantizer noise for weak signals, and also on the signal amplitude and the false alarm probability for non-weak signals. Improvement in detector performance stems primarily from quantization and to a lesser extent from the optimization of quantizer noise. For most input noise pdfs, the performance of the SSR detector is very close to that of the optimum detector.

Comment on “Stochastic analysis of recurrence plots with applications to the detection of deterministic signals” by Rohde et al. [Physica D 237 (2008) 619–629

In the recent article “Stochastic analysis of recurrence plots with applications to the detection of deterministic signals” (Physica D 237 (2008) 619–629), Rohde et al. stated that the performance of RQA in order to detect deterministic signals would be below traditional and well-known detectors. However, we have concerns about such a general statement. Based on our own studies we cannot confirm their conclusions. Our findings suggest that the measures of complexity provided by RQA are useful detectors outperforming well-known traditional detectors, in particular for the detection of signals of complex systems, with phase differences or signals modified due to the measurement process. Nevertheless, we also clearly assert that an uncritical application of RQA may lead to wrong conclusions.

A novel weak chirp typed blind watermarking detection algorithm based on wavelet and duffing oscillators

To enhance the robustness of the Chirp typed watermark,propose an algorithm based on Duffing Oscillators.First we change the Chirp signal which was embedded into the low frequency band of the host image in the wavelet domain into single frequency periodic signal,then we detect the periodic signal by the Duffing oscillators.The model of deterministic signal detection with unknown parameters is utilized to formulate the watermark detection.Experiments show that the detector perform effectively when the signal-to-noise ratio is greater than-40dB.

Stochastic analysis of recurrence plots with applications to the detection of deterministic signals

Recurrence plots have been widely used for a variety of purposes such as analyzing dynamical systems, denoising, as well as detection of deterministic signals embedded in noise. Though it has been postulated previously that recurrence plots contain time correlation information here we make the relationship between unthresholded recurrence plots and the covariance of a random process more precise. Computations using examples from harmonic processes, autoregressive models, and outputs from nonlinear systems are shown to illustrate this relationship. Finally, the use of recurrence plots for detection of deterministic signals in the presence of noise is investigated and compared to traditional signal detection methods based on the likelihood ratio test. Results using simulated data show that detectors based on certain statistics derived from recurrence plots are sub-optimal when compared to well-known detectors based on the likelihood ratio.

Bayesian Fusion Performance and System Optimization for Distributed Stochastic Gaussian Signal Detection Under Communication Constraints

The problem of decentralized detection and fusion of a Gaussian signal is considered under the assumption of analog relay-amplifier local processing. It is shown that under an average global (system) power constraint, there always exists an optimal number of nodes that achieves the best possible performance under both orthogonal and nonorthogonal sensor-to-fusion center communication. Any increase in the number of nodes beyond the optimal value leads to degraded performance. This implies that each node needs to maintain a certain minimum received power level at the fusion center in order to make a useful contribution to the final decision. This is contrasted with the monotonic performance improvement observed under individual node power constraints as well as in the case of deterministic signal detection under a global power constraint. Three communication scenarios are studied in detail: 1) orthogonal; 2) equicorrelated; and 3) random signaling waveforms. In each case, error exponents and resulting bounds for Bayesian fusion performance are derived. A sensor system optimization method based on Bhattacharya error exponent, that leads to simple rules for determining the optimal number of nodes under a global average power constraint is also proposed

On LLRT detection of deterministic signals in multiplicative noise

The LLRT detector for a known deterministic signal in the presence of multiplicative noise is studied. An interesting property of this “multiplicative” detector is discovered. For the exponential class of noise covariances, it is shown that an unrestricted increase of output SNR (detection index) can be achieved when increasing the sampling rate. Such effect does not occur in the case of LLRT detector in the presence of additive noise, where the detection index is limited by the noise correlation time.

Maximum likelihood method in the problem of adaptive detection of signals with unknown noninformative parameters

A new algorithm of signal detection is synthesized with an estimate of signal noninformative parameters against the noise background with an arbitrary distribution law. It has been shown by a simple example of Gaussian clutter that the efficiency of the synthesized detector approaches the efficiency of deterministic signal detection.

Optical preamplifier receiver for spectrum-sliced WDM

Spectrum-slicing provides a low-cost alternative to the use of multiple coherent lasers for wavelength division multiplexing (WDM) applications by utilizing spectral slices of a single broadband noise source for creating the multichannel system. In this paper we analyze the performance of both p-i-n and optical preamplifier receivers for spectrum-sliced WDM using actual noise distributions, and the results are compared with those using the Gaussian approximation. This extends prior results of Marcuse for the detection of deterministic signals in the presence of optical amplifier and receiver noise. Although the methodology is similar, the results are considerably different when the signal is itself noise-like. For the case of noise-like signals, it is shown that when an optical preamplifier receiver is used, there exists an optimum filter bandwidth which minimizes the detection sensitivity for a given error probability. Moreover the evaluated detection sensitivity, in photons/bit, represents an order of magnitude (>10 dB) improvement over conventional detection techniques that employ p-i-n receivers. The Gaussian approximation is shown to be overly conservative when dealing with small ratios of the receiver optical to electrical bandwidth, for both p-i-n and preamplifier receivers.

Estimation and detection in non-Gaussian noise using higher order statistics

One of the primary applications of higher order statistics has been for detection and estimation of nonGaussian signals in Gaussian noise of unknown covariance. This is motivated by the fact that higher order cumulants of Gaussian processes vanish. We study the opposite problem, namely, detection and estimation in nonGaussian noise. We estimate cumulants of nonGaussian processes in the presence of unknown deterministic and/or Gaussian signals, which allows either parametric or nonparametric estimation of the covariance of the nonGaussian noise. Our approach is to augment existing second-order detection methods using cumulants. We propose solutions for detection of deterministic signals based on matched filters and the generalized likelihood ratio test which incorporate cumulants, where the resulting solutions are valid under either detection hypotheses. This allows for single record detection and obviates the need for noise-only training records. The problem of estimating signal strength in the presence of nonGaussian noise of unknown covariance is also considered, and a cumulant-based solution is proposed which uses a single data record. Examples are used throughout to illustrate our proposed methods.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Approximately optimum detection of deterministic signals in Gaussian and compound Poisson noise

An approximate but explicit likelihood ratio is derived for detecting deterministic signals in Gaussian and compound Poisson noise. The approximation in the derivation is based on the assumption that the localized noise elements rarely overlap each other. The derived log-likelihood ratio consists of two distinct parts. One is the conventional correlation detector for detecting deterministic signals in Gaussian noise. The other is a nonlinear processor which compensates for the degradation of the correlation detector caused by the localized noise, and is activated only by the presence of the localized noise. As such, it involves covariance operators of both the Gaussian and the localized noise, and is obtained by using the simultaneous diagonalization and orthogonalization of quadratic forms in function space involving eigenfunctions of certain composite operators.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The square root of f power-spectrum centroid detector: system considerations, implementation, and performance.

Operation of the √f centroid detector with various doppler systems is discussed, and its design, implementation, and performance are described. It is determined that the detector can be employed in directional detection schemes to measure spectral moments and centroids with correct polarity and with no degradation in accuracy. Narrow- and wideband deterministic signal detection of both stationary and FM information is investigated, and it is found that the centroid detector can also serve as an FM demodulator with high AM rejection. A versatile √f detector was realized in discrete form and evaluated with deterministic and random signals, and its measured variance agreed closely with the theoretical values. The validity and application of the noise-reduction method was verified on deterministic and random doppler signals. Applications of the detector and the noise-reduction method to blood-flow and velocity measurements are demonstrated.

The √f power-spectrum centroid detector: System considerations, implementation, and performance

Operation of the √f centroid detector with various doppler systems is discussed, and its design, implementation, and performance are described. It is determined that the detector can be employed in directional detection schemes to measure spectral moments and centroids with correct polarity and with no degradation in accuracy. Narrow- and wideband deterministic signal detection of both stationary and FM information is investigated, and it is found that the centroid detector can also serve as an FM demodulator with high AM rejection. A versatile √f detector was realized in discrete form and evaluated with deterministic and random signals, and its measured variance agreed closely with the theoretical values. The validity and application of the noise-reduction method was verified on deterministic and random doppler signals. Applications of the detector and the noise-reduction method to blood-flow and velocity measurements are demonstrated.

On robust detection of discrete-time stochastic signals

The problem of designing robust systems for the detection of stochastic signals in noise is considered for the large-sample-size, small-signal case. By applying two previously-established models for the detection of stochastic signals, known results for the robust detection of deterministic signals are extended on a limited basis to the stochastic- signal case. The proposed detectors are seen to be robust over a class of possible noise statistics, based on a Huber-Tukey mixture model, which contains noises characterized by heavy-tailed probability density functions. In addition, numerical results are presented which verify the robustness property of the proposed detectors over wider classes of noise mixtures.

Energy Detection of Unknown Deterministic Signals in the Presence of Jamming

Urkowitz [1]has discussed the detection of a deterministic signal of unknown structure in the presence of flat, band-limited, Gaussian noise of known power density. That analysis is extended here to the case where jamming or other conditions preclude knowledge of the noise power density. The chi-square statistic of Urkowitz is replaced with Fisher's variance-ratio statistic, using a separate set of noise samples to estimate the unknown noise power density. Curves are given to show the additional degradation of perform over that due to ignorance of the signal structure, caused by ignorance of the noise power density.

Energy detection of unknown deterministic signals

By using Shannon's sampling formula, the problem of the detection of a deterministic signal in white Gaussian noise, by means of an energy-measuring device, reduces to the consideration of the sum of the squares of statistically independent Gaussian variates. When the signal is absent, the decision statistic has a central chi-square distribution with the number of degrees of freedom equal to twice the time-bandwidth product of the input. When the signal is present, the decision statistic has a noncentral chi-square distribution with the same number of degrees of freedom and a noncentrality parameter λ equal to the ratio of signal energy to two-sided noise spectral density. Since the noncentral chi-square distribution has not been tabulated extensively enough for our purpose, an approximate form was used. This form replaces the noncentral chi-square with a modified chi-square whose degrees of freedom and threshold are determined by the noncentrality parameter and the previous degrees of freedom. Sets of receiver operating characteristic (ROC) curves are drawn for several time-bandwidth products, as well as an extended nomogram of the chi-square cumulative probability which can be used for rapid calculation of false alarm and detection probabilities. Related work in energy detection by J. I. Marcum and E. L Kaplan is discussed.

Correlation detection of signals perturbed by a random channel

We show that the concept of correlation detection of deterministic signals in additive Gaussian noise can be extended in a natural manner to the detection of signals that are transmitted through a "Gaussian" random channel besides being corrupted by additive Gaussian noise. Such situations are typical in communication over scatter-multipath channels (with or without a specular component). In the deterministic case, the receiver essentially crosscorrelates the received signal with the signal before the additive noise was introduced. When a random channel is present, however, this latter signal, i.e., the output of the random channel, is not known at the receiver, However, knowing the statistics of the channel and the noise, the receiver can make an estimate of it from the received signal on the hypothesis that a particular signal was transmitted. The optimum receiver then crosscorrelates this estimate with the received signal.