Random Signal Model Research Articles

EM and SAGE Algorithms for DOA Estimation in the Presence of Unknown Uniform Noise.

The existing expectation maximization (EM) and space-alternating generalized EM (SAGE) algorithms are only applied to direction of arrival (DOA) estimation in known noise. In this paper, the two algorithms are designed for DOA estimation in unknown uniform noise. Both the deterministic and random signal models are considered. In addition, a new modified EM (MEM) algorithm applicable to the noise assumption is also proposed. Next, these EM-type algorithms are improved to ensure the stability when the powers of sources are not equal. After being improved, simulation results illustrate that the EM algorithm has similar convergence with the MEM algorithm, the SAGE algorithm outperforms the EM and MEM algorithms for the deterministic signal model, and the SAGE algorithm cannot always outperform the EM and MEM algorithms for the random signal model. Furthermore, simulation results show that processing the same snapshots from the random signal model, the SAGE algorithm for the deterministic signal model can require the fewest computations.

Statistically robust estimation of source bearing via minimizing the Bhattacharyya distance.

Source bearing estimation is a common technique in acoustic array processing. Many methods have been developed and most of them exploit some underlying statistical model. When applied to a practical system, the robustness to model mismatch is of major concern. Traditional adaptive methods, such as the minimum power distortionless response processor, are notoriously known for their sensitivity to model mismatch. In this paper, a parameter estimator is developed via the minimum Bhattacharyya distance estimator (MBDE), which provides a measure of the divergence between the assumed and true probability distributions and is, thus, capable of statistically matching. Under a Gaussian random signal model typical of source bearing estimation, the MBDE is derived in terms of the data-based and modeled covariance matrices without involving matrix inversion. The performance of the MBDE, regarding the robustness and resolution, is analyzed in comparison with some of the existing methods. A connection with the Weiss-Weinstein bound is also discussed, which gives the MBDE an interpretation of closely approaching a large-error performance bound. Theoretical analysis and simulations of bearing estimation using a uniform linear array show that the proposed method owns a considerable resolution comparable to an adaptive method while being robust against statistical mismatch, including covariance mismatch caused by snapshot deficiency and/or noise model mismatch.

Incoherence is Sufficient for Statistical RIP of Unit Norm Tight Frames: Constructions and Properties

In this work, we show that the incoherence alone is sufficient to establish the statistical restricted isometry property (StRIP) and statistical incoherence property (SInCoP) for unit norm tight frames (UNTFs). Further, we derive three simple properties that binary matrices need to satisfy, in order to produce incoherent UNTFs (IUNTFs) with high redundancy (ratio of the number of columns to the number of rows) via an existing embedding operation. We show that biadjacency matrices corresponding to biregular graphs satisfy the required properties. Thereby, we provide a connection between graph theory and the construction of IUNTFs. We also provide a bouquet of constructions of IUNTFs from finite fields and combinatorial designs. Another important aspect of our construction is that the sparse recovery guarantees for the embedded IUNTFs can in fact be translated to the constituent binary matrix. We show that if the constituent m×M binary matrix has constant row and column weight, it can support sparse recovery through <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -minimization for all but an ε-fraction of t-sparse signals chosen from a random signal model, provided m=O(t(log(M/ε)) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ), which is a significant improvement over the existing m=O(t <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) bound, where m denotes the number of measurements. Also, the StRIP and SInCoP based approach results in matrices whose column size is exponential in the fourth root of the row size. To the best of our knowledge, this is the first construction of deterministic matrices satisfying StRIP and SInCoP with such high redundancy.

Multi-Target Robust Waveform Design Based on Harmonic Variance and Mutual Information

Cognitive radar is an intelligent radar system, and adaptive waveform design is one of the core problems in cognitive radar research. In the previous studies, it is assumed that the prior information of the target is known, and the definition of target spectrum variance has not changed. In this paper, we study on robust waveform design problem in multiple targets scene. We hope that the upper and lower bounds of the uncertainty range of robustness are more close to the actual situation, and establish a finite time random target signal model based on mutual information (MI). On the basis of the optimal transmitted waveform and robust waveform based on MI, we redefine the target spectrum variance as harmonic variance, and propose a novel robust waveform design method based on harmonic variance and MI. We compare its performance with robust waveform based on original variance. Simulation results show that, in the situation of multiple targets, compared to the original variance, the MI lifting rate of robust waveform based on harmonic variance relative to the optimal transmitted waveform in the uncertainty range has great improvement. In certain circumstances, robust waveform based on harmonic variance and MI is more suitable for more targets.

Phosphorus Versus Arsenic: Role of the Photodiode Doping Element in CMOS Image Sensor Radiation-Induced Dark Current and Random Telegraph Signal

This work investigates the role of the phosphorus doping element in the radiation-induced dark current in a CMOS image sensor (CIS) photodiode. The neutron and proton irradiations on shallow arsenic-based photodiode CISs and deep phosphorus-based photodiodes CISs have been performed. The results highlight the applicability of the same dark current increase and random telegraph signal (RTS) models. Already verified on other photodiode structures, these results further extend the universality of these analytic tools. Moreover, it emphasizes that the phosphorus element does not play a significant role either in the radiation-induced dark current increase or in the dark current RTS. The results on RTS after annealing reveal the same recovery dynamic than those already observed in irradiated image sensors, suggesting that the phosphorus element does not play a significant role after annealing. Therefore, this work is a piece of experimental evidence supporting the idea that RTS induced by displacement damage is principally due to defect clusters mainly constituted of intrinsic silicon defects such as clusters of vacancies and interstitials.

Construction of highly redundant incoherent unit norm tight frames as a union of orthonormal bases

Unit norm tight frames are useful in providing stable reconstruction. Incoherence, restricted isometry property and statistical restricted isometry property of a frame provide performance guarantees of sparse signal recovery algorithms in compressed sensing. Equiangular tight frames, mutually unbiased bases and chirp matrices are well known incoherent unit norm tight frames that exhibit near optimal sparse recovery guarantees. The dimension of frame elements belongs to some particular family of numbers and the number of elements in these frames is in the order of square of the dimension of the underlying space. In the present work, we construct incoherent unit norm tight frames for more general dimensions with higher redundancy than these frames. One of the important features of our construction is that it produces incoherent unit norm tight frames that are a union of orthonormal bases. In addition, the incoherent unit norm tight frames that we construct possess the statistical restricted isometry property and statistical incoherence property. As a result they exhibit near optimal theoretical guarantees in recovering sparse signals obtained from a generic random signal model. Using simulations, we demonstrate the efficacy of the constructed tight frames as good candidates for recovering sparse signals as against partial Fourier matrices and with existing constructions of incoherent unit norm tight frames.

Semiparametric CRB and Slepian-Bangs Formulas for Complex Elliptically Symmetric Distributions

The main aim of this paper is to extend the semiparametric inference methodology, recently investigated for Real Elliptically Symmetric (RES) distributions, to Complex Elliptically Symmetric (CES) distributions. The generalization to the complex field is of fundamental importance in all practical applications that exploit the complex representation of the acquired data. Moreover, the CES distributions has been widely recognized as a valuable and general model to statistically describe the non-Gaussian behaviour of datasets originated from a wide variety of physical measurement processes. The paper is divided in two parts. In the first part, a closed form expression of the constrained Semiparametric Cram\'{e}r-Rao Bound (CSCRB) for the joint estimation of complex mean vector and complex scatter matrix of a set of CES-distributed random vectors is obtained by exploiting the so-called \textit{Wirtinger} or $\mathbb{C}\mathbb{R}$-\textit{calculus}. The second part deals with the derivation of the semiparametric version of the Slepian-Bangs formula in the context of the CES model. Specifically, the proposed Semiparametric Slepian-Bangs (SSB) formula provides us with a useful and ready-to-use expression of the Semiparametric Fisher Information Matrix (SFIM) for the estimation of a parameter vector parametrizing the complex mean and the complex scatter matrix of a CES-distributed vector in the presence of unknown, nuisance, density generator. Furthermore, we show how to exploit the derived SSB formula to obtain the semiparametric counterpart of the Stochastic CRB for Direction of Arrival (DOA) estimation under a random signal model assumption. Simulation results are also provided to clarify the theoretical findings and to demonstrate their usefulness in common array processing applications.

An analytical model for regular respiratory signal.

In disaster rescue, breathing motion detection is an important approach to searching survivors trapped under debris. Detection of breathing motion is realized by detecting the respiratory signal acquired by the sensing system. In this paper, modeling the regular respiratory signal is studied. Firstly, a preliminary model is built based on power of absolute value of cosine function. Then, this preliminary model is improved in terms of some practical considerations, such as the DC-component of the respiratory signal often is removed by signal processing, and a phase uncertainty occurs due to the data acquisition. Finally, an analytical harmonic-based random respiratory signal model is derived, which can be used as the signal model in the future research about breathing motion detection.

Source localization and calibration using TDOA and FDOA measurements in the presence of sensor location uncertainty

Source localization accuracy is very sensitive to sensor location error. This paper performs analysis and develops a solution for locating a moving source using time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements with the use of a calibration emitter. Using a Gaussian random signal model, we first derive the Cramer-Rao lower bound (CRLB) for source location estimate in this scenario. Then we analyze the differential calibration technique which is commonly used in Global Positioning System. It is indicated that the differential calibration cannot attain the CRLB accuracy in most cases. A closed-form solution is then proposed which takes a calibration emitter into account to reduce sensor location error. It is shown analytically that under some mild approximations, our approach is able to reach the CRLB accuracy. Numerical simulations are included to corroborate the theoretical developments.

On U-Statistics and Compressed Sensing I: Non-Asymptotic Average-Case Analysis

Hoeffding's U-statistics model combinatorial-type matrix parameters (appearing in CS theory) in a natural way. This paper proposes using these statistics for analyzing random compressed sensing matrices, in the non-asymptotic regime (relevant to practice). The aim is to address certain pessimisms of "worst-case" restricted isometry analyses, as observed by both Blanchard & Dossal, et. al. We show how U-statistics can obtain "average-case" analyses, by relating to statistical restricted isometry property (StRIP) type recovery guarantees. However unlike standard StRIP, random signal models are not required; the analysis here holds in the almost sure (probabilistic) sense. For Gaussian/bounded entry matrices, we show that both l1-minimization and LASSO essentially require on the order of k \cdot [\log((n-k)/u) + \sqrt{2(k/n) \log(n/k)}] measurements to respectively recover at least 1-5u fraction, and 1-4u fraction, of the signals. Noisy conditions are considered. Empirical evidence suggests our analysis to compare well to Donoho & Tanner's recent large deviation bounds for l0/l1-equivalence, in the regime of block lengths 1000-3000 with high undersampling (50-150 measurements); similar system sizes are found in recent CS implementation. In this work, it is assumed throughout that matrix columns are independently sampled.

Classical signal model reproducing quantum probabilities for single and coincidence detections

We present a simple classical (random) signal model reproducing Born's rule. The crucial point of our approach is that the presence of detector's threshold and calibration procedure have to be treated not as simply experimental technicalities, but as the basic counterparts of the theoretical model. We call this approach threshold signal detection model (TSD). The experiment on coincidence detection which was done by Grangier in 1986 [22] played a crucial role in rejection of (semi-)classical field models in favour of quantum mechanics (QM): impossibility to resolve the wave-particle duality in favour of a purely wave model. QM predicts that the relative probability of coincidence detection, the coefficient g(2) (0), is zero (for one photon states), but in (semi-)classical models g(2)(0) ≥ 1. In TSD the coefficient g(2)(0) decreases as 1/ε2d, where εd > 0 is the detection threshold. Hence, by increasing this threshold an experimenter can make the coefficient g(2) (0) essentially less than 1. The TSD-prediction can be tested experimentally in new Grangier type experiments presenting a detailed monitoring of dependence of the coefficient g(2)(0) on the detection threshold. Structurally our model has some similarity with the prequantum model of Grossing et al. Subquantum stochasticity is composed of the two counterparts: a stationary process in the space of internal degrees of freedom and the random walk type motion describing the temporal dynamics.

Optimum Quantization Scaling for Noisy Signals in UWB Scenarios

The influence of quantization scaling is seldom considered in narrow band (NB) communications, because a high resolution analogue-to-digital converter (ADC) can be generally employed. In ultra-wideband (UWB) systems, however, the resolution of ADC is required to be low to reduce complexity, cost and power consumption. Consequently, the influence of quantization scaling is significant and should be taken into account. In this letter, effects of quantization scaling are analyzed in terms of signal to noise ratio (SNR) loss based on an uniformly distributed random signal model. For the effects of quantization scaling on bit error rate (BER) performance, however, theoretical analysis is too complicated since quantization is a nonlinear operation, hence we employ here a simulation method. The simulation results show there exists an optimum scaling to minimize BER performance for a fixed-resolution receiver; the optimum scaling power is related to the SNR of input noisy signal and the resolution of ADC.

Increasing the sine-cosine transformation accuracy in signal approximation and interpolation

Sine-cosine transformations on the interval −0.5T ≤ t ≤ 0.5T, which are equivalent to a cosine transformation on the interval 0 ≤ t ≤ T, are considered. Relationships for the error variance of signal reconstruction are obtained. Depending on the a priori information on the signal, the relationships make it possible to choose for its representation the most suitable orthogonal expansion. A stationary random signal model is used for comparing the expansion with a conventional sine-cosine transformation.

Passive Source Localization Using Time Differences of Arrival and Gain Ratios of Arrival

A source signal will be subject to different amounts of time-delay as well as attenuation when it reaches a number of spatially separated sensors. Both time-delay and attenuation are dependent on the distance between the source and the receivers. This paper performs a fundamental investigation of whether the gain ratios of arrival (GROAs), defined here as the ratio of the received signal amplitudes at the referenced sensor to the other sensors, can be utilized in conjunction with the time differences of arrival (TDOAs) to improve the source localization accuracy. We begin with a Gaussian random signal model and derive the Cramer-Rao lower bound (CRLB) of a source location estimate based on both GROAs and TDOAs. Our conclusion is that the improvement from GROAs increases when the factor c/omegao increases, where c is the signal propagation speed and omegao is the signal bandwidth. The paper proceeds to develop an algebraic closed-form solution for the source location using GROAs and TDOAs. The algebraic solution is proved theoretically to reach the CRLB accuracy under the Gaussian data model. Numerical simulations are included to support and corroborate the theoretical developments.

System-Orthogonal Functions for Sound Speed Profile Perturbation

Empirical orthogonal functions (EOFs) are typically derived from direct measurements of the sound speed profile (SSP) and they are orthogonal in regard to the statistics of the SSP uncertainty. Viewed from the output end of a particular sonar system, however, the effect of an error in one EOF is usually coupled with the effect of the error in another due to the strongly nonlinear relation between the SSP parameters and the system response. In this paper, a new set of basis functions, orthogonal in regard to sonar performance measure, is developed to characterize SSP perturbations. The performance measure used is the Cramer-Rao bound (CRB) for SSP expansion coefficients derived from a full-field random Gaussian signal model; a closed-form, analytical solution is obtained for both the range-independent and adiabatically range-dependent environments. The derived functions make the CRB matrix diagonal, decoupling the errors in the estimation of the expansion coefficients. Compared to the EOFs, the new set of basis functions depends on both the statistics of the sound speed uncertainty and the sound waveguide propagation property; it incorporates the measurement noise as well. The development makes possible the investigation of the relative significance of the individual basis functions in system response; it also provides a novel framework for optimum acoustic parameterization in adaptive rapid environmental assessment

Bayesian Bounds for Matched-Field Parameter Estimation

Matched-field methods concern estimation of source locations and/or ocean environmental parameters by exploiting full wave modeling of acoustic waveguide propagation. Because of the nonlinear parameter-dependence of the signal field, the estimate is subject to ambiguities and the sidelobe contribution often dominates the estimation error below a threshold signal-to-noise ratio (SNR). To study the matched-field performance, three Bayesian lower bounds on mean-square error are developed: the Bayesian Crame/spl acute/r-Rao bound (BCRB), the Weiss-Weinstein bound (WWB), and the Ziv-Zakai bound (ZZB). Particularly, for a multiple-frequency, multiple-snapshot random signal model, a closed-form minimum probability of error associated with the likelihood ratio test is derived, which facilitates error analysis in a wide scope of applications. Analysis and example simulations demonstrate that 1) unlike the local CRB, the BCRB is not achieved by the maximum likelihood estimate (MLE) even at high SNR if the local performance is not uniform across the prior parameter space; 2) the ZZB gives the closest MLE performance prediction at most SNR levels of practical interest; 3) the ZZB can also be used to determine the necessary number of independent snapshots achieving the asymptotic performance of the MLE at a given SNR; 4) incoherent frequency averaging, which is a popular multitone processing approach, reduces the peak sidelobe error but may not improve the overall performance due to the increased ambiguity baseline; and finally, 5) effects of adding additional parameters (e.g., environmental uncertainty) can be well predicted from the parameter coupling.

A Bound on Mean-Square Estimation Error With Background Parameter Mismatch

In typical parameter estimation problems, the signal observation is a function of the parameter set to be estimated as well as some background (environmental/system) parameters assumed known. The assumed background could differ from the true one, leading to biased estimates even at high signal-to-noise ratio (SNR). To analyze this background mismatch problem, a Ziv-Zakai-type lower bound on the mean-square error (MSE) is developed based on the mismatched likelihood ratio test (MLRT). At high SNR, the bound incorporates the increase in MSE due to estimation bias; at low SNR, it includes the threshold effect due to estimation ambiguity. The kernel of the bound's evaluation is the error probability associated with the MLRT. A closed-form expression for this error probability is derived under a random signal model typical of the bearing estimation/passive source localization problem. The mismatch is then analyzed in terms of the related ambiguity functions. Examples of bearing estimation with system (array shape) mismatch demonstrate that the developed bound describes the simulations of the maximum-likelihood estimate well, including the sidelobe-introduced threshold behavior and the bias at high SNR.

A model subspace method for matched field source localization in a shallow-water acoustic waveguide

Model subspace methods for parameter estimation can yield promising results when temporal or spatial variability dominate the model inputs. Application of Gaussian signal detection theory, summarized by Van Trees, is applied to the localization problem. Model inputs, such as the sound velocity profile in water, bottom properties, and array position, rather than being deterministic, are characterized using a Gaussian random vector. This, in turn, yields a random signal model which is represented as a vector space. Detection and localization via a maximum-likelihood estimator becomes a question of whether the received signal fits the subspace defined by the random signal model.

System-orthogonal functions for sound velocity profile perturbation

Empirical orthogonal functions (EOFs) are derived from direct measurements of the sound velocity profile (SVP) and they are orthogonal in regard to the statistics of the SVP uncertainty. Viewed from the sonar output end, however, the effect of an error in one EOF is usually coupled with the effect of the error in another due to the nonlinear physical constraints. Thus the traditional EOF is not an optimum basis set to characterize the SVP uncertainty in regard to sonar performance measure. To obtain a system-orthogonal SVP representation, a new set of orthonormal functions is derived for SVP perturbations in a water column. The performance measure used is the Cramer–Rao bound (CRB) for SVP expansion coefficients, and a full-field random Gaussian signal model is assumed. The derived functions make the CRB matrix diagonal, decoupling the errors in the estimation of the expansion coefficients. Compared to the traditional EOFs, the new set of SVP basis functions depends on both the statistics of the sound speed uncertainty and the sound waveguide propagation property. It also includes the noise effect in measurements. Using this system-orthogonal function set makes possible the investigation of the relative significance of the individual basis functions. [Work supported by ONR.]

Observation and modeling of random telegraph signals in the gate and drain currents of tunneling metal–oxide–semiconductor field-effect transistors

Parallel measurements of random telegraph signals (RTS) in the gate and drain currents of n-metal–oxide–semiconductor field-effect transistors with 1.3-nm-thin gate oxides are presented. RTS appear simultaneously in both currents. Contrary to what could be expected, the signals have opposite signs in the gate and drain currents. A model is proposed to explain this phenomenon by the Schottky effect. The relative amplitude of the signal fluctuation in the gate current is significantly higher than that in the drain current. Therefore, the gate current is a much more sensitive indicator for RTS than the drain current.