Cross-borehole ground-penetrating radar (GPR) is one of the most effective tools available to detect underground cavities. These cavities are often detected from zero-offset profiling (ZOP) measurements, where the transmitter and receiver are always at the same depth; the other common alternative is to use multiple-offset gathers (MOG), such that a measurement is recorded with the transmitter and receiver at every pair of depths. While the latter strategy sometimes allows one to compute a tomographic inversion and in general gives strictly more information, it is often prohibitively expensive to carry out such a survey, and the utility of many of these measurements is limited. ZOP measurements, on the other hand, are comparatively cheap to carry out, yet under certain conditions it may not be possible to use these measurements alone to detect cavities with the required degree of accuracy. In this paper, the use of measurements with a small offset in depth between the receiver and transmitter is investigated, and it is shown that the use of only these measurements is a very favorable point in the expense-utility tradeoff. Along the way, it is shown that the manner in which traveltime is measured must be appropriate for the noise regime in which the GPR operates.

One of the most difficult sensorimotor behaviors exhibited by flying animals is the ability to track another flying animal based on its sound emissions. From insects to mammals, animals display this ability in order to localize and track conspecifics, mate or prey. The pursuing individual must overcome multiple non-trivial challenges including the detection of the sounds emitted by the target, matching the input received by its (mostly) two sensors, localizing the direction of the sound target in real time and then pursuing it. All this has to be done rapidly as the target is constantly moving. In this project, we set to mimic this ability using a physical bio-mimetic autonomous drone. We equipped a miniature commercial drone with our in-house 2D sound localization electronic circuit which uses two microphones (mimicking biological ears) to localize sound signals in real-time and steer the drone in the horizontal plane accordingly. We focus on bat signals because bats are known to eavesdrop on conspecifics and follow them, but our approach could be generalized to other biological signals and other man-made signals. Using two different experiments, we show that our fully autonomous aviator can track the position of a moving sound emitting target and pursue it in real-time. Building an actual robotic-agent, forced us to deal with real-life difficulties which also challenge animals. We thus discuss the similarities and differences between our and the biological approach.

We present a novel method to detect underground cavities using cross-borehole ground-penetrating radar (GPR). We model the propagation of a GPR signal across a cavity and find that the spectrum of the signal will be distorted in a specific low-pass manner. Comparing the spectra of received signals with the predicted spectrum using a hypothesis-testing approach allows us to detect cavities with high probability. The proposed method is validated on both simulated and real measurements. Our approach generally remains effective even when conventional methods fail; our method can also be combined with conventional methods in order to more successfully distinguish between cavities and geologic clutter.

We consider the design of a single moving sensor trajectory for the purpose of optimally localizing a stationary emitter based on time-of-arrival measurements, which are deteriorated by oscillator instability. The localization error covariance matrix is predicted by the Cramér-Rao bound. In order to optimize the localization, we propose the minimization of the largest eigenvalue of the bound matrix, or, equivalently, the maximization of the smallest eigenvalue of the associated Fisher information matrix. Two different cases are discussed. In the first case, a pre-mission path design is considered where the path is optimized for locating an emitter in the vicinity of a postulated location. In the second case, the path is designed in real time, as the sensor moves, using measurements collected online. Using robust optimization methods, the best next way-point is chosen, considering the uncertainty in the emitter location. Constraints rising from speed and maneuvering limitations, and restricted regions are treated. Since these optimization problems are non-convex, we use semi-definite relaxation. We demonstrate that in many scenarios, the proposed algorithms yield near optimal results.

The core component of a cognitive radio is its detector. When a device is equipped with multiple antennas, the detection method is usually based on an eigenvalue analysis. This paper explores the performance of the most common largest eigenvalue detector, for the case of a narrowband temporally white signal and calibrated receiver noise. In contrast to popular Gaussian assumption, our performance bounds are valid for any signal and noise that belong to the wide class of sub-Gaussian random processes. Moreover, the results are given in closed-form for any finite number of observations and antennas, in contrary to the widespread asymptotic analysis approach.

The most common methods for localization of radio frequency transmitters are based on two processing steps. In the first step, parameters such as angle of arrival or time of arrival are estimated at each base station independently. In the second step, the estimated parameters are used to determine the location of the transmitters. The direct position determination approach advocates using the observations from all the base stations together in order to estimate the locations in a single step. This single-step method is known to outperform two-step methods when the signal-to-noise ratio is low. In this paper, we propose a direct-position-determination-based method for localization of multiple emitters that transmit unknown signals. The method does not require knowledge of the number of emitters. It is based on minimum-variance-distortionless-response considerations to achieve a high resolution estimator that requires only a two-dimensional search for planar geometry, and a three-dimensional search for the general case.

The direct position determination (DPD) approach is a single-step method, which uses the maximum likelihood estimator to localize sources emitting electromagnetic energy using combined data from all available sensors. The DPD is known to outperform the traditional two-step methods under low signal-to-noise ratio conditions. We propose an improvement to the DPD approach, using the well-known minimum-variance-distortionless-response (MVDR) approach. Unlike maximum likelihood, the number of sources needs not be known before applying the method. The combination of both the direct approach and MVDR yields unprecedented localization accuracy and resolution for weak sources. We demonstrate this approach on the problem of multistatic radar, but the method can easily be extended to general localization problems.

Multiple antenna techniques are used to enhance wireless links and therefore have been studied extensively. Many practical systems that differ from ideal schemes have been discussed in the literature. One example is a system that lacks precise channel information at the transmitter. We evaluate analytically the performance of a multiple input multiple output (MIMO) technique that uses partial channel knowledge. Specifically, we analyze a scheme with M transmit antennas and N receive antennas, employing eigenbeamforming at the transmitter and MRC at the receiver. We assume that only partial channel matrix is known to the transmitter, specifically only P out of N rows of the channel matrix are known. We derive the optimal beamformer for a single stream transmission case and show that it is the singular vector of the known channel submatrix. We show that the diversity order of a transmission scheme where such a precoder is used is MP+N-P and further show that increasing the value of P by one increases the diversity order by M-1. We also derive the array gain for this scheme. All the results are supported by simulations.

We consider estimation of a set of tent-map chaotic sequences. These sequences are obtained by iterating a one dimensional chaotic function in the (-1,1) domain. We demonstrate how to construct a set of n sequences, in which information in the form of n arbitrary samples in the (-1,1) domain is embedded. Additionally the signs of all sequences jointly form a valid digital codeword. Each sequence in the set consists of m elements, hence the set of sequences is equivalent to a rate \lm analog error correcting-code. We present performance in terms of coding gain when maximum likelihood (ML) and minimum-mean-square-error (MMSE) estimation approaches are employed.

Discrete-input two-dimensional (2D) Gaussian channels with memory represent an important class of systems, which appears extensively in communications and storage. In spite of their widespread use, the workings of 2D channels are still very much unknown. In this work, we try to explore their properties from the perspective of estimation theory and information theory. At the heart of our approach is a mapping of a 2D channel to an undirected graphical model, and inferring itsaposterioriprobabilities (APPs) using generalized belief propagation (GBP). The derived probabilities are shown to be practically accurate, thus enabling optimal maximumaposteriori(MAP) estimation of the transmitted symbols. Also, the Shannon-theoretic information rates are deduced either via the vector-wise Shannon-McMillan-Breiman (SMB) theorem, or via the recently derived symbol-wise Guo-Shamai-Verdu (GSV) theorem. Our approach is also described from the perspective of statistical mechanics, as the graphical model and inference algorithm have their analogues in physics. Our experimental study, based on common channel settings taken from cellular networks and magnetic recording devices, demonstrates that under nontrivial memory conditions, the performance of this fully tractable GBP estimator is almost identical to the performance of the optimal MAP estimator. It also enables a practically accurate simulation-based estimate of the information rate. Rationalization of this excellent performance of GBP in the 2-D Gaussian channel setting is addressed.

We discuss the challenge of node localization in ad-hoc wireless networks using range measurements and a few anchors. The measurements are assumed to be noisy with unknown bias. We propose an iterative Maximum Likelihood algorithm that is statistically efficient under these conditions. The algorithm is related to phase retrieval and can be viewed as an adaptation of the Gerchberg-Saxton Iterations alternating projection procedure. As a byproduct the algorithm estimates the bias of the range measurements. Closed form expressions for the Fisher Information Matrix are derived. Finally, simulations are used to corroborate the analysis.

Abstract Given a network of stations with incomplete and possibly imprecise inter‐station range measurements, it is required to find the relative positions of the stations. Several models for the bias in the range estimates are discussed. We present a set of iterative algorithms that cope successfully with the various bias models and provide Maximum Likelihood position estimates. Proof of convergence is provided. A procedure, albeit designed for precise measurements, is also proposed for the initialization of the iterative algorithms. We also present compact, matrix form expression for the Cramér—Rao Bound (CRB). Numerical examples are provided to corroborate the results. Copyright © 2007 John Wiley & Sons, Ltd.

Fundamental limitations on estimation accuracy are well known and include a variety of lower bounds including the celebrated Cramer Rao Lower Bound. However, similar theoretical limitations on resolution have not yet been presented. We exploit results from detection theory for deriving fundamental limitations on resolution. In this paper we discuss the resolution of two zero mean complex random Gaussian signals with a general and predefined covariance matrix observed with additive white Gaussian noise. The results are not based on any specific resolution technique and thus hold for any method and any resolution success rate. The theoretical limit is a simple expression of the observation interval, the user's pre-specified resolution success rate and the second derivative of the covariance matrix. We apply the results to the bearing resolution of two emitters with closely spaced direction of arrival impinging on an array of sensors. The derived limits are verified experimentally by model order selection methods such as the Akaike Information Criterion and the Minimum Description Length.

Orthogonal frequency division multiplexing (OFDM) is a modulation technique that is used in many modern digital communication systems and has been explored in numerous publications. Specifically, the tradeoff between throughput and ICI/ISI (intercarrier interference/intersymbol interference), which affects the length of the guard interval (GI) is well known. Many equalization methods that decrease the interference for a given (short) GI have been proposed. However, it seems that the exact expressions for the ICI and ISI have never been derived. In this paper these expressions are derived for a general (per tone equalization) setup. Often, the matched filter bound (MFB) for single carrier systems is used for OFDM systems. We make two new observations. First, we prove that under mild conditions, met in common scenarios, the ICI power and the ISI power are approximately equal. Second, we show by example that the MFB does not necessarily hold for OFDM. Both cyclic prefix (CP) and zeros prefix (ZP) are examined.

Fundamental limitations on estimation accuracy are well known and include a variety of lower bounds including the celebrated Cramer Rao Lower Bound. However, similar theoretical limitations on resolution have not yet been presented. We exploit results from detection theory for deriving fundamental limitations on resolution. The results are general and are not based on any specific resolution technique and therefore hold for any method and for any resolution success rate. We show that for signals with additive white Gaussian noise the resolution is given by a simple expression related to signal to noise ratio, the signals waveforms and the resolution success rate. As an example, we discuss the resolution of two sinusoids with closely spaced frequencies. The result is compared with the empirical performance of the Akaike information criterion, and the Minimum Description Length criterion for model order selection.

This contribution focuses on error-correcting codes for analog signals. Generally, error-correcting codes exhibit a threshold effect, which degrades performance at the low SNR range. We propose two error correction alternatives based on chaotic dynamical systems, which improve threshold performance relative to previously proposed methods. The first one, which is based on principles of diversity, exhibits a very simple decoder. The second alternative, which is based on a low-density parity-check code, attains a significantly lower threshold. Theoretical analysis and simulations are provided.

This paper focuses on error-correcting codes for analog signals. Generally, error-correcting codes exhibit a threshold effect, which degrades performance at the low signal-to-noise ratio (SNR) range. We propose two error-correction alternatives based on chaotic dynamical systems, which improve threshold performance relative to previously proposed methods. The first one, which is based on principles of diversity, exhibits a very simple decoder. The second alternative, which is based on a low-density parity-check (LDPC) code, attains a significantly lower threshold. Theoretical analysis and simulations are provided.

We analyze the parameter estimation mean square error when the Fisher information measure is zero at some points within the parameter space. At these points the Cramer-Rao lower bound diverges and no unbiased estimator can achieve a finite mean square error. Under mild regularity conditions the maximum likelihood estimator is known to be asymptotically unbiased and therefore lower bounded by the Cramer-Rao lower bound. It is therefore of interest to examine the maximum likelihood estimator performance in the presence of vanishing Fisher information measure. We provide new theoretical and practical results. All results are corroborated by simulations

The most common methods for localization of radio signal emitters are based on measuring a specified parameter such as signal angle-of-arrival (AOA) or time-of-arrival (TOA). The measured parameters are then used to estimate the transmitter location. Since the measurements are done at each base station independently, without using the constraint that all AOA/TOA estimates must correspond to the same transmitter, they are sub-optimal. Moreover, if the number of array elements at each base station is M, the number of cochannel simultaneous transmitters that can be localized is M-1. We propose a technique that uses exactly the same data as the common AOA/TOA methods, but the position determination is direct. The proposed method can handle LM-1 cochannel simultaneous signals, using L base stations. Although there are many stray parameters, only a two-dimensional search is required for a planar geometry and a three-dimensional search for the general case. The technique exploits the principles of the MUSIC algorithm, and provides a natural solution to the measurements-sources association problem that is encountered in AOA/TOA based systems.

The most common methods for location of communications or radar transmitters are based on measuring a specified parameter such as signal angle-of-arrival or time-of-arrival. The measured parameters are then used to estimate the transmitter location. These methods are sub-optimal since they are indirect and involve two separate estimation steps. We propose a technique that uses exactly the same data as the common methods but the estimation of location is based on maximum-likelihood and the location determination is direct. Although there are many stray parameters, including the attenuation coefficients and the signal waveform, the method requires only a two-dimensional search. Monte-Carlo simulations indicate that the accuracy is superior to angle-of-arrival, time-of arrival and their combination.

We propose a generalized belief propagation (GBP) receiver for two-dimensional (2D) channels with memory, which is applicative to 2D intersymbol interference (ISI) equalization and multiuser detection (MUD). Our experimental study demonstrates that under non-trivial interference conditions, the performance of this fully tractable GBP receiver is almost identical to the performance of the optimal maximum a-posteriori (MAP) receiver.

The most common methods for location of communications or radar transmitters are based on measuring a specified parameter such as signal angle of arrival (AOA) or time of arrival (TOA). The measured parameters are then used to estimate the transmitter location. Since the AOA/TOA measurements are done at each base station separately, without using the constraint that all measurements must correspond to the same transmitter, they are suboptimal. We propose a technique that uses exactly the same data as the common methods, except that the estimation of location is based on exact maximum likelihood, and the location determination is direct. Although there are many stray parameters, including the attenuation coefficients and the signal waveform, the method requires only a two-dimensional search. Monte Carlo simulations indicate that the accuracy is equivalent to AOA, TOA, and their combination for high SNR, while for low SNR, the accuracy of the proposed method is superior.

A new Cramer-Rao lower bound for symbol timing recovery of linearly modulated (quadrature amplitude modulation) signals is presented. Contrary to some other works on the subject, the transmitted data is assumed to be unknown at the receiver. The bound is derived from a likelihood function that includes the symbol randomness. For large number of symbols, the bound is achievable at any signal-to-noise ratio. The separation of symbol timing recovery and phase recovery schemes is investigated using the new results. It is shown that the separation of these operations causes a degradation of less than 0.3 dB compared to joint phase and timing recovery. The bound is derived for symbol shaping limited to a single symbol length (i.e., no intersymbol interference.) Simulations for longer pulse shapes demonstrate that the new results provide better performance prediction than other known techniques.

Synchronous code-division multiple-access (CDMA) techniques possess intrinsic protection against cochannel interference when orthogonal spreading codes are used. However, in the presence of multipath propagation, the signals lose their orthogonality property, leading to increased cross correlation. In these cases, channel estimation may be needed in order to improve detection. We propose and compare several algorithms for channel estimation of a synchronous CDMA point-to-multipoint link (downlink) that uses aperiodic spreading waveforms. We compare by simulation and analysis a subspace approach, a pilot-aided approach, and a decision-based approach.

We consider the problem of localizing multiple narrow-band stationary signals using an arbitrary time-varying array such as an array mounted on a moving platform. We assume a Gaussian stochastic model for the received signals and employ the generalized least squares (GLS) estimator to get an asymptotically-efficient estimation of the model parameters. In case the signals are a-priori known to be uncorrelated, this estimator allows one to exploit this prior knowledge to its benefit. For the important case of translational motion of a rigid array, a computationally-efficient spatial-smoothing method is presented. Simulation results confirming the theoretical results are included.

A new method for localizing multiple signals in spatially-colored background noise using an arbitrary passive sensor array is presented. The method enables also to exploit prior knowledge that the signals are uncorrelated, in case such information is available, so as to improve the performance and allow localization even if the number of signals exceeds the number of sensors. The estimation is based on the generalized least squares criterion, and is both consistent and efficient. Simulation results confirming the theoretical results are included.

We consider the problem of separating and estimating the waveforms of superimposed signals received using an array of uncalibrated sensors. The array elements are assumed to have the same unknown gain pattern, up to an unknown multiplicative factor. The phases of the elements are arbitrary and unknown. In this paper we analyze the quality of the estimated signal in terms of the output signal to interference ratio (SIRO) and output signal to noise ratio (SNRO). It is shown that uncalibrated arrays can be used successfully for signal separation and estimation using only second order moments. The analysis is verified by Monte Carlo experiments using an algorithm for steering vector estimation.

The Gaussian and deterministic maximum likelihood (ML) direction of arrival (DOA) estimates are examined for several cases of a-priori noise statistics. The structures of the Gaussian and the deterministic log-likelihood functions are compared, and it is shown that, for unknown noise spectrum, both estimators minimize the entropy of the measurements. It is also shown that the Gaussian log-likelihood function includes an additional term, which is the entropy of the projection of the measurements onto the signal subspace. General conditions under which the deterministic ML estimate is also an extremum of the Gaussian likelihood function are derived, and it is shown that the asymptotic (large K) limit of these conditions guarantees equal asymptotic performances. It is also shown that the asymptotic performance is not affected by prior knowledge of the noise spectrum.>

A new direction finding algorithm is derived for multiple wideband signals received by an arbitrary array, and its performance is analyzed. Using an interpolation technique, a set of virtual arrays is generated, each for a direct frequency band, having the same array manifold. The covariance matrices of these arrays are added up to produce a composite covariance matrix. Direction of arrival estimates are obtained by eigendecomposition of this composite covariance matrix using the narrowband MUSIC algorithm or its variants. By choosing the virtual arrays to be linear and equally spaced, one can apply the root-MUSIC algorithm to this problem. Closed-form expressions for the asymptotic covariance matrix of the direction of arrival (DOA) estimation errors are derived using a perturbation analysis.>

The performance of direction finding systems in a correlation signal environment utilizing diversely polarized antenna arrays is investigated. The Cramer-Rao bound (CRB) is used to evaluate the accuracy of the estimated directions of arrival. Compact closed form formulas are presented for the CRB corresponding to the joint estimation of the directions of arrival, signal covariance matrix, signal polarization parameters, and noise variance. The CRB is evaluated numerically for selected examples, to provide insights into the potential improvement in direction finding accuracy due to polarization diversity.>

The interpolated spatial smoothing algorithm is a computationally efficient method for estimating the directions of arrival (DOAs) of signals, some of which may be perfectly correlated. It extends the spatial smoothing method to arbitrary array geometrics. A performance analysis is outlined for this algorithm. Closed form expressions for the covariance matrix of the DOA estimation errors are derived using a perturbation analysis.>

The technique of interpolated arrays is applied to ESPRIT-type direction-finding methods. The resulting method uses sensor arrays with arbitrary configuration, thus eliminating the basic restrictive requirement of ESPRIT for two (or more) identical arrays. The approach allows for resolving D narrowband signals if the number of sensors is at least D+1, while the original ESPRIT method requires at least 2D sensors. Moreover, it is shown that while ESPRIT performs poorly for signals propagating in parallel (or close to parallel) with the array-displacement vector, this technique does not exhibit such weakness. While using two subarrays ESPRIT cannot resolve azimuth and elevation, even when the sensors are not collinear. The interpolated ESPRIT procedure resolves azimuth and elevation using only a single array. These advantages are obtained with a reasonable increase in computation load, thus preserving the basic and most outstanding advantage of ESPRIT.>

An eigenstructure-based method for direction finding in the presence of sensor gain and phase uncertainties is presented. The method provides estimates of the directions of arrival (DOA) of all the radiating sources as well as calibration of the gain and phase of each sensor in the observing array. The technique is not limited to a specific array configuration and can be implemented in any eigenstructure-based DOA system to improve its performance.>

Sensor location uncertainty can severely degrade the performance of direction finding systems. An exact maximum-likelihood method for simultaneously estimating directions of arrival (DOA) and sensor locations is developed to alleviate this problem. The case of nondisjoint sources, i.e., sources observed in the same frequency cell and at the same time, is emphasized. The algorithm is iterative and converges to the global maximum of the likelihood function is the initial conditions are good enough. Selected numerical examples demonstrate that the proposed technique is capable of correcting severe errors in the DOA estimates due to sensor location uncertainty.>

A general class of Bayesian lower bounds on moments of the error in parameter estimation is formulated, and it is shown that the Cramer-Rao, the Bhattacharyya, the Bobrovsky-Zakai, and the Weiss-Weinstein lower bounds are special cases in the class. The bounds can be applied to the estimation of vector parameters and any given function of the parameters. The extension of these bounds to multiple parameter is discussed.>

We formulate a general class of lower bounds on the attainable mean square error (MSE) in parameter estimation, and show that the Cramer-Rao, the Bhattacharyya and the Bobrovsky-Zakai lower bounds are special cases in the class. We then propose a lower bound in the class that is often significantly tighter than the above mentioned bounds. The proposed bound is simple to analyze and compute; it is free from bias and regularity assumptions; it readily incorporates a priori information; and it readily generalizes to the estimation of vector parameters and any given function of the parameters.

A general class of lower bounds on the mean square error (mse) in random parameter estimation is formulated. These bounds are generated using functions of the parameter and the data that are orthogonal to the data. A particular choice in the class yields a new lower bound which is superior to both the Cramer-Rao and Bobrovsky-Zakai lower bounds.

A new lower bound on mean-square error in parameter estimation is presented. The bound is tighter than the Cramér-Rao and Bobrovsky-Zakai lower bounds. It requires no bias or regularity assumptions, it is computationally simple, and it can be applied to estimates of vector parameters or functions of the parameters.

The Ziv-Zakai Lower Bound (ZZLB) on the mean square error (m.s.e.) of time delay estimators is compared with theoretical and computer simulation results for time delay estimation via cross-correlation. Comparisons are made for both lowpass and narrowband signal spectra. For both signal spectra it is shown that for sufficiently large time-bandwidth product the correlator performance is very close to the ZZLB in both the small and large error regions. This establishes the cross-correlator as an optimal instrumentation (in the m.s.e. sense) while demonstrating that the ZZLB is an extremely tight lower bound. The ZZLB is further used to accurately predict the threshold signal-to-noise ratio (SNR) above which the cross-correlator performance is closely characterized by the Cramer-Rao Lower Bound (CRLB).

The location of a radiating source can be determined by measuring the relative time-delay of its signal wavefront to several spatially separated receivers. A new technique is presented to investigate the performance of time-delay measurement schemes based on a modified version of the Ziv-Zakai lower bound. This technique is shown to yield a tight bound on the attainable mean-square measurement error for any prespecified signal-to-noise ratio conditions.