The Bayesian Cramér-Rao bound (BCRB) is a crucial tool in signal processing for assessing the fundamental limitations of any estimation problem as well as benchmarking within a Bayesian frameworks. However, the BCRB cannot be computed without full knowledge of the prior and the measurement distributions. In this work, we propose a fully learned Bayesian Cramér-Rao bound (LBCRB) that learns both the prior and the measurement distributions. Specifically, we suggest two approaches to obtain the LBCRB: the Posterior Approach and the Measurement-Prior Approach. The Posterior Approach provides a simple method to obtain the LBCRB, whereas the Measurement-Prior Approach enables us to incorporate domain knowledge to improve the sample complexity and interpretability. To achieve this, we introduce a Physics-encoded score neural network which enables us to easily incorporate such domain knowledge into a neural network. We study the learning errors of the two suggested approaches theoretically, and validate them numerically. We demonstrate the two approaches on several signal processing examples, including a linear measurement problem with unknown mixing and Gaussian noise covariance matrices, frequency estimation, and quantized measurement. In addition, we test our approach on a nonlinear signal processing problem of frequency estimation with real-world underwater ambient noise.

This paper proposes a cognitive beamforming method for target tracking using multiple-input multiple-output (MIMO) radar. This method minimizes a Bayesian performance criterion on direction-of-arrival (DOA) estimation error with respect to the transmit signal auto-correlation matrix. Traditionally, the Bayesian Cramér-Rao bound (BCRB) serves as an optimization criterion for cognitive radars. However, when the corresponding deterministic Fisher information is parameter-dependent, the BCRB is unachievable, even asymptotically. In order to obtain a reliable criterion in the asymptotic region, the semi-expected Cramér-Rao bound (SECRB) is adopted. Our approach utilizes the SECRB for target tracking as a criterion in order to sequentially determine the transmit signal auto-correlation matrix based on past measurements. Simulations indicate that the proposed method outperforms DOA estimation using the BCRB-based cognitive approach and MIMO radar with orthogonal signals. This paper demonstrates that the proposed method automatically focuses the transmit beampattern towards the target direction within fewer steps compared to the BCRB-based cognitive approach.

We introduce the Generative Barankin Bound (GBB), a learned Barankin Bound, for evaluating the achievable performance in estimating the direction of arrival (DOA) of a source in non-asymptotic conditions, when the statistics of the measurement are unknown. We first learn the measurement distribution using a conditional normalizing flow (CNF) and then use it to derive the GBB. We show that the resulting learned bound approximates the analytical Barankin bound well for the case of a Gaussian signal in Gaussian noise, Then, we evaluate the GBB for cases where analytical expressions for the Barankin Bound cannot be derived. In particular, we study the effect of non-Gaussian scenarios on the threshold SNR.

The Misspecified Cramér-Rao lower bound (MCRB) provides a lower bound on the performance of any unbiased estimator of parameter vector θ under model misspecification. An approximation of the MCRB can be numerically evaluated using a set of i.i.d samples of the true distribution at θ. However, obtaining a good approximation for multiple values of θ requires collocating an unrealistically large number of samples. In this paper, we present a method for approximating the MCRB using a Generative Model, referred to as a Generative Misspecified Lower Bound (GMLB), in which we train a generative model on data from the true measurement distribution. Then, the generative model can generate as many samples as required for any θ, and therefore the GMLB can use a limited set of training data to achieve an excellent approximation of the MCRB for any parameter. We demonstrate the GMLB on two examples: a misspecified Linear Gaussian model; and a Non-Linear Truncated Gaussian model. In both cases, we empirically show the benefits of the GMLB in accuracy and sample complexity. In addition, we show the ability of the GMLB to approximate the MCRB on unseen parameters.

Real-time analysis and forecasting of rain-induced attenuation patterns in terrestrial microwave links has gained increasing attention in the field of communication and meteorology, enabling preparation for upcoming events. This paper presents an empirical study of model-based and data-driven techniques applied to multi-step predictions of rain attenuation in terrestrial microwave links. Data-driven approaches have been adopted in many research fields, including time series forecasting, which allows the modeling of complex data patterns without assuming a particular model representation. However, the superiority of such algorithms over traditional time series model-based methods has yet to be resolved for short-term rain attenuation predictions. We provide a comprehensive evaluation through empirical analysis using real-world measurements by comparing the performances of six main state-of-the-art algorithms involving two dimensions: the available training dataset and forecast horizon. The empirical results demonstrate the superiority of data-driven algorithms over model-based methods with an increasing gap as the forecast horizon grows, reaching over 20% gain in the RMSE. Nevertheless, adopting data-driven algorithms in rainfall prediction requires a sufficient amount of available data and typically requires a significant number of observed rainfall hours, highlighting the challenge when the dataset is limited or unavailable.

The spatial structure of rain fields is important to the understanding of their effects on ground-level aspects, such as runoff generation, and is considered crucial information for the accurate reconstruction of these fields. It is commonly characterized by a simplified spatial autocorrelation function (ACF). The near-ground ACF, and—particularly—its decorrelation distance, is evaluated from point measurements (rain gauges and distrometers). However, the spatial representation of such measurements is limited and therefore rarely sufficient for reliable ACF estimation. The emerging use of commercial microwave links (CMLs) for near-ground rain retrieval, and their spatial abundance, suggests using them for ACF estimation. In this study, we propose a method for extracting spatial features of a rain field, and in particular its decorrelation distance, from CML measurements. When sampled by path integration, the rain measurements acquire a distortion as a result of the averaging of a once fluctuating signal, where extreme rain intensities are being smeared. When evaluating the AFC from CMLs’ measurements, this effect needs to be compensated for. We propose methods for retrieving the original parameters characterizing the AFC and validate them on semisynthetic simulated data, based on actual rain events. The error was found to be 5%.

The use of recurrent neural networks (RNNs) to utilize measurements from commercial microwave links (CMLs) has recently gained attention. Whereas previous studies focused on the performance of methods for wet-dry classification, here we propose an RNN algorithm for estimating the rain-rate. We empirically analyzed the proposed algorithm, using real data, and compared it with the traditional power-law (PL)-based algorithm, commonly used for estimating rain from CML attenuation measurements. Our analysis shows that the data-driven RNN algorithm, when properly trained, outperforms the PL algorithm in terms of accuracy. On the other hand, the PL algorithm is simpler and more robust when dealing with a large variety of corruptions and adverse conditions. We then introduced a time normalization (TN) layer for controlling the trade-off between performance and robustness of the RNN methods, and demonstrated its performance.

A Power-Law relation between attenuation and rain rate has proven to be a useful tool in wireless network design at microwave and mmWave frequencies. In the last decade this relation has also been used for estimating rain from signal level measurements in Commercial Microwave Links (CMLs). In this paper we empirically show that while the power-law relation provides good approximation for relating attenuation and rain-rate in terrestrial microwave links of length 1-20Km, for links shorter than 1km, widely used in 5G technologies, it shows significant errors. We then suggest a recurrent neural network (RNN) approach to relate attenuation with rain rate and we show that it overcomes the uncertainties in short links.

Modern infrastructures support smart-city operations, which are based on short millimeter-waves wireless links connected by a dense network. These links are sensitive to hydrometeors, and their signals attenuated by rain. In this study, we demonstrate that standard signal-level measurements being collected by the network can be used to estimate the movement of an ongoing storm. Parameters characterizing the movements of the frontal rain cell, as its velocity and direction, can be accurately estimated. We first estimate the differential time of arrival of the attenuated signals between pairs of links, from which we extract the parameters of interest. We demonstrate our results using actual measurements from an operating system in the city of Rehovot, Israel.

In this paper we apply statistical signal processing methodologies on a real-world application of using Commercial Microwave Links (CMLs) as opportunistic sensors for rain monitoring. We formulate an appropriate parameter estimation problem, taking advantage on the empirically evaluated statistics of the rain, and present a new methodology for rain estimation given only the quantized minimum and maximum radio signal level measurements, which are being logged regularly by the network management systems. Our method transforms measurements taken from any single CML, without the need for training series, nor any prior or side information, into rainfall estimates, that is - to a virtual rain gauge. The operation of the proposed method was demonstrated using actual CMLs in Israel in a semiarid climate zone, and shows that the achieved rain estimates agrees with near-by dedicated rain gauges.

In the last decade, commercial microwave links (CMLs) have been treated as opportunistic near-ground rain sensors, and successfully used for the retrieval of 2-D near-ground rain fields in several countries. In spite of the path integration of a CML, most studies represent the rainfall measured by a CML as a single virtual rain gauge (VRG) in the center of the path. Here, we study the performance of spatial reconstruction of rain fields by an inverse distance weighting (IDW) spatial interpolation method. We compare the case where each CML is represented by a single VRG with the case where it is represented by several VRGs along its path. A synthetic rain field was produced, simplified to a single rain cell, and sampled by a synthetic CML network that was built according to statistics of actual CMLs. A Monte Carlo simulation study yielded a quantitative and specific set of metrics showing that the rain-retrieval results are scenario-dependent and can be used to design a rain-retrieval system. In particular, we show that if the rain-cell dimensions are in the order of the average length of the CMLs, using several VRG with the iterative algorithm can significantly improve the retrieval performance, whereas the performance gain is small otherwise.

The ground level rainfall at a given time is modeled as a 2-D spatial random process r(x, y), the rain field. Existing measurement equipment, such as rain gauges, weather stations, or recently proposed microwave links, samples r(x, y) spatially in specific points or along lines. Given these samples, our purpose is to reconstruct r(x, y). In this paper, we study the question: “under what conditions can a given topology of ground measurements guarantee reconstructability of the rain field?” Based on the assumption that rain fields are sparse, we present a statistical approach to this problem by first characterizing the statistics of the measurements, and then answering the question by applying methods from compressed sensing theory, and in particular Donoho and Tanner's phase transition diagram for sparse recovery. We conclude by suggesting a solution in a form of a simple diagram, allowing one to evaluate the potential reconstruction of r(x, y) in different resolutions without the need for computations.

Cellular backhaul networks usually consist of commercial microwave links, known to be sensitive to weather conditions. The management network systems usually provide records of measurements of the transmitted and the received signals levels from the different microwave links for monitoring and analyzing the network performance. Many of them log only the minimum and the maximum levels of the transmitted and the received signals in pre-set intervals (usually 15-minute). Moreover, only quantized version of these measurements are logged. In the last decade it has been proposed to use these existing measurements for rainfall monitoring. In this paper we analyze the effects of the quantizer and the min/max operators on commercial microwave links signals levels measurements. We show that the quantization process, in combination with the min/max operators, adds bias to the measurements which can be significant. We then propose a method to calculate this bias, and demonstrate our findings using measurements from actual commercial microwave links.

This letter deals with the case where parameter estimation is required, but only observations of extreme values (i.e., the minimum observed value and/or the maximum observed value per interval) are available. We describe the theoretical grounds of the three leading methodologies of estimation from extremes, discuss the relations between them, and analyze the tradeoffs of the different methodologies with respect to the performance (accuracy), complexity, and robustness of the estimates. We then demonstrate our evaluations via a specially designed simulation, which validates our results.

Atmospheric conditions are known to affect the Received Signal Level (RSL) in commercial microwave links (MWLs), that operate at frequencies of tens of GHz. Study of these effects is of great importance both for communication engineers and for environmental monitoring. In this paper we study the phenomenon of a wet antenna. During periods of high relative humidity (RH), a thin layer of water may collect on the outside cover of the microwave units, resulting in increased signal attenuation. Here, we focus on the estimation of the signal power loss caused due to this phenomenon. We used a generalized likelihood ratio test (GLRT) to detect transient signal loss of unknown arrival time and duration, based on existing measurements from a network of commercial MWLs, used in for cellular backhauling. The results indicate the ability of the proposed algorithm to detect and estimate the signal loss of antenna moistening. Beyond its value for commercial microwave networks design, this information holds potential for the detection of dew, which is of great environmental importance.

A common way to describe the relation between rain-rate R [mm/h] and attenuation A [dB] in radio signal is the Power-Law A = aRb, where a and b are the Power-Law parameters, which depend on the radio signal (frequency, polarization) and on some properties of the specific environmental conditions. These parameters are usually set off-line using special purpose equipment and are used from existing tables. However, such tables provide averaged, approximated values to the Power-Law parameters. Using these values for local network design and/or for rainfall estimation can cause inaccuracies. In this paper we propose a new method for calibrating the power law parameters locally, in almost real time, using standard equipment - that is, measurements from rain-gauges and from existing commercial microwave networks deployed in cellular backhauling systems. We suggest an estimation procedure and demonstrate its operation using real scenario in the south of Israel.

Optimal parameter estimation requires simultaneous processing of all available measurements. The complexity of this task may become too large when measurements from two or more multimodal sensor networks are available. In such cases, fusion of estimates obtained from each data set separately may be practical. In this paper, we derive the optimal linear combination of the possibly non-linear estimators, and propose sub-optimal weightings. We analyze the asymptotic performance gain of the first sub-optimal approach with respect to the individual optimal estimates. The theoretical results are supported by simulations.

Recently, it has been demonstrated that Commercial Microwave Networks (CMN) can be considered as an opportunistic sensor networks for rainfall monitoring, and in particular, for rain fields reconstruction. While different rainfall mapping techniques have been proposed, their absolute performance has never been evaluated. This paper presents a novel algorithm, which generates an accurate reconstruction of rain field maps, given measurements from commercial microwave links (ML). The accuracy is achieved by using the sparse properties of the rain field, which enables an optimal and unique recovery of the rain rates along the ML, under certain regularity conditions. We demonstrate that the performance of the proposed algorithm is close to the actual measurements of the rain intensity in a given location, and that it outperforms the reconstruction done by the Radar, almost uniformly. The proposed approach is not restricted to the specific application of rainfall mapping. It can also be used for reconstructing images, especially sparse images, which are sampled by projections on arbitrary lines.

This paper studies the problem of competitive spectrum management in the presence of channel estimation errors. In particular, we study the effect of the channel estimation error on the Bayesian Interference Game (BIG), in which two selfsh wireless systems (players) share the same frequency band, where each player knows its own channel gains but does not know the other players channel gains. In the case where the channel is estimated perfectly, the BIG is known to have a spectrally effcient equilibrium point, which produces a higher payoff to both players than the trivial equilibrium, in which both players always interfere with each other. However, the assumption that each player knows its own channel gains impeccably is not practical due to estimation error. The latter leads to payoff perturbations, which can reduce spectral effciency by driving the spectrally effcient equilibrium point unstable. In this paper, we show that the spectral effciency is robust to small estimation errors; i.e., the BIGs spectrally effcient equilibrium point preserves its properties in the presence of estimation errors.

Commercial wireless microwave links have been recently proven to be an effective tool for precipitation monitoring, mainly for accurate rainfall estimation and high-resolution rainfall mapping. This paper focuses on the challenge of precipitation classification from the measurements of received signal level (RSL) in several commercial wireless microwave links, by suggesting a tree of classification based on the physical features that distinguish between different phenomena. Wet periods are first identified, followed by a classification of the wet periods into pure rain or sleet. The classification is based on the kernel Fisher discriminant analysis, followed by a decision-making process. The suggested procedure is tested on real data, and its performance is evaluated. It is shown that the proposed classification is in very good agreement (85%) with that of a special-purpose meteorological device called disdrometer.

This letter presents an extension of the Multifamily Likelihood Ratio Test (MFLRT) so it can be applied for detection of a deterministic signal of unknown waveform using measurements from multiple sensors. The extended MFLRT is applied for precipitation detection from noisy measurements of the received signal level (RSL), taken from commercial microwave links (ML). The extended MFLRT shows improved detection performance compared with the existing standard Generalized Likelihood Ratio Test (GLRT), while offering also the ability to estimate the signal waveform.

We address the problem of detecting the presence of a recurring stimulus by monitoring the voltage on a multiunit electrode located in a brain region densely populated by stimulus reactive neurons. Published experimental results suggest that under these conditions, when a stimulus is present, the measurements are gaussian with typical second-order statistics. In this letter we systematically derive a generic, optimal detector for the presence of a stimulus in these conditions and describe its implementation. The optimality of the proposed detector is in the sense that it maximizes the life span (or time to injury) of the subject. In addition, we construct a model for the acquired multiunit signal drawing on basic assumptions regarding the nature of a single neuron, which explains the second-order statistics of the raw electrode voltage measurements that are high-pass-filtered above 300 Hz. The operation of the optimal detector and that of a simpler suboptimal detection scheme is demonstrated by simulations and on real electrophysiological data.

This paper deals with multidimensional ICA and its performance analysis, applied to cosmological observations. Our purpose is the separation of the cosmic microwave background radiation from the Galactic emission, in a noise-free setup, using a model of correlated sources. Since the Galactic emission does not obey this model, we propose a method to select the effective model order. As there are more detectors than signal-space dimensions, a dimension reduction scheme is derived. Our simulations show a good match between the closed-form analytical expression for the error and its empirical counterpart. This analytical expression is compact and involves inversions only of small matrices. Therefore, it can serve as a reliable predictor of the separation error without resorting to exhaustive Monte-Carlo trials.

This paper discusses a real time stimulus timing detection for a Brain-Machine-Interface (BMI). We present a low complexity detector for detecting the stimulus onset time from real multichannel, multi-unit electro-physiological data, recorded from a brainstem area called Pontine Nucleus (PN). The detector contains a novel pre-processing block, which takes advantage of the high coherence between different channels during response, in order to enhance the Signal-to- Noise Ratio (SNR), as well as to achieve higher detection rates. An intuitive effective method for fusion and combination of different channels based on spike counts is used. A full detailed description of the algorithm blocks is presented, along with its optimized parameters according to real data performance evaluation.

This paper considerers a symmetric Gaussian interference game with incomplete information where players choose between frequency division multiplexing (FDM) and full spread (FS) of their transmit power. Previously, the only known Nash equilibrium point for this game was the point where players mutually choose FS and interfere with each other. This point may lead to undesirable outcome from global network point of view and even for each user individually. It happens when mutual FDM is better to both users than mutual FS. In this paper, we show that if users agree to use different sub-bands in the case of FDM, then there exist a non pure-FS Nash equilibrium point, i.e. an equilibrium point where players choose FDM for some channel realizations and FS for the others. This Nash equilibrium point increases each user's throughput and therefore improves the spectrum utilization. Furthermore, to reach this point, the only instantaneous channel state information (CSI) required by each user is its interference-to-signal ratio.

Electromagnetic waves are known to be influenced by atmospheric conditions. Therefore, wireless communications, in which electromagnetic signals carry the information, can be used in environmental studies. In a recently published paper, it has been demonstrated that received signal level (RSL) measurements from fixed terrestrial line-of-sight microwave links, deployed by cellular operators, can be used to estimate space-time rainfall intensities [1]. In this follow-up paper we present recent real data results based on a rigorous algorithm which converts received signal level measurements from a set microwave links in an arbitrary geometry, lengths and frequencies into a two dimensional rain map. As such, the great potential of using globally spread wireless communication systems for accurate two dimensional rainfall monitoring has is exploited.

The problem of detecting muons in a particle detector is considered. The tracks of high momentum muons can be considered as straight lines, and thus well known techniques for line detection, such as the Hough transform, can be used. In this paper, we show that the Hough transform, which is commonly used in high energy physics, can be interpreted as an approximation of the generalized likelihood ration test (GLRT). We consider the case of a muon detector which consists of a set of sub-detectors, where each sub-detector provides a random activity measurement. Using the probability density functions of these activity measurements, a GLRT for muon detection is calculated, and its performance - when approximated by the Hough transform - is demonstrated.

Direct sequence code division multiple access (CDMA) systems that use non-continuous transmission were considered throughout the history of spread spectrum systems, but gained renewed interest with the emergence of impulse radio (IR) technology. Recently, several works had shown that in non- continuous CDMA, the transmission duty cycle (or transmission probability) has a significant effect on system performance. In this work we address the optimization of the performance of CDMA systems with adjustable transmission probabilities. We consider CDMA systems that implement non-continuous transmission by random puncturing, and study the system optimization with respect to both transmission powers (termed power control) and transmission probabilities (termed probability control). We show that the joint optimization has a significant performance advantage over the optimization with respect to transmissions powers only. For some cases we even show that the optimization with respect to transmission probabilities alone is sufficient to achieve optimal performance. In this part, we demonstrate the importance of probability control, by studying the case of frequency-flat slow-fading multiple access channel (MAC) and no spreading. We prove, for this special case, that mutual information rate optimization is achieved by probability control only, while power control is redundant. The theory is supported by simulation results, which show that the achievable rates of all users are better in a system that uses probability control instead of power control.

Code division multiple access (CDMA) systems commonly use power control mechanism to reduce the amount of interference between the users. In part I of this paper, we introduced the concept of probability control that optimizes system performance with respect to the users' transmission probabilities. The importance of probability control was demonstrated by proving that probability control alone optimizes the mutual information rates over a frequency-flat slow-fading multiple access channel. In this part we extend this result to the optimization of the average signal-to-noise plus interference ratio (SIR) in a CDMA system over a frequency-selective slow- fading channel model and any network topology. We prove that there is a group of CDMA receivers, in which the average SIR (ASIR) of all users is maximized using probability control (while all users transmit their maximal allowed power). This receivers group includes, among others, the common matched filter (MF) RAKE receiver, as well as the sophisticated minimal mean square error (MMSE) RAKE receiver. Simulations demonstrate for a 2- users scenario that both users achieve significantly higher ASIR using probability-control instead of power-control. Results are applicable both for CDMA and impulse radio (IR) systems.

Signal-to-noise ratio (SNR) estimation is considered for phase-shift keying communication systems in time-varying fading channels. Both data-aided (DA) estimation and nondata-aided (NDA) estimation are addressed. The time-varying fading channel is modeled as a polynomial-in-time. Inherent estimation accuracy limitations are examined via the Cramer-Rao lower bound, where it is shown that the effect of the channel's time variation on SNR estimation is negligible. A novel maximum-likelihood (ML) SNR estimator is derived for the time-varying channel model. In DA scenarios, where the estimator has a simple closed-form solution, the exact performance is evaluated both with correct and incorrect (i.e., mismatched) polynomial order. In NDA estimation, the unknown data symbols are modeled as random, and the marginal likelihood is used. The expectation-maximization algorithm is proposed to iteratively maximize this likelihood function. Simulation results show that the resulting estimator offers statistical efficiency over a wider range of scenarios than previously published methods.

This paper studies the fundamental transmission limits for ultra wideband (UWB) downlink broadcast channels. The significant contribution of this article is demonstrating the effectiveness of adaptive frequency allocation in UWB systems. We derive an expression for the ergodic sum-rate capacity of an UWB channel with perfect channel knowledge, and show the advantage of an adaptive system that uses channel state information (CSI), over a conventional, non-adaptive system. A capacity achieving system is also proposed. In this system, the transmitter assigns each frequency band to the user that has the best channel gain, and adaptively changes the bandwidth allocation according to the known channel state. The sum-rate capacity can be achieved in a fast fading channel. For a slow fading channel the system must apply fair scheduling to ensure service to all users, and the optimization must be performed for each channel realization. In this case, we also take advantage of the wide bandwidth of the UWB system and show the advantage of an frequency adaptive systems over non frequency adaptive systems

Signal processing, and especially statistical signal processing, is a field in which generic tools for modeling, analysis and processing of signals are developed. Traditionally, it has been used in technology, and most modern technological systems apply advanced signal processing. However, the post-genomic era introduces challenges which, from a signal processing point of view, may lead to new understanding and promising results. We propose to apply statistical signal processing tools to the problem of DNA repair, where nature operates as a master engineer. The DNA repair process consists of small machines (proteins, enzymes), which continuously transmit and receive signals from each other. The system regulates its operation; it has feedback loops and backup paths. We suggest modeling the components of the DNA repair system by a probability Markov state diagram.

Impulse radio (IR) systems have drawn attention during the last few years. These systems are planned to coexist with narrowband systems without interfering them. Nevertheless, the narrowband systems can cause interference which may jam the IR receiver. This letter analyzes a low-complexity narrowband interference (NBI)-mitigation algorithm for IR systems, based on minimal mean-square error combining. Theoretical analysis reveals that these algorithms nearly eliminate the NBI. The concept is also extended to the case where the receiver has more correlators than channel taps.

Semi blind impulse radio (IR) is a low complexity receiver, which improves performance by employing prior knowledge of the pulse transmission times of all other users. In this paper we investigate the optimization of the operation of a semi-blind IR system as a multiuser, multiple-access system. We show that optimal semi-blind IR has significant performance improvement over a code division multiple access (CDMA) system. This performance increase is measured by the achievable rate region, and it is shown that using semi-blind IR, the rate of at least one of the users can be made higher, without decreasing the rate of any user.

In this paper, we consider training-based symbol timing synchronization for continuous phase modulation over channels subject to flat, Rayleigh fading. A high signal-to-noise-ratio maximum-likelihood estimator based on a simplified channel correlation model is derived. The main objective is to reduce algorithm complexity to a single-dimensional search on the delay parameter, similar to that of the static-channel (slow fading) estimator. The asymptotic behavior of the algorithm is evaluated, and comparisons are made with the Cramer-Rao lower bound for the problem. Simulation results demonstrate highly improved performance over the conventional, static-channel delay estimator.

Detecting the number of sources is a well known and a well investigated problem. In this problem, the number of sources impinging on an array of sensors is to be estimated. The widely used processor is based on the Minimum Description Length (MDL) criterion where the array is assumed unstructured and the radiating sources are assumed Gaussian. This paper presents an asymptotic analysis of the performance of a different estimator, when some a-priori information is utilized: In particular, the performance of the MDL estimator which assumes Gaussian sources and a structured array when applied to Gaussian sources is analyzed. It is shown that appropriate use of the prior knowledge about the array geometry can lead to significant improvement in the detection performance. Simulation results show good fit between the empirical and the theoretical results.

Data-Aided Signal-to-Noise-Ratio (SNR) estimation is considered for time selective fading channels whose time variation is described by a polynomial time model. The inherent estimation accuracy limitations associated with the problem are quantified via a Cramer-Rao Bound analysis. A maximum likelihood type class of estimators is proposed and its exact, non-asymptotic performance is computed. The standard, constant channel SNR estimator performance is determined in the presence of channel polynomial order mismatch. Simulations results are presented which verify the effectiveness of the technique as well as its performance advantage over previously proposed methods.

Non-data-aided (NDA) signal-to-noise-ratio (SNR) estimation is considered for binary phase shift keying systems where the data samples are governed by a normal mixture distribution. Inherent estimation accuracy limitations are examined via a simple, closed-form approximation to the associated Cramer-Rao bound which eliminates the need for numerical integration. The expectation-maximization algorithm is proposed to iteratively maximize the NDA likelihood function. Simulation results show that the resulting estimator offers statistical efficiency over a wider range of scenarios than previously published methods.

This letter addresses the problem of consistent constant false-alarm rate (CFAR) detection based on partially consistent observations. The term "partially consistent observations" refers to the fact that the number of unknown parameters increases with the number of samples, and therefore, the number of observed samples is insufficient for consistent estimation of all parameters. Specifically, the problem of detecting a deterministic signal with unknown linear parameters in nonstationary white Gaussian noise is addressed. Two families of CFAR detectors are proposed; their consistency is discussed; and their performance is examined.

In many applications there exists an array of cells (or bins), each containing either an activity (signal) plus noise, or noise only. A common problem is to identify the active bins, assuming that the noise level in the array is unknown. In this paper we present a novel approach for solving this problem. The approach is based on two steps. In the first, we estimate the noise level and in the second we perform a sequential test to decide, for each bin, whether it is active or not. We show that the proposed algorithm collapses to well known special cases. The performance of the proposed algorithm is analyzed analytically and is demonstrated via simulation results.

We define a generalized scattering function for the spatio-temporal propagation channel. The definition is free of the restrictive assumption that there is a finite number of scatterers. We derive the time-varying vector channel between the source and the array in a unified manner and define a correlation function and a power spectrum that incorporate the spatial parameter-directly giving rise to the new scattering function of the spatio-temporal channel. In practice, the scattering function can be estimated by applying a well-known non-parametric spectrum estimation method to data obtained from an appropriately designed channel sounding experiment. The estimator's performance is evaluated theoretically and by simulation.

In this paper we consider a time synchronization problem for a minimum shift keying (MSK) signal received over a time-selective, fast fading channel. We calculate the Cramer Rao bound (CRB) for the case when the transmitted data bits are a-priori known and examine the effects of parameters such as signal-to-noise ratio (SNR) and temporal correlation of the channel on the synchronization performance. In addition, we derive an explicit high SNR approximation to the CRB. Lastly, we use the bound to study how the choice of transmitted bits (the training sequence) influences synchronization performance thus enabling us to identify the best and worst case bit sequences.

Estimating the parameters of a skewed /spl alpha/-stable distribution calls for estimation of four unknown parameters of the probability density function (PDF): the location parameter, the scale parameter, the characteristic exponent and the skewness parameter. We present cumulative distribution function (CDF) based estimators for either the location parameter, the skewness parameter, or the characteristic exponent. The estimators are simple, consistent and their asymptotic performance is analyzed. Of a particular interest is the new estimator for the skewness parameter which is given in a closed form, as a function of the other parameters. As such, it can be used for reducing the search dimension when joint parameter estimation of a skewed stable distribution is called for.

The problem of using antenna array measurements to estimate the bearing of a mobile communications user surrounded by local scatterers is considered. The concept of "partial coherence" is introduced to account for the temporal as well as spatial correlation effects often encountered in mobile radio propagation channels. A simple, intuitive parametric model for temporal channel correlation is presented. The result is an overall spatio-temporal channel model which is more realistic than formerly proposed models (which assume either full or zero temporal channel correlation). Thus, previously posed bearing estimation problems for a "distributed" or "scattered" source are generalized to a joint spatio-temporal parameter estimation problem. A study of the associated Cramer-Rao Bound for the case of known transmitted signal of constant modulus indicates that the inherent accuracy limitations associated with this generalized problem lie somewhere between the cases of zero and full temporal correlation and become more severe as temporal channel correlation increases.

A new approach for estimating the number of radiating, not fully correlated sources using the data received by an array of sensors is presented. The common approach is to apply information theoretic criteria, such as the minimum description length (MDL) or the Akaike information criterion (AIC), on the received data. Alternatively, we suggest to apply these criteria on the ordered eigenvalues of the sample data covariance matrix. While asymptotically, as the number of snapshots tends to infinity, the two approaches converge, we demonstrate that for any finite number of samples there exist physical conditions for which the proposed approach outperforms the traditional one. These cases are associated with spatially close sources, or with highly correlated sources, or with the case of sources with very different signal-to-noise ratio (SNR).

The problem of passive localization of coherently scattered sources with an array of sensors is considered. The spatial extent of such a source is typically characterized by an angular mean and an angular spreading parameter. The maximum likelihood (ML) estimator for this problem requires a complicated search of dimension equal to twice the number of sources. However, a previously reported sub-optimal MUSIC type method reduces the search dimension to two (independently of the number of sources). In this paper, the search over the angular mean parameter in the above MUSIC type technique is replaced by a possibly more efficient polynomial rooting procedure. Computer simulations verify the effectiveness of the proposed method compared to the performance of the ML and MUSIC estimators as well as to the Cramer-Rao bound.

This paper deals with the effect of sampling the continuous observations on parameter estimation errors. In particular, we study the problem of estimating the time of arrival (TOA) of a continuous, deterministic signal in noise. For this problem, the sampling procedure transforms the continuous parameter space into a discrete one, resulting in inherent estimation errors. We introduce a general tool for evaluating the achievable performance for any parameter estimation problem at a given sampling rate. For TOA estimation with a Gaussian-shaped signal, we show that one can undersample with a factor up to 3 times the Nyquist rate with an average TOA estimation performance reduction of less than 3 dB.

It is not possible, in practice, to precisely model a complex propagation channel, such as shallow water. This lack of accuracy causes a deterioration in the performance of the optimal detector and motivates the search for sub-optimal detectors which are insensitive to uncertainties in the propagation model. We present a novel, robust detector, which measures the degree of spatial-stationarity of the received field, exploiting the fact that a signal propagating in a bounded channel induces non-spatial-stationarity. The performance of the proposed detector is evaluated using both simulated data and experimental data collected in the Mediterranean Sea. This performance is compared to those of three other detectors, employing different extents of prior information. It is shown that when the propagation channel is not completely known, as is the case of the experimental data, the novel detector outperforms the others. That is, this detector couples good performance with robustness to propagation uncertainties.

The Barankin (1949) bound is a realizable lower bound on the mean-square error (MSE) of any unbiased estimator of a (nonrandom) parameter vector. We present a Barankin-type bound which is useful in problems where there is a prior knowledge on some of the parameters to be estimated. That is, the parameter vector is a hybrid vector in the sense that some of its entries are deterministic while other are random variables. We present a simple expression for a positive-definite matrix which provides bounds on the covariance of any unbiased estimator of the nonrandom parameters and an estimator of the random parameters, simultaneously. We show that the Barankin bound for deterministic parameters estimation and the Bobrovsky-Zakai (1976) bound for random parameters estimation are special cases of our proposed bound.

This paper presents a new, non-parametric test for detecting modeling mismatches in a propagation medium, as shallow water. The test is based on the fact that if there are no model uncertainties, the corresponding modal spectrum of the received signal is strictly band-limited to an a-priori known band. Any mismatches in the assumed model cause the modal spectrum out of this band to be non-zero. To make the test independent of the emitters characteristic we use the generalized likelihood ratio test which uses maximum likelihood estimate of the unknown modal spectrum. We demonstrate the operation of the proposed test by applying it (via computer simulations) to a complex, practical scenario.

We use the term hybrid parameter vector to refer to a vector which consists of both random and non-random parameters. We present a novel Barankin-type lower bound which bounds the estimation error of a hybrid parameter vector. The bound is expressed in a simple matrix form which consists of a non-Bayesian bound on the non-random parameters, a Bayesian bound on the random parameters, and the cross terms. We show that the non-Bayesian Barankin (1949) bound for deterministic parameters estimation and the Bobrovsky-Zakai (1976) Bayesian bound for random parameters estimation are special cases of the new bound. Also, the multi-parameter Cramer-Rao bound, in its Bayesian or non-Bayesian versions, are shown to be special cases of the new bound.

This paper presents a robust maximum-likelihood estimator for matched-field source localization in the presence of uncertainties in the ocean environment. The method is based on a decomposition of the field into predictable and unpredictable subspaces of the acoustic normal mode representation. The performance of the method is evaluated and compared to other matched-field methods using simulations and acoustic array data from the Mediterranean Sea. The algorithm has superior probability of correct localization than the maximum-likelihood, matched-mode-processing, and Bartlett methods.

We report results of a research in which we studied the problem of determining the threshold signal to noise ratio (SNR) between large and small errors in the estimation of the direction of arrival (DOA) of a radiating, far-field source in the presence of another. Using the Barankin lower bound (BB) we examine the conditions under which achievable mean square error (MSE) performance of any unbiased DOA estimator deviates substantially from the Carmer-Rao lower bound (CRB). We present expressions for the threshold SNR as a function of the source-array geometry and the sources SNR where one and two sources, of known/unknown spectral parameters and DOAs, are present.

Source localization in a waveguide involves a multidimensional search procedure. The authors propose a new algorithm, in which the search in the depth direction is replaced by polynomial rooting. The proposed algorithm decreases the search dimension to one for a 2D localization problem (range and depth) and to two for a 3D one (range, depth) and direction-of arrival (DOA), independently of the number of sources. Consequently, the presented algorithm requires significantly less computation.

For the detection of a not-perfectly-known signal in noise, usually no uniformly most powerful test exists, and thus a detector performance depends on the signal representation. The use of the wavelet representation of signals to perform a new detection scheme is discussed. The advantage of using this particular representation is shown. It is shown that prior information regarding the relative bandwidth and the time-bandwidth-product of the signal to be detected is efficiently incorporated into the detection problem formulation. Thus, the proposed detection scheme is most suitable for detection of unknown transient signals when prior information about the signal time-bandwidth product and relative bandwidth exists. In these cases, the wavelet-representation-based detector performs better than any other. The structure of the proposed detectors is discussed and its performance is evaluated using Monte Carlo simulations.>

The authors compare the output of a certain generalized matched filter to a threshold for detection of a signal of known waveshape, but unknown arrival time and time-scaling factor in white Gaussian noise. It is shown that this generalized matched filter is actually the wavelet transform, and the authors suggest implementing the proposed detector using the discrete wavelet transform. The performance of the proposed detector is studied, and it is shown that, under proper design of the parameter grid, its performance is near-optimal.>

A method of detecting arbitrary random signals in the presence of additive Gaussian noise is discussed. The method is based on eigendecomposition of the noise probability subspace. This decomposition leads to unique detector structure, invariant with respect to the signal distribution. The resulting detection scheme uses a variable number of terms per decision, but any decision made is exactly the same as the one produced by the optimal detector. The scheme is found to be computationally efficient, and well suited for generalization to the case of unknown (or only partially known) statistics. The efficiency of the algorithm is demonstrated in a typical example, with the aid of computer simulations.>

The effect of timing-error (jitter) on the bispectrum (third-order spectrum) is discussed. Expressions for the bispectrum of jittered sampled data are derived under different models of the jitter process. Under the assumption that the timing errors are independent and identically distributed random variables, these expressions are studied for typical jitter distributions. It is shown that while the unjittered discrete bispectrum is zero in a triangle that is a proper subset of the principal domain triangle, the jittered bispectrum is not. A closed-form expression for the additive bispectrum due to small jitter of any symmetric distribution is presented, and its validity is demonstrated.>

Optimal detection of a multitone signal in Gaussian noise and its relation to bispectral analysis are addressed. Using hypothesis testing methods the optimal detector of a multitone signal with random phases and (known) harmonic relations is derived. It is shown that the optimal receiver consists of a power spectrum block, and a block which deals with the phase coupling. Under a low signal-to-noise ratio (SNR) assumption, this extra block is closely related to a processor based on the bispectral analysis. Thus, a detector which is based on a superposition of the output of the conventional noncoherent detector and the bispectrum estimate of the input signal is a suboptimal one, approaching optimal performance in the low SNR case.>

A summary of results concerning passive array calibration using far-field sources in known/unknown directions and/or near-field sources in known/unknown locations is presented. All possible combinations of the four different types of sources are referred to. For each of them, the minimal number of sources of each kind which enable array calibration is established. Pathological geometries under which array calibration fails are presented. The justification of the results is purely geometrical so no statistical assumptions concerning the source signals and/or the sensor locations uncertainties are needed.>

The authors present the maximum-likelihood (ML) time-delay estimator (TDE) for a special class of non-Gaussian signals, when the radiated signal is a harmonically related random multitone signal. For this case they show that when the signal has a nonzero bispectrum (i.e. in the case of phase coupling), the ML TDE consists of the noncoherent estimator plus an extra processor that is, at least for low SNR, directly related to the signal bispectrum. The performance of the TDE is analyzed by using the Cramer-Rao lower bound, and it is shown that the improved processor is superior.>

The authors present a closed-form, simple expression for a lower bound on the variance of an unbiased estimator of the bearing of a narrowband source in the presence of any number of interfering sources received by an arbitrary M-sensor array. The sources radiate narrowband, statistically independent Gaussian signals. The spectral levels of all signals are unknown a priori. The bound is a good approximation of the Cramer-Rao lower bound (CRLB) in large signal-to-noise-ratio (SNR) and/or observation time conditions. Since the CRLB is used as a measure of efficiency for source location estimation algorithms, the bound gives some insight into the asymptotic properties of an optimal estimator. It shows that the estimation of the bearing of the ith source is inversely proportional to the SNR of this source and is not a function of the SNRs of the other sources. The incremental error due to the presence of other sources is uniquely determined by the beam pattern of the conventional array and its first derivative at the different source spatial separations.>

The problem of estimating directions of multiple broadband sources using the eigenstructure of the tempospatial data covariance matrix (TSCM) is dealt with. K.M. Buckley and L.J. Griffiths (1986) suggested that, similarly to the narrowband case, the eigenstructure of this covariance matrix can be used to estimate the signal-only (or noise-only) subspace and then use it for direction estimation. However, even for a single source and a given arbitrary array geometry, the eigenvalues of the signal-only tempospatial covariance matrix (TSCM), and therefore its effective rank, depend on the source direction as well as on its spectral level. This leads to serious difficulties in the implementation of Buckley and Griffiths' algorithm. The authors show here that by using a special array geometry, namely a two dimensional circular array, the eigenvalues of the signal-only TSCM for one source are practically independent of the source direction. Based on this property, they suggest a more feasible algorithm for parameter estimation of multiple broadband sources using an array of circular geometry.>

Implementation of the Complex Cepstrum (CC) and its inverse, using processors based on surface acoustic waves (SAW) devices, is presented. Design considerations based on theoretical analysis are given. The performance of the processor, partly built and totally simulated, is demonstrated as applied to recovering of a signal corrupted by multipath echoes.