We derive fundamental accuracy limits for distributed localization when a fusion center has access only to independently rate–distortion (RD)-optimally compressed versions of multi-sensor observations, under a line-of-sight propagation model with a Gaussian wideband waveform. Using the Gaussian RD test-channel model together with a Whittle spectral Fisher-information characterization, we obtain an explicit frequency-domain Cramér–Rao lower bound. A two-band, two-level specialization yields closed-form expressions and reveals a rate-induced regime change: RD-optimal compression under a squared-error distortion measure can eliminate localization-informative spectral content. A simple band-selective scheme can outperform RD compression by orders of magnitude at the same rate, motivating localization-aware compression for networked sensing and integrated sensing and communication systems.

The need to digitize signals with intricate spectral characteristics often challenges traditional analog-to-digital converters (ADCs). The recently proposed modulo-ADC architecture offers a promising alternative by leveraging inherent features of the input signals. This approach can dramatically reduce the number of bits required for the conversion while maintaining the desired fidelity. However, the core algorithm of this architecture, which utilizes a prediction filter, functions properly only when the respective prediction error is bounded. In practice, this assumption may not always hold, leading to considerable instability and performance degradation. To address this limitation, we propose an enhanced modulo-unfolding solution without this assumption. We develop a reliable detector to successfully unfold the signals, yielding a robust solution. Consequently, the reinforced system maintains proper operation in scenarios where the original approach fails, while also reducing the quantization noise. We present simulation results that demonstrate the superior performance of our approach in a representative setting.

The ubiquitous time-delay estimation (TDE) problem becomes nontrivial when sensors are non-co-located and communication between them is limited. Building on the recently proposed "extremum encoding" compression-estimation scheme, we address the critical extension to complex-valued signals, suitable for radio-frequency (RF) baseband processing. This extension introduces new challenges, e.g., due to unknown phase of the signal of interest and random phase of the noise, rendering a naïve application of the original scheme inapplicable and irrelevant. In the face of these challenges, we propose a judiciously adapted, though natural, extension of the scheme, paving its way to RF applications. While our extension leads to a different statistical analysis, including extremes of non-Gaussian distributions, we show that, ultimately, its asymptotic behavior is akin to the original scheme. We derive an exponentially tight upper bound on its error probability, corroborate our results via simulation experiments, and demonstrate the superior performance compared to two benchmark approaches.

Motivated by the proliferation of mobile devices, we consider a basic form of the ubiquitous problem of time-delay estimation (TDE), but with communication constraints between two non co-located sensors. In this setting, when joint processing of the received signals is not possible, a compression technique that is tailored to TDE is desirable. For our basic TDE formulation, we develop such a joint compression-estimation strategy based on the notion of what we term "extremum encoding", whereby we send the index of the maximum of a finite-length time-series from one sensor to another. Subsequent joint processing of the encoded message with locally observed data gives rise to our proposed time-delay "maximum-index"-based estimator. We derive an exponentially tight upper bound on its error probability, establishing its consistency with respect to the number of transmitted bits. We further validate our analysis via simulations, and comment on potential extensions and generalizations of the basic methodology.

Learning the physical environment is an important yet challenging task in reverberant settings such as the underwater and indoor acoustic domains. The locations of reflective boundaries, for example, can be estimated using echoes and leveraged for subsequent, more accurate localization. Current boundary estimation methods are constrained to a regime of high signal strength, or mitigate noise with heuristic (suboptimal) filters. These limitations can lead to fragile estimators that fail under non-ideal conditions. Furthermore, many algorithms in the literature also require a correct assignment of echoes to boundaries, which is combinatorially hard. To evade these limitations, we develop a convolutional neural network method for robust 2D boundary estimation, given known emitter and receiver locations. Our method uses as its input data format transform images, which are the potential boundary locations mapped into curves. We demonstrated in simulations that the proposed neural network method outperforms alternative state-of-the-art algorithms.

We study the single-channel source separation problem involving orthogonal frequency-division multiplexing (OFDM) signals, which are ubiquitous in many modern-day digital communication systems. Related efforts have been pursued in monaural source separation, where state-of-the-art neural architectures have been adopted to train an end-to-end separator for audio signals (as 1-dimensional time series). In this work, through a prototype problem based on the OFDM source model, we assess—and question—the efficacy of using audio-oriented neural architectures in separating signals based on features pertinent to communication waveforms. Perhaps surprisingly, we demonstrate that in some configurations, where perfect separation is theoretically attainable, these audio-oriented neural architectures perform poorly in separating co-channel OFDM waveforms. Yet, we propose critical domain-informed modifications to the network parameterization, based on insights from OFDM structures, that can confer about 30 dB improvement in performance.

Key challenges in developing underwater acoustic localization methods are related to the combined effects of high reverberation in intricate environments. To address such challenges, recent studies have shown that with a properly designed architecture, neural networks can lead to unprecedented localization capabilities and enhanced accuracy. However, the robustness of such methods to environmental mismatch is typically hard to characterize, and is usually assessed only empirically. In this work, we consider the recently proposed data-driven method [18] based on a deep convolutional neural network, and demonstrate that it can learn to localize in complex and mismatched environments. To explain this robustness, we provide an upper bound on the localization mean squared error (MSE) in the "true" environment, in terms of the MSE in a "presumed" environment and an additional penalty term related to the environmental discrepancy. Our theoretical results are corroborated via simulation results in a rich, highly reverberant, and mismatch channel.

A bilateral (i.e., upper and lower) bound on the mean-square error under a general model mismatch is developed. The bound, which is derived from the variational representation of the chi-square divergence, is applicable in the Bayesian and nonBayesian frameworks to biased and unbiased estimators. Unlike other classical MSE bounds that depend only on the model, our bound is also estimator-dependent. Thus, it is applicable as a tool for characterizing the MSE of a specific estimator. The proposed bounding technique has a variety of applications, one of which is a tool for proving the consistency of estimators for a class of models. Furthermore, it provides insight as to why certain estimators work well under general model mismatch conditions.

We propose a new method for separating superimposed sources using diffusion-based generative models. Our method relies only on separately trained statistical priors of independent sources to establish a new objective function guided by $\textit{maximum a posteriori}$ estimation with an $\textit{$\alpha$-posterior}$, across multiple levels of Gaussian smoothing. Motivated by applications in radio-frequency (RF) systems, we are interested in sources with underlying discrete nature and the recovery of encoded bits from a signal of interest, as measured by the bit error rate (BER). Experimental results with RF mixtures demonstrate that our method results in a BER reduction of 95\% over classical and existing learning-based methods. Our analysis demonstrates that our proposed method yields solutions that asymptotically approach the modes of an underlying discrete distribution. Furthermore, our method can be viewed as a multi-source extension to the recently proposed score distillation sampling scheme, shedding additional light on its use beyond conditional sampling. The project webpage is available at https://alpha-rgs.github.io.

We study the problem of extracting biometric information of individuals by looking at shadows of objects cast on diffuse surfaces. We show that the biometric information leakage from shadows can be sufficient for reliable identity inference under representative scenarios via a maximum likelihood analysis. We then develop a learning-based method that demonstrates this phenomenon in real settings, exploiting the subtle cues in the shadows that are the source of the leakage without requiring any labeled real data. In particular, our approach relies on building synthetic scenes composed of 3D face models obtained from a single photograph of each identity. We transfer what we learn from the synthetic data to the real data using domain adaptation in a completely unsupervised way. Our model is able to generalize well to the real domain and is robust to several variations in the scenes. We report high classification accuracies in an identity classification task that takes place in a scene with unknown geometry and occluding objects.

We study the potential of data-driven deep learning methods for separation of two communication signals from an observation of their mixture. In particular, we assume knowledge on the generation process of one of the signals, dubbed signal of interest (SOI), and no knowledge on the generation process of the second signal, referred to as interference. This form of the single-channel source separation problem is also referred to as interference rejection. We show that capturing high-resolution temporal structures (nonstationarities), which enables accurate synchronization to both the SOI and the interference, leads to substantial performance gains. With this key insight, we propose a domain-informed neural network (NN) design that is able to improve upon both “off-the-shelf” NNs and classical detection and interference rejection methods, as demonstrated in our simulations. Our findings highlight the key role communication-specific domain knowledge plays in the development of data-driven approaches that hold the promise of unprecedented gains.

In a growing number of applications, there is a need to digitize a (possibly high) number of correlated signals whose spectral characteristics are challenging for traditional analog-to-digital converters (ADCs). Examples, among others, include multiple-input multiple-output systems where the ADCs must acquire at once several signals at a very wide but sparsely and dynamically occupied bandwidth supporting diverse services. In such scenarios, the resolution requirements can be prohibitively high. As an alternative, the recently proposed modulo-ADC architecture can in principle require dramatically fewer bits in the conversion to obtain the target fidelity, but requires that spatiotemporal information be known and explicitly taken into account by the analog and digital processing in the converter, which is frequently impractical. Building on our recent work, we address this limitation and develop a blind version of the architecture that requires no such knowledge in the converter. In particular, it features an automatic modulo-level adjustment and a fully adaptive modulo-decoding mechanism, allowing it to asymptotically match the characteristics of the unknown input signal. Simulation results demonstrate the successful operation of the proposed algorithm.

One-bit quantization has recently become an attractive option for data acquisition in cutting edge applications, due to the increasing demand for low power and higher sampling rates. Subsequently, the rejuvenated one-bit array processing field is now receiving more attention, as "classical" array processing techniques are adapted / modified accordingly. However, array calibration, often an instrumental preliminary stage in array processing, has so far received little attention in its one-bit form. In this paper, we present a novel solution approach for the blind calibration problem, namely, without using known calibration signals. In order to extract information within the second-order statistics of the quantized measurements, we propose to estimate the unknown sensors' gains and phases offsets according to a Kullback-Leibler Divergence (KLD) covariance fitting criterion. We then provide a quasi-Newton solution algorithm, with a consistent initial estimate, and demonstrate the improved accuracy of our KLD-based estimates in simulations.

Blind calibration of sensors arrays (without using calibration signals) is an important, yet challenging problem in array processing. While many methods have been proposed for "classical" array structures, such as uniform linear arrays, not as many are found in the context of the more "modern" sparse arrays. In this paper, we present a novel blind calibration method for 2-level nested arrays. Specifically, and despite recent contradicting claims in the literature, we show that the Least-Squares (LS) approach can in fact be used for this purpose with such arrays. Moreover, the LS approach gives rise to optimally-weighted LS joint estimation of the sensors' gains and phases offsets, which leads to more accurate calibration, and in turn, to higher accuracy in subsequent estimation tasks (e.g., direction-of-arrival). Our method, which can be extended to K-level arrays (K > 2), is superior to the current state of the art both in terms of accuracy and computational efficiency, as we demonstrate in simulation.

We study the blind calibration problem of uniform linear arrays of acoustic vector sensors for narrowband Gaussian signals, and propose an improved, asymptotically optimal blind calibration scheme. Following recent work by Ramamohan et al., we exploit the special (block-Toeplitz) structure of the underlying signals' spatial covariance matrix. However, we offer a substantial improvement over their ordinary Least Squares (LS)-based approach: Using asymptotic approximations we obtain Optimally-Weighted LS estimates of the sensors' gains and phases offsets. We show via simulations that our estimates exhibit near-optimal performance, with improvements reaching more than an order of magnitude in the mean squared estimation errors of the calibration parameters, as well as in directions of-arrival estimation.

We address the problem of source separation from noisy mixtures in a semi-blind scenario, with stationary, temporally-diverse Gaussian sources and known spectra. In such noisy models, a dilemma arises regarding the desired objective. On one hand, a "maximally separating" solution, providing the minimal attainable Interference-to-Source-Ratio (ISR), would often suffer from significant residual noise. On the other hand, optimal Minimum Mean Square Error (MMSE) estimation would yield estimates which are the "least distorted" versions of the true sources, often at the cost of compromised ISR. Based on Maximum Likelihood (ML) estimation of the unknown underlying model parameters, we propose two ML-based estimates of the sources. One asymptotically coincides with the MMSE estimate of the sources, whereas the other asymptotically coincides with the (unbiased) "least-noisy maximally-separating" solution for this model. We prove the asymptotic optimality of the latter and present the corresponding Cramér-Rao lower bound. We discuss the differences in principal properties of the proposed estimates and demonstrate them empirically using simulation results.

A novel blind estimate of the number of sources from noisy, linear mixtures is proposed in this letter. Based on Székely et al.'s distance correlation measure, we define the sources' dependence criterion (SDC), from which our estimate arises. Unlike most previously proposed estimates, the SDC estimate exploits the full independence of the sources and noise, as well as the non-Gaussianity of the sources (as opposed to the Gaussianity of the noise), via implicit use of high-order statistics. This leads to a more robust, resilient, and stable estimate w.r.t. the mixing matrix and the noise covariance structure. Empirical simulation results demonstrate these virtues on top of superior performance in comparison with current state-of-the-art estimates.

Tensor decompositions are regarded as a powerful tool for multidimensional signal processing. In this contribution, we focus on the well-known Canonical Polyadic (CP) decomposition and present a first-order perturbation analysis of the SEmi-algebraic framework for approximate CP decompositions via SImultaneous matrix diagonalization with Generalized Unfoldings (SECSI-GU), which is advantageous for tensors of an order higher than three. Numerical results indicate that the analytical relative Mean Square Factor Error (rMSFE) of the estimated factor matrices resulting from each generalized unfolding considered in SECSI -GU matches the empirical rMSFE very well. As SECSI -GU considers all possible partitionings of the tensor modes resulting in a large number of candidate factor matrix estimates, an exhaustive search-based criterion to select the final factor matrix estimates leads to a prohibitive computational complexity. The accurate performance prediction achieved by the first-order perturbation analysis conducted in this paper will significantly facilitate the selection of the final factor matrix estimates in an efficient manner and will therefore contribute to a low-complexity enhancement of SECSI-GU.

Electrocardiography (ECG) measured using wearable wireless sensors is already commonly used for several years, as one of the products of the emerging Telemedicine field, which is one the main branches in eHealth applications. In this work we address the problem of missing samples recovery of such ECG (digital) signals, resulting from temporally-local communication dropouts. We propose a new model for the ECG signal based on its conspicuous quasi-periodical characteristics in short time intervals, along with a compatible estimation procedure tailored to the proposed model. We extend the autoregressive (AR) model, previously proposed by Prieto-Guerrero et al., to a cyclostationary AR model, and our proposed estimation scheme incorporates a first phase of model parameters estimation, followed by a Linear Minimum Mean Squared Error (LMMSE) estimation phase of the missing samples. We demonstrate significant improvement compared to the AR method in simulation experiments using real ECG data.

In its basic, fully blind form, Independent Component Analysis (ICA) does not rely on a particular statistical model of the sources, but only on their mutual statistical independence, and therefore does not admit a Maximum Likelihood (ML) estimation framework. In semi-blind scenarios statistical models of the sources are available, enabling ML separation. Quasi-ML (QML) methods operate in the (more realistic) fully-blind scenarios, simply by presuming some hypothesized statistical models, thereby obtaining QML separation. When these models are (or are assumed to be) Gaussian with distinct temporal covariance matrices, the (quasi-)likelihood equations take the form of a “Sequentially Drilled Joint Congruence” (SeDJoCo) transformation problem. In this work we state some mild conditions on the sources' true and presumed covariance matrices, which guarantee consistency of the QML separation when the SeDJoCo solution is asymptotically unique. In addition, we derive a necessary “Mutual Diversity” condition on these matrices for the asymptotic uniqueness of the SeDJoCo solution. Finally, we demonstrate the consistency of QML in various simulation scenarios.

Joint EigenValue Decomposition (JEVD) algorithms are widely used in many application scenarios. These algorithms can be divided into different categories based on the cost function that needs to be minimized. Most of the frequently used algorithms in the literature use indirect least square (LS) criteria as a cost function. In this work, we perform a first order perturbation analysis for the JEVD algorithms based on the indirect LS criterion. We also present closed-form expressions for the eigenvector and eigenvalue matrices. The obtained expressions are asymptotic in the signal-to-noise ratio (SNR). Additionally, we use these results to obtain a statistical analysis, where we only assume that the noise has finite second order moments. The simulation results show that the proposed analytical expressions match well to the empirical results of JEVD algorithms which are based on the LS cost function.

The “Sequentially Drilled” Joint Congruence (SeDJoCo) transformation is a set of matrix transformation equations, which coincide with the Likelihood Equations for semi-blind source separation, when each source is modeled as a zero-mean Gaussian process with a known (and distinct) temporal covariance matrix. Therefore, with such a model a solution of SeDJoCo can lead to the Maximum Likelihood (ML) estimate of the separating matrix, which is asymptotically optimal. However, as we have shown in previous work, multiple solutions of SeDJoCo may exist, and the selection of the optimal solution among these (corresponding to the global maximum of the likelihood function) is therefore of considerable interest. In this paper we further extend our results by proposing a new ML approach for the identification and correction of a sub-optimal solution, assuming sources of unrestricted, general temporal covariance structures. We demonstrate the resulting improvement in simulation with non-stationary sources.