A Geometric Approach to Covariance Matrix Estimation and its Applications to Radar Problems

A new class of disturbance covariance matrix estimators for radar signal processing applications is introduced following a geometric paradigm. Each estimator is associated with a given unitary invariant norm and performs the sample covariance matrix projection into a specific set of structured covariance matrices. Regardless of the considered norm, an efficient solution technique to handle the resulting constrained optimization problem is developed. Specifically, it is shown that the new family of distribution-free estimators shares a shrinkagetype form; besides, the eigenvalues estimate just requires the solution of a one-dimensional convex problem whose objective function depends on the considered unitary norm. For the two most common norm instances, i.e., Frobenius and spectral, very efficient algorithms are developed to solve the aforementioned one-dimensional optimization leading to almost closed form covariance estimates. At the analysis stage, the performance of the new estimators is assessed in terms of achievable Signal to Interference plus Noise Ratio (SINR) both for a spatial and a Doppler processing assuming different data statistical characterizations. The results show that interesting SINR improvements with respect to some counterparts available in the open literature can be achieved especially in training starved regimes.Comment: submitted for journal publicatio

Power-Aperture Resource Allocation for a MPAR with Communications Capabilities

Multifunction phased array radars (MPARs) exploit the intrinsic flexibility of their active electronically steered array (ESA) to perform, at the same time, a multitude of operations, such as search, tracking, fire control, classification, and communications. This paper aims at addressing the MPAR resource allocation so as to satisfy the quality of service (QoS) demanded by both line of sight (LOS) and non line of sight (NLOS) search operations along with communications tasks. To this end, the ranges at which the cumulative detection probability and the channel capacity per bandwidth reach a desired value are introduced as task quality metrics for the search and communication functions, respectively. Then, to quantify the satisfaction level of each task, for each of them a bespoke utility function is defined to map the associated quality metric into the corresponding perceived utility. Hence, assigning different priority weights to each task, the resource allocation problem, in terms of radar power aperture (PAP) specification, is formulated as a constrained optimization problem whose solution optimizes the global radar QoS. Several simulations are conducted in scenarios of practical interest to prove the effectiveness of the approach.Comment: 12 pages, 14 figure

Power-Aperture Resource Allocation for a MPAR with Communications Capabilities

Multifunction phased array radars (MPARs) exploit the intrinsic flexibility of their active electronically steered array (ESA) to perform, at the same time, a multitude of operations, such as search, tracking, fire control, classification, and communications. This paper aims at addressing the MPAR resource allocation so as to satisfy the quality of service (QoS) demanded by both line of sight (LOS) and reflective intelligent surfaces (RIS)-aided non line of sight (NLOS) search operations along with communications tasks. To this end, the ranges at which the cumulative detection probability and the channel capacity per bandwidth reach a desired value are introduced as task quality metrics for the search and communication functions, respectively. Then, to quantify the satisfaction level of each task, for each of them a bespoke utility function is defined to map the associated quality metric into the corresponding perceived utility. Hence, assigning different priority weights to each task, the resource allocation problem, in terms of radar power aperture (PAP) specification, is formulated as a constrained optimization problem whose solution optimizes the global radar QoS. Several simulations are conducted in scenarios of practical interest to prove the effectiveness of the approach

Power-Aperture Product Resource Allocation for Radar ISAC

This article deals with the problem of power aperture product (PAP) management in a multifunction phased array radar (MPAR) performing sensing in both line of sight (LOS) and non line of sight (NLOS), and communications. To this end, two different quality metrics are introduced, namely the range where the cumulative detection probability (for sensing) and the channel capacity per bandwidth (for communications) attain a specified value. Then, suitable utility functions are defined to map the quality index relative to the corresponding perceived utility for each task. The resource allocation is hence formulated as a constrained optimization problem whose solution optimizes the global radar quality of service (QoS). The method is finally validated by means of numerical simulations

New Methods for MLE of Toeplitz Structured Covariance Matrices with Applications to RADAR Problems

This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced and two iterative algorithms are proposed for the optimization of the equivalent statistical learning framework. Both the strategies are based on the Majorization Minimization (MM) paradigm and hence enjoy nice properties such as monotonicity and ensured convergence to a stationary point of the equivalent MLE problem. The proposed framework is also extended to deal with MLE of other practically relevant covariance structures, namely, the banded Toeplitz, block Toeplitz, and Toeplitz-block-Toeplitz. Through numerical simulations, it is shown that the new methods provide excellent performance levels in terms of both mean square estimation error (which is very close to the benchmark Cram\'er-Rao Bound (CRB)) and signal-to-interference-plus-noise ratio, especially in comparison with state of the art strategies.Comment: submitted to IEEE Transactions on Signal Processing. arXiv admin note: substantial text overlap with arXiv:2110.1217

Non-cooperative code design in radar networks: a game-theoretic approach

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Statistical Hypothesis Testing Based on Machine Learning: Large Deviations Analysis

We study the performance -- and specifically the rate at which the error probability converges to zero -- of Machine Learning (ML) classification techniques. Leveraging the theory of large deviations, we provide the mathematical conditions for a ML classifier to exhibit error probabilities that vanish exponentially, say $\sim \exp\left(-n\,I + o(n) \right)$, where $n$ is the number of informative observations available for testing (or another relevant parameter, such as the size of the target in an image) and $I$ is the error rate. Such conditions depend on the Fenchel-Legendre transform of the cumulant-generating function of the Data-Driven Decision Function (D3F, i.e., what is thresholded before the final binary decision is made) learned in the training phase. As such, the D3F and, consequently, the related error rate $I$, depend on the given training set, which is assumed of finite size. Interestingly, these conditions can be verified and tested numerically exploiting the available dataset, or a synthetic dataset, generated according to the available information on the underlying statistical model. In other words, the classification error probability convergence to zero and its rate can be computed on a portion of the dataset available for training. Coherently with the large deviations theory, we can also establish the convergence, for $n$ large enough, of the normalized D3F statistic to a Gaussian distribution. This property is exploited to set a desired asymptotic false alarm probability, which empirically turns out to be accurate even for quite realistic values of $n$. Furthermore, approximate error probability curves $\sim \zeta_n \exp\left(-n\,I \right)$ are provided, thanks to the refined asymptotic derivation (often referred to as exact asymptotics), where $\zeta_n$ represents the most representative sub-exponential terms of the error probabilities

3D Localization and Tracking Methods for Multi-Platform Radar Networks

Multi-platform radar networks (MPRNs) are an emerging sensing technology due to their ability to provide improved surveillance capabilities over plain monostatic and bistatic systems. The design of advanced detection, localization, and tracking algorithms for efficient fusion of information obtained through multiple receivers has attracted much attention. However, considerable challenges remain. This article provides an overview on recent unconstrained and constrained localization techniques as well as multitarget tracking (MTT) algorithms tailored to MPRNs. In particular, two data-processing methods are illustrated and explored in detail, one aimed at accomplishing localization tasks the other tracking functions. As to the former, assuming a MPRN with one transmitter and multiple receivers, the angular and range constrained estimator (ARCE) algorithm capitalizes on the knowledge of the transmitter antenna beamwidth. As to the latter, the scalable sum-product algorithm (SPA) based MTT technique is presented. Additionally, a solution to combine ARCE and SPA-based MTT is investigated in order to boost the accuracy of the overall surveillance system. Simulated experiments show the benefit of the combined algorithm in comparison with the conventional baseline SPA-based MTT and the stand-alone ARCE localization, in a 3D sensing scenario

Radar detection performance prediction using measured UAVs RCS data

This paper presents measurements of Radar Cross Section (RCS) of five Unmanned Aerial Vehicles (UAVs), comprising both consumer grade and professional small drones, collected in a semi-controlled environment as a function of azimuth aspect angle, polarization and frequency in the range 8.2-18 GHz. The experimental setup and the data pre-processing, which include coherent background subtraction and range gating procedures, are illustrated in detail. Furthermore, a thorough description of the calibration process, which is based on the substitution method, is discussed. Then, a first-order statistical analysis of the measured RCSs is provided by means of the Cramér-von Mises (CVM) distance and the Kolmogorov-Smirnov (KS) test. Finally, radar detection performance is assessed on both measured and bespoke simulated data (leveraging the results of the developed statistical analysis), including, as benchmark terms, the curves for non-fluctuating and Rayleigh fluctuating targets