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In this paper, the design of binary sequences exhibiting low values of aperiodic/periodic correlation functions, in terms of Integrated Sidelobe Level (ISL), is pursued via a learning-inspired method. Specifcally, the synthesis of either a single or a burst of codes is addressed, with reference to both Single-Input Single-Output (SISO) and Multiple-Input Multiple-Output (MIMO) radar systems. Two optimization machines, referred to as two-layer and single-layer Binary Sequence Correlation Network (BiSCorN), able to learn actions to design binary sequences with small ISL/Complementary ISL (CISL) for SISO and MIMO systems are proposed. These two networks differ in terms of the capability to synthesize Low-Correlation-Zone (LCZ) sequences and computational cost. Numerical experiments show that proposed techniques can outperform state-of-the-art algorithms for the design of binary sequences and Complementary Sets of Sequences (CSS) in terms of ISL and, interestingly, of Peak Sidelobe Level (PSL).

This article deals with the synthesis and analysis of quasi-orthogonal nonlinear frequency modulation (NLFM) waveforms to mitigate the impairments of ambiguous returns in quadrature-polarimetric (quad-pol) synthetic aperture radars (SARs). To this end, focusing on signals with a continuous piecewise linear instantaneous frequency, the design of a waveform pair exhibiting both a low cross correlation energy (CCE) and low peak to sidelobe ratios (PSLRs), is considered. To handle the resulting nondeterministic polynomial (NP) hard problem, a coordinate descent (CD) method is employed, where, at each step, the marginal minimization is tackled via a MATLAB optimization toolbox. Hence, transmission/reception schemes jointly capitalizing quasi-orthogonal NLFM waveforms and azimuth phase coding (APC) techniques are proposed to suppress ambiguity interference. Moreover, a systematic framework for the evaluation of the resulting azimuth ambiguity-to-signal ratio (AASR) and range ambiguity-to-signal ratio (RASR) is provided. Finally, detailed simulation experiments based on the LuTan (LT-1) parameters are carried out to verify the practicability and effectiveness of the newly proposed transceiver schemes.

This article outlines the archetype of a novel SpaceBorne Radar (SBR) in the Ka-band for space situational awareness (SSA) based on a code-division multiplexing (CDM) multiple-input-multiple-output (MIMO) payload transceiver. Considering small-size hypervelocity debris, the functional architecture of the fully polarimetric SBR is described, including key comparisons with previous works based on single-input-multiple-output (SIMO) configurations. SBR operations are clarified via timing hierarchies in surveillance mode, the complex data hypercube structure, and the low pulse repetition frequency (L-PRF) range and range rate search (RRRS) entailing a track while simultaneous search (TWSS) contacts collection strategy. Ancillary details on the SBR functional architecture provide paramount insights to ponder critical MIMO aspects and pave the way for key research and development efforts. Finally, numerical results provide a proof of concept for the signal processor upstream the constant false alarm rate-like (CFAR-like) detection block.

This article deals with the problem of angle and incremental range (i.e., the target range offset with respect to the center of the cell under test) estimation with a frequency diverse array multiple-input multiple-output (FDA-MIMO) radar exploiting a single data snapshot as observable. Starting from the observation that the maximum likelihood (ML) estimation entails a 2-D grid search over the parameters of interest, three approximated ML techniques are designed resorting to the coordinate descent algorithm and the adaptive monopulse criterion (employing either real or complex slope/bias corrections). At the analysis stage, the estimation performance of the proposed methods, including the tapered and double-step monopulse versions, is also assessed in comparison with the Cramér-Rao lower bound. Numerical results corroborate the effectiveness of the considered estimation strategies in some diverse simulated scenarios.

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.

This paper deals with joint adaptive radar detection and target bearing estimation in the presence of mutual coupling among the array elements. First of all, a suitable model of the signal received by the multichannel radar is developed via a linearization procedure of the Uniform Linear Array (ULA) manifold around the nominal array looking direction together with the use of symmetric Toeplitz structured matrices to represent the mutual coupling effects. Hence, the Generalized Likelihood Ratio Test (GLRT) detector is evaluated under the assumption of homogeneous radar environment. Its computation leverages a specific Minorization-Maximization (MM) framework, with proven convergence properties, to optimize the concentrated likelihood function under the target presence hypothesis. Besides, when the number of active mutual coupling coefficients is unknown, a Multifamily Likelihood Ratio Test (MFLRT) approach is invoked. During the analysis phase, the performance of the new detectors is compared with benchmarks as well as with counterparts available in the open literature which neglect the mutual coupling phenomenon. The results indicate that it is necessary to consider judiciously the coupling effect since the design phase, to guarantee performance levels close to the benchmark., submitted to IEEE Transactions on Signal Processing

A new algorithm for passive bistatic radar (PBR) localization is proposed via joint exploitation of multiple illuminators of opportunity and measurements gathered by a colocated active radar. Ad-hoc constraints within the localization process are bestowed accounting for both a priori information on the PBR receive antenna main-beam size and the uncertainty characterizing active radar data, i.e., the root mean square error (RMSE) of range/bearing measurements. Hence, the estimation task is cast as an elliptic positioning problem, according to the constrained least squares framework. The resulting non-convex optimization problem is globally solved providing a closed-form estimate in Cartesian coordinates. The performance of the proposed estimator, in terms of RMSE, exhibits sensible improvement with respect to counterparts. The proposed technique is also applied to the case of a dynamic scenario for a bi-sensor surveillance system, where the active rotating platform acquires measurements at each scanning period. The results show the localization performance improvement achieved when the system is complemented with a PBR staring in a specific search sector of interest.

This paper deals with the use of Reconfigurable Intelligent Surfaces (RISs) for radar surveillance in Non-Line Of Sight (N-LOS) scenarios. First of all, the geometry of the scene and the new system concept is described with emphasis on the required operative modes and the role played by the RIS. Then, the specific radar equation (including the RIS effect) is developed to manage the coverage requirements in the challenging region where the LOS is not present. Both noise and clutter interference cases (pulse length-limited and beamwidth-limited surface clutter as well as volume clutter) are considered. Hence, a digression on the use of the radar timeline for the new operative mode is presented together with the data acquisition procedure and the resolution issues for the range, azimuth, and Doppler domains. Finally, the interplay among the system parameters and, in particular, those involving the RIS is discussed and analyzed via numerical simulations., Comment: typo corrected in the first equation on page 6

This paper is focused on the detection and resolution of Unmanned Aerial Vehicles (UAVs) via a multi-channel phased-array radar with emphasis on the challenging situation where multiple targets are unresolved in the range-Doppler domain and closely spaced in angle. An adaptive processor is devised which, after triggering a detection in a given range-Doppler cell, implements a binary decision about the presence of a single or multiple targets. In the former situation, the plain monopulse algorithm is used to estimate the target azimuth whereas, in the latter case, a super-resolution technique is activated to get the angular parameters of the UAVs. The performance of the signal processor is assessed both on simulated and on measured data (endowed by ground-truth) collected by a 12-channel phased-array radar operating in the C-band. The results highlight the capabilities of the architecture to detect the presence of targets, to discriminate the single from the multiple targets scenario, and to resolve the UAVs in angle domain when they are unresolved in range and Doppler.

Following governmental strategies to acquire “…capability to watch for objects and natural phenomena that could harm satellites in orbit,” a number of ground-based radars (GBRs) have been deployed for space situational awareness (SSA). In particular, networks of GBRs support the characterization of possible collision trajectories for different types of debris against orbital assets. On the other side, despite increasing demands for augmenting space-based monitoring capabilities for near-earth SSA, there is no evidence of operative SpaceBorne Radars (SBRs) for debris detection and tracking. In the absence of experimental data, one may ponder the design of a novel SBR payload transceiver with specific benefits for SSA, especially if compared to GBRs inference capabilities. In line with this reasoning, this article provides, for the first time, a holistic and harmonizing ontological framework for possible environmental scenarios that an SBR may have to cope with. The objective of such an ontology is related to the conceptual modeling of both channel and target phenomenology as well as target motion models. This, in turn, paves the way for reasonable mathematical formulations and architectural paradigms for framing SBR-based detection and tracking techniques, mostly with respect to small-size hypervelocity targets.

Due to increasing demands for spectral resources in both communication and radar systems, the radio frequency electromagnetic spectrum is becoming more and more crowded with interfering nuisances. In order to tackle the scarcity of available spectral intervals, in recent years a multitude of sensing algorithms have been developed for improving spectrum sharing. Among these, two-dimensional (2-D) spectrum sensing can be used to obtain space-frequency electromagnetic spectrum awareness. Specifically, this approach makes it possible to optimize the spectrum usage of certain spectrum portions whose occupancy varies both temporally and spatially. In this article, we evaluate the effectiveness of certain space-frequency map recovery algorithms relying on the use of commercially available hardware. To this end, we employ an inexpensive four-channel coherent receiver, using software-defined radio components, for emitter localization. Hence, after proper calibration of the receiving system, the acquired samples are used to evaluate the performance of different signal processing strategies which exploits the inherent block-sparsity of the overall profile. At the analysis stage, results reveal the effectiveness of such algorithms.

This article considers target separation detection (TSD) in the presence of homogeneous Gaussian interference. The problem is formulated as a hypothesis test for two typical situations: 1) the use of a low range-resolution radar or fast-track update rate; 2) the use of a high-resolution radar or low-track update rate. At the design stage, TSD tests are devised according to the generalized likelihood ratio test criterion. The computation of each decision statistic requires the solution of a semidefinite programming problem obtained leveraging the relationship among linear matrix inequalities and nonnegative trigonometric polynomials. All the obtained decision rules ensure the bounded constant false alarm rate property. At the analysis stage, the performance of some benchmark detectors is given in terms of detection and false alarm probabilities. Finally, numerical examples are provided to show the performance of the proposed tests as compared with the benchmarks as well as the gain achievable over some counterparts devised to monitor a separation event.

Radar operation in a spectrally dense environment is nowadays a very challenging problem due to the increasing demand of spectral resources for defence/surveillance applications, remote sensing capabilities, and civilian wireless services. This article explores the technical feasibility of radar waveforms capable of ensuring spectral coexistence with overlaid emitters via a modern digital arbitrary waveform generator. To this end, a specific hardware-in-the-loop test bed is designed to mimic the perception-action cycle necessary for the agile management of the radio spectrum. Then, a spectrum analyzer (SA) and a digital oscilloscope (DO) are used to demonstrate the compliance of the synthesized waveforms with the theoretical counterparts. In particular, the SA is used to establish if the synthesized waveforms fulfil the spectral requirements forced at the design stage. The DO, instead, is used to assess the adherence of synthesized signals ambiguity function (AF) with the theoretical one. For the considered case studies, results highlight that the synthesized waveforms enable spectral compatibility between radar and communication systems and exhibit desirable AF properties.

A new algorithm for 3D localization in multiplatform radar networks, comprising one transmitter and multiple receivers, is proposed. To take advantage of the monostatic sensor radiation pattern features, ad-hoc constraints are imposed in the target localization process. Therefore, the localization problem is formulated as a non-convex constrained Least Squares (LS) optimization problem which is globally solved in a quasi-closed-form leveraging Karush-Kuhn-Tucker (KKT) conditions. The performance of the new algorithm is assessed in terms of Root Mean Square Error (RMSE) in comparison with the benchmark Root Cramer Rao Lower Bound (RCRLB) and some competitors from the open literature. The results corroborate the effectiveness of the new strategy which is capable of ensuring a lower RMSE than the counterpart methodologies especially in the low Signal to Noise Ratio (SNR) regime.

This article deals with the effects of plasma turbulence on the detection performance of spaceborne radars (SBRs) for space situational awareness (SSA). Physical insights on both channel and target phenomenology lead to reasonable statistical models with a focus on the fading occurrence probability (FOP) in case of weak scintillation. Consequently, the performance analysis of conventional radar detectors in additive white Gaussian noise (AWGN) is provided in a monostatic configuration for either Rayleigh or Rice fluctuating targets, and considering Rice plasma scintillation as a function of the scintillation index $s_{4}$. Numerical results identify a paramount framework to characterize the influence of plasma turbulence on SBR detection performance for SSA. Finally, ancillary notes make provision for tailoring the performance analysis also in the case of bistatic radar configurations.

This article deals with the effects of power amplifiers (PAs) on radar waveforms designed to ensure spectral compatibility with other radio frequency wireless systems cohabitating in the same frequency band. To this end, a specific hardware-in-the-loop testbed composed of a personal computer, an arbitrary waveform generator, a nonlinear PA, and a signal analyzer is designed. It allows to gather measurements of the amplified signal and to grasp unwanted modifications of its spectral features due to the PA nonlinear distortion. Besides, it permits a quantitative assessment of the discrepancies between the nominal and the actual interference power injected by the radar in the shared frequency bandwidths. To alleviate the spectral distortions induced by the PA and improve spectral coexistence, the use of a digital predistortion (DPD) stage upstream the PA is investigated. Modeling techniques together with parameter inference are discussed and applied to the measured waveforms. The obtained experimental results highlight that pairing a suitable waveform design strategy with DPD processing represents a viable means to mitigate the PA distortions and to realize spectral coexistence.

This paper addresses adaptive detection of range spread targets in the presence of thermal noise, jammer, and clutter. After motivating the study, a set of clutter-free training (CFT) data is considered to assist radar detection in absence of conventional secondary data sharing the same spectral properties as the interference of the cells under test. To this end, a maximum likelihood (ML) estimate of the unknown parameters is derived under the alternative hypothesis by leveraging the primary data and the CFT data simultaneously. Subsequently, the ML estimate is used to design decision rules based on generalized likelihood ratio, complex parameter Wald, and complex parameter Gradient test criteria. Furthermore, conditions guaranteeing the constant false alarm rate (CFAR) property of the proposed detectors are discussed. At the analysis stage, numerical examples are presented to evaluate the effectiveness of the proposed detectors in comparison with other detection schemes available in the literature.

This paper deals with the synthesis of constant modulus waveforms that optimize radar performance while satisfying multiple spectral compatibility constraints. For each shared band, a precise control is imposed on the injected interference energy. Furthermore, the compliance with amplifiers operating in saturation is ensured at the design stage where phase-only waveforms are considered. To tackle the resulting NP-hard optimization problem, an iterative procedure based on the coordinate descent method is introduced. The overall computational burden of the algorithm is linear with respect to the code length as well as the number of iterations and less then cubic with reference to the number of spectral constraints. Hence, some case studies are reported to highlight the effectiveness of the technique.

Following a geometric paradigm, the estimation of a Toeplitz structured covariance matrix is considered. The estimator minimizes the distance from the Sample Covariance Matrix (SCM) while complying with some specific constraints modeling the covariance structure. The resulting constrained optimization problem is solved globally resorting to the Dykstra’ projection framework. Each step of the procedure involves the solution of two convex sub-problems, whose minimizers are available in closed form. Simulation results related to typical radar environments highlight the effectiveness of the devised method.

This paper studies adaptive radar detection of range distributed targets in the presence of Gaussian interference and possible diffuse multipath returns modeled as independent zero-mean complex circular Gaussian random vectors with unknown covariance matrices. For this problem, an adaptive constrained generalized likelihood ratio (ACGLR) test is devised, where in each range cell of the primary data the covariance matrix (due to both multipath and disturbance echoes) is forced to belong to a neighborhood of the secondary data sample covariance. The size of the uncertainty set is determined adaptively employing jointly a union-intersection test and an expectation likelihood (EL)-based estimate. Besides, an adaptive detector based on the complex parameter Rao test criterion is derived. Remarkably, both the two new architectures possess the desired constant false alarm rate (CFAR) property with respect to the disturbance covariance. Finally, their detection performance is assessed and validated via numerical examples.

This letter deals with similarity parameter selection for knowledge-aided covariance matrix estimation in adaptive radar signal processing. Starting from the observation that the maximum likelihood estimate of the interference covariance matrix under a similarity constraint admits a closed-form expression, which depends on the similarity parameter, an adaptive procedure is devised to get a parameter free estimator. The technique is based on the expected likelihood principle and requires the solution of an implicit equation, which can be efficiently pursued via the bisection method due a monotonicity property. The analysis of the estimator, conducted also in comparison with the counterpart based on the cross-validation method confirms its effectiveness in terms of both performance and computational complexity.

Two-dimensional (2-D) spectrum sensing is addressed in the context of a cognitive radar to gather real-time space-frequency electromagnetic awareness. Assuming a sensor equipped with multiple receive antennas, a discrete-time sensing signal model formally accounting for multiple snapshots of observations is introduced. Hence, a new signal processing strategy exploiting the inherent block-sparsity of the overall profile is developed to glean a reliable 2-D occupancy awareness. Specifically, the proposed approach resorts to the regularized maximum likelihood estimation paradigm including a term promoting the block-sparsity of the 2-D profile so as to automatically foster this peculiarity in the profile evaluation. Some illustrative examples (both on simulated and measured data) are provided to compare the novel strategy with a relevant counterpart available in the open literature and highlight the effectiveness of the developed approach.

In principle, the Automatic Identification System (AIS) makes covert rendezvous at sea, such as smuggling and piracy, impossible; in practice, AIS can be spoofed or simply disabled. Previous work showed a means whereby such deviations can be spotted. Here we play the opponent's side, and describe the least-detectable trajectory that the elusive vessel can take. The opponent's route planning problem is formalized as a non-convex optimization problem capitalizing the Kullback-Leibler (KL) divergence between the statistical hypotheses of the nominal and the anomalous trajectories as key performance measure. The velocity of the vessel is modeled with an Ornstein-Uhlenbeck (OU) mean reverting stochastic process, and physical and practical requirements are accounted for by enforcing several constraints at the optimization design stage. To handle the resulting non-convex optimization problem, we propose a globally-optimal and computationally-efficient technique, called the Non-Convex Optimized Stealth Trajectory (N-COST) algorithm. The N-COST algorithm consists amounts to solving multiple convex problems, with the number proportional to the number of segments of the piecewise OU trajectory. The effectiveness of the proposed approach is demonstrated through case studies and a real-world example.

This paper focuses on the joint synthesis of constant envelope transmit signal and receive filter aimed at optimizing radar performance in signal-dependent interference and spectrally contested-congested environments. To ensure the desired Quality of Service (QoS) at each communication system, a precise control of the interference energy injected by the radar in each licensed/shared bandwidth is imposed. Besides, along with an upper bound to the maximum transmitted energy, constant envelope (with either arbitrary or discrete phases) and similarity constraints are forced to ensure compatibility with amplifiers operating in saturation regime and bestow relevant waveform features, respectively. To handle the resulting NP-hard design problems, new iterative procedures (with ensured convergence properties) are devised to account for continuous and discrete phase constraints, capitalizing on the Coordinate Descent (CD) framework. Two heuristic procedures are also proposed to perform valuable initializations. Numerical results are provided to assess the effectiveness of the conceived algorithms in comparison with the existing methods., Comment: Submitted to IEEE Transactions on Signal Processing

Structured covariance matrix estimation in the presence of missing-(complex) data is addressed in this paper with emphasis on radar signal processing applications. After a motivation of the study, the array model is specified and the problem of computing the maximum likelihood estimate of a structured covariance matrix is formulated. A general procedure to optimize the observed-data likelihood function is developed resorting to the expectation-maximization algorithm. The corresponding convergence properties are thoroughly established and the rate of convergence is analyzed. The estimation technique is contextualized for two practically relevant radar problems: beamforming and detection of the number of sources. In the former case an adaptive beamformer leveraging the EM-based estimator is presented; in the latter, detection techniques generalizing the classic Akaike information criterion, minimum description length, and Hannan–Quinn information criterion, are introduced. Numerical results are finally presented to corroborate the theoretical study.

This article delves into a novel spaceborne radar payload transceiver for augmenting space-based monitoring capabilities for near-Earth space situational awareness. The sensor complex data hypercube structure and sensor timing hierarchies in surveillance mode are addressed along with a suitable low pulse repetition frequency range and range-rate search with a pause while scan collection strategy. A bespoke active electronically scanned array-based Pulse Doppler Radar sensor in the Ka-band is then defined in order to cope with the significant Doppler stress characterizing a burst of echoes from hypervelocity debris targets. Before feeding the onboard Bayesian tracker, the complex data hypercube is processed by means of a Doppler filter bank including pulse compression in cascade with a constant false alarm rate-like block.

This paper addresses adaptive detection of a range distributed target in the presence of dominant heterogeneous clutter, which is (possibly) low-rank and lies in a known subspace, plus Gaussian thermal noise. First, this problem is transformed into an equivalent binary hypothesis test with observations having block-diagonal covariance matrices. Then an invariance analysis is conducted on the resulting hypothesis test. Data and unknown parameters are compressed into a maximal invariant and an induced maximal invariant, respectively, w.r.t. a suitable transformation group. This suggests to focus attention on invariant detectors and to establish the relationship between invariance and constant false alarm rate (CFAR) property. According to this guideline, two tunable invariant detectors exploiting the aforementioned covariance structure are devised, and they are shown to ensure bounded CFAR and standard CFAR properties, respectively. Finally, the CFAR behavior of the proposed detectors as well as their detection performance is assessed via numerical simulations.

This article deals with the problem of adaptive target detection in the presence of homogeneous Gaussian interference with frequency diverse array multiple-input multiple-output radar. Adaptive detectors are devised according to the generalized likelihood ratio test criterion, where the position of the target within each range cell is assumed unknown. To obtain the maximum likelihood estimate of the target incremental range under the $H_1$ hypothesis, three different optimization strategies are pursued. They are, respectively, based on semidefinite programming, discrete grid search, and Newton method. At the analysis stage, a detection performance comparison is carried on among the new proposed adaptive detectors, benchmark, and mismatched receivers. Numerical results corroborate the effectiveness of the developed receivers.

This paper is focused on the design of phase sequences with good (aperiodic) autocorrelation properties in terms of Peak Sidelobe Level (PSL) and Integrated Sidelobe Level (ISL). The problem is formulated as a bi-objective Pareto optimization forcing either a continuous or a discrete phase constraint at the design stage. An iterative procedure based on the coordinate descent method is introduced to deal with the resulting optimization problems which are non-convex and NP-hard in general. Each iteration of the devised method requires the solution of a non-convex min-max problem. It is handled either through a novel bisection or an FFT-based method for the continuous and the discrete phase constraint, respectively. Additionally, a heuristic approach to initialize the procedures employing the lp-norm minimization technique is proposed. Simulation results illustrate that the proposed methodologies can outperform some counterparts providing sequences with good autocorrelation features especially in the discrete phase/binary case.

This paper deals with constant modulus waveform design in spectrally dense environments assuming a discrete phase code alphabet. The goal is to optimize the radar detection performance while rigorously controlling the injected interference energy within each shared band and enforcing a similarity constraint to manage some relevant signal features. To tackle the resulting NP-hard optimization problem, an iterative procedure characterized by a polynomial computational complexity, is introduced leveraging the coordinate descent method. Numerical results are provided to show the effectiveness of the technique in terms of detection performance, spectral shape and autocorrelation features.

This letter studies the conformity with the reciprocity theorem on the measured polarimetric synthetic aperture radar (SAR) data. The problem is formalized via a binary hypothesis test where the reciprocity assumption is tested versus its alternative (absence of reciprocity). The generalized likelihood ratio (GLR) is used as design criterion and the resulting decision rule ensures the constant false alarm rate (CFAR) property. At the analysis stage, the performance of the GLR statistic is analyzed on the simulated data as well as on two different measured data sets (collected by two systems) thus highlighting the effectiveness of the approach.

This letter deals with the robust joint design of radar transmit waveform and receive filter bank in a background of range unambiguous signal-dependent clutter. Assuming an unknown Doppler shift for the target, the worst-case Signal-to-Interference-plus-Noise-Ratio (SINR) at the output of the receive filter bank is considered as the figure of merit. The transceiver design is pursued considering a max-min optimization problem with some constraints on the transmit energy, similarity, and signal dynamic range. Hidden convexity is shown and a procedure to derive optimal waveform and filters is given. Simulation results highlight the effectiveness of the devised method.

Covariance matrix estimation is a crucial task in adaptive signal processing applied to several surveillance systems, including radar and sonar. In this paper we propose a dynamic learning strategy to track both the covariance matrix of data and its structure (class). We assume that, given the class, the posterior distribution of the covariance is described through a mixture of inverse Wishart distributions, while the class evolves according to a Markov chain. Hence, we devise a novel and general filtering strategy, called multi-class inverse Wishart mixture filter, able to capitalize on previous observations so as to accurately track and estimate the covariance. Some case studies are provided to highlight the effectiveness of the proposed technique, which is shown to outperform alternative methods in terms of both covariance estimation accuracy and probability of correct model selection. Specifically, the proposed filter is compared with class-clairvoyant covariance estimators, e.g., the maximum likelihood and the knowledge-based recursive least square filter, and with the model order selection method based on the Bayesian information criterion.

This paper is focused on noncooperative target position estimation via the joint use of two-dimensional (2-D) hyperbolic and elliptic passive location techniques based on time difference of arrival (TDOA) and passive coherent locator (PCL) measurements, respectively. A fusion strategy is laid down at the signal processing level to obtain a reliable estimate of the current target position. With reference to the scenario with a single transmitter of opportunity, the mathematical model for joint exploitation of TDOA and PCL strategies is formulated. Then, the Cramer-Rao lower bound (CRLB) for the Cartesian coordinates of the target is established and the theoretical performance gains achievable over the localization technique using only TDOA or PCL observations are assessed. Finally, TDOA-PCL hybrid 2-D localization algorithms are provided and their performance in terms of root-mean-square error is compared with the square root of the CRLB.

This paper is focused on simultaneous target detection and angle estimation with a multichannel phased array radar. Resorting to a linearized expression for the array steering vector around the beam pointing direction, the problem is formulated as a composite binary hypothesis test where the unknowns, under the alternative hypothesis, include the target directional cosines displacements with respect to the array nominal coarse pointing direction. The problem is handled via the Generalized Likelihood Ratio (GLR) criterion (both one-step and two-step) where decision statistics leveraging the Maximum Likelihood Estimates (MLEs) of the parameters are compared with a detection threshold. If crossed, target presence is declared and the MLEs of the aforementioned displacements directly provide target angular position with respect to the pointing direction. From the analytic point of view, ML estimation involves a constrained fractional quadratic optimization problem whose optimal solution can be found via the Dinkelbach's algorithm or approximated through a fast-converging procedure based on a Coordinate Descent (CD) optimization. The performance analysis of the proposed architectures as well as the corresponding discussion is developed in terms of computational complexity, Constant False Alarm Rate (CFAR) behavior, detection performance, and angular estimation accuracy, also in comparison with some counterparts available in the open literature and theoretical benchmark limits.

A new algorithm for Passive Bistatic Radar (PBR) localization exploiting multiple illuminators of opportunity is proposed. To capitalize a-priori information on the receiving antenna main-lobe extent, specific constraints are forced to the target localization process. At the estimator design process the elliptic positioning problem is formulated according to the constrained Least Squares (LS) framework. Hence, the resulting non-convex optimization problem is globally solved providing a closed-form estimate to the target Cartesian coordinates. At the analysis level, the performance of the new estimator is assessed in terms of Root Mean Square Error (RMSE) behavior. The results highlight that interesting MSE improvements with respect to some counterparts available in the open literature can be achieved especially at low Signal to Noise Ratio (SNR) values.

This paper considers the design of robust filters for radar pulse-Doppler processing when the interference is a wide sense stationary random process. The figure of merit which is optimized is the signal-to-interference-plus-noise ratio (SINR) at the filter output under a multitude of constraints accounting for Doppler filter sidelobes as well as uncertainties both in the received useful signal component and interference covariance matrix. The design is analytically formulated as a constrained optimization problem whose solvability is thoroughly studied. Precisely, a polynomial-time solution technique to get the optimal filter is proposed exploiting the representation of non-negative trigonometric polynomials via linear matrix inequalities, the spectral factorization theorem, and the duality theory. Last but not least, a detailed analysis of the optimum filter performance is provided showing the tradeoffs involved in the design and the gain achievable over some already known counterparts.

Random and unwanted fluctuations, which perturb the phase of an ideal reference sinusoidal signal, may cause significant performance degradation in radar systems exploiting coherent integration techniques. To quantify the resulting performance loss, we develop a fast-time/slow-time data matrix radar signal representation, modeling the undesired phase fluctuations via multivariate circular distributions and describing the phase noise power spectral density (PSD) through a composite power-law model. Hence, we accurately predict the performance degradation experienced by moving target indication (MTI) algorithms for clutter cancellation, providing a closed form expression for the improvement factor I. The subsequent analysis shows that phase noise affects I directly through its characteristic function (CF). Additionally, I shares a robust behavior with respect to the actual phase noise multivariate circular distribution, as long as the phase noise PSD correctly represents the available measurements.

Random and unwanted fluctuations that perturb the phase of an ideal reference sinusoidal signal may cause significant performance degradation in radar systems employing coherent integration techniques. In this second part of the study, resorting to the fast-time/slow-time data matrix representation developed in "Part I" of this two-part study, we assess the performance of both pulse Doppler processing (PDP) algorithms and sidelobe blanker (SLB) techniques when phase noise and Gaussian interference (clutter plus noise) impair the data. Specifically, we derive analytically manageable expressions for: 1) the probability of false alarm and the probability of detection of PDP algorithms; 2) the probability of false alarm, the probability of blanking a coherent repeater interference, and the probability of blanking a target in the mainlobe of SLB processors. Simulation results show that phase noise may slightly degrade the performance of PDP and SLB processors as long as its power spectral density correctly represents the available measurements. Additionally, the matched filter receiver ensures a high level of robustness against phase noise, highlighting its robustness against steering and covariance matrix mismatches, a property that we formally prove in the paper.

The problem of high range resolution profile (HRRP) estimation is considered in this paper. In particular, stepped frequency waveforms are devised to enhance the target range profile (RP) estimation accuracy. The basic idea relies on the dynamic optimization of the probing waveform accounting for some feedback information to minimize the profile estimation error. The transmitted frequency hopping pattern is selected so as to minimize the predicted Cramer–Rao lower bound (CRLB) associated with the amplitudes and locations of the scattering centers falling in the coarse range bin under test (i.e., the target profile). Specifically, it is assumed that the target imaging is initially performed via a conventional linear stepped frequency transmission, hence, based on the collected data, an initial prediction of the target profile is derived (perception). Then, the RP estimation is enhanced progressively according to the cognitive paradigm, via a specific frequency pattern selection at the next transmission (action). The results highlight the capabilities of the cognitive approach to provide interesting benefits with respect to the classic linear stepped frequency strategy.

In this study, authors address high-range-resolution (HRR) profile reconstruction, when stepped-frequency waveforms are eventually used to maintain a narrow instantaneous bandwidth, resorting to the sparse learning via iterative minimisation (SLIM) paradigm, a regularised minimisation approach with an l(q)-norm constraint (for 0 < q

The authors deal with the robust design of multiple-input–multiple-output (MIMO) space–time transmit code (STTC) and space–time receive filter (STRF) for a point-like target embedded in signal-dependent interference. Specifically, they assume that the radar exploits knowledge provided by dynamic environmental database, to roughly predict the actual scattering scenario. Then, they devise an iterative method to optimise the (constrained) STTC and the (constrained) STRF which sequentially improves the worst-case (over interfering scatterers statistics) signal-to-interference-plus-noise ratio (SINR). Each iteration of the algorithm is handled via solving two (hidden) convex optimisation problems. The resulting computational complexity is linear with the number of iterations and polynomial with the sizes of the STTC and the STRF. At the analysis stage, they assess the performance of the proposed algorithm in terms of the achieved SINR. They show that properly exploiting the spatial degrees of freedom offered by the MIMO system, it is possible to obtain considerable SINR gains with respect to the conventional single-input–single-output system. Moreover, their results highlight the capability of the proposed method to robustify the performance of the designed system against possible knowledge inaccuracies.

This study deals with the problem of adaptive radar detection when a limited number of training data, due to environmental heterogeneity, is present. Suppose that some a priori spectral models for the interference in the cell under test and a lower bound on the power spectral density (PSD) of the white disturbance term are available. Hence, generalised likelihood ratio test-based detection algorithms have been devised. At the design stage, the basic idea is to model the actual interference inverse covariance as a combination of the available a priori models and to account for the available lower bound on the PSD. At the analysis stage, the capabilities of the new techniques have been shown to detect targets when few training data are available as well as their superiority with respect to conventional adaptive techniques based on the sample covariance matrix.

Radar signal design in a spectrally crowded environment is a very challenging and topical problem due to the increasing demand for both military surveillance/remote-sensing capabilities and civilian wireless services. This paper deals with the synthesis of optimized radar waveforms ensuring spectral compatibility with the overlayed licensed electromagnetic radiators. A priori information, for instance, provided by a radio environmental map (REM), is exploited to force a spectral constraint on the radar waveform, which is thus the result of a constrained optimization process aimed at improving some radar performances (such as detection, sidelobes, resolution, tracking). The feasibility of the waveform optimization problem is extensively studied, and a solution technique leading to an optimal waveform is proposed. The procedure requires the relaxation of the original problem into a convex optimization problem and involves a polynomial computational complexity. At the analysis stage, the waveform performance is studied in terms of trade-off among the achievable signal to interference plus noise ratio (SINR), spectral shape, and the resulting autocorrelation function (ACF). © 2014 IEEE.

We read with great interest the recently published paper [1] (together with some additional technical details in [2]) dealing with an important topic for the radar signal processing Community.With regret, we noticed that the mentioned reference [1] provides some claims which do not agree with what we proved in paper [3]; contains some technical inconsistencies from the optimization theory point of view. Thus, respectfully, we feel obliged to provide the necessary clarifications and corrections. Specifically, this "comments on" paper has the following technical purposes: a) to rectify some untrue claims by the Authors of [1] about reference [3]; b) to show that the optimization problem arising in [1] (eq. (17)) is a special instance of the more general optimization problem addressed in [3] (eq. (13)); c) to prove that the solution of the waveform design problem in [1] (eq. (25)) given by eq. (36) is not generally correct. [1] P. Setlur and M. Rangaswamy, "Waveform Design for Radar STAP in Signal Dependent Interference," IEEE Transactions on Signal Processing, vol. 64, no. 1, pp. 19-34, Jan. 2016. [2] P. Setlur and M. Rangaswamy, Joint Filter and Waveform Design for Radar STAP in Signal Dependent Interference, Tech. Rep. DTIC, available at : https: // arxiv.org/abs/ 1510. 00055, US Air Force Res. Lab., Sensors Directorate, WPAFB, Dayton, OH, 2014. [3] A. Aubry, A. De Maio, A. Farina, and M. Wicks, "Knowledge-Aided (Potentially Cognitive) Transmit Signal and Receive Filter Design in Signal-Dependent Clutter," IEEE Transactions on Aerospace and Electronic Systems, vol. 49, no. 1, pp. 93-117, Jan. 2013.