A polarimetric synthetic aperture radar (PolSAR) system, which uses multiple images acquired with different polarizations in both transmission and reception, has the potential to improve the description and interpretation of the observed scene. This is typically achieved by exploiting the polarimetric covariance or coherence matrix associated with each pixel, which is processed to meet a specific goal in Earth observation. This paper presents a design framework for selecting the structure of the polarimetric covariance matrix that accurately reflects the symmetry associated with the analyzed pixels. The proposed methodology leverages both polarimetric and temporal information from multipass PolSAR images to enhance the retrieval of information from the acquired data. To accomplish this, it is assumed that the covariance matrix (of the overall acquired data) is given as the Kronecker product of the temporal and polarimetric covariances. An alternating maximization algorithm, known as the flip-flop method, is then developed to estimate both matrices while enforcing the symmetry constraint on the polarimetric covariance. Subsequently, the symmetry structure classification is formulated as a multiple hypothesis testing problem, which is solved using model order selection techniques. The proposed approach is quantitatively assessed on simulated data, showing its advantages over its competitor, which does not exploit temporal correlations. For example, it reaches accuracies of 94.6% and 92.0% for the reflection and azimuth symmetry classes, respectively, while the competitor achieves 72.5% and 72.6% under the same simulation conditions. Moreover, the proposed method can realize a Cohen’s kappa coefficient of 0.95, which significantly exceeds that of its counterpart equal to 0.78. Finally, the effectiveness of the proposed framework is further demonstrated using measured RADARSAT-2 data, corroborating the results obtained from the simulations. Specifically, tests conducted applying the Freeman-Durden Wishart classification have proved that the new approach greatly enhances the accuracy of pixel classification. For instance, in areas dominated by surface scattering, it boosts the percentage of correctly classified pixels from 68.23%, achieved using the classic method, to 91.65%.

The design of bespoke adaptive detection schemes relying on the joint use of multistatic/polarimetric measurements requires a preliminary statistical inference on the clutter interference environment. This is of paramount importance to develop an analytic model for the received signal samples, which is mandatory for the synthesis of radar detectors. In this respect, the aim of this paper is the development of suitable learning tools to study some important statistical features of the sea-clutter environment perceived at the nodes of a multistatic/polarimetric radar system. Precisely, stationarity of the data in the slow-time domain is first assessed resorting to Generalized Inner Product (GIP) based statistics. Then, the possible presence of structural symmetries in the clutter covariance matrices is investigated. Finally, relationships between some statistical parameters characterizing the sea-clutter returns on the bistatic polarimetric channels are explored via a specific sequential hypothesis testing. This research activity is complemented by the use of radar returns measured via the Netted RADar (NetRAD), which collects simultaneously monostatic and bistatic polarimetric measurements. The results indicate that the analyzed data can be modeled as drawn from a stationary Gaussian process within the coherence time. Additionally, the bistatic returns on the different polarimetric channels can be assumed statistically independent with speckle components possibly exhibiting proportional/equal covariance matrices depending on the transmit/receive polarization and bistatic geometry.

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 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 Cramér-Rao Bound (CRB)) and signal-to-interference-plus-noise ratio, especially in comparison with state-of-the art strategies. Moreover, the estimation task is accomplished with a remarkable reduction in computational complexity compared with a standard approach relying on a Semidefinite Programming (SDP) solver.

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 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 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 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.

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 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.

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 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.

A new derivation of the Capon spectral estimator is provided in this letter enriching the set of its possible interpretations. Specifically, it is shown that it defines the best rank-one approximation (according to any distance measure induced by a unitary invariant norm) of the data covariance matrix along the dyadic product specified by the useful signal direction. Remarkably, the Capon power estimate is obtained as solution to a convex optimization problem, which represents the starting point toward the development of a new class of robust estimators.

Radar signal design in spectrally dense environments is a very challenging and topical problem. This letter deals with the synthesis of waveforms optimizing radar performance while satisfying multiple spectral compatibility constraints. Unlike some counterparts available in the open literature, a specific control on the interference energy radiated on each shared bandwidth is enforced. To tackle the resulting NP-hard optimization problem, a polynomial computational complexity procedure based on semidefinite relaxation (SDR) and randomization is developed. Hence, some numerical results are shown to highlight the effectiveness of the new technique to devise high-performance radar waveforms complying with the spectral compatibility requirements.

We develop a polynomial-time procedure to handle a class of generalized fractional programming (GFP) problems with Toeplitz-Hermitian quadratics exploiting the linear matrix inequality (LMI) representation of the finite autocorrelation sequences cone, the spectral factorization theorem, and the Dinkelback's algorithm. For the special case of fractional quadratic programming (FQP) problems, we also provide a SemiDefinite programming (SDP) reformulation of the resulting non-convex optimization by means of the Charnes-Cooper transformation. Finally, we focus on an interesting radar signal processing application to assess the effectiveness of the devised optimization tool.

This letter deals with adaptive radar detection of targets embedded in Gaussian clutter plus range-distributed subspace-structured jamming by exploiting the invariance theory. The class of invariant detectors which ensure the constant false alarm rate property has been characterized by designing the maximal invariant statistic for the studied detection problem. The achievement of this letter is the coincidence of the obtained maximal invariant with that derived assuming range-concentrated jamming.

In this work we propose an adaptive receiver with enhanced range estimation capabilities, which jointly exploits the over-sampling of the noisy returns and the spillover of target energy to adjacent range samples. To this end, a proper discrete-time model for the received signal is introduced. Then, the Generalized Likelihood Ratio Test (GLRT) is derived and assessed. The performance analysis highlights that better detection performances and increased range estimation accuracies can be achieved exploiting the oversampling at the price of an additional processing cost.

In this paper, we study the joint design of Doppler robust transmit sequence and receive filter to improve the performance of an active sensing system dealing with signal-dependent interference. The signal-to-interference-plus-noise ratio (SINR) of the filter output is considered as the performance measure of the system. The design problem is cast as a max-min optimization problem to robustify the system SINR with respect to the unknown Doppler shifts of the targets. To tackle the design problem, we devise a novel method to obtain optimized pairs of transmit sequence and receive filter sharing the desired robustness property.

In this letter, we devise an adaptive decision scheme for point-like targets capable of handling the joint presence of homogeneous clutter and structured interference in the primary and secondary data. To this end, we resort to a design procedure based on the method of sieves: the usual generalized likelihood ratio test (GLRT) is modified constraining the unknown parameters to belong to a suitable subset of the original space ensuring unique solutions for the involved optimizations. Remarkably, the proposed receiver possesses the constant false alarm rate (CFAR) property with respect to the unknown covariance matrix of the unstructured interference. At the analysis stage, closed-form expressions for the false alarm and detection probabilities are derived.

In this paper, we provide an information-theoretic analysis of a Gaussian multiple-input multiple-output multiple access channel (MIMO MAC) with imperfect channel knowledge at the receiver. In particular, we derive inner and outer bounds for the MIMO MAC rate region when the inputs are Gaussian. We then apply these bounds to a Gaussian interference network with receiver cooperation, in which a central processor with incomplete channel state information must jointly decode all the received signals. Then, in the case where the channel knowledge at the receiver is obtained through training signals, we derive the structure of the optimum training signals for all users under a definite and semidefinite rank constraint. Numerical results show that the bounds we derive can be quite tight, confirming the asymptotic analysis conducted for the finite case. Finally, we also investigate the low-SNR and high-SNR regimes, specifically analyzing the minimum required energy per information bit and the wideband slope region in the first case, and the high-SNR slope in the second.

In this work we provide an information-theoretic analysis of a Gaussian multiple-input multiple-output multiple access channel (MIMO MAC) with imperfect channel knowledge at the receiver. In particular we derive inner and outer bounds for the rate region of the MIMO MAC when the inputs are Gaussian. In the case where the channel knowledge at the receiver is obtained through training signals, we derive the structure of the optimum training signals for all users under a definite and semi-definite rank constraint. Numerical results show that the bounds we derive can be quite tight. Finally, we also investigate the low-SNR regime, specifically analyzing the minimum required energy per information bit and the wideband slope region.

In this paper, we consider a multiple-input-multiple-output (MIMO) detection problem withMwidely spaced transmit antennas andLwidely spaced receive antennas, and we study the problem of designing the signal waveforms transmitted by each source node under non-Gaussian target scattering and temporally correlated Gaussian clutter. Two figures of merit are investigated for space-time code (STC) optimization under a semidefinite rank constraint: 1) the lower Chernoff bound (LCB) to the detection probability for fixed probability of false alarm, and 2) the mutual information (MI) between the observations available at the receive nodes and the “channel response” generated by a point-like target, assumed present tout court. Both receive and transmit power constraints are discussed. If the scattering distribution possesses some suitably defined properties of unitary invariance (see Section II-B), both MI-optimal and LCB-optimal STCs have a simple canonical structure: the same set of (clutter dependant) temporal codewords are employed at the transmit nodes, the only difference among the many solutions being the amount of power radiated by each antenna. Such a spatial power allocation critically depends upon the adopted figure of merit, the specified power constraint, and the underlying scattering model. Sufficient conditions to determine the optimal power allocation for all design criteria are provided. Asymptotic power distributions are also derived in the limit of vanishingly small and increasingly large signal-to-clutter ratios, proving that assuming Gaussian scattering at the design stage is a robust choice. A case study of relevant practical interest is examined in depth so as to compare the proposed design criteria and to assess the impact of signal non-Gaussianity on the system performances.

We consider a multiple-input multiple-output (MIMO) detection problem with widely-spaced antennas at both the transmitter and the receiver, and we assume that target scattering is modeled as an exchangeable and unitarily-invariant process. We illustrate optimal signal design (i.e., space-time coding) at the transmitter for two criteria, i.e. the lower Chernoff bound (LCB) to the detection probability for fixed probability of false alarm and the mutual information (MI) between the observations and the target scattering matrix, under a semi-definite rank constraint and a transmit power constraint, showing that the Gaussian scattering assumption is robust. A by-product, of not secondary importance, of our derivation is the proof of a number of new properties concerning concavity and Schur-concavity of MI and LCB.

Coordinating the reception and transmission of signals across spatially distributed base stations has been shown to improve sum-rate performance by mitigating the effects of intercell interference in Multiple-Input-Multiple-Output (MIMO) cellular networks. Relying on recent results on the freeness of certain non-Gaussian random matrices, we provide an information theoretic analysis of cooperative MIMO networks. This analysis applies to the case where full channel state information is known at a subset of the bases and where statistical information is known at all others. Tools for evaluating random matrix transforms traditionally exploited in Mean Square Error (MSE) and mutual information analysis are provided, and the general model formulation paves the way for future work, where specific scheduling and/or power assignment schemes could be embodied in the newly presented framework.