Model order selection in multi-baseline interferometric radar systems

Synthetic aperture radar interferometry (InSAR) is a powerful technique to derive three-dimensional terrain images. Interest is growing in exploiting the advanced multi-baseline mode of InSAR to solve layover effects from complex orography, which generate reception of unexpected multicomponent signals that degrade imagery of both terrain radar reflectivity and height. This work addresses a few problems related to the implementation into interferometric processing of nonlinear algorithms for estimating the number of signal components, including a system trade-off analysis. Performance of various eigenvalues-based information-theoretic criteria (ITC) algorithms is numerically investigated under some realistic conditions. In particular, speckle effects from surface and volume scattering are taken into account as multiplicative noise in the signal model. Robustness to leakage of signal power into the noise eigenvalues and operation with a small number of looks are investigated. The issue of baseline optimization for detection is also addressed. The use of diagonally loaded ITC methods is then proposed as a tool for robust operation in the presence of speckle decorrelation. Finally, case studies of a nonuniform array are studied and recommendations for a proper combination of ITC methods and system configuration are given

Semiparametric CRB and Slepian-Bangs formulas for Complex Elliptically Symmetric Distributions

The main aim of this paper is to extend the semiparametric inference methodology, recently investigated for Real Elliptically Symmetric (RES) distributions, to Complex Elliptically Symmetric (CES) distributions. The generalization to the complex field is of fundamental importance in all practical applications that exploit the complex representation of the acquired data. Moreover, the CES distributions has been widely recognized as a valuable and general model to statistically describe the non-Gaussian behaviour of datasets originated from a wide variety of physical measurement processes. The paper is divided in two parts. In the first part, a closed form expression of the constrained Semiparametric Cram\'{e}r-Rao Bound (CSCRB) for the joint estimation of complex mean vector and complex scatter matrix of a set of CES-distributed random vectors is obtained by exploiting the so-called \textit{Wirtinger} or $\mathbb{C}\mathbb{R}$-\textit{calculus}. The second part deals with the derivation of the semiparametric version of the Slepian-Bangs formula in the context of the CES model. Specifically, the proposed Semiparametric Slepian-Bangs (SSB) formula provides us with a useful and ready-to-use expression of the Semiparametric Fisher Information Matrix (SFIM) for the estimation of a parameter vector parametrizing the complex mean and the complex scatter matrix of a CES-distributed vector in the presence of unknown, nuisance, density generator. Furthermore, we show how to exploit the derived SSB formula to obtain the semiparametric counterpart of the Stochastic CRB for Direction of Arrival (DOA) estimation under a random signal model assumption. Simulation results are also provided to clarify the theoretical findings and to demonstrate their usefulness in common array processing applications.Comment: Submitted to IEEE Transactions on Signal Processing. arXiv admin note: substantial text overlap with arXiv:1807.08505, arXiv:1807.0893

Spectrum Sensing and Sharing for Cognitive Radar Systems

The IEEE 802.22 standard specifies the air interface, including the cognitive medium access control layer (MAC) and physical layer (PHY), of point-to-multipoint wireless regional area networks (WRAN) comprised of a professional fixed Base Station (BS) with fixed and portable user terminals, referred as the Customer Premise Equipment (CPE) devices, operating in the white spaces in the VHF/UHF TV broadcast bands while avoiding interference to the incumbent broadcast services. This work focuses on a Passive Coherent Location (PCL) system that exploits the signals emitted by IEEE 802.22 devices and is referred hereafter as a White Space PCL (WS-PCL) system. To cope with the very low transmitted EIRP of the IEEE 802.22 emitters, we focus on the design of a WS-PCL system that exploits all the useful signals received in each frame, and therefore the signals emitted from both the BS and CPEs. In this work we study the feasibility of the WS-PCL system, we derive the Receiver Operating Characteristic (ROC) of the WS-PCL receiver and we define a multistatic velocity profiling algorithm for the estimation of the target velocity vector. The performances of the proposed receiver are compared with those of a WS-PCL system that exploits only the signal emitted by the BS

Adaptive Sparse Array Beamformer Design by Regularized Complementary Antenna Switching

In this work, we propose a novel strategy of adaptive sparse array beamformer design, referred to as regularized complementary antenna switching (RCAS), to swiftly adapt both array configuration and excitation weights in accordance to the dynamic environment for enhancing interference suppression. In order to achieve an implementable design of array reconfiguration, the RCAS is conducted in the framework of regularized antenna switching, whereby the full array aperture is collectively divided into separate groups and only one antenna in each group is switched on to connect with the processing channel. A set of deterministic complementary sparse arrays with good quiescent beampatterns is first designed by RCAS and full array data is collected by switching among them while maintaining resilient interference suppression. Subsequently, adaptive sparse array tailored for the specific environment is calculated and reconfigured based on the information extracted from the full array data. The RCAS is devised as an exclusive cardinality-constrained optimization, which is reformulated by introducing an auxiliary variable combined with a piece-wise linear function to approximate the $l_0$-norm function. A regularization formulation is proposed to solve the problem iteratively and eliminate the requirement of feasible initial search point. A rigorous theoretical analysis is conducted, which proves that the proposed algorithm is essentially an equivalent transformation of the original cardinality-constrained optimization. Simulation results validate the effectiveness of the proposed RCAS strategy

Copolar Calibration of Multistatic Radar in the Presence of Multipath

This paper addresses the Polarimetrie calibration of the nodes of a multistatic radar system, by using a reference object with known scattering matrix, such as a metallic sphere. A calibration technique is proposed and its experimental validation performed in a realistic scenario, by accounting also for the multipath effect. The intensity of the signal scattered by a metallic sphere and received by the monostatic and bistatic nodes of the NetRAD system is measured, by varying the antenna height, the object range and the bistatic angle. The adopted calibration technique shows a quite good accuracy, as the calibrated values of the radar cross section of the reference object are close to the theoretical ones, after the compensation of the multipath effect

Semiparametric Inference and Lower Bounds for Real Elliptically Symmetric Distributions

This paper has a twofold goal. The first aim is to provide a deeper understanding of the family of the Real Elliptically Symmetric (RES) distributions by investigating their intrinsic semiparametric nature. The second aim is to derive a semiparametric lower bound for the estimation of the parametric component of the model. The RES distributions represent a semiparametric model where the parametric part is given by the mean vector and by the scatter matrix while the non-parametric, infinite-dimensional, part is represented by the density generator. Since, in practical applications, we are often interested only in the estimation of the parametric component, the density generator can be considered as nuisance. The first part of the paper is dedicated to conveniently place the RES distributions in the framework of the semiparametric group models. The second part of the paper, building on the mathematical tools previously introduced, the Constrained Semiparametric Cram\'{e}r-Rao Bound (CSCRB) for the estimation of the mean vector and of the constrained scatter matrix of a RES distributed random vector is introduced. The CSCRB provides a lower bound on the Mean Squared Error (MSE) of any robust $M$-estimator of mean vector and scatter matrix when no a-priori information on the density generator is available. A closed form expression for the CSCRB is derived. Finally, in simulations, we assess the statistical efficiency of the Tyler's and Huber's scatter matrix $M$-estimators with respect to the CSCRB.Comment: This paper has been accepted for publication in IEEE Transactions on Signal Processin

Channel parameters estimation for cognitive radar systems

This paper deals with the problem of a cognitive radar system that shares the same frequency band with a communication system, supposed to be the primary user of channel. A cognitive algorithm is proposed to estimate the channel parameters that describe the behaviour of the primary user and how to exploit these estimates to minimize the interference between the radar and the communication system. The performance of the proposed algorithm are assessed in terms of probability of collision, that is the probability that the radar transmits when the primary user already occupies the channel, and probability to lose a spectrum opportunity, that is the probability that the radar does not transmit when the channel is free