Vincenzo Carotenuto

Optimality Claims for the FML Covariance Estimator with respect to Two Matrix Norms

In this correspondence we prove two interesting properties of the fast maximum likelihood (FML) covariance matrix estimator proposed in [1] under the assumption of zero-mean complex circular Gaussian training data sharing the same covariance matrix. The new properties represent optimality claims regardless of the statistical characterization of the data and, in particular, of the multivariate Gaussian assumption for the observables. The optimality is proved with respect to two cost functions involving either the Frobenius or the spectral norm of an Hermitian matrix.

Forcing Multiple Spectral Compatibility Constraints in Radar Waveforms

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.

Invariant Rules for Multipolarization SAR Change Detection

This paper deals with coherent (in the sense that both amplitudes and relative phases of the polarimetric returns are used to construct the decision statistic) multipolarization synthetic aperture radar (SAR) change detection assuming the availability of reference and test images collected from N multiple polarimetric channels. At the design stage, the change detection problem is formulated as a binary hypothesis testing problem, and the principle of invariance is used to come up with decision rules sharing the constant false alarm rate property. The maximal invariant statistic and the maximal invariant in the parameter space are obtained. Hence, the optimum invariant test is devised proving that a uniformly most powerful invariant detector does not exist. Based on this, the class of suboptimum invariant receivers, which also includes the generalized likelihood ratio test, is considered. At the analysis stage, the performance of some tests, belonging to the aforementioned class, is assessed and compared with the optimum clairvoyant invariant detector. Finally, detection maps on real high-resolution SAR data are computed showing the effectiveness of the considered invariant decision structures.

Space-Time Transmit Code and Receive Filter Design for Colocated MIMO Radar

This paper deals with the design of multiple-input multiple-output radar space-time transmit code (STTC) and space-time receive filter (STRF) to enhance moving targets detection in the presence of signal-dependent interferences. An iterative procedure, whose convergence is analytically proved, is devised to maximize the Signal to interference plus noise ratio (SINR) accounting for both a similarity constraint and a constant modulus requirement on the probing waveform. Each iteration of the algorithm involves the solution of hidden convex problems. Specifically, both a convex problem (whose solution is provided in closed form) and a set of fractional programming problems, that can be globally solved in polynomial time via the Dinkelbacks procedure, are settled. The computational complexity is linear with the number of iterations and polynomial with the sizes of the STTC and the STRF. In particular, the proposed technique provides a monotonic SINR improvement without limitations on the size of the similarity constraint and ensures convergence to a stationary point filling these important gaps in the open literature. Besides, the reported results highlight that the new devised procedure outperforms both in the optimized SINR value and the computational complexity than the available counterparts.

Optimization theory-based radar waveform design for spectrally dense environments

The radio frequency (RF) electromagnetic spectrum is a limited natural resource necessary for an ever-growing number of services and systems. It is used in several applications, such as mobile communications, radio and television broadcasting, as well as remote sensing. Together with oil and water, the RF spectrum now represents one of the most important, significant, crucial, and critical commodities due to the huge impact of radio services on society. Both high-quality/high-rate wireless services (4G and 5G) as well as accurate and reliable remote-sensing capabilities (air traffic control (ATC), Earth geophysical monitoring, defense and security applications) call for increased amounts of bandwidth [1], [2]. Besides, basic electromagnetic considerations, such as good foliage penetration [3], low path loss attenuation, and reduced sizes of the devices push some systems to coexist in the same frequency band [4] (for instance VHF and UHF). As a result, the RF spectrum congestion problem has been attracting the interest of many scientists and engineers during the last few years and is currently becoming one of the hot topics in both regulation and research fields [5], [6].

Forcing Scale Invariance in Multipolarization SAR Change Detection

This paper considers the problem of coherent (in the sense that both amplitudes and relative phases of the polarimetric returns are used to construct the decision statistic) multipolarization synthetic aperture radar change detection starting from the availability of image pairs exhibiting possible power mismatches/miscalibrations. The principle of invariance is used to characterize the class of scale-invariant decision rules which are insensitive to power mismatches and ensure the constant false alarm rate property. A maximal invariant statistic is derived together with the induced maximal invariant in the parameter space which significantly compresses the data/parameter domain. A generalized likelihood ratio test is synthesized both for the cases of two- and three-polarimetric channels. Interestingly, for the two-channel case, it is based on the comparison of the condition number of a data-dependent matrix with a suitable threshold. Some additional invariant decision rules are also proposed. The performance of the considered scale-invariant structures is compared to those from two noninvariant counterparts using both simulated and real radar data. The results highlight the robustness of the proposed method and the performance tradeoff involved.

Performance prediction of the incoherent detector for a weibull fluctuating target

We deal with performance prediction of the incoherent radar receiver (i.e., squared law plus integrator) in the presence of independent nonidentically distributed (non-id)Weibull target echoes. First, we provide the probability density function (pdf) for the sum of independent but non-idWeibull random variables in terms of an infinite sum of Gamma pdfs. Then we develop an analytic expression for the detection probability as a fast converging series of functions. Finally, we study the approximation error and convergence rate of the quoted series, and evaluate the impacts on the detection performance of non-idWeibull target parameters.

Space-time transmit code and receive filter design for colocated MIMO radar

This paper considers the design problem of Multiple-Input Multiple-Output (MIMO) radar space-time transmit code (STTC) and space-time receive filter (STRF) for a moving point-like target in the presence of signal-dependent interference. An iterative procedure, whose convergence is analytically proved, is devised to maximize the Signal to Interference plus Noise Ratio (SINR) accounting for both a similarity constraint and constant modulus requirements on the probing waveform. Each iteration of the algorithm, involves the solution of hidden convex problems. Specifically, both a convex problem (whose solution is provided in closed form) and a set of fractional programming problem, that can be globally solved in polynomial time via the Dinkelbacks procedure, are solved. The computational complexity is linear in the number of iterations and polynomial with the sizes of the STTC and the STRF. Finally, numerical results are provided to assess the quality of the devised procedure.

Radar phase noise modeling and effects–part I: MTI filters

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.

New Results on Generalized Fractional Programming Problems With Toeplitz Quadratics

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 Dinkelbacks 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.