Augusto Aubry

Knowledge-Aided (Potentially Cognitive) Transmit Signal and Receive Filter Design in Signal-Dependent Clutter

We consider the problem of knowledge-aided (possibly cognitive) transmit signal and receive filter design for point-like targets in signal-dependent clutter. We suppose that the radar system has access to a (potentially dynamic) database containing a geographical information system (GIS), which characterizes the terrain to be illuminated, and some a priori electromagnetic reflectivity and spectral clutter models, which allow the raw prediction of the actual scattering environment. Hence, we devise an optimization procedure for the transmit signal and the receive filter which sequentially improves the signal- to-interference-plus-noise ratio (SINR). Each iteration of the algorithm, whose convergence is analytically proved, requires the solution of both a convex and a hidden convex optimization problem. The resulting computational complexity is linear with the number of iterations and polynomial with the receive filter length. At the analysis stage we assess the performance of the proposed technique in the presence of either a homogeneous ground clutter scenario or a heterogeneous mixed land and sea clutter environment.

Maximum Likelihood Estimation of a Structured Covariance Matrix With a Condition Number Constraint

In this paper, we deal with the problem of estimating the disturbance covariance matrix for radar signal processing applications, when a limited number of training data is present. We determine the maximum likelihood (ML) estimator of the covariance matrix starting from a set of secondary data, assuming a special covariance structure (i.e., the sum of a positive semi-definite matrix plus a term proportional to the identity), and a condition number upper-bound constraint. We show that the formulated constrained optimization problem falls within the class of MAXDET problems and develop an efficient procedure for its solution in closed form. Remarkably, the computational complexity of the algorithm is of the same order as the eigenvalue decomposition of the sample covariance matrix. At the analysis stage, we assess the performance of the proposed algorithm in terms of achievable signal-to-interference-plus-noise ratio (SINR) both for a spatial and a Doppler processing. The results show that interesting SINR improvements, with respect to some existing covariance matrix estimation techniques, can be achieved.

Radar waveform design in a spectrally crowded environment via nonconvex quadratic optimization

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).

A new radar waveform design algorithm with improved feasibility for spectral coexistence

Radar signal design in a spectrally crowded environment is currently a challenge due to the increasing requests for spectrum from both military sensing applications and civilian wireless services. The goal of this paper is to improve a previously devised algorithm for the synthesis of optimized radar waveforms fulfilling spectral compatibility with overlaid licensed radiators. The new technique achieves an enhanced spectral coexistence with the surrounding electromagnetic environment through a suitable modulation of the transmitted waveform energy, which was kept fixed at the maximum level in the previously devised algorithm. 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), also in situations where the previous technique cannot be applied.

Ambiguity Function Shaping for Cognitive Radar Via Complex Quartic Optimization

In this paper, we propose a cognitive approach to design phase-only modulated waveforms sharing a desired range-Doppler response. The idea is to minimize the average value of the ambiguity function of the transmitted signal over some range-Doppler bins, which are identified exploiting a plurality of knowledge sources. From a technical point of view, this is tantamount to optimizing a real and homogeneous complex quartic order polynomial with a constant modulus constraint on each optimization variable. After proving some interesting properties of the considered problem, we devise a polynomial-time waveform optimization procedure based on the Maximum Block Improvement (MBI) method and the theory of conjugate-partial-symmetric/conjugate-super-symmetric fourth order tensors. At the analysis stage, we assess the performance of the proposed technique showing its capability to properly shape the range-Doppler response of the transmitted waveform.

Radar Detection of Distributed Targets in Homogeneous Interference Whose Inverse Covariance Structure is Defined via Unitary Invariant Functions

In this paper we deal with the problem of detecting an extended target embedded in homogeneous Gaussian interference with unknown but structured covariance matrix. We model the possible target echo, from each range bin under test, as a deterministic signal with an unknown scaling factor accounting for the target response. At the design stage, we exploit some a-priori knowledge about the operating environment enforcing the inverse interference plus noise covariance matrix to belong to a set described via unitary invariant continuous functions. Hence, we derive the constrained Maximum Likelihood (ML) estimates of the unknown parameters, under both the H0 and H1 hypotheses, and design the Generalized Likelihood Ratio Test (GLRT) for the considered decision problem. At the analysis stage, we assess the performance of the devised GLRT for some covariance matrix uncertainty sets of practical relevance both for spatial and Doppler processing. The results highlight that correct use of the a-priori knowledge can lead to a detection performance quite close to the optimum receiver which supposes the perfect knowledge of the interference plus noise covariance matrix.

A Doppler Robust Design of Transmit Sequence and Receive Filter in the Presence of Signal-Dependent Interference

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-noise-plus-interference (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, which belongs to a class of NP-hard problems, we devise a novel method (which we call DESIDE) to obtain optimized pairs of transmit sequence and receive filter sharing the desired robustness property. The proposed method is based on a cyclic maximization of SINR expressions with relaxed rank-one constraints, and is followed by a novel synthesis stage. We devise synthesis algorithms to obtain high quality pairs of transmit sequence and receive filter that well approximate the behavior of the optimal SINR (of the relaxed problem) with respect to target Doppler shift. Several numerical examples are provided to analyze the performance obtained by DESIDE.

Cognitive radar waveform design for spectral coexistence in signal-dependent interference

In this paper, we deal with cognitive design of the transmit signal and receive filter optimizing the radar detection performance without affecting spectral compatibility with some licensed overlaid electromagnetic radiators. We assume that the radar is embedded in a highly reverberating environment and exploit cognition provided by Radio Environmental Map (REM), to induce spectral constraints on the radar waveform, by a dynamic environmental database, to predict the actual scattering scenario, and by an Electronic Support Measurement (ESM) system, to acquire information about hostile active jammers. At the design stage, we develop an optimization procedure which sequentially improves the Signal to Interference plus Noise Ratio (SINR). Moreover, we enforce a spectral energy constraint and a similarity constraint between the transmitted signal and a known radar waveform. At the analysis stage, we assess the effectiveness of the proposed technique to optimizing SINR while providing spectral coexistence.

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.

Optimizing Radar Waveform and Doppler Filter Bank via Generalized Fractional Programming

Assuming unknown target Doppler shift, we focus on robust joint design of the transmit radar waveform and receive Doppler filter bank in the presence of signal-dependent interference. We consider the worst case signal-to-interference-plus-noise-ratio (SINR) at the output of the filter bank as the figure of merit to optimize under both a similarity and an energy constraint on the transmit signal. Based on a suitable reformulation of the original non-convex max-min optimization problem, we develop an optimization procedure which monotonically improves the worst-case SINR and converges to a stationary point. Each iteration of the algorithm, involves both a convex and a generalized fractional programming problem which can be globally solved via the generalized Dinkelbachs procedure with a polynomial computational complexity. Finally, at the analysis stage, we assess the performance of the new technique versus some counterparts which are available in open literature.