Marco Piezzo

Design of Optimized Radar Codes With a Peak to Average Power Ratio Constraint

This paper considers the problem of radar waveform design in the presence of colored Gaussian disturbance under a peak-to-average-power ratio (PAR) and an energy constraint. First of all, we focus on the selection of the radar signal optimizing the signal-to-noise ratio (SNR) in correspondence of a given expected target Doppler frequency (Algorithm 1). Then, through a max-min approach, we make robust the technique with respect to the received Doppler (Algorithm 2), namely we optimize the worst case SNR under the same constraints as in the previous problem. Since Algorithms 1 and 2 do not impose any condition on the waveform phase, we also devise their phase quantized versions (Algorithms 3 and 4, respectively), which force the waveform phase to lie within a finite alphabet. All the problems are formulated in terms of nonconvex quadratic optimization programs with either a finite or an infinite number of quadratic constraints. We prove that these problems are NP-hard and, hence, introduce design techniques, relying on semidefinite programming (SDP) relaxation and randomization as well as on the theory of trigonometric polynomials, providing high-quality suboptimal solutions with a polynomial time computational complexity. Finally, we analyze the performance of the new waveform design algorithms in terms of detection performance and robustness with respect to Doppler shifts.

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.

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.

Intrapulse radar-embedded communications via multiobjective optimization

We deal with the problem of intrapulse radar-embedded communication and propose a novel waveform design procedure based on a multiobjective optimization paradigm. More specifically, under both energy and similarity constraints, we devise signals according to the following criterion: constrained maximization of the signal-to-interference ratio and constrained minimization of a suitable correlation index (which is related to the possibility of waveform interception). This is tantamount to jointly maximizing two competing quadratic forms under two quadratic constraints so that the problem can be formulated in terms of a nonconvex multiobjective optimization. In order to solve it, we resort to the scalarization technique, which reduces the vectorial problem into a scalar one using Pareto weights defining the relative importance of the two objectives. At the analysis stage, we assess the performance of the proposed waveform design scheme in terms of symbol error rate and the so-called intercept metric.

Performance Prediction of the Incoherent Radar Detector for Correlated Generalized Swerling-Chi Fluctuating Targets

We deal with the performance prediction of the incoherent radar receiver in the presence of arbitrary correlated, possibly nonidentically-distributed target backscattered echoes. The problem is of interest in some common scenarios that account for frequency agility, and polarization, as well as for spatial diversity. We develop analytic expressions for the detection probability in terms of function series, assuming that a generalized Swerling-chi distribution models the first order probability density function (pdf) of the target amplitude. Moreover, we study the speed of convergence of the resulting series and assess the impact on the detection performance of both the correlation and the nonidentical distribution of the target returns.

A Doppler Robust Max-Min Approach to Radar Code Design

This correspondence considers the problem of robust waveform design in the presence of colored Gaussian disturbance under a similarity and an energy constraint. We resort to a max-min approach, where the worst case detection performance (over the possible Doppler shifts) is optimized with respect to the radar waveform under the previously mentioned constraints. The resulting optimization problem is a non-convex Quadratically Constrained Quadratic Program (QCQP) with an infinite number of constraints, which is NP-hard in general and typically difficult to solve. Hence, we propose an algorithm with a polynomial computational complexity to generate a good sub-optimal solution for the aforementioned QCQP. The analysis, conducted in comparison with some known radar waveforms, shows that the sub-optimal solutions by the algorithm lead to high-quality radar signals.

Adaptive Detection of Point-Like Targets in the Presence of Homogeneous Clutter and Subspace Interference

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.

Non-cooperative code design in radar networks: a game-theoretic approach

A network of radars sharing the same frequency band, and using properly coded waveforms to improve features attractive from the radar point of view is considered in this article. Non-cooperative games aimed at code design for maximization of the signal-to-interference plus noise ratio (SINR) of each active radar are presented. Code update strategies are proposed, and, resorting to the theory of potential games, the existence of Nash equilibria is analytically proven. In particular, we propose non-cooperative code update procedures for the cases in which a matched filter, a minimum integrated sidelobe level filter, and a minimum peak to sidelobe level filter are used at the receiver. The case in which the received data contain a non-negligible Doppler shift is also analyzed. Experimental results confirm that the proposed procedures reach an equilibrium in few iterations, as well as that the SINR values at the equilibrium are largely superior to those in the case in which classical waveforms are used and no optimization of the radar code is performed.

Cognitive radar waveform design for spectral coexistence

In the present paper, the synthesis of optimized radar waveforms ensuring spectral compatibility with the overlayed electromagnetic radiators is addressed. Cognition provided by a Radio Environmental Map (REM) is exploited so as to induces dynamic spectral constraints on the radar waveform. A waveform optimization aiming at improving some radar performances is proposed, whose feasibility is extensively studied. 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).