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The aim of the present work of thesis is to investigate the potentiality o�ffered by waveform design and waveform diversity. In particular, the essence is the possible application of the Optimization Theory so as to the devise high performing transmit signal/receeive fi�lter design techniques. Verily, once a certain �figure of merit has been chosen and properly described by the mathematial language, and once the necessary data have been collected, many problems of practial interest in radar �field can be modeled in terms of an optimization problem, where the main purpose is to optimize the system performance under some constraints imposed by interference, clutter and, more in general, the operating environment.

This paper considers the design of robust filters for radar pulse-Doppler processing when the interference is a wide sense stationary random process. The figure of merit which is optimized is the signal-to-interference-plus-noise ratio (SINR) at the filter output under a multitude of constraints accounting for Doppler filter sidelobes as well as uncertainties both in the received useful signal component and interference covariance matrix. The design is analytically formulated as a constrained optimization problem whose solvability is thoroughly studied. Precisely, a polynomial-time solution technique to get the optimal filter is proposed exploiting the representation of non-negative trigonometric polynomials via linear matrix inequalities, the spectral factorization theorem, and the duality theory. Last but not least, a detailed analysis of the optimum filter performance is provided showing the tradeoffs involved in the design and the gain achievable over some already known counterparts.

In this study, the authors consider the problem of cognitive transmit signal and receive filter design for a point-like target embedded in a high-reverberating environment. The authors focus on phase-only waveforms, sharing either a continuous or a finite alphabet phase, hence they devise constrained optimisation procedures that sequentially improve the Signal to Interference plus Noise Ratio (SINR), accounting for a similarity constraint between the transmitted signal and a prescribed radar waveform. The computational complexity of the proposed algorithms is linear with the number of iterations and polynomial with the receive filter length. At the analysis stage, the performance of the techniques is assessed in the presence of a homogeneous clutter scenario.

This correspondence deals with the design of radar receive filters for pulse compression which optimize either the L-p-norm of the vector containing the filter sidelobe energies or the inverse signal-to-noise power ratio (ISNR) under an upper-bound constraint on the previously mentioned L-p-norm. In both the cases, we prove that the filter design can be formulated as a convex optimization second-order cone programming (SOCP) problem which can be efficiently solved with a polynomial time computational complexity resorting to interior point methods. At the analysis stage, we assess the performance of the receive filters in correspondence of different values of the parameter highlighting the performance compromises between the integrated sidelobe level (ISL), the peak sidelobe level (PSL), and the ISNR. Finally, we study the effects of the filter length on the performance as well as the Doppler tolerance of the devised filters. The results show that the proposed technique leads to satisfactory performance levels and good Doppler tolerances.

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.

This paper considers the design of robust filters for radar pulse-Doppler processing when the interference is a wide sense stationary random process. The Signal-to-Interference-plus-Noise Ratio (SINR) at the filter output is considered as the figure of merit to optimize under a multitude of requirements accounting for Doppler filter sidelobes as well as uncertainties both in the received useful signal component and interference covariance matrix. The design is analytically formulated as a constrained optimization problem whose solvability is thoroughly studied. Specifically, a polynomial time solution technique to get the optimal filter is proposed exploiting the representation of non-negative trigonometric polynomials via linear matrix inequalities, the spectral factorization theorem, and the duality theory. Last but not least, a detailed analysis of the optimum filter performance is provided showing the trade-offs involved in the design and the gain achievable over some already known counterparts.

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.

In this paper, we consider the problem of knowledge-aided transmit signal and receive filter design for a point-like target embedded in a high reverberating signal-dependent environment. We focus on phase-only waveforms and devise a constrained optimization procedure which sequentially improves the Signal to Interference plus Noise Ratio (SINR), forcing a similarity constraint between the transmitted signal and a known radar waveform sharing a good ambiguity function. The computational complexity of the proposed algorithm is linear with the number of iterations and polynomial with the receive filter length. At the analysis stage, the performances of the technique are assessed in the presence of a homogeneous clutter scenario.

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.

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. Firstly, we focus on the selection of the radar signal optimizing the Signal to Noise Power Ratio (SNR) for a given target Doppler frequency (Algorithm 1). Then, we devise its phase quantized version (Algorithm 2), which forces the waveform phase to lie within a finite alphabet. Both the problems are formulated in terms of NP-hard non-convex quadratic optimization programs; in order to solve them, we resort to Semidefinite Programming (SDP) relaxation and randomization techniques, providing provable-quality sub-optimal solutions with a polynomial time computational complexity. Finally, we analyze the performance in terms of detection capability and robustness with respect to Doppler shifts.

Design of Pareto-Optimal Radar Receive Filters This paper deals with the design of radar receive filters jointly optimized with respect to sidelobe energy and sidelobe peaks via Pareto-optimal theory. We prove that this criterion is tantamount to jointly minimizing two quadratic forms, so that the design can be analytically formulated in terms of a multi-objective optimization problem. In order to solve it, we resort to the scalarization technique, which reduces the vectorial problem into a scalar one using a Pareto weight defining the relative importance of the two objective functions. At the analysis stage, we assess the performance of the receive filters in correspondence of different values of the Pareto weight highlighting the performance compromises between the Integrated Sidelobe Level (ISL) and the Peak Sidelobe Level (PSL).

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 non-convex 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.

This paper deals with the problem of estimating the disturbance covariance matrix when a limited number of training data, due to environmental heterogeneity, is present. To this end, we suppose that some a-priori spectral models for the the disturbance in the cell under test are available and determine the Maximum Likelihood (ML) estimate of the actual inverse covariance (and hence of the covariance itself) as a suitable combination of the a-priori models. At the analysis stage, we show the capabilities of the new technique to track the actual clutter Power Spectral Density (PSD) and its superiority with respect to adaptive techniques based on the sample covariance matrix.

This study deals with the problem of Pareto-optimal waveform design in the presence of coloured Gaussian noise, under a similarity and an energy constraint. At the design stage, the authors, determine the optimal radar code according the following criterion: constrained maximisation of the detection performance and constrained minimisation of the Cramer-Rao lower bound (CRLB) on the Doppler estimation accuracy. This is tantamount to jointly maximising two quadratic forms under two quadratic constraints, so that the problem can be formulated in terms of a non-convex multi-objective optimisation problem. In order to solve it, the authors resort to the scalarisation technique, which reduces the vectorial problem into a scalar one using a Pareto weight defining the relative importance of the two objective functions. At the analysis stage, the authors assess the performance of the proposed waveform design scheme in terms of detection performance, region of achievable Doppler estimation accuracy and ambiguity function. In particular, the authors analyse the role of the Pareto weight in the optimisation process.