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In the present chapter, we have addressed radar waveform optimization in spectrally crowded scenarios via constrained quadratic programming techniques. First of all, we have defined a taxonomy of performance measures which are to be optimized and/or controlled in the waveform synthesis: SINR, signal energy, similarity constraint, interference constraint for spectral compatibility, and quality constraint for bandwidth selection. Then, we have formulated the radar waveform design as a nonconvex QCQP problem and have exploited a specific methodology leveraging rank-one matrix decomposition tools to prove the hidden convexity of some instances of the waveform optimization or to build solution procedures ensuring good quality radar waveforms.

This paper considers the design problem of constant modulus sequence set which could be applied in multiple-input multiple-output (MIMO) radar and communication societies, to achieve desired correlation properties.A new and general weighted integrated sidelobe level (WISL) accounting for both auto- and cross-correlation functions is proposed.An iteration algorithm based on iteration direct search is devised to optimizes the WISL without limitations on the weightslling the gap in the open literature and involves the FFT operation at each iteration ensuring the convergence speed.Results highlight that the proposed algorithm possesses excellent superiority both in correlation properties and computation complexity compared with the related WeCAN algorithm. This paper considers the design problem of constant modulus sequence set which could be applied in multiple-input multiple-output (MIMO) radar and communication societies, to achieve desired correlation properties. An iteration algorithm based on iteration direct search is devised to minimize a new and general weighted integrated sidelobe level (WISL) accounting for both auto- and cross-correlation functions. At each iteration of the proposed algorithm, we sequentially optimize each code element of the sequence while fixing remained code elements; to this end, we split the multi-dimensional problem into multiple one-dimension problems with closed-form solutions for continues phase case and optimal solutions for finite phase case via one-dimensional search. In particular, the proposed algorithm directly optimizes the WISL without limitations on the weights filling the gap in the open literature and involves the FFT operation at each iteration ensuring the convergence speed. The numerical simulations validate the effectiveness of the proposed algorithm.

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.

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). © 2014 IEEE.

The work presented here focuses on the performance analysis of the sidelobe blanking (SLB) system with noncoherent integration in the presence of white Gaussian noise and jammer entering through the sidelobes of the antenna. Closed-form performance probabilities, in terms of either the generalized Marcum or Nuttall Q-function, are derived for nonfluctuating target and jammer, both in the blanking and the detection regions. The analysis is then extended to account for arbitrary correlated, possibly nonidentically distributed, fluctuating target and/or jamming returns among a given number of integrated pulses. Finally, several numerical results are given, and the effects of typical SLB parameters are discussed.

[This corrects the article DOI: 10.18632/oncotarget.25874.].

Radar signal design in a spectrally dense environment is a very challenging and topical problem due to the increasing demand of both defence surveillance/remote sensing capabilities and civilian wireless services. This chapter describes an optimization theory-based radar waveform design to deal with the spectrum congestion problem. Cognition provided by a radio environmental map paves the way for an intelligent dynamic spectrum allocation. It pushes for dynamic spectral constraints on the radar waveform which is thus the result of a constrained optimization process aimed at improving some radar performance (such as detection, classification and tracking capabilities) while ensuring spectral compatibility with the surrounding radio frequency licensed systems. Finally, some spectrally crowded illustrative scenarios are analyzed to show the effectiveness of the considered optimization theory-based approach.

In this paper, the synthesis of optimized radar waveforms ensuring spectral compatibility with the overlayed electromagnetic radiators is addressed. For the first time the quality of the bandwidths available for transmission is accounted for at the design stage via a specific constraint measuring their purity. To this end, cognition provided by a Radio Environmental Map (REM) is exploited so as to induce dynamic spectral constraints on the radar waveform as well as on the quality of bandwidths free from cooperative transmissions. A waveform optimization aiming at improving some radar performances is proposed. It 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 spectral shape and auto-ambiguity features.

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.

Effects of Mutual Coupling of Radiating Antennas on an Adaptive Radar Detector In this paper, we address the adaptive detection/classification of signals in a homogenous interference environment. We refer to a radar system equipped with a phased array antenna and account for both the presence of mutual coupling between radiating antennas and a possible coherent interferer impinging on the array mainbeam. To deal with this scenario, we adopt a two-stage detection/classification scheme, enjoying the Costant False Alarm Rate (CFAR) property, to discriminate between target detection and coherent interferer rejection. Finally, we evaluate the system performance via Monte Carlo simulations. The results show that our system has interesting rejection capabilities and satisfactory detection levels. As a consequence, it could be successfully applied in real scenarios where mutual coupling is present.

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 multi-objective optimization. Precisely, under both energy and similarity constraints, we devise orthogonal signals aiming at maximization of the Signal-to-Interference Ratio (SIR) and minimization of a suitable correlation index (related to the possibility of waveform interception). The problem can be cast into a non-convex multi-objective optimization and solved via the so-called scalarization technique. Finally, performance of the proposed waveform design scheme is assessed in terms of both Symbol Error Rate (SER) and the so-called “intercept metric”.

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.

In this paper, the problem of cognitively designing the transmit signal and the receive filter for a point-like target embedded in a high reverberating environment is addressed. Precisely, a dynamic environmental database on the actual scattering environment is assumed available. Then, an optimization procedure which sequentially improves the Signal to Interference plus Noise Ratio (SINR), exploiting the aforementioned information, is presented. A quantized phase-only condition, and a similarity constraint between the transmitted signal and a known radar waveform sharing a good ambiguity function, are enforced. 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 in the presence of a homogeneous clutter scenario are assessed.

In this paper we deal with the performance prediction of the incoherent radar receiver in the presence of arbitrary correlated, possibly non-identically distributed target backscattered echoes. The problem is of interest in some common scenarios accounting for frequency agility, polarization as well as spatial diversity. We develop analytic expressions for the detection probability in terms of power series, assuming that a Generalized Swerling-Chi distribution models the first order probability density function (pdf) of the target amplitude. We also provide an interesting interpretation of the derived formulas. Finally, we assess the impact on the detection performance of both the correlation and the non-identical distribution of the target returns.

This paper is focused on the performance analysis of the Sidelobe Blanking (SLB) system with non-coherent integration in the presence of white Gaussian noise and jammer entering through the antenna sidelobes. In the blanking region, closed-form performance probabilities, in terms of the generalized Marcum Q -function, are derived for arbitrary correlated, possibly non-identically distributed fluctuating target and/or jamming returns. Finally, several numerical results are given and the effects of typical SLB parameters are discussed.

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.

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.

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).

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.

This paper considers sidelobe blanking (SLB) system design in the presence of both homogeneous Gaussian clutter plus noise and jammer entering through the sidelobes of the antenna. A coherent SLB structure using Kelly's receiver [6] on the two channels is introduced and analyzed. Closed-form performance probabilities in the blanking and detection regions are derived and the Constant False Alarm Rate (CFAR) behavior of the architecture is remarked. Finally, several numerical simulations of the proposed SLB system with typical parameters are obtained and discussed.

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. © 2013 Piezzo et al.; licensee Springer.

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.

This paper considers the robust waveform design of multiple-input multiple-output (MIMO) radar to enhance targets detection in the presence of signal-dependent interferences assuming the knowledge of steering vectors is imprecise. Specifically, resorting to semidefinite programming (SDP)-related technique, we first maximize the worst-case signal-to-interference-plus-noise ratio (SINR) over uncertain region to optimize waveform covariance matrix forcing a uniform elemental power requirement. Then, based on least square (LS) approach, we devise the waveform accounting for constant modulus and similarity constraints by the obtained waveform covariance matrix using cyclic algorithm (CA). Finally, we assess the effectiveness of the proposed technique through numerical simulations in terms of non-uniform point-like clutter and uniform clutter.