Problem Of Radar Waveform Design Research Articles

LPI Radar Waveform Design With Desired Cyclic Spectrum and Pulse Compression Properties

This paper considers the practical LPI radar waveform design problem for jointly achieving a desired cyclic spectrum and pulse compression properties. In this work, the weighted cyclic frequency sidelobe (WCFS) level is minimized to achieve the LPI purpose while the similarity constraint regarding a known radar waveform that occupies the desired detection properties is considered. The waveform design problem is then formulated as a quartic optimization problem with heterogeneous quadratic inequality constraints. These properties make the problem NP-hard in general. To solve this problem efficiently, by introducing necessary auxiliary variables, the original problem is converted into several quadratic optimization problems with respect to each independent variable under a separated linear inequality constraint, which can be efficiently solved by leveraging the alternation direction method of multipliers (ADMM) framework. Finally, the performance of the proposed method is demonstrated via numerical examples.

Probabilistically Robust Radar Waveform Design for Extended Target Detection

We address radar waveform design problem for extended targets under the Peak-to-Average Ratio (PAR) constraint. Based on the stochastic model of the Target Impulse Response (TIR), the distribution of output Signal-to-Interference-pulse-Noise Ratio (SINR) is derived. After that, a novel waveform design metric, named Probabilistically Robust Detection (PRD), is proposed to improve the stability of detection performance against the stochastic TIR. The geometric and limit interpretations for the PRD metric are given to show its rationality. Leveraging on the Semi-Definite Relaxation schemes and the Dinkelbach's algorithm, we devise algorithms to optimize waveform covariance matrix based on the proposed metric in high and low SINR situations, respectively. It is theoretically proved that the global optimal waveform covariance matrix can be achieved in high SINR situations. On the contrary, only the sub-optimal waveform covariance matrix can be obtained in low SINR situations. The transmit waveform is synthesized from the optimized waveform covariance matrix through randomization schemes. Numerical experiments are carried out to evaluate the PRD metric as well as the proposed algorithms. Results verify the effectiveness of the proposed algorithms. Compared with the current design metric, the proposed PRD metric exhibits strong probabilistic robustness on detecting extended targets.

Waveform Optimization for Multistatic Radar Imaging Using Mutual Information

This article addresses the problem of radar waveform design for imaging targets in a cluttered environment. A multistatic radar scenario is considered for sparse and random sensor positions. The target impulse response is modeled using the simulated frequency response of a buried metallic mine, and the clutter is modeled using the compound Gaussian (CG) distribution. We explore novel waveform design techniques with respect to the mutual information (MI) criterion based on the CG clutter. The first method presents a waveform that exploits the CG distribution of the scene reflectivity function when projected onto a sparse basis. This is compared to the second method, called the target-specific approach that uses knowledge of the target and clutter frequency responses to optimize a matched illumination waveform. In both cases, the Taguchi and particle swarm optimization solvers are employed for MI-based waveform design optimization. To validate and compare the effectiveness of the optimized waveforms, the resulting scene reflectivity function is estimated using the sparsity-driven regularization radar imaging method. Our experimental results demonstrate that both waveform optimization techniques result in significantly better image reconstruction performance than the traditional linear-frequency-modulated waveform, and that the target-specific approach additionally suppresses clutter information in the scene.

Adaptive Radar Waveform Design Based on Weighted MI and the Difference of Two Mutual Information Metrics

This study deals with the problem of radar waveform design based on the weighted mutual information (MI) and the difference of two mutual information metrics (DMI) in signal-dependent interference. Since the target and clutter information are included in the received signal at the beginning of the design, DMI-based waveform is designed according to the following criterion: maximizing the MI between the received signal and target impulse response while minimizing the MI between the received signal and the clutter impulse response. This criterion is equivalent to maximizing the difference between the first MI and the second MI. Then maximizing the difference of two types of MI is used as the objective function, and the optimization model with the transmitted waveform energy constraint is established. In order to solve it, we resort to maximum marginal allocation (MMA) method to find the DMI-based waveform. Since DMI-based waveform does not allocate energy to the frequency band where the clutter power spectral density (PSD) is greater than the target PSD, we propose to weight the MI-based waveform and DMI-based waveform to synthesize the final optimal waveform. It could provide different trade-offs between two types of MI. Simulation results show the proposed algorithm is valid.

Multi-Target Adaptive Radar Waveform Design Based on SINR

Aiming at the radar waveform design problem of detecting multiple targets in the presence of clutter, a novel algorithm based on linear probability-weighted summation (PWS) of multi-target impulse response of signal to interference plus noise ratio (SINR) is proposed. In view of the traditional water-filling algorithm, the multi-target detection algorithm is further studied in a new way to improve the overall performance of the system. This method uses Jensen’s inequality to make a lot of derivations to determine the target function of the algorithm and the constraints. Simulation results show that the proposed algorithm has better detection performance and more accurate target information.

High-Resolution Radar Waveform Design Based on Target Information Maximization

Although the transmit radar waveform design problem for maximizing target information has been studied widely in the past, the resolution requirement is normally ignored in such designs. Using maximizing target information as a criterion, a new radar waveform design method meeting the high-resolution requirement is proposed in this article, which makes no assumptions on the statistical distribution of target scattering. The objective function is proposed by maximizing the Pearson correlation coefficient and the design is then transformed into an optimization problem, which is solved in two steps. First, a closed-form expression for the discretized waveform with constant power constraint is derived in the time domain. Second, based on the bandwidth analysis of the optimal solution, a resolution improvement method considering information distortion is introduced and a suboptimal waveform is proposed while satisfying the constant power and resolution requirements. Finally, performance of the proposed radar waveform in terms of information acquisition, classification, and resolution is analyzed and compared with the classic high-resolution linear frequency modulated waveform (LFMW). Simulation results show that the resolution of the suboptimal waveform is slightly lower than the LFMW, but more desirable in terms of peak sidelobe ratio, information acquisition, and classification.

Optimization of a new Golay sequences shaping for low sidelobe radar ambiguity function

This work addresses the radar waveform design problem using phase-coded waveforms especially Golay complementary pair (GCP). Thus, a new shaping of GCP is proposed and the good performance of this shaping in terms of ambiguity function sidelobe (SL) rejection is shown. With the new shaping, a gain of at least 10 dB is easily obtained in comparison with the standard GCP. In order to improve the performance of the proposed waveform, two optimization algorithms are proposed to deal with low sidelobe ambiguity function problem, a very hard combinatorial optimization problem. The first one is the simulated annealing algorithm, a local search algorithm. The second represents the genetic algorithm-based global search strategy. Simulation results are provided and demonstrate that both types of algorithms decrease the SL rejection of the ambiguity function for all tested instances.

Unimodular Waveform Design With Desired Ambiguity Function for Cognitive Radar

In this correspondence, we target the problem of radar waveform design based on the ambiguity function. The problem is formulated as an optimization, where the nonconvex unimodularity constraint is also considered. The problem is solved by successive application of majorization minimization (MM) and projected gradient descent algorithm (PGD). The proposed method has the unprecedented ability to synthesize nonzero subregions. The superiority of the proposed algorithm in achieving zero subregions is confirmed through simulation, where a suppression superiority of at least 6 dB is evident compared to the best state-of-the-art benchmark.

Efficient low‐PAR radar waveform design method based on the alternating direction method of multipliers for multiple missions

This study addresses the low-peak-to-average power ratio (PAR) radar waveform design problem to optimise the detection and estimation performance simultaneously in the presence of signal-dependent clutter. The aim is to realise an effective trade-off between maximising the output signal-to-interference-plus-noise ratio (SINR) and mutual information (MI) under a low-PAR constraint. In the existing method, this problem is solved via convex optimisation, but the high computational complexity of this method limits its application. Motivated by the decomposability and superior convergence of the alternating direction method of multipliers, the authors propose an efficient method to obtain the optimal waveform by converting the original non-convex problem into simpler convex sub-problems that can be solved efficiently. The simulation results illustrate that the optimal waveform can be obtained efficiently within the given low-PAR range and that the synthesised waveform can provide a reasonable trade-off between the detection and estimation performances. Compared with the existing method, the proposed method has reduced computational complexity without SINR and MI performance degradations.

Alternating direction method of multipliers for radar waveform design in spectrally crowded environments

This paper addresses the radar waveform design problem in spectrally crowded environments. The aim is to maximize the output signal-to-interference-plus-noise ratio (SINR) of the waveform under spectral and similarity constraints. The existing algorithm proposes to tackle such a problem via semidefinite relaxation (SDR) and rank-one decomposition, resulting in high complexity and limited applications. Motivated by the decomposability and superior convergence properties of alternating direction method of multipliers (ADMM), we propose a novel algorithm to tackle the waveform optimization problem. Since simpler subproblems are involved at each iteration and they can be tackled efficiently, the proposed algorithm has a much lower computational complexity than the existing algorithm. Numerical examples demonstrate the effectiveness of the proposed algorithm.

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.

MIMO Radar Waveform Design via Alternating Projection

Waveform design is essential to unleash the performance advantages promised by multiple-input multiple-output (MIMO) radar, and this topic has attracted a lot of attention in the recent years. Revisiting an earlier examined MIMO radar waveform design problem that optimizes both minimum mean-square error estimation (MMSE) and mutual information (MI), in this correspondence we formulate a new waveform design problem and provide some further results, which complement the previous study. More specifically, we present an iterative optimization algorithm based on the alternating projection method to determine waveform solutions that can simultaneously satisfy a structure constraint and optimize the design criteria. Numerical examples are provided, which illustrate the effectiveness of the proposed approach. In particular, we find that the waveform solutions obtained through our proposed algorithm can achieve very close and virtually indistinguishable performance from that predicted in the previous study.

MIMO radar waveform design based on mutual information and minimum mean-square error estimation

This paper addresses the problem of radar waveform design for target identification and classification. Both the ordinary radar with a single transmitter and receiver and the recently proposed multiple-input multiple-output (MIMO) radar are considered. A random target impulse response is used to model the scattering characteristics of the extended (nonpoint) target, and two radar waveform design problems with constraints on waveform power have been investigated. The first one is to design waveforms that maximize the conditional mutual information (MI) between the random target impulse response and the reflected waveforms given the knowledge of transmitted waveforms. The second one is to find transmitted waveforms that minimize the mean-square error (MSE) in estimating the target impulse response. Our analysis indicates that under the same total power constraint, these two criteria lead to the same solution for a matrix which specifies the essential part of the optimum waveform design. The solution employs water-filling to allocate the limited power appropriately. We also present an asymptotic formulation which requires less knowledge of the statistical model of the target

Radar Waveform Design and the Heisenberg Group

This paper presents a number of constructions based on the Heisenberg group that are relevant to the problem of radar waveform design. All of the constructions are based on the modification of the Weil transform of a waveform.