Waveform Design Method Research Articles

Stochastic radiation field optimization for microwave staring correlated imaging via spatial correlation minimization

Microwave staring correlated imaging (MSCI) is a staring high-resolution microwave imaging technique, employing the temporal–spatial stochastic radiation field (TSSRF). The imaging capability of MSCI depends on the spatial correlation of the TSSRF, which is equivalent to the incoherence of the sensing matrix in discrete form. A waveform design method for MSCI using multifrequency signals to reduce the spatial correlation of the TSSRF is proposed. The amplitude of each frequency component in the multifrequency signals serves as the design variable. Considering the power and the amplitude constraints in the practical radar system, we first form the waveform design as a constrained optimization problem. Then, it is reformulated as a nonsmooth unconstrained optimization problem by the penalty function method. With the smoothing approximation, the reformulated problem is solved by alternating minimization. Numerical experiments show that the proposed method can decrease the spatial correlation of the TSSRF and improve the imaging performance of MSCI as a result.

Designing Unimodular Waveform(s) for MIMO Radar by Deep Learning Method

A fast and excellent unimodular waveform with good autocorrelation and cross-correlation design method for the multiple-input multiple-output radar is devised. Unlike the existing methods that only optimize partial metrics or only optimize the short sequence in acceptable time, we propose a comprehensive waveform design method to minimize the weighted sum of almost entirely metrics under the constant modulus constraint. Then, a deep learning framework, named as the comprehensive optimization network, is derived to handle the problem. Numerical results show that the proposed method has superior performance and acceptable optimization time compared with the existing methods.

Secure hybrid pulse compression as a technique against jamming in radar systems

In this paper, we propose a secure hybrid pulse compression method for radar waveform design. This method uses a confidential code as the phase-code for the binary-shift keying modulation. We also use another confidential code for the frequency-code. This code is replaced in the frequency control register of a direct digital synthesizer to perform the narrow-band frequency-shift keying. We exploit the output of an encryption algorithm, e.g. a block cipher, as the binary code, which fulfills security and confidentiality requirements of electronic warfare scenarios. In contrast to other proposals that use only confidential phase-codes, we propose a method that considers both the frequency and phase codes to be confidential. We evaluate the proposed method’s performance in the presence of a jammer for three cases: where the jammer has access only to the phase-code, only the frequency code, and has access to neither. Our method effectively decreases the probability of false alarms, while improving detection probability.

Distributed Target Detection in Communication Interference and Noise Using OFDM Radar

In this letter, the distributed target detection in a mixture of unknown communication interference and noise using the orthogonal frequency division multiplexing (OFDM) radar is considered. A closed-form detector is not tractable, instead, an efficient expectation maximization-based generalized likelihood ratio test (GLRT) detector is developed. The ideal GLRT detector with the complete knowledge of communication signal is also derived as a contrast. Besides, an information theoretic waveform design method by maximizing Kullback-Leibler divergence is addressed to improve the detection performance, in which the subcarrier power ratio is used as a constraint. Simulations show the superiority of the addressed detectors and method.

Multi-Target Robust Waveform Design Based on Harmonic Variance and Mutual Information

Cognitive radar is an intelligent radar system, and adaptive waveform design is one of the core problems in cognitive radar research. In the previous studies, it is assumed that the prior information of the target is known, and the definition of target spectrum variance has not changed. In this paper, we study on robust waveform design problem in multiple targets scene. We hope that the upper and lower bounds of the uncertainty range of robustness are more close to the actual situation, and establish a finite time random target signal model based on mutual information (MI). On the basis of the optimal transmitted waveform and robust waveform based on MI, we redefine the target spectrum variance as harmonic variance, and propose a novel robust waveform design method based on harmonic variance and MI. We compare its performance with robust waveform based on original variance. Simulation results show that, in the situation of multiple targets, compared to the original variance, the MI lifting rate of robust waveform based on harmonic variance relative to the optimal transmitted waveform in the uncertainty range has great improvement. In certain circumstances, robust waveform based on harmonic variance and MI is more suitable for more targets.

An analytical method of switching waveform design for selective harmonic elimination

The paper proposes an analytical approach to the design of switching waveforms to eliminate harmonics and thereby improve THD (Total Harmonic Distortion) in power converters. Generally, numerical solutions are used to obtain the switching angles to eliminate targeted harmonics and the solution requires guessing of an initial value and a valid modulation index, m (a ratio of the fundamental to the dc input). Both of these values affect solution convergence whereas, such difficulties do not arise in analytical solutions. The closed-form solutions obtained through the analytical approach also determine the valid range of m. Due to the closed form, this method is suitable for real-time applications where a microcontroller can be programmed, thus making it attractive for low-cost applications. A PWM (Pulse Width Modulation) signal with even–odd symmetry has been selected to minimize the complexity of the solution. The approach requires the solution of transcendental equations associated with Fourier coefficients of a periodic waveform. Chebyshev expansion is used to convert the transcendental equations to power-sum non-linear polynomials. A successive polynomial simplification method has been used that lead to a set of elementary functions in closed-form, which are used to generate a polynomial and its roots are the desired optimal switching angles. In this paper, the proposed approach has been examined through a fourth-order, three-phase system for bipolar and multistep waveforms. The approach is equally applicable to other types of PWM systems. Simulation results verify the harmonic cancellations.

An Adaptive Multi-Target Jamming Waveform Design Based on Power Minimization.

With increasing complexity of electronic warfare environments, smart jammers are beginning to play an important role. This study investigates a method of power minimization-based jamming waveform design in the presence of multiple targets, in which the performance of a radar system can be degraded according to the jammers’ different tasks. By establishing an optimization model, the power consumption of the designed jamming spectrum is minimized. The jamming spectrum with power control is constrained by a specified signal-to-interference-plus-noise ratio (SINR) or mutual information (MI) requirement. Considering that precise characterizations of the radar-transmitted spectrum are rare in practice, a single-robust jamming waveform design method is proposed. Furthermore, recognizing that the ground jammer is not integrated with the target, a double-robust jamming waveform design method is studied. Simulation results show that power minimization-based single-robust jamming spectra can maximize the power-saving performance of smart jammers in the local worst-case scenario. Moreover, double-robust jamming spectra can minimize the power consumption in the global worst-case scenario and provide useful guidance for the waveform design of ground jammers.

Robust interference waveform design in fuzzy colored noise based on mutual information

Traditional waveform design methods mostly assume that the noise in the environment is Gaussian white noise. However, as the electronic warfare environment for the jammer becomes increasingly complicated, there is more likely to be a noise source that can emit fuzzy colored noise and a situation where the radar and jammer game, and the existing waveform design methods cannot meet jammer’s performance demand. Therefore, to reduce the radar’s estimation performance in complex environments, a fuzzy colored noise environment and a robust interference waveform design method under the hierarchical game model between the radar and jammer are proposed successively, which can minimize the mutual information of the radar echo signal and the target impulse response. Extensive simulation experiments show that the designed robust interference waveform can finally optimize the strategy of the jammer and provide a meaningful reference for the interference waveform energy allocation strategy in the future.

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.

Spatial–temporal waveform design for MIMO radar without approximating the covariance matrix

In this study, a transmit waveform design method based on spatial-temporal optimisation for multiple-input multiple-output (MIMO) radar is proposed. The goal is not only to design the waveforms for beampattern matching, but also to minimise the autocorrelation sidelobes of the spatial synthesis signals of interested direction. Especially, to synthesise the constant envelope waveform directly, an improved sequential convex algorithm is proposed to tackle the non-convex problem in spatial optimisation. Then the autocorrelation sidelobes are reduced by using the steepest descent algorithm in temporal optimisation. Finally, the authors assess the effectiveness of the proposed technique through numerical simulations in comparison with the traditional and the alternating direction method of multipliers method.

Waveform Analytic Design Method for Transmit Beampattern Synthesis of Circulating Coded MIMO Radar

The transmit beampattern of multiple-input and multiple-output (MIMO) radar can be controlled by transmitting properly designed correlated waveforms. However, most of the correlated waveform design methods proposed in recent years are computational complex. For real time application, the low computational complex waveform design technique has become the interest of research. In this article, we present a waveform analytic design method for the transmit beampattern synthesis of circulating coded MIMO radar. The relationship between the parameters of linear frequency modulated (LFM) waveform and the instantaneous beam pointing angle of circulating coded MIMO radar is developed. Based on such a relationship, the analytic solutions to the parameters of LFM waveform are derived for arbitrary transmit beampattern synthesis. The computational burden of this method is negligible. Numerical simulation results demonstrate the performance of the proposed method.

An Optimizing Method of OFDM Radar Communication and Jamming Shared Waveform Based on Improved Greedy Algorithm

Orthogonal frequency division multiplexing (OFDM) has been widely used as radar, communication, and jamming shared waveform. To improve the power utilization and efficiency of radar, communication, and jamming integrated system, we propose an adaptive OFDM shared waveform design method. Considering the problem of jamming path propagation loss and sensitivity of frequency response error of radar and communication channels, we propose a robust OFDM shared waveform design method. Firstly, the suppressed jamming entropy model, the detection probability (Pd) of the stationary point target model, the data information rate (DIR) model with a given bit error rate (BER) are formulated. With the constraints on total power and BER, the adaptive and the robust OFDM optimization problems are formulated. Then we derive the Karush-Kuhn-Tucker (KKT) conditions of the two optimization problems and an improved greedy algorithm is proposed to solve the optimization problems, and the optimal power and bit allocation schemes for the two problems are obtained. Finally, we present several numerical results to demonstrate the effectiveness of the proposed method.

Closed-Form Waveform Design for MIMO Radar Transmit Beampattern Synthesis via Integral Equality

Recently, due to the adequate use of waveform diversity, MIMO technology has been widely adopted, resulting in the waveform design for MIMO radar beampattern synthesis becoming a hot issue. However, most previous works regarding this problem optimize the waveform by introducing the global mean squared error (MSE) as the cost function, this requires large computation in applications. Different from these works, we adopt the idea from the shaped beampattern synthesis problem of 2-D array in this paper, that is, to form a flat-top beampattern in the desired area with small ripple. By considering the physical meaning of the flat-top beampattern from scratch, the MIMO waveform design problem is turned to designing the waveforms that make its beampattern integral (i.e. the energy transmitted by array) equal in the desired area. Subsequently, we put forth a closed-form method and give its mathematical proof. Numerical simulations and comparisons to known MIMO radar waveform design methods are provided to verify its effectiveness and outperformance.

Radar Waveform Optimization for Joint Radar Communications Performance

We develop and present a radar waveform design method that optimizes the spectral shape of the radar waveform so that joint performance of a cooperative radar communications system is maximized. The continuous water-filling (WF) spectral-mask shaping method presented in this paper is based on the previously derived spectral-mask shaping technique. However, the method presented in this paper is modified to utilize the continuous spectral water-filling algorithm to improve communications performance. We also introduce additional practical system constraints on the autocorrelation peak side-lobe-to-main-lobe ratio and radar waveform spectral leakage. Finally, we perform a numerical study to compare the performance of the continuous WF spectral-mask-shaping method with the previously derived method. The global estimation rate, which also accounts for non-local estimation errors, and the data rate capture radar and communications performance respectively.

Adaptive chaotic MIMO radar based on DPMM clustering and Kalman filtering technique.

A novel scheme to optimize the adaptive transmit waveform of chaotic multiple-input multiple-output (MIMO) radar is developed. The main objective of this work is to achieve high ability in target discrimination by using a Dirichlet process mixture model (DPMM)-based clustering method based on nonparametric Bayesian theory and to improve the capability of target detection by minimizing the mean square error of radar channel response via Kalman filtering (KF) technique. The two stages are the discrimination of multiple range-extended targets and the optimization of the adaptive chaos-based waveform for transmission. The adaptive chaotic MIMO waveform optimization scheme overcomes the problem of target discrimination and detection in an intelligent transportation system, where there is a need for extracting the feature of target information achieved from vehicle-mounted sensor. As the number of iterations increases, simulation experiments demonstrate better target discrimination capability provided by the proposed DPMM-KF technique as compared with the traditional waveform design method. In addition, the proposed DPMM-KF technique leads to improved target detection probability and receiver operating characteristics in the interference environment.

Research on Radar Waveform Design Strategy under Game Condition

In order to improve missile-borne radar detection performance in modern electronic warfare, a radar waveform design method based on Nash equilibrium is proposed. Firstly, the radar and jammer game signal models are established in electronic warfare. Based on maximum Signal-to-Interference-plus-Noise Ratio (SINR), waveform strategies of radar and jammer are designed respectively. Secondly, the existence of Nash equilibrium solution is demonstrated by mathematical derivation and verified in experimental simulation. A multiple iterative water-filling method which repeatedly eliminates strict disadvantages is designed to achieve Nash equilibrium. The maxmin scheme of disequilibrium game is deduced by two-step water-filling method. Finally, the radar detection performance of optimization strategies is tested by simulation experiments. Simulation results reveal that the radar waveform design based on Nash equilibrium is beneficial to improve the radar detection performance under game conditions. Compared with no-game and maxmin strategies, the radar detection probability of Nash equilibrium strategy can be increased by 12.02% and 3.82%, respectively. It is proved that the Nash equilibrium strategy of this paper is closer to the Pareto optimality.

Mutual-Information-Based OFDM Waveform Design for Integrated Radar-Communication System in Gaussian Mixture Clutter

Existing studies on joint radar and communication systems are mainly based on a common assumption: Gaussian environment. Nevertheless, this does not hold in many complicated scenarios. In this letter, mutual information (MI)-based waveform design method for the integrated orthogonal frequency division multiplexing radar-communication system in Gaussian mixture (GM) clutter is investigated. First, from the statistical perspective, the approximate differential entropy of received signal in GM clutter is derived. Subsequently, an adaptive waveform design method is proposed by maximizing the MI, subject to three metrics: communication channel capacity; subcarrier power ratio; and energy constraint. Simulation shows the tradeoff among the above metrics.

Information theoretic waveform design for OFDM radar‐communication coexistence in Gaussian mixture interference

In this study, mutual information (MI)-based waveform design methods for the coexistence between orthogonal frequency division multiplexing (OFDM) radar system and communication system corrupted by Gaussian mixture interference are investigated for the first time. Firstly, the received signal is formulated as a Bayesian linear model. Subsequently, from a statistical perspective, the approximate differential entropy of received signal is derived, followed by three different approximate MIs and corresponding theoretic upper bounds. After that, two adaptive waveform design methods are proposed by maximising MI and minimising radar transmitted power, respectively. The numerical results show that exploiting the reflected communication signals helps to obtain higher MI value and reduce radar transmitted power. Besides, by maximising the MIs, the optimised radar waveforms remarkably outperform the fixed ones, which benefits the estimation performance.

Radar Waveform Optimization for Target Parameter Estimation in Cooperative Radar-Communications Systems

The coexistence between radar and communications systems has received considerable attention from the research community in the past years. In this paper, a radar waveform design method for target parameter estimation is proposed. Target time delay parameter is used as an example. The case where the two systems are not colocated is considered. Radar waveform optimization is performed using statistical criteria associated with estimation performance, namely Fisher Information (FI) and Cramer–Rao Bound (CRB). Expressions for FI and CRB are analytically derived. Optimization of waveforms is performed by imposing constraints on the total transmitted radar power, constraints on the interference caused to the communications system, as well as constraints on the subcarrier power ratio (SPR) of the radar waveform. The frequency-domain SPR is different than the peak-to-average power ratio, which is computed in time domain. It is shown, using simulation results, that the proposed optimization strategies outperform other strategies in terms of estimation error. It is also shown that the SPR constraint reduces the delay domain ambiguities.

Range sidelobe suppression for OFDM‐integrated radar and communication signal

To improve the RadCom system of performing both data transmission and radar-sensing functions, here a waveform design method for orthogonal frequency division multiplexing (OFDM) signal is proposed to solve the problem of high range sidelobe level in radar detection process while maintaining a reasonable channel capacity. The method only transmits data in the sub-channels with preferable channel quality. Then, calculate the weight of the chosen subcarriers through the convex optimisation method to traditionally minimise the peak-to-sidelobe (PSL) ratio. Simulation results prove that, compared with traditional range sidelobe suppression method, this algorithm is more suitable for RadCom system.