Adaptive waveform design for radar target classification

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.

Waveform design is a commonly used approach to enhance target classification in high resolution radar systems. In the monostatic case of detecting some extended target, inherent to many of these system models is an assumption of a known target impulse or frequency response. A practical issue with this method is that for nonsimple target cases, such a response can change drastically for varying aspect or viewing angles. In this paper, we first develop a sparse regression method for classifying target class and aspect angle. Next, we derive matched filters tailored to dictionaries of target response profiles representing these variations in aspect angle. The desirable goal of real-time classification is met by suitably reducing the computational cost and not relying on a series of measurement and adaption cycles to achieve classification. The result is a series of filters matched to the target dictionary data and can be used in a hypothesis testing approach to classification. Results are shown for radar cross-sectional data generated from computer-aided design models of different targets.

A new scheme based on Kalman filtering to optimize the waveforms of an adaptive multi-antenna radar system for target impulse response (TIR) estimation is presented. This work aims to improve the performance of TIR estimation by making use of the temporal correlation between successive received signals, and minimize the mean square error (MSE) of TIR estimation. The waveform design approach is based upon constant learning from the target feature at the receiver. Under the multiple antennas scenario, a dynamic feedback loop control system is established to real-time monitor the change in the target features extracted form received signals. The transmitter adapts its transmitted waveform to suit the time-invariant environment. Finally, the simulation results show that, as compared with the waveform design method based on the MAP criterion, the proposed waveform design algorithm is able to improve the performance of TIR estimation for extended targets with multiple iterations, and has a relatively lower level of complexity.

The use of information theory to design waveforms for the measurement of extended radar targets exhibiting resonance phenomena is investigated. The target impulse response is introduced to model target scattering behavior. Two radar waveform design problems with constraints on waveform energy and duration are then solved. In the first, a deterministic target impulse response is used to design waveform/receiver-filter pairs for the optimal detection of extended targets in additive noise. In the second, a random target impulse response is used to design waveforms that maximize the mutual information between a target ensemble and the received signal in additive Gaussian noise. The two solutions are contrasted to show the difference between the characteristics of waveforms for extended target detection and information extraction. The optimal target detection solution places as much energy as possible in the largest target scattering mode under the imposed constraints on waveform duration and energy. The optimal information extraction solution distributes the energy among the target scattering modes in order to maximize the mutual information between the target ensemble and the received radar waveform. >

This study investigates the problem of low probability of intercept (LPI)-based distributed multiple-input multiple-output (MIMO) radar waveform design against barrage jamming in signal-dependent clutter and coloured noise. Given the priori knowledge of the extended target impulse response, signal-dependent clutter, barrage jamming signals and coloured noise, the LPI-based scheme for optimal radar waveform design is proposed to minimise the total power consumption of the MIMO radar system by optimising the transmitted waveforms of different transmitters with a predetermined mutual information (MI) constraint for target characterisation performance. Firstly, the MI between the received echoes from the target at each receiver and the target impulse response is derived as a practical metric to characterise the parameter estimation performance of a target. Then, the LPI-based distributed MIMO radar waveform design strategy is developed. The resulting radar waveform optimisation problem is convex and solved analytically, whose solutions represent the optimum power allocation for each transmitter in the MIMO radar system. With the aid of numerical simulations, it is illustrated that to minimise the total transmission power, the optimal waveform should match with the target, clutter, jamming and coloured noise. In addition, it is also demonstrated that the LPI performance of the MIMO radar system can be significantly improved by employing the proposed radar waveform design scheme.

Shallow-water horizontal underwater acoustic (UWA) channels are characterized by a time-varying multipath structure with a long delay spread. This causes significant signal distortion in phase coherent transmissions by introducing intersymbol interference (ISI), which can span several hundreds of symbols. The multipath structure is usually very sparse. This paper proposes an adaptive sparse partial response equalizer (SPRE) well matched with the channel characteristics to mitigate the ISI efficiently, and communicate reliably. Unlike the conventional equalizers that try to eliminate the ISI completely, the proposed structure performs equalization in two steps. In the first step, the channel is equalized to a judiciously chosen target impulse response (TIR), thereby leaving controlled residual ISI at the output of the SPRE. In the second step, the residual ISI is further mitigated by a near-optimal, graph-based, low-complexity symbol detection algorithm known as belief propagation (BP). We demonstrate that due to the sparse nature of the long ISI channel, and the well-matched adaptive TIR, this two-step equalization process is particularly useful. The idea here can be compared to what is done in the magnetic recording literature [i.e., partial response maximum-likelihood (ML) equalization] to avoid excessive noise enhancement, with the difference that the TIR needs to be designed adaptively using training symbols and that in the second step, instead of using a ML detector, a BP algorithm is used. The proposed SPRE algorithm is designed for a general multiple-input-multiple-output (MIMO) system and it provides soft outputs for the transmitted bits as a by-product of the BP-type equalization algorithm. Hence, it can be efficiently employed in coded systems (e.g., turbo or low-density-parity-check-coded, interleaved systems) with an iterative decoding/equalization scheme, providing significant improvements in achievable error rates. Finally, we note that the proposed SPRE scheme also incorporates a phase locked loop (PLL) structure so as to track the Doppler shift introduced by the channel. To evaluate the effectiveness of the proposed equalizer, we compare it with several decision feedback equalizers (DFEs) proposed by Stojanovic (J. Ocean. Eng. vol. 19, no. 1, pp. 100-111, Jan. 1994), Roy (Proc. MTS/IEEE TECHNO-OCEAN Conf., vol. 1, pp. 26-33, Nov. 2004), and Roy (J. Ocean. Eng., vol. 32, no. 3, pp. 663-688, Jul. 2004) both through simulations and experimental results. The results demonstrate that the SPRE receiver outperforms the decision-feedback-based receivers when the channel has long, yet sparse (possibly, nonminimum phase) structure, by reducing the frame error rates (FERs), improving the post-equalization signal-to-noise ratio (SNR), and decreasing the required number of turbo iterations (reduced latency).

Radar networks are proven to have numerous advantages over traditional monostatic and bistatic radar. With recent developments, radar networks have become an attractive platform due to their low probability of intercept (LPI) performance for target tracking. In this paper, a joint sensor selection and power allocation algorithm for multiple-target tracking in a radar network based on LPI is proposed. It is found that this algorithm can minimize the total transmitted power of a radar network on the basis of a predetermined mutual information (MI) threshold between the target impulse response and the reflected signal. The MI is required by the radar network system to estimate target parameters, and it can be calculated predictively with the estimation of target state. The optimization problem of sensor selection and power allocation, which contains two variables, is non-convex and it can be solved by separating power allocation problem from sensor selection problem. To be specific, the optimization problem of power allocation can be solved by using the bisection method for each sensor selection scheme. Also, the optimization problem of sensor selection can be solved by a lower complexity algorithm based on the allocated powers. According to the simulation results, it can be found that the proposed algorithm can effectively reduce the total transmitted power of a radar network, which can be conducive to improving LPI performance.

The target classification of unknown classes using radar sensor data is discussed. The neural network‐based classifier shows high classification accuracy for the learned class targets. However, there is a risk of false decision for the untrained class target owing to an overconfidence problem. The output confidence of the classifier is calibrated using the deep convolutional neural network ensemble structure to propose a method to set the proper threshold for output confidence to decide unknown class targets. When using the proposed method, the accuracy of the learned target is maintained similar to that of the existing single neural network‐based classifier, whereas the unknown class target is better identified. Further analysis verifies the effectiveness of the proposed method using commercial automotive radar. The proposed method can classify learned targets with an accuracy of 95% and distinguish unknown class targets with an accuracy of at least 85%. Based on the interaction with other sensors, individual sensors need to make reserved decisions about uncertain information. It is expected that the proposed ensemble network will be efficient in designing the classifier to perform target classification including unknown class decision.

A cognitive radar (CR) system is one that observes and learns from the environment; then uses a dynamic closed-loop feedback mechanism to adapt the illumination waveform so as to provide system performance improvements over traditional radar systems. Romero et al. recently developed a CR system that performs multiple hypothesis target classification and exploits the spectral sparsity of correlated narrowband target responses to achieve significant performance improvements over traditional radars that use wideband illumination pulses. This CR system was designed for Gaussian target responses. This research generalizes the CR system to deal effectively with arbitrary non-Gaussian distributed target responses via two key contributions: (1) an important statistical expected value operation that is usually evaluated in closed form is evaluated numerically using an ensemble averaging operation, and (2) a powerful new statistical sampling algorithm and a kernel density estimator are applied to draw complex target samples from target distributions specified by both a desired power spectral density and an arbitrary desired probability density function. Simulations using non-Gaussian targets demonstrate very effective algorithm performance.

The problems of multiple-input multiple-output (MIMO) radar adaptive waveform design in additive white Gaussian noise channels and multitarget recognition based on sequential likelihood ratio test are jointly addressed in this paper. Two information-theoretic waveform design strategies, namely, the optimal waveform for maximizing the mutual information (MI) between the extended target impulse response and the target echoes and the optimal waveform for maximizing the Kullback-Leibler (KL) divergence (or relative entropy), are applied in the multitarget recognition application. For multitarget case, two adaptive waveform design methods for all possible targets based on the current knowledge of each hypothesis are proposed. Method 1 is the probability weighted waveform method. Method 2 is the probability weighted target signature method. The optimal waveform is transmitted and adaptively changed such that a decision is made based on the likelihood ratio after several illuminations. Numerical results demonstrate that the best waveform is the KL divergence-based optimal waveform using Method 1 as it has the lowest average illumination number and the highest correct decision rate for target recognition. By optimally designing and adaptively changing the transmitted waveform, the average number of illuminations required for multitarget recognition can be much reduced.

Information theory, and particularly the mutual information (MI), has provided fundamental guidance for communications research. In Bell's 1993 paper, the MI was first applied to radar waveform design. Similar to its communications counterpart, the solution comes in a water-filling form. However, the practical meaning of MI in the sensing context remains unclear to date. Recently, Yang and Blum's 2007 paper shows that under the white noise assumption, the optimum water-filling scheme simultaneously maximizes the MI and minimizes the estimation minimum mean square error (MMSE). Such an equivalence, however, does not hold when the target parameter statistics are not perfectly known as shown in Yang and Blum's subsequent work. To further the understanding of the practical meaning of MI and to establish a connection between the MI and commonly adopted MSE measures for sensing, this paper takes a fresh look at the target estimation problem. We consider the general colored noise, incorporate the normalized MSE (NMSE), and develop joint robust designs for both the transmitter (waveforms) and the receiver (estimator) under various target and noise uncertainty models. Our results show that i) the optimum waveform designs resulted from the MI, MMSE and NMSE criteria are all different and ii) compared to MMSE, the NMSE-based designs share more similarities with the MI-based ones, especially when the target and noise statistics are not perfectly known.

Motivated by dual use of OFDM signal format for communications and radar in ever-worsening Electromagnetic (EM) coexistence environments, this paper deals with transmit waveform design problem considering multiple design objectives. Spectral nulling is a typical way for friendly coexistence with narrow band systems. However, a Non-Contiguous Orthogonal Frequency-Division Multiplexing (NC-OFDM) waveform generated by turning off the interfering sub-carriers does not lead to satisfactory results. In this paper a convex optimization based waveform design framework is used to achieve deep spectral nulling while retaining low waveform autocorrelation side lobes and good range resolution. Because of dual use of the waveform, the data blocks to transmit are either unknown or chosen from a known dataset. Optimal sub-carrier weights are obtained for given transmission data blocks. In addition, waveform design for unknown data blocks are discussed and examined.

We propose an information theoretic waveform design algorithm for target tracking in a low-grazing angle (LGA) scenario. We incorporate realistic physical and statistical effects, such as Earth's curvature, vertical refractivity gradient of lower atmosphere, and compound-Gaussian characteristics of sea-clutter, into our model. We employ a co-located multiple-input-multiple-output (MIMO) radar configuration using wideband orthogonal frequency division multiplexing (OFDM) signalling scheme. The frequency diversity of OFDM provides richer information about the target as different scattering centers resonate at different frequencies. Additionally, we use polarization-sensitive transceivers to resolve the multipath signals with small separation angles. Thus, we track the scattering coefficients of the target at different frequencies along with its position and velocity. We apply a sequential Monte Carlo method (particle filter) to track the target. Our tracker works in a closed-loop fashion with an integrated optimal waveform design technique based on mutual information (MI) criterion. We seek the optimal OFDM waveform at the current pulse duration to maximize the MI between the state and measurement vectors at the next pulse duration utilizing all the measurement history up to the current pulse. Our numerical examples demonstrate the importance of realistic physical modeling, effects of frequency diversity through OFDM MIMO configuration, and achieved performance improvements due to adaptive OFDM waveform design.

Waveform design over two consecutive transmission time instants or epochs is the focus of this paper. The waveforms are designed to maximize the mutual information (MI) over the two time epochs. For a single epoch, maximizing the MI is equivalent to waterfilling. In this paper it is shown that for two epochs, the designed waveforms must satisfy two criteria. The first is waterfilling, and the other is that the waveforms must place energies in those spectral bands which offer maximum un-correlated target scattering responses. The interplay of these two criteria causes the waveforms to be distinct from those designed by the single-epoch waterfilling-based systems. Comparisons of the waveforms designed over one epoch, and over two epochs are shown through simulations.

The problem of adaptive orthogonal frequency division multiplexing (OFDM) waveform design in the case of stochastic extended targets in the presence of strong and nonstationary interferences is an essential part of a cognitive radar system. In this article, a new approach is developed based on maximizing the mutual information between the random target impulse response and the received echoes with respect to the transmitted waveform. We use the advantage of OFDM signals and present an adaptive structure to match the complex weights of OFDM signal with the radar scene for making complete use of the transmission power. The interference reflections are utilized rather than eliminating them to design the weights of the transmitted OFDM signal. The optimization algorithm for designing transmitted signals is based on adaptive learning whose essential information is obtained by a feedback between receiver and transmitter. This feedback includes essential target and interference characteristics which extracted from the reflected echoes. Based on changes in interference features, the weights of the transmitted OFDM signal on each subcarrier are designed and transmitted in the next coherent processing interval. Experimental results reveal that the proposed approach achieves a higher rate of performance compared to nonadaptive waveform design approaches.