Waveform Optimization for Multistatic Radar Imaging Using Mutual Information

The typical approach to radar target classification is to image the target with waveforms that provide high resolution and low sidelobes, and then to compare the target images to a template library. In this chapter, we reconsider whether imaging-based metrics for waveform design are best for target classification, and develop alternative design strategies that result in waveforms with improved classification ability, but not necessarily a good ambiguity function by traditional notions. After presenting waveform design strategies based on optimizing signal-to-noise ratio or mutual information from a wide-sense stationary (WSS) ensemble of target impulse responses, we apply the design methods to the problem of radar target classification through a two-step process. The first step is to modify the design methodology that was based on WSS targets to account for the finite duration of practical target responses. The second step is to use the target class probabilities and impulse response library to calculate a weighted power spectral variance over target classes, which is then substituted into the design equations. The use of target class probabilities enables the waveform to be adapted in response to previous transmissions. Waveform behaviour and performance are studied over several different clutter and noise scenarios. The target impulse response library for these studies is based on finite-difference time-domain (FDTD) simulation of a publically available CAD model of an F-16 aircraft.

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.

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.

Over the last decade, research on multistatic radar waveform design has attracted significant consideration among the radar system designers.Among the waveform design techniques, linear frequency modulated waveforms are widely used, but the problem associated with it is range Doppler coupling and complexity in achieving adequate pulse-to-pulse diversity. In this letter, an orthogonal linear frequency modulated (OLFM) waveform has been used as the transmitted waveforms, which has good correlation properties and large time bandwidth product. The ambiguity function (AF), which is the output of the matched filter, is used to analyze the target resolution capabilities of the OLFM waveforms. The mathematical expressions of the AF with OLFM waveforms for the multistatic architecture are represented based on the target fluctuations observed at the receiver. These expressions allow the ambiguity in resolving target position and velocity vectors for any transmitted waveform in the multistatic topology. The normalized cross-correlation value of the LFM waveforms is compared with the OLFM waveforms, which signify the isolation factor between two transmitted waveforms at the receiver. A performance comparison has been made based on the probability of target detection for various multistatic scenarios under numerous signal-to-noise ratio (SNR) conditions.

Detection of weak moving targets with a low signal-to-clutter ratio (SCR) in heavy-tailed non-Gaussian sea clutter is a challenge problem in radar signal processing. In this study, an easily implementable suboptimum detector in compound-Gaussian (CG) clutter is proposed based on suprathreshold stochastic resonance (SSR). The structure of the locally optimum coherent detector for weak target detection in CG clutter is first analysed and the authors proved that it can be implemented using a pre-processing system followed by the adaptive matched filter (AMF) used in Gaussian backgrounds. A suboptimum pre-processing system is designed using the SSR system consisting of a parallel array of quantisers, which overcomes the high computation cost caused by the calculation of the data-dependent threshold for optimum detectors. Its input–output characteristic can be adjusted by adding different quantiser noise at the input of the system, making it suitable to be used for different distributions of input clutter. The gain of the SSR pre-processing system is introduced and the parameter determination for quantiser noise is analysed. Experiments on both simulated clutter and real sea clutter data in the Council for Scientific and Industrial Research's database and Intelligent PIXel Grimsby database have shown that the proposed detector based on SSR could achieve robust detection performance and perform better than the existing methods.

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.

It was recently shown that MIMO radars with sparse sensing and matrix completion (MC) can significantly reduce the volume of data required by MIMO radars for accurate target detection and estimation. In MIMO-MC radars, the subsampled target returns are forwarded by the receive antennas to a fusion center, partially filling a matrix, referred to as the data matrix. The data matrix is first completed via MC techniques and then used to estimate the target parameters via standard array processing methods. This paper studies the applicability of MC theory on the data matrix arising in colocated MIMO radars using uniform linear arrays. It is shown that the data matrix coherence, and consequently the performance of MC, is directly related to the transmit waveforms. Among orthogonal waveforms, the optimum choices are those for which, any snapshot across the transmit array has a flat spectrum. The problem of waveform design is formulated as an optimization problem on the complex Stiefel manifold, and is solved via the modified steepest descent method, or the modified Newton algorithm with nonmonotone line search. Although the optimal waveforms are designed for the case of targets falling in the same range bin, sensitivity analysis is conducted to assess the performance degradation when those waveforms are used in scenarios in which the targets fall in different range bins.

In the past decades, there has been an extensive research interest in the areas of both waveform diversity/design and advanced signal processing algorithms departing from the more classical solutions based on Linear Frequency Modulated (LFM) pulses and Matched Filters (MF). In the waveform diversity community, especially within the context of spectrum sharing, MIMO and cognitive radars, several waveform optimization and design methodologies have been studied, see [1], [2] and references therein. In parallel to waveform design, several signal processing techniques have also been proposed which exploit some kind of prior knowledge and/or iterative algorithms to improve the performance of the more classical MF, such as the Adaptive Pulse Compression(APC) [3], MUSIC [4], CLEAN [5] and Sparse Signal Processing (SSP) [6], [7]. In this paper we present some results and examples to show how the combination of waveform design with SSP can lead to improved performance in radar compared to the more classical approach.

We consider waveform design for colocated multiple-input, multiple-output (MIMO) radar systems where the signal phase is subject to random phase perturbations during propagation. We formulate an iterative algorithm to obtain both waveform parameters and the space-time adaptive weights to maximize the signal-to-interference-plus-noise ratio (SINR). We ensure that the impact of the chosen waveforms on the interference signal is accounted for when modeling the second-order interference statistics. The waveform design technique is then extended to include peak-to-average power constraints. An example of a clutter and target model is provided to show how the optimal waveform design improves radar detection performance in the presence of the signal phase randomization.

Waveform optimization is a crucial step in the design of a multiple-input multiple-output system. This letter considers the joint optimization of constant modulus waveforms and mismatched (or matched) receive filters to suppress the auto- and cross correlations using the minimax ( $\ell _{\infty }$ -norm) design criterion. For practical waveform length and system size, the waveform design problem becomes quite challenging due to the large problem size (more than $10^5$ unimodular complex variables and $10^7$ nonlinear constraints). In addition to the large size, this problem is nonconvex, nonsmooth, and as such, cannot be handled effectively by the existing waveform design algorithms or off-the-shelve optimization tools. This letter develops an efficient primal–dual type algorithm with low per-iteration complexity to solve this problem. Numerical comparison shows that the waveforms based on the minimax design outperform those obtained from the existing $\ell _2$ -norm design by 4–5 dBs in terms of peak sidelobe levels.

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.

This paper addresses the problem of adaptive sequential waveform design for system parameter estimation. This problem arises in several applications such as radar, sonar, or tomography. In the proposed technique, the transmit/input signal waveform is optimally determined at each step, based on the measurements in the previous steps. The waveform is determined to minimize the Bayesian Cramer-Rao bound (BCRB) for estimation of the unknown system parameter at each step. The algorithm is tested for spatial transmit waveform design in multiple-input multiple-output radar target angle estimation at very low signal-to-noise ratio. The simulations show that the proposed adaptive waveform design achieves significantly higher rate of performance improvement as a function of the pulse index, compared to identical signal transmission.

We introduce a novel generalization of the compound Gaussian (CG) (or Gaussian Scale Mixture [1]) distribution which extends the Gaussian component of the CG model to a multilinear distribution. The resulting model, which we call the Multilinear Compound Gaussian (MCG) distribution, subsumes both GSM [1] and the previously developed MICA [3-4] distributions as complementary special cases; thereby allowing us to model a richer class of stochastic phenomena. First we derive the structural characterization of the MCG distribution and develop some of its important theoretical properties. Thereafter we describe a parameter estimation algorithm for learning this model from sample data, and then deploy this for modeling textures, including natural (i.e. optical) and SAR images. Our simulation results demonstrate how, for each case, we obtain improved performance over the CG model; thus indicating the versatility of the MCG model in accurately modeling various natural phenomena of interest.

This paper deals with the weak target detection and tracking for airborne radar in compound Gaussian with inverse Gaussian texture (IGCG) distribution sea clutter. Combine with the characteristics of IGCG distribution clutter and the airborne radar, a track-before-detect algorithm based on dynamic programming (DP-TBD) is proposed in this paper. In this algorithm, the multi-frame test statistic based on generalized likelihood ratio test (GLRT) under the track-before-detect (TB-D) framework is derived, and then the dynamic programming (DP) algorithm is used to give the specific realization method for detecting and tracking target in the range-azimuth-doppler domain. Compared with the traditional algorithms, simulation results show that the proposed algorithm can effectively improve the detection and tracking performance for airborne radar in IGCG distribution clutter.

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.