MIMO Radar Adaptive Waveform Design for Extended Target Recognition

In the field of target detection and tracking, the resolvability of multiple closely located targets is a significant criterion for measuring the sensing ability of radar and other sensing systems. This paper considers the problem of adaptive radar waveform design to maximize the practical resolvability of closely located targets. Conventional ambiguity function (AF)-based radar resolution considers only the waveform, regardless of the influence of noise. However, noise grreatly influences the achievable resolution as well as radar detection and tracking performance. As a result of this deficiency in conventional radar resolution, Kullback-Leibler Divergence (KLD) is introduced in this paper in order to quantify the “distance” between two probability density functions (PDFs) of radar measurements, and thus to represent practical radar resolution, which includes not only the effect of the waveform but also the signal-to-noise ratio (SNR) and measurement model. Consequently, a new adaptive radar waveform design criterion is proposed, which aims to maximize the practical radar resolution. Simulation results show the effectiveness of the proposed adaptive waveform design method.

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.

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 address the problem of adaptive waveform design for extended target recognition in cognitive radar networks. A closed-loop active target recognition radar system is extended to the case of a centralized cognitive radar network, in which a generalized likelihood ratio (GLR) based sequential hypothesis testing (SHT) framework is employed. Using Doppler velocities measured by multiple radars, the target aspect angle for each radar is calculated. The joint probability of each target hypothesis is then updated using observations from different radar line of sights (LOS). Based on these probabilities, a minimum correlation algorithm is proposed to adaptively design the transmit waveform for each radar in an amplitude fluctuation situation. Simulation results demonstrate performance improvements due to the cognitive radar network and adaptive waveform design. Our minimum correlation algorithm outperforms the eigen-waveform solution and other non-cognitive waveform design approaches.

The 18 papers in this issue focus on the following areas: waveform design; adaptive waveform design; surveillance and classification in radar; multiple-input multiple-output (MIMO) radar systems; and wireless communications.

In this paper, an optimal waveform design method for target recognition is proposed based on the relative entropy. Since the target recognition can be considered as a hypothesis test procedure, the detection probability could be the cost function to characterize the recognition performance. Then the cost function associated with the relative entropy is maximized to optimize the waveform for improving the recognition performance. The most proposed optimal waveform design methods just only consider the energy constraint. However, only the energy constraint is impractical. In this paper, we do not only consider the total energy limit, but also add the constant modulus constraint from the practice side to design the optimal waveform, since the radar systems commonly require constant modulus waveforms in order to utilize nonlinear power amplifiers. Finally, the simulation results show the effectiveness of the proposed algorithm.

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.

A simple and successful design for an adaptive radar phase-coded waveform is presented. The optimised phase-coded waveform is designed by the phase-only conjugate gradient method. The signal-to-interference-plus-noise ratio of the optimised phase-coded waveform is compared with an optimal waveform and good approximation is achieved.

For chaotic trajectories, when the system parameters are fixed, they are generally confined in a bounded state space. In this paper, we propose an adaptive regularized particle filter (RPF), which makes the best of this inherent characteristic, for identical synchronization of chaotic Colpitts circuits combating additive white Gaussian noise (AWGN) channel distortion. This proposed filter incorporates RPF that resamples from a continuous approximation of the posterior density to avoid sample impoverishment and then utilizes the revised Kullback–Leibler distance (KLD) sampling to adaptively select the number of particles used. Compared with the existing particle filters (PFs) with fixed large number of particles, this proposed adaptive RPF propagates less number of particles with similar performance and thus provides a much more efficient solution for this problem.

: Calculating the amount of information about a random function contained in another random function has important uses in communication theory. An expression for the mutual information for continuous time random processes has been given by Gelfand and Yaglom, Chiang, and Perez by generalizing Shannon's result in a natural way. Under a condition of absolute continuity of measures the continuous time expression has the same form as Shannon's result. For two Gaussian processes Gelfand and Yaglom express the mutual information in terms of a mean square estimation error. We generalize this result to diffusion processes and express the solution in a different form which is more naturally related to a corresponding filtering problem. We also use these results to calculate some information rates.

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.

In this paper, the problem of adaptive waveform design for cognitive radar (CR) in signal-dependent interference, as well as additive channel noise is investigated. With constraints on waveform energy and bandwidth, a flexible waveform optimization method taking both detection and range resolution into account is proposed. Unlike existing optimal waveforms designed by a single design criterion, waveform designed by the proposed method can be updated according to the environment information fed back by receiver and radar performance demands simultaneously at each cycle of CR. Simulations are conducted to illustrate that CR with the proposed waveform performs better than traditional radar system with fixed waveform, and offers more practical and flexible.

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.

This study addresses the challenge of cognitive waveform design for multiple-input–multiple-output (MIMO) radar systems operating in cluttered environments. It focuses on the key practical requirements for transmitting time-domain waveforms and proposes a novel approach. This method first determines the optimal frequency-domain waveform and then designs a time-domain waveform that closely approximates the frequency-domain solution. The primary objective is to enable MIMO radar systems to transmit orthogonal waveforms while accommodating various constraints. A frequency-domain waveform optimization model was initially developed using the principle of maximizing dual mutual information (DMI), and the energy spectral density (ESD) of the optimal waveform was derived using the water-filling method. Next, a time-domain waveform approximation model is constructed based on the minimum mean square error (MMSE) criterion, which incorporates constant modulus and peak-to-average power ratio (PAPR) constraints. To minimize the performance degradation of the waveform, an improved adaptive gradient descent genetic algorithm (GD-AGA) was proposed to synthesize multichannel orthogonal time-domain waveforms for MIMO radars. The simulation results demonstrate the effectiveness of the proposed model for enhancing the performance of MIMO radar. Compared with traditional genetic algorithms (GA) and two enhanced GA alternatives, the proposed algorithm achieves a lower ESD loss and better orthogonal performance.

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.