In this paper, we exploit the concept of identical partitioning of an integer set to support orthogonal radar waveforms with non-overlapping slow-time pulses. The set of slow-time pulses in a coherent processing interval (CPI) is partitioned into multiple identical subsets, and each subset is used to design sparse slow-time pulses for a single radar with low lag redundancy. Such waveform design based on integer set partitioning not only allows co-existence of multiple radars over a particular CPI, but also ensures that each radar unit can enjoy an extended dwell time, thereby maintaining a high-resolution estimation of the target Doppler frequencies. A modified difference co-chirp-based approach is exploited for range-Doppler estimation of targets with a low computational complexity.

When using a distributed multiple-input multiple-output (MIMO) radar system, one must account for nonideal and unknown effects due to the electronics, cables, antennas, and so on. This article addresses the problem of estimating the MIMO system transfer function coefficients of a linear time-invariant (LTI) MIMO system. The system is considered to be uncalibrated in that its MIMO transfer function, receiver noise powers, and noise spatial correlations are unknown. The problem of estimating the MIMO system transfer function coefficients is shown to be nontrivial due to its inherent Kronecker structure and is shown to be of the form of a class of unsolved problems. Three approaches for estimating the transfer function are derived and shown to achieve good performance in simulation. The first approach relaxes the constraints and finds the corresponding (relaxed) maximum likelihood estimator (MLE). The second approach projects the relaxed MLE solution into the constraint (Kronecker) set. The third approach makes use of the fact that the original transfer function MLE problem is biconvex in the transmit and receive transfer functions, respectively, and employs an alternating minimization algorithm to find them directly.

In classical parameter estimation settings, sensor observation models are often assumed to be known. However, when the sensors themselves become unreliable, the traditional observation models may no longer hold. It is then expected that estimation performance would degrade due to the abnormal behavior of sensor observations. We formulate the estimation problem as a two-person zero-sum game and propose a mini-max estimator with the optimization goal to minimize the worst possible estimation error. We show that there exists a saddle-point solution for a single sensor observation. We then apply our result and characterize the estimation performance for networks with multiple sensors.

We consider the case where there are outliers in the observations and evaluate two robust detectors, namely the Clipped Log-Likelihood Ratio Detector inspired by Huber’s ratio test, and a $\alpha$–Trimmed Sum Detector. The detector’s robustness and performance in the presence of outliers are analyzed. We show these detectors provide reasonably good performance despite the presence of outliers in the observations. We also analyze the detectors breakdown points where the detectors can not yield any meaningful results.

This paper considers the detection of a target in a distributed radar system, wherein the received reflections from the said target are contaminated with heterogeneous clutter returns. We model this clutter, and possibly additional interference, as a superposition of an auto-regressive process and deterministic interference coming from a known subspace. Parametric adaptive detectors for this scenario are derived based on the Generalized Likelihood Ratio (GLR), Rao, and Wald tests, and are analyzed and compared with their non-adaptive, clairvoyant counterparts, which assume a priori knowledge of the auto-regressive process parameters. Using numerical simulations, the proposed detectors are shown to have detection performances that are robust to strong subspace interference.

Target geo-location is an important task in over-the-horizon radar. A useful approach is based on the Doppler signatures of the micro-multipath signals which reveal target motion and enable target state estimation. Target Doppler signatures, however, are sensitive to irregular target motions, thereby complicating the Doppler signature analyses. In this paper, we consider the Doppler signatures of micro-multipath signals for a target that moves with a constant altitude but its azimuth velocity and altitude are perturbed. We analyze the effect of such velocity and altitude variations in the resulting Doppler signatures. The Doppler frequency difference is estimated using the self-stationarized signals.

We derive several parametric detectors for the case of a ground-based distributed multiple-input multiple-output radar system with colocated transmitters and receivers. The proposed detectors are based on exact and approximate generalized likelihood ratio tests. For the transmit–receive paths, which start and end at the same node, we incorporate the constraint of spectral symmetry, meaning that the clutter returns are assumed to have a power spectral density that is symmetric around the zero Doppler, which is motivated by statistical analyses performed on measured clutter radar data. Our numerical simulations suggest that the proposed parametric detectors, which incorporate the physics-based spectral symmetry constraint on clutter returns, achieve better performance than previously investigated parametric detection approaches which do not incorporate this constraint.

An automatic target recognition (ATR) differential game between a radar that moves with simple motion and a turn-constrained target is examined in which a radar continuously acquires information about a target until the prescribed information requirement is fulfilled. The radar strives to satisfy the information requirement in minimum time while the target strives to prolong the engagement for as long as possible where the information collection rate is dependent on the relative geometry of the system. We develop the regular equilibrium conditions and the singular solution conditions for the nine singular surfaces within the global solution. We provide illustrative examples of equilibrium state trajectories that are constructed by solving a multipoint boundary value problem where we combine regular and singular solution segments in a piecewise manner. Using the singular surfaces within the global solution of the game, we synthesize the equilibrium feedback controller for the target. The performance of alternative, subequilibrium radar controllers is tested against the synthesized controller to show the Nash equilibrium of the calculated equilibrium control strategies.

Doppler frequency analysis is important in over-the-horizon radar (OTHR) in order to determine important target parameters such as the target altitude. In this paper, we analyze the Doppler signatures of OTHR signals propagated through both ordinary and extraordinary electromagnetic modes. As the signals following the two propagation modes undergo different group delays, the Doppler frequencies of a target associated with these two modes differ from each other. The frequency analysis of the resulting Doppler signatures becomes challenging when the Doppler components associated with these two modes are closely separated or even partially overlapping. In this paper, we develop a low-complexity sparsity-based method to resolve the Doppler signatures corresponding to the two propagation modes. It is based on a Lasso-based approach and the computational complexity is effectively reduced by employing a frequency focusing transform. To demonstrated the effectiveness of the proposed approach, simulation results are presented for challenging scenarios where the multipath Doppler signatures corresponding to the two propagation modes are interlaced or very close to each other.

This paper considers the detection of a target in a distributed radar system, wherein the received reflections from the said target are contaminated with clutter returns. We model this clutter, as well as additional interference, as a superposition of an auto-regressive process and deterministic interference coming from a known subspace. A parametric adaptive detector is derived for this scenario based on an approximate generalized likelihood ratio test (GLRT), and is shown to have a detection performance that is robust to strong subspace interference.

In this paper, we examine the Doppler signatures of local-multipath signals in over-the-horizon radar for a target that moves with a constant horizontal velocity but experiences altitude perturbation. In practice, the target altitude may deviate from its scheduled altitude due to, e.g., flight dynamics. After describing the Doppler signatures for a target that maintains a constant altitude without perturbation, we develop the mathematical framework for target Doppler signature analysis that includes target altitude perturbations. It is observed that altitude variations result in spreading of Doppler frequencies, and the bias is associated with the average target altitude. It is observed that, for mild target altitude perturbations, existing analysis methods remain effective for local-multipath Doppler frequency estimation. The Doppler frequency estimation capability and performance are verified using simulation results.

Target localization, especially the estimation of target altitude, is a challenging task in over-the-horizon radar (OTHR) because of the narrow signal bandwidth as well as the complexity and uncertainty involved in the ionosphere conditions. This task becomes further complicated when the height of the ionosphere layer varies over time. Therefore, it is important to jointly estimate the instantaneous height of the ionosphere and the target altitude as well as other motion parameters. In this article, we achieve these objectives by analyzing the Doppler frequencies of the target local-multipath signals and the clutter. We reveal that the change of the ionosphere height can either enhance or deteriorate the performance of target parameter estimation depending on its direction of motion relative to the target’s motion profile. In addition, it is found that the received target and clutter Doppler signatures follow the chirp signal profile at the OTHR receiver. Based on these observations, we develop a general framework that achieves joint target and ionosphere parameter estimation and accounts for the velocity and accelerations of both target and ionosphere layer. Unlike existing time-frequency-based strategies for target localization and tracking in OTHR, where the Doppler signatures only directly determine target vertical velocity and the target altitude is estimated indirectly, the proposed model enables direct estimation of target altitude and ionosphere parameters. The parameter estimation problem in the proposed strategy is analytically derived and the effectiveness is verified using extensive simulation results.

Doppler signatures of local multipath signals provide useful information for target altitude estimation in over-the-horizon radar surveillance. In this paper, we develop a method to improve the resolution of these multipath Doppler signatures and enable enhanced altitude estimation of aircraft target which maintains a constant altitude. Moreover, we consider the impact of ionospheric layer motion on target parameter estimation and show that target parameters can be estimated under both stationary as well as time-varying ionospheric layer conditions. In order to improve the resolution and estimation accuracy of the target parameters and ionosphere velocity with a significantly reduced complexity, we exploit a frequency focused transform to the de-chirped target signals for dimension reduction before applying a least absolute shrinkage and selection operator (LASSO)-based high-resolution spectrum estimation technique. The proposed strategy outperforms fractional Fourier transform and classical subspace-based frequency estimation methods with a much lower computational complexity. The effectiveness of the proposed approach is especially evident for challenging cases where the multipath signal components have spectrally close Doppler signatures. Simulation results confirm the effectiveness of the proposed method.

In this paper, we examine the problem of velocity estimation for a moving object using distributed measurements. The system employs a non-cooperative transmitter and multiple receivers to collect targets echoes. The problem is formulated by modelling the unknown transmitted waveform as a deterministic process. The exact maximum likelihood estimator (MLE) is developed which requires a multi-dimensional search procedure. To reduce the computational load, an efficient two-step estimator (TSE) is proposed. The TSE first finds the maximum likelihood estimates of pairwise differences of the Doppler frequencies observed by the receivers. Then, the target velocity can be estimated from the frequency differences in closed-form. We show that the maximum likelihood estimation of each frequency difference reduces to a cross-correlation process followed by peak finding, which can efficiently be implemented by the fast Fourier transform (FFT). As a result, the TSE is significantly more efficient than the MLE. Numerical results show the TSE achieves a similar estimation accuracy as that of the MLE except for very low signal-to-noise ratio (SNR) scenarios.

Doppler signature analysis of targets, particularly micro-multipath signals, plays an important role in target trajectory analysis and tracking in over-the-horizon radar. In this paper, we examine the Doppler signatures of micro-multipath signals for a target that moves with a constant altitude but its velocity varies due to, for example, turbulence. We first describe the effect of such velocity variation in the resulting Doppler signatures under the micro-multipath model. Noticing that the velocity variation changes the Doppler signatures of all micro-multipath components in a similar manner, the self-stationarization approach is applied to provide a robust Doppler difference estimation.

In this article, we consider the problem of estimating the location and velocity of a moving source using a distributed passive radar sensor network. We first derive the maximum likelihood estimator (MLE) using direct sensor observations, when the source signal is unknown and modeled as a deterministic process. Since the MLE obtains the source location and velocity estimates through a search process over the parameter space and is quite computationally intensive, we also developed an efficient algorithm to solve the problem using a two-step approach. The first step finds the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) estimates for each sensor with respect to a reference sensor by using a two-dimensional fast Fourier transform and interpolation, while the second step employs an iterative reweighted least square (IRLS) approach with a varying weighting matrix to determine the source location and velocity. To benchmark the performance of the proposed methods, a constrained Cramér-Rao bound (CRB) for the considered source localization problem is derived. Numerical results show that the IRLS approach has a lower signal-to-noise ratio threshold phenomenon compared with several recent TDOA/FDOA-based methods, especially when the source is considerably farther away from some sensors than others, creating a larger disparity in the quality of sensors observations.

A new target detection and interference mitigation approach is proposed for future artificial intelligence (AI) - based radar. Targets in AI radar systems are detected based on target and interference classification without removing interference, in contrast to interference cancelation processing in traditional radar target detection approaches. The general AI target detection approach is presented and demonstrated to be more robust and effective in target detection in unknown environments.