This study focuses on multiple target detection in the presence of signal-dependent clutter using a Multiple-Input Multiple-Output (MIMO) radar system. The problem is formulated as worst-case SINR maximization (max-min optimization), which is a function of the MIMO waveform, under the hardware-inspired constant modulus constraint (CMC). While existing approaches invariably rely on computationally expensive iterative optimization over the waveform variable, we develop a model-based deep learning algorithm that shifts the computational burden to the neural network training, yielding fast inference. We utilize a surrogate cost function – the sum of SINR-Reciprocals (SRs) – that enables converting the max-min problem into the minimization of the sum of SRs. Our model-based learner unrolls an iterative optimization method that utilizes the SR descent vectors but with novel inter-target and inter-step parameters. The inter-target parameter weighs the SR descent vectors so that the net descent direction is dominated by the vector associated with the largest SR, thereby focusing on the worst-case SINR. The inter-step parameter ensures the update between the steps encourages a monotonic decrease in the cost function. To effectively guide the parameter learning, we introduce regularizers aligned with the learning goals, and consequently, we term the proposed method Regularized Weighted Descent (RWD). We demonstrate that the RWD achieves a larger worst-case SINR value (superior solution quality) in a shorter time (lower computational complexity) compared to the state-of-the-art alternatives.

In this paper, we present a Situational Awareness based Resource Allocation (SA-RA) strategy for multi-target tracking (MTT) in distributed radar networks, where both the resource utilization and overall MTT accuracy can be improved. The fusion rule with probabilistic data association (PDA) is used to associate cumulative data with measurement data from radar nodes. We also further derive the Bayesian Cramér-Rao Lower Bound (BCRLB) under the PDA fusion rule. For the proposed SA-RA strategy, the targets behavior is analyzed to determine their importance weights, expected tracking accuracy, and the allocated beams for each target. Utilizing the PDA-BCRLB and the importance weights, the objective function of the SA-RA strategy is formulated as a weighted sum of target utility functions. By addressing this objective function, the optimal transmission power is determined. Simulation results verify the superiority both in terms of tracking performance and resource allocation.

Automotive radar sensors are vital for enhancing vehicle safety and autonomy, enabling functionalities such as adaptive cruise control and collision avoidance. The performance of these radar systems is highly dependent on the selected waveform. There are several waveform options for automotive radars, including Frequency Modulated Continuous Wave (FMCW), Phase Modulated Continuous Wave (PMCW), Orthogonal Frequency Division Multiplexing (OFDM), and Orthogonal Time Frequency Space (OTFS). Each offers unique benefits and tradeoffs concerning range resolution, Doppler resolution, resistance to multipath fading, and complexity. Notably, OTFS, as a promising technique in Integrated Sensing And Communication (ISAC), outperforms OFDM in high-mobility scenarios for communication systems. In this paper, we design a phase-perturbation matrix using the Coordinate Descent (CD) framework, to optimize the range Integrated Side-lobe Level (ISL) of OTFS waveform in automotive radar applications. We also examine the Ambiguity Function (AF) characteristics of OTFS compared to OFDM, PMCW, and FMCW. The simulation results demonstrate an improvement in the ISL values of the designed OTFS waveforms.

As an extension of the phased-array (PA) and frequency diverse array multi-input multi-output (FDA-MIMO) radars, the coherent FDA (C-FDA) radar simultaneously enjoys the merits from a higher coherent array gain and range-dependency, especially the range-angle decoupling. Based on these properties, C-FDA radar is potential to implement more robust target tracking. This paper proposes a subspace-based range-angle tracking method, including the subspace tracking and range-angle estimation. We first design a data processing structure for C-FDA radar, separating the range-dependent data from the angle-dependent data. Then we use the exponential decay function inspired from the information geometry to achieve fast convergence for the subspace tracking. Numerical results describe the range-angle tracking trajectories of C-FDA radar by using the proposed algorithm, indicating its superiority through the root mean square error (RMSE) and the subspace estimation performance (SEP).

Coherently distributed (CD) sources are typically characterized by their direction of arrival (DOA) and angular spread. Traditional distributed signal parameter estimation (DSPE) methods for CD sources rely on a computationally intensive two-dimensional spectral search, which limits their suitability for real-time applications. In this letter, we propose a simple yet effective method to decouple the angular parameters of CD sources. By projecting the sample covariance matrix onto Toeplitz space, DOA information is approximately extracted. The DOAs are then estimated by a polynomial root-finding approach, followed by a one-dimensional DSPE spectral search to determine the angular spread. Simulation results demonstrate that the proposed method achieves performance comparable to existing approaches while significantly enhancing computational efficiency.

This paper presents hole-free lengthened coprime arrays with reduced mutual coupling (rLCAs). Based on the$k$-times extended coprime array structure, the rLCAs are designed by positioning two sparse subarrays outside the original aperture. An enhanced rLCA is further derived via locating and rearranging an inessential sensor. This enhanced rLCA is able to increase the number of degrees of freedom (DOFs). Compared with other arrays, the proposed rLCAs exhibit more DOFs and significantly reduced mutual coupling. The achievable DOFs of the rLCAs are derived and analyzed in detail. Finally, numerical examples show that the proposed rLCAs provide reduced mutual coupling and higher estimation accuracy.

In this paper, we analyze the effect of sensor placement to the achievable number of degrees-of-freedom (DOFs) when the sensors deviate from a half-wavelength grid. More specifically, we consider two variations of a uniform linear array (ULA), namely, when one or more sensors are shifted from half-wavelength grid positions and when the inter-element spacing of the ULA is smaller than a half-wavelength. The numerical rank and the rank-revealing QR factorization of the array data covariance matrix are examined and the number of DOFs of the array is studied in terms of the rank of the array data covariance matrix. A threshold based on the rank-revealing QR factorization is proposed to separate the eigenvalues respectively corresponding to the signal and noise subspaces, and thus the numerical rank of the array data covariance matrix is estimated. Simulation results are provided to justify the findings and provide insights on sensor placements to preserve the array DOFs.

The holes in difference coarrays (DCA) of coprime arrays (CA) limit the extension of the aperture thus causing the waste of resources. In this paper, we propose a generalized hole-filling strategy for hole-existing CAs with overlapping subarrays, which allows to extend the aperture completely and achieves a larger hole-free DCA. First, we summarize a generalized CA configuration based on the existing CAs with overlapping subarrays and derive the symmetric relationship between holes and non-consecutive lags in DCA. Then, we propose a hole-free coprime array by arranging a third subarray outside the original configurations, where the first element location is determined by the symmetric relationship. Furthermore, we derive the optimal parameters that produce the largest hole-free DCA with a given number of sensors. Theoretical derivations and simulations are provided to demonstrate that the proposed hole-free coprime configurations overcome the original coprime arrays in terms of uniform degrees of freedom and direction-of-arrival estimation performance.

In this paper, we propose a novel reduced-dimensional decomposition method of coherent sources with arbitrary rectangle arrays, namely RD-MUSIC. Compared with the orientational invariance structure of two-dimensional spatial smoothing methods, the proposed RD-MUSIC utilizes the orthogonally similar transformation to achieve the real-valued decomposition only with a half dimension, which can be extended to arbitrary rectangle arrays. Simulation results demonstrate the satisfactory estimation accuracy and improved resolution.

In this paper, a power optimization (PO) strategy is proposed to combat deception jamming in multi-radar systems (MRSs) performing multi-target tracking (MTT). As a crucial parameter for distinguishing between physical and false targets in MRS under deception jamming, we propose integrating the deception range into the augmented target state to be estimated. The posterior Cramér-Rao lower bound (PCRLB) of the target location parameter is adopted as the tracking performance metric. Using the predicted PCRLB of deception range in the augmented target state, a discriminator is designed to improve the rejection probability of false target. Tracking PCRLBs for physical targets and rejection probabilities for false targets are calculated and used to build the objective function. Considering resource constraints, the anti-deception jamming PO problem is formulated and solved. Numerical results demonstrate the effectiveness of the presented PO strategy for MTT in discriminating false targets.

Due to the characteristics of light weight, low cost, and high resolution, millimeter wave (MMW) multiple-input multiple-output (MIMO) radars are widely applied in remote sensing and automotive systems. The MMW MIMO radar orthogonal waveform design is a key issue based on dechirp-on-receive technique to acquire high degree of freedom (DOF). In this paper, we propose an optimized interleaved orthogonal frequency division multiplexing (I-OFDM) chirp waveform design scheme using unequal sub-chirp duration and sparse sub-band constraint to further reduce the mutual interference (MI) between waveforms, and analyze the orthogonality of the original and optimized I-OFDM chirp waveform for MMW MIMO radar based on dechirp processing from various aspects. The simulation results show the effectiveness of the proposed method.

Joint sensing and communication (JSAC) has emerged as a promising technology in autonomous driving, as it allows simultaneous road sensing and two-way communication using a single shared platform. Meanwhile, intelligent reflective surface (IRS) enables sensing enhancement and communication with targets in a blind zone. In this paper, we propose an IRS-assisted JSAC design to address two issues of the limited sensing range of automotive radar and the likely occlusion among road targets. We co-design the IRS’ reflection coefficient vector to steer the beam towards the directions of radar targets as well as embed the communication symbols into the reflected signals. Considering the phase-only property of the passive IRS, we establish a constant modulus co-design problem. We seek to optimize the covariance matrix first and then obtain the optimal reflection coefficient vector via matrix decomposition. Subsequently we transform the constant modulus constraint into a rank-1 semidefinite programing (SDP) problem and solve it iteratively. Simulation results demonstrate the effectiveness of the proposed IRS-assisted JSAC design.

To achieve full coherence, it is indispensable for distributed coherent aperture radar (DCAR) to estimate coherence parameters (CPs) using orthogonal waveforms in MIMO mode. However, incomplete orthogonality between waveforms and initial time and phase synchronization errors between the subapertures introduce estimation errors, which degrade full coherence performance. To tackle these issues, we propose an orthogonal waveform design framework based on ambiguity function (AF) shaping to improve CPs’ estimation accuracy. We combine the alternating direction method of multipliers (ADMM) and the majorization-minimization (MM) algorithm to transform the nonconvex quartic optimization problem into a quadratic optimization problem. Numerical simulation results show that the optimized waveforms significantly enhance the estimation accuracy of CPs.

The interrupted sampling repeater jamming (ISRJ) is a widely used coherent jamming technique. A proper waveform design can effectively suppress or mitigate the ISRJ. Even if several phase-coded waveform design methods have been proposed for this purpose, frequency modulation (FM) waveforms remain the most common choice for high-power transmitters, as they do not introduce significant distortions in real radar systems. In this letter, we propose a design method for multiple-input multiple-output (MIMO) radar that simultaneously derives the optimal polyphase-coded FM (PCFM) waveforms and the receive filters to mitigate the ISRJ. Specifically, we first model the joint design problem as a nonconvex bivariate optimization problem and we minimize the matching error between the desired and practical transmit-receive correlation functions for different channels. Subsequently, we adopt an alternating strategy to update the PCFM waveforms and receive filters sequentially. More specifically, gradient-based algorithms in Euclidean space and Riemannian manifold space are adopted to derive the optimal waveforms and filters, respectively. The proposed method is characterized by a low computational cost, thanks to its FFT-based implementation. Numerical analysis shows the effectiveness of the proposed method.

In this letter, we propose a robust direction of arrival (DOA) estimation method for mixed circular and noncircular incoherently distributed (ID) sources in impulsive noise. This approach incorporates an outlier-robust extended bounded nonlinear covariance to alleviate the impact of impulsive noise, and we demonstrate its applicability for DOA estimation of ID sources. Subsequently, we determine the DOAs and angular spreads of mixed circular and noncircular ID sources in a closed form via array shift invariance. Numerical simulations illustrate that our proposed method outperforms alternatives in terms of both effectiveness and robustness.

With the development of miniaturized millimeter wave (MMW) frequency-modulated continuous-wave (FMCW) radar, the dechirp-on-receive technique has been widely used. Due to the limitations of highly integrated radar hardware, it is difficult to further increase the bandwidth of the transmitted signal. Therefore, enhanced range resolution in MMW synthetic aperture radar (SAR) imaging can be achieved only thanks to suitable post-processing. In this paper, we propose a method for range resolution enhancement based on the principle of wavenumber shift with application to cross-track miniature MMW multiple-input and multiple-output (MIMO)-SAR systems. An improved orthogonal waveform design scheme of multi-subband chirp waveforms with chirp rate changes between waveforms is proposed, which is suitable for dechirp processing. In addition, given the constraint of the position of the equivalent SAR platform of MIMO-SAR, which leads to the lack of range-dimensional spectrum, a spectral data interpolation method based on autoregressive (AR) modeling in the time-frequency (TF) domain is proposed. The effectiveness of the proposed method is verified by numerical simulation and experimental data processing.

Optimizing a transmit MIMO radar waveform subject to the non-convex constant modulus constraint remains a problem of enduring interest. The past decade has seen a variety of tailored iterative approaches with various performance-complexity trade-offs. Despite promising work, iterative algorithms have a speed handicap and require meticulous parameter tuning. Once trained, a deep network can quickly regress the desired waveform coefficients, but it is a black box and may excel only when generous training is available. We present a fast, learned, and - for the first time - interpretable (FLI) deep learning approach by unrolling a state-of-the-art iterative optimization approach. We particularly leverage the recently proposed projection, descent, and retraction (PDR) algorithm and design a deep network where each PDR step is mapped to a layer in the neural network while preserving the non-convex constant modulus constraint. FLI breaks the trade-off between complexity and performance. It is near real-time with boosted performance – fidelity to the desired beampattern – compared to the state-of-the-art alternatives.

In this paper, we develop a deep learning framework to optimize the compressive sampling matrix in a massive multiple-input multiple-output (MIMO) system. The optimized compressive sampling matrix is utilized to project high-dimensional data received at the massive MIMO system into a lower-dimensional space so that the directions of arrival and other signal parameters can be efficiently obtained with a reduced hardware complexity. The proposed deep learning approach for optimizing the compressive measurement matrix increases its robustness and generalizability.

Existing stochastic Ziv-Zakai bound (ZZB) for compressive time delay estimation from compressed measurement relies on a Gaussian approximation, which makes it inaccurate in the asymptotic region when the stochastic component dominates the received signals. In this letter, we apply different random projections on zero-mean Gaussian received signal to obtain multiple compressed measurements, based on which the log-likelihood ratio test is exactly formulated as the difference of two generalized integer Gamma variables. Accordingly, we further derive the exact expression of the stochastic ZZB for compressive time delay estimation from zero-mean Gaussian signal. Simulation results show that the derived ZZB is globally tight to accurately predict the estimation performance regardless of the number of compressed measurements, and it can also accurately predict the threshold signal-to-noise ratio for the estimator when the number of compressed measurements is large.

Massive multi-input-multi-output (MMIMO) cognitive radar can enhance the target detection ability in a dynamic environment via a continuous "perception-action" cycle. In our previous work, we proposed a reinforcement learning (RL) based approach for multi-target detection in MMIMO. However, this method shows poor detection performance for weak targets attributed to its imperfect action and reward mechanisms. In this paper, we propose an improved RL based method to enhance the detection probability of weak targets. In the action stage, the transmit power is divided into omni-directional and directional components, the former significantly reduces the missed detection probability of weak targets and the latter improves the detection probability by focusing more power on weak targets. Moreover, the reward mechanism of RL is modified to further improve the detection performance. In addition, the transmit weight matrix is designed by an optimum combination of the beampatterns of all unit orthogonal transmit waveforms, thus greatly reducing the computational complexity. Simulation results are provided to demonstrate the effectiveness of the improved RL based method for weak target detection.

It is well-known that the multiple signal classification (MUSIC) algorithm is computationally time-consuming because it requires a complex-valued full-dimension eigenvalue decomposition (EVD) and a complex-valued spectral searching. In this paper, we exploit the virtual signal model of forward/backward average of array covariance matrix (FBACM) to show that its real part (R-FBACM) is a real symmetric matrix. Based on that, we prove that by evaluating two half-dimension EVD after an orthogonally similar transformation performed on the estimated R-FBACM, we are able to reconstruct the original eigenspace whereas the maximum number of estimated sources is reduced as compared to the upper limit$\mathit{M}-\text{1}$for original MUSIC. Numerical results show that the proposed method provides satisfactory estimation accuracy and improved resolution with reduced complexity.

Beampattern synthesis of frequency diverse arrays (FDAs) has recently raised increased attention attributed to their range-dependent beampattern. The transmit beampattern of uniform FDA appears$S$-shaped, which implies coupling in the range-angle domain and thus causing unwanted energy leakage into the area of non-interest. In this work, we propose a joint optimization of sparse FDAs to synthesize a decoupled transmit beampattern from the perspective of spatial-frequency virtual array. Specifically, both spatial and spectral configuration of FDAs are optimized via joint antenna-frequency selection. In order to solve the resultant NP-hard combinatorial optimization problem, we propose an iterative reweighting strategy to transform the original problem into a convex optimization. Further, we proceed to synthesize a time-invariant decoupled beampattern by designing a time-varying unit frequency step. Comparative simulations are provided to manifest the superior performance of the proposed FDA in the metric of normalized peak sidelobe level (NPSLL) of transmit beampatterns.

In this article, a composed resource optimization (CRO) scheme is developed for an active and passive radar network engaged in multiple target tracking (MTT). The motivation of the CRO scheme is to collaboratively optimize the transmit resources of active radars, as well as the receiving processing resources of passive radars, to improve the overall MTT performance. We utilize the predicted conditional Cramér–Rao lower bound to evaluate the impact of allocation strategies on tracking performance and formulate the CRO as a mixed-integer nonlinear program problem since the adaptable parameters w.r.t. the target selection process are in binary form. To solve the problem, we propose an alternating direction method of multiplier-based algorithm. This algorithm transforms the original problem into an equality constrained problem by introducing two auxiliary vectors. In such a case, the CRO problem can be tackled by alternately solving several simple subproblems. Specifically, the subproblem w.r.t. the resource vector is convex, and the subproblems w.r.t. the auxiliary vectors are separable. Simulation results demonstrate that the proposed CRO scheme outperforms the traditional allocation schemes in terms of MTT performance. In addition, the performance of the CRO scheme is close to the optimal performance provided by the exhaustive method, but the computation load of the CRO scheme is lower than that of the exhaustive method. Finally, physical interpretations are presented to support our conclusions.

This work focuses on target detection in a colocated MIMO radar system. Instead of exploiting the "classical’ temporal domain, we propose to explore the spatial dimension (i.e., number of antennas M) to derive asymptotic results for the detector. Specifically, we assume no a priori knowledge of the statistics of the autoregressive data generating process and propose to use a mispecified Wald-type detector, which is shown to have an asymptotic χ-squared distribution as M → ∞. Closed-form expressions for the probabilities of false alarm and detection are derived. Numerical results are used to validate the asymptotic analysis in the finite system regime. It turns out that, for the considered scenario, the asymptotic performance is closely matched already for M ≥ 50.

Focusing on the signal-to interference-plus-noise ratio (SINR) maximization in colocated multiple-input multiple-output (MIMO) radars, using the covariance matrix design of transmitted waveforms, we propose a kind of transmit covariance matrix (TCM)$\mathrm{R}_{pm}$with the form of symmetrical Toeplitz matrix, whose full rank characteristic firstly can sufficiently exploit the waveform diversity advantage of MIMO radar to further suppress the maximum number of interfering sources. Meanwhile, the positive semi-definition characteristic of$\sin((\pi/2)\mathrm{R}_{pm})$guarantees that these TCMs can be synthesized with binary phase shift keying (BPSK) waveforms in closed form. Furthermore, employing certain proposed TCM, higher SINR level can be yielded, and lower sidelobe levels (SLLs) can be obtained for the unwanted sidelobe interference suppression. Simulation results validate the better performance of our proposed TCMs in comparison with the phased array, omnidirectional MIMO radar and the recently proposed TCMs.

The aim of this letter is to provide a constrained version of the misspecified Cramér-Rao bound (MCRB). Specifically, the MCRB is a lower bound on the error covariance matrix of any unbiased (in a proper sense) estimator of a deterministic parameter vector under misspecified models, i.e., when the true and the assumed data distributions are different. Here, we aim at finding an expression of the MCRB for estimation problems involving continuously differentiable equality constraints. Our proof generalizes the derivation of the classical constrained CRB (CCRB) by showing that the constrained MCRB (CMCRB) can be obtained by exploiting the building blocks of its unconstrained counterpart and a basis of the null space of the constraint's Jacobian matrix. The conditions for the existence of the CMCRB are also discussed.

This paper deals with the problem of estimating the Directions of Arrival (DOA) of multiple source signals from a single observation of an array data. In particular, an estimation algorithm based on the emerging theory of Compressed Sensing (CS) is analyzed and its statistical properties are investigated. We show that, unlike the classical Fourier beamformer, a CS-based beamformer (CSB) has some desirable properties typical of the adaptive algorithms (e.g. Capon and MUSIC). Particular attention will be devoted to the super-resolution property. Theoretical arguments and simulation analysis are provided in order to prove that the CSB can achieve a resolution below the classical Rayleigh limit.

Compressed Sensing is a new signal processing methodology that allows to reconstruct sparse signals using a relatively small number of samples in the form of random projections. These samples are collected at a much lower rate than Nyquist rate. This paper focuses on the application of Compressed Sensing in Cognitive Radar systems that use wide operating frequency bandwidths for spectrum sensing and sharing. Compressed sensing can provide a significant reduction in acquisition time reducing the cost for high resolution analog-to-digital converters with large dynamic range, and high speed signal processors.

This work deals with the analysis of a multisensor radar system in the context of maritime border control scenario. The system is composed by a receiver that exploits the signal emitted by two non co-operative transmitters of opportunity: a UMTS base station and a FM radio station. An algorithm for selecting the transmitter for the tracking of a radar target is proposed. This algorithm can provide a significant aid to harbour protection and can reduce the computational load of surveillance operations.

This work deals with the Sequential Cramér-Rao Lower Bound (SCRLB) for sequential target state estimators for a bistatic tracking problem. In the context of tracking, the SCRLB provides a powerful tool, enabling one to determine a lower bound on the optimal achievable accuracy of target state estimation. The bistatic SCRLBs are analyzed and compared to the monostatic counterparts for a fixed target trajectory. Two different kinematic models are analyzed: constant velocity and constant acceleration. The derived bounds are also valid when the target trajectory is characterized by the combination of these two motions.

In this paper we compare two radar target direction-of-arrival (DOA) estimation algorithms, the classical moving window (MW) and the asymptotic maximum likelihood (AML) estimators. The first technique for azimuth DOA estimation exploits multiple detections in the same time-on-target and the second one exploits the fact that the radar antenna mechanical scanning impresses an amplitude modulation on the signals backscattered by the target. Performances of the estimators are numerically investigated through Monte Carlo simulation in terms of root-mean-square-error (RMSE), probability of detection for a fixed probability of false alarm, and probability of "splitting". The obtained results show that the asymptotic maximum likelihood estimator generally outperforms the classical moving window estimator.

This paper deals with the problem of modeling high-resolution synthetic aperture radar clutter data from different vegetated areas. We analyzed moving and stationary target recognition (MSTAR) data sets focusing on histograms, moments, and covariance of clutter amplitude, texture, and speckle. The most celebrated statistical models are tested on real data of grass field or wood and trees to validate the goodness of fit of the compound Gaussian model in different scenarios. The results demonstrate that for grass fields, the compound Gaussian model provides a good data fitting. This is not the case for woods images where the speckle is not more Gaussian distributed. Covariance analysis and concluding remarks complete this paper

In this work, we deal with the problem of modeling SAR clutter data from different vegetated areas. We analyzed MSTAR dataset by means of histogram, moment analysis and covariance estimation. Some results are shown in this summary

In this work we deal with the problem of analyzing and modeling marine (lake) surface scattering as seen by high resolution radars, with the aim of highlighting, where possible, the differences due to changes in the range resolution and polarization.

This work deals with the problem of detecting and estimating multiple radar targets present in the same range-azimuth resolution cell of a surveillance radar system with a mechanically rotating antenna. First, the target parameters are estimated assuming a maximum number of possible targets. To this purpose we use the asymptotic maximum likelihood (AML) RELAX estimator derived in the first part (for pt. 1 see ibid., p. 529-532 (2003)). Subsequently, these estimates are used in a sequential hypotheses test (SHT) procedure. The statistic of the test at each step of the SHT procedure is derived using an asymptotic expression of the generalized likelihood ratio test (GLRT) statistic. An upper bound of the false alarm probability is derived in closed form, whereas detection performance of the proposed SHT detector is investigated through Monte Carlo simulation.