Frequency Diverse Array Multiple-input Multiple-output Radar Research Articles

Adaptive target detection for an FDA-MIMO radar in a mainlobe deceptive jamming and a partially homogeneous noise

In this paper, we investigate the adaptive target detection problem for a collocated frequency diverse array multiple-input multiple-output (FDA-MIMO) radar in the presence of mainlobe deceptive jamming and partially homogeneous noise with an unknown covariance matrix and scaling factor. Precisely, we establish a received signal model that includes the true target and false counterparts echoes in the presence of Gaussian noise (it includes thermal noise, interference suppression, and clutter after range compensation.). Furthermore, we consider that the range information of the true target and mainlobe deceptive targets is not identical. Therefore, we project the corresponding transmit steering vectors onto different subspaces with known subspace matrices but unknown coordinates. On the other hand, the true and false targets' receive steering vectors are considered to be from the same subspace. Finally, following the generalized likelihood ratio test (GLRT), the Rao and the Wald criteria, we design three adaptive detectors with two-step criteria, i.e., TGLRT, TRao, and TWald. We note that the proposed detectors maintain a constant false alarm rate (CFAR) against the scaling factor and the noise covariance matrix. The extensive numerical simulation results have validated the effectiveness of the proposed detectors.

Reinforcement Learning for FDA-MIMO Radar Power Allocation in Congested Spectral Environments

This paper studies the coexistence problem of frequency diverse array multiple-input multiple-output (FDA-MIMO) radar and communication systems. The communication system and radar share the same frequency band, and the overlap of the frequency spectrum will interfere with each other's performance, which constitutes a dynamic non-cooperative coexistence problem. We model the FDA-MIMO radar interference suppression process as a Markov decision process (MDP). The interference signals received by FDA-MIMO radar are generated by the communication system, including constant interference, frequency-hopping interference, and intermittent interference. FDA-MIMO radar realizes flexible transmission waveform spectrum control through transmission power allocation. Reinforcement learning (RL) is applied to obtain the optimal power allocation strategy of FDA-MIMO radar, and it is compared with the Sense and Avoid (SSA) algorithm. The simulation results show that the FDA-MIMO radar power allocation method based on reinforcement learning can effectively suppress the communication system's interference and improve the radar's signal-to-interference-and-noise ratio (SINR) and range resolution.

Moving-Target Detection for FDA-MIMO Radar in Partially Homogeneous Environments

This paper delves into the problem of moving-target detection in partially homogeneous environments (PHE) with unknown Gaussian disturbance using a frequency diverse array multiple-input multiple-output (FDA-MIMO) radar. Using training data, we have derived expressions for four adaptive detectors, including the one-step and two-step generalized likelihood ratio test (GLRT), two-step Rao (TRao) test, and two-step Wald (TWald) test criteria, respectively. All the proposed detectors are characterized by the constant false-alarm rate (CFAR). The theoretical analysis and simulation results validate the effectiveness of the proposed detectors.

Joint Range and Angle Estimation by FDA-MIMO Radar With Unknown Mutual Coupling

Frequency diverse array-multiple-input multiple-output (FDA-MIMO) radar is characterized by a range-angle-dependent transmit antenna beampattern, where both range and angle of the target can be jointly estimated. However, the performance of existing estimation algorithms degrades in the presence of mutual coupling effect. To overcome this drawback, this paper deals with the problem of joint range and angle estimation by FDA-MIMO radar with unknown mutual coupling. At the design stage, the mutual coupling matrices (MCM) are constructed in both transmit and receive arrays, exploiting the banded symmetric Toeplitz structure, where the mutual coupling effect is eliminated by transforming the MCM into a diagonal matrix with a selection matrix. Subsequently, the range ambiguity is resolved by setting two linear coprime frequency increments, which locates the true target at the overlap of the peaks corresponding to the two spatial spectra. Furthermore, to reduce the computational cost resulted from the two-dimensional (2-D) grid search, an iterative procedure based on the coordinate descent (CD) algorithm is considered by alternating between the optimization over one variable keeping the other fixed. At the analysis stage, the closed-form solutions of the mutual coupling coefficients are given by utilizing the estimated range and angle. Moreover, a comparison in terms of estimation performance in different coupling scenarios is carried out, where the Cramér-Rao lower bound is provided as the benchmark. Numerical results verify the effectiveness of the considered estimation strategy in multiple simulated scenarios.

Adaptive Target Detection With Polarimetric FDA-MIMO Radar

The problem of adaptive radar detection with a polarimetric Frequency Diverse Array Multiple-Input Multiple-Output (FDA-MIMO) radar is addressed in this paper. At the design stage, the target detection problem is formulated as a composite hypothesis test, with the unknowns given by the target angle, incremental range (target displacement with respect to the center of the occupied range cell), and scattering matrix, as well as the interference covariance matrix. The formulated detection problem is handled by resorting to sub-optimal design strategies based on the Generalized Likelihood Ratio (GLR) criterion. The resulting detectors demand, under the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\mathrm{{1}}$</tex-math></inline-formula> hypothesis, the solution of a box-constrained optimization problem for which several iterative techniques, i.e., the Linearized Array Manifold (LAM), the Gradient Projection Method (GPM), and the Coordinate Descent (CD) algorithms, are exploited. At the analysis stage, the performance of the proposed architectures, which ensure the bounded CFAR property, is evaluated via Monte Carlo simulations and compared with the benchmarks in both white and colored disturbance.

Joint range, angle and polarization estimation in polarimetric FDA-MIMO radar based on Tucker tensor decomposition

Frequency diverse array multiple-input multiple-output (FDA-MIMO) radar is an emerging technology to offer range-angle-dependent beampattern. Polarimetric FDA-MIMO radar can sense additional polarization information to improve target identification capability. In this article, we investigate the problem of joint range, angle and polarization parameter estimation in a monostatic polarimetric FDA-MIMO radar with an FDA at transmitter and a cross-dipole array at receiver. Unlike the conventional methods in which the multidimensional data structure is rearranged into vectors or matrices by stacking operation, we propose a Tucker tensor decomposition-based scheme, which can reserve the original data structure and avoid spoiling the inherent characteristics of interest, especially when the number of snapshots is small. The third-order tensor model of the observed data is constructed. Two approaches named as Tucker covariance reconstruction and Tucker signal subspace are presented using the fourth-order covariance tensor decomposition. The Cramér–Rao bound for range, angle and polarization estimation is also provided. Numerical experiments demonstrate the superiorities of the proposed approaches. Specifically, two targets with identical range and close angles are effectively distinguished.

Discrimination of Target and Mainlobe Jammers With FDA-MIMO Radar

This letter focuses on discriminating true target from mainlobe jammers using a frequency diverse array-multiple-input multiple-output (FDA-MIMO) radar. To this end, a three-stage detection and discrimination architecture is proposed. Specifically, mainlobe jammers caused by large time delays can be discriminated from the true target based on the range degrees-of-freedom (DOFs) of FDA-MIMO radar, while the true target and jammers generated with small time delays are distinguishable in the fast time domain. In particular, a binary hypothesis test is formulated for discrimination, where the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{1}$</tex-math></inline-formula> hypothesis contains the true target, while the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{0}$</tex-math></inline-formula> hypothesis contains the unknown mainlobe jammer. The mainlobe jammer can be formulated as either a known subspace model or an unknown rank-one model. The former leads to a subspace-based selective detector (SSD) and the latter generates a rank-one-based SD (ROSD). Then, the formulated tests are handled using the generalized likelihood ratio test (GLRT) criterion. At the analysis stage, the selectivity and detection performance are compared with the conventional GLRT and selective receivers. Simulation results validate that the proposed detectors achieve satisfactory detection performance while providing the selectivity to mainlobe jammers.

Improved MUSIC Method against Range Dimension Deceptive Jamming Based on FDA-MIMO

Frequency diverse array-multiple-input multiple-output (FDA-MIMO) radar makes it transmit beam range–angle two-dimensional freedom by attaching a small frequency offset increment between the array elements. With the widespread use of digital radio frequency memory (DRFM) technology, it is able to delay the false target to any range bin and doppler unit by delaying and forwarding the radar transmits signals, resulting in the deceptive jamming effect of range dimension. To this end, based on the research of the existing main-lobe deceptive interference methods, this paper proposes a new improved MUSIC method based on the FDA-MIMO radar against deceptive jamming in the range dimension. Firstly, the range information of target and jamming is determined through spatial spectrum search by using the mismatch of jamming in the airspace position and range bin position, and then the process of range dimension deceptive jamming suppression is given. The simulation analysis results show that the proposed anti-jamming method can effectively mitigate against range dimension deceptive jamming.

Research on the Compound Jamming Method against FDA-MIMO Beamforming

Frequency diverse array multiple-input multiple-output (FDA-MIMO) radar solves the problem of angle pointing and range pointing during beam transmission due to its unique range-angle dimension dependent, which gives it good characteristics against main lobe deceptive jamming. Moreover, the current single range dimension deceptive jamming is easy to be identified and cannot form an effective jamming effect on FDA-MIMO radar. To address this problem, this paper proposes a compound jamming method of suppression and range deceptive against FDA-MIMO beamforming. Compared with the traditional deceptive jamming method, this method can reasonably utilize the beam gain, and minimum variance distortionless response (MVDR) adaptive beamforming cannot significantly reduce the power of the jamming, thus avoiding the jamming being weakened at the beamforming level, and the jamming may appear in different range bins, causing significant suppression and range deceptive compound jamming effects on FDA-MIMO radar in the range dimension. The simulation verified that the compound jamming method can effectively interfere with the FDA-MIMO radar at the beam-forming level, and the jamming effect is good.

Search-Free Angle, Range, and Velocity Estimation for Monostatic FDA-MIMO

The monostatic frequency diverse array multiple-input multiple-output (FDA-MIMO) has attracted much attention recently. However, much research is concentrated on the estimation of angle-range parameters based on the FDA-MIMO radar, and the velocity has not been considered. In this study, we propose a search-free method to estimate these parameters. To overcome the problem of the high computational complexity associated with the searching estimation algorithms, the parallel factor (PARAFAC) decomposition is introduced to estimate the space-time steering vector. Next, we can utilize the least square method to solve the angle, range, and velocity of each target. In addition, the Cramér–Rao bounds (CRBs) of angle, range, and velocity are derived. Besides, the other performance analysis consists of the root mean square error, and complexity is derived. We compare the PARAFAC decomposition algorithm with the estimation of signal parameters via the rotational invariance techniques (ESPRIT) algorithm, and our method owns a superior performance. Finally, the proposed method is verified by simulations and has the ability to achieve greater estimation accuracy than existing algorithms.

Adaptive Distributed Target Detection for FDA-MIMO Radar in Gaussian Clutter Without Training Data

Since frequency diverse array multiple-input multiple-output (FDA-MIMO) radar possesses additional target range information for potential performance improvement, this article studies adaptive distributed targets detection for FDA-MIMO radar, where the targets are embedded in Gaussian clutter with unknown covariance matrix. The proposed FDA-MIMO radar detection model considers also the distributed targets occupying several secondary range cells, which is different from the classic detection models in multiple-input multiple-output (MIMO) and/or phase array (PA) radars that discuss only point-like targets. By exploiting the FDA-MIMO radar framework for distributed target detection, we propose the detector through a two-step generalized likelihood ratio test criteria without the need of training data and/or a priori covariance matrix. Moreover, closed-form expressions for the probability of false alarm and detection probability are derived, respectively. The proposed detector adheres to the property of a constant false alarm rate because its probability of false alarm is not restricted by the covariance matrix. The proposed method together with all theoretical analysis are verified by numerical results.

FDA-MIMO radar detection for independent and nonidentically distributed fluctuating targets

Due to its range-dependent target response, frequency diverse array multiple-input multiple-output (FDA-MIMO) radar systems enable superior detection capabilities as compared with conventional phased-array radars. This paper proposes an incoherent detector for airborne FDA-MIMO radar to detect independent but possibly non-identically distributed fluctuating targets. For FDA-MIMO, variations in the target's flight attitude result in different distributions of the target radar cross section (RCS) for different pulses. In order to allow the FDA-MIMO RCS to vary due to the large frequency increments across the array antennas, we formulate a statistical FDA-MIMO RCS model for the reflected signal. We further derive the analytical detection probability for an FDA-MIMO radar measuring independent and non-identically distributed fluctuating targets. The resulting expression takes the form of an infinite sum; to enable evaluation in practice, an upper bound of the truncation error is also derived. The proposed method and all theoretical analysis are verified by numerical results, which provides theoretical basis and guidance for FDA-MIMO system implementation and design in independent and non-identically distributed fluctuating targets detection.

Discrimination of Mainlobe Deceptive Target With Meter-Wave FDA-MIMO Radar

Frequency diverse array multiple-input multiple-output (FDA-MIMO) communication regime has received a lot of attention in the field of point-to-point communication and interference suppression due to its degrees of freedom in the range domain. Previous researches have mainly considered non-coherent source scenarios. However, FDA-MIMO communication system in low-elevation is subject to multipath effects in addition to the potential threats within the mainlobe. The discrimination of true and false targets using meter-wave FDA-MIMO radar in low-elevation scenarios is still a problem that needs to be addressed. This letter mainly derives the signal model of the mainlobe deceptive jamming acting on the meter-wave FDA-MIMO radar and proposes a method for the discrimination of true and false targets. Simulation results verify the effectiveness of the proposed method.

Low elevation and range joint estimation method with metre wave frequency diverse array‐multiple input multiple output radar based on sparse array

Frequency diverse array-multiple input multiple output (FDA-MIMO) radar not only has the advantage of waveform diversity but also can realise azimuth-range correlation map, so it can realise high precision azimuth-range joint estimation and has the ability to distinguish different range unit targets in the same azimuth. However, the existing research mainly adopts uniform linear array (ULA) model and mainly focusses on incoherent targets. At present, the elevation-range joint estimation algorithm of metre wave FDA-MIMO radar based on ULA has the problems of sharp decline in angle-range measurement accuracy of ultra-low altitude targets and large fluctuation of elevation-range measurement accuracy with changing elevation. In order to solve the above difficult problems, starting from the perspective of reducing the influence of multipath effect by array structure, this paper innovatively combines sparse array with FDA-MIMO radar, establishes the low elevation-range joint estimation model of metre wave FDA-MIMO radar based on sparse array, and puts forward the low elevation-range joint estimation method suitable for this model, and it fills the gap of low elevation-range measurement method based on sparse array metre wave FDA-MIMO radar. Simulation experiments compare two typical sparse arrays with ULA of equal array elements, which verify the superiority of low elevation-range measurement performance of monostatic metre wave FDA-MIMO radar based on sparse array and the effectiveness of the proposed method.

Joint Angle and Range Estimation in Monostatic FDA-MIMO Radar via Compressed Unitary PARAFAC

In this paper, we study the joint range and angle estimation problem based in monostatic frequency diverse-array multiple-input multiple-output (FDA-MIMO) radar, and propose a method for range and angle estimation base on compressed unitary parallel factor (PARAFAC). First, the received complex signal matrix is stacked into a third-order complex signal tensor. Then, we can transform the obtained third-order complex signal tensor into a third-order real-valued signal tensor by employing forward–backward and unitary transformation techniques. Next, a smaller third-order real-valued signal tensor is composed by using compressing the third-order real-valued signal tensor. After that, PARAFAC decomposition is applied to obtain the direction matrix. Lastly, the angle and range are estimated by employing the least square (LS) fitting. The estimation error of the proposed method is about 10% lower than that of the traditional PARAFAC method under the low number of snapshots. When the number of snapshots is high, the performance of the two methods is close. Moreover, the computational complexity of the proposed method is nearly 96% less than those of the traditional PARAFAC methods in the case of low snapshots, while the gap is larger in the case of high snapshots. The superiority and effectiveness of the method are proved by complexity analysis and simulation experiments.

Covariance Matrix Estimation for FDA-MIMO Adaptive Transmit Power Allocation

Frequency diverse array multiple-input multiple-output (FDA-MIMO) radar produces an angle-range-dependent and time-varying transmit beampattern due to the small frequency increment across its array elements, which provides potential applications in new radar techniques. In this paper, we first establish a FDA-MIMO radar receiver model in the presence of spectral interferences, which focuses on the interference covariance matrix structure when the transmitted baseband signals are time- or frequency-domain orthogonal. Then, we show that the FDA-MIMO radar has a capability in suppressing spectral interferences with low computational complexity. Specifically, we propose an adaptive transmit weight vector for element-wise power allocation through maximizing the output signal-to-interference-plus-noise ratio (SINR). Furthermore, we propose a shrinkage-to-tapering algorithm for covariance matrix estimation in a coherent process interval. The interference-plus-noise covariance matrix is reconstructed accordingly with prior knowledge including the target, interference and noise covariance matrix structures. Numerical results demonstrate that the FDA-MIMO radar with adaptive power allocation can suppress spectral interferences by the developed method and high output SINR is achieved.

Resolving Doppler Ambiguity of High-Speed Moving Targets via FDA-MIMO Radar

To address the problem of Doppler ambiguity in low pulse repetition frequency (PRF) radar, we propose the use of frequency diverse array multiple-input multiple-output (FDA-MIMO) radar to detect high-speed moving targets. This method does not require the radar to transmit multiple-PRF pulses. The possible Doppler ambiguity is resolved by exploiting the multicarrier characteristics of FDA-MIMO radar. The effectiveness of the proposed method is verified by simulation results.

FDA-MIMO Beampattern Synthesis with an Analytical Method

Since the beampattern has the characteristics of range-angle dependence, frequency diverse array multiple-input multiple-output (FDA-MIMO) radar has a good application prospect. There have been many studies to improve the performance of the beampattern by optimizing the frequency offset. However, on the basis of fully understanding the time parameters, the relationship between the array element frequency offset and the beampattern performance still needs to be clarified. Based on a new FDA-MIMO radar framework, this paper presents an analytical solution of the beampattern, which removes the influence of the time parameter. Taking the minimum main lobe as the objective function, an analytical method for solving a better frequency offset is given. Then, a method of using the window function was proposed to reduce the high side lobes of the range dimension. Comparing with the existing FDA radar beampattern design methods, it can achieve a more focusing beampattern. The simulation results verify the correctness of the theory.

Joint Transmit and Receive Beamforming for Cognitive FDA-MIMO Radar With Moving Target

Cognitive radars can possess intelligent active sensing ability and adapt complex variable environment. Inspired by this technology, a cognitive frequency diverse array multiple-input multiple-output (FDA-MIMO) radar is proposed to apply for surveillance and detect the moving target timely. FDA-MIMO radar is a novel array structure which employs the small frequency offset across the transmit waveform to produce the range-angle dependent beampattern. The range-angle dependent beampatterns have ability to suppress the jammers when they are located at the same angle of the target. To obtain the maximum signal-to-interference-plus-noise-ratio (SINR) and suppress the jammers effectively, we consider the transmit and receive beamforming filters design and proposed an iterating optimization algorithm to obtain optimal beamforming filters. For the moving target, the Extended Kalman filter (EKF) method is utilized to update the position of the target and the new position information is applied for the filters design to obtain optimal performance of SINR timely. In addition, expressions for the detection probability and SINR are deduced for the FDA-MIMO radar target detection. Finally, numerical results show that the proposed cognitive FDA-MIMO radar can effectively suppress the jammers and detect the moving target.

FDA-MIMO radar covariance matrix estimation via shrinkage processing

Frequency diverse array multiple-input multiple-output (FDA-MIMO) produces an angle-range-dependent and time-varying transmit beampattern due to the small frequency increment across its array elements, which provides potential applications in new radar techniques. Due to this particularity, multiple signal classification (MUSIC) algorithm can be used to simultaneously estimate the angle and range of the target through a two-dimensional search. The MUSIC need to estimate the covariance matrix. In this paper, we introduce a shrinkage processing for estimating large covariance matrices when the number of samples is substantially fewer than the number of variables which is more common in FDA-MIMO than phase array (PA). Firstly, we propose a receiving model of multi-channel mixing multi-matched filter to eliminate time-varying effect. Secondly, the taper processing, Toeplitz rectification processing and shrinkage-to-identity processing are analyzed. Then, we propose two algorithms, namely, shrinkage-to-taper and shrinkage-to-Toeplitz-rectification on the basis of these algorithms. The proposed processing method improves upon both shrinkage and Toeplitz rectification or tapering processing by shrinking the sample covariance matrix (SCM) to its Toeplitz rectification or tapered version. Thirdly, a closed form expression of shrinkage coefficient for the shrinkage-to-Toeplitz-rectification, and shrinkage-to-taper are used. Finally, simulations results for FDA-MIMO radar show that the proposed algorithm is superior to the sample covariance matrix, shrinkage LW algorithm proposed by Ledoit-Wolf and shrinkage RBLW algorithm which is improved shrinkage LW according to the Rao-Blackwell theorem, in the sense of minimum mean-squared error (MMSE).