Frequency Diverse Array Multiple-input Multiple-output Research Articles

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.

Robust Suppression of Deceptive Jamming with VHF-FDA-MIMO Radar under Multipath Effects

Frequency diverse array multiple-input multiple-output (FDA-MIMO) radar has received a lot of attention due to the advantages of waveform diversity. Suppression of mainlobe deceptive jamming can be effectively achieved with the degree of freedom (DOF) in the range domain. However, the existing research mainly focuses on non-coherent signals. The echo signal of VHF-FDA-MIMO radar for low elevation has its own unique characteristics. False targets cannot be suppressed with conventional beamforming methods. Thus, a signal model for VHF-FDA-MIMO radar subjected to deceptive jamming is established. The reconstruction of the covariance matrix and the estimation of the steering vector are implemented with the generalized MUSIC algorithm. In addition, a matching Capon reconstruction method is proposed to finish the robust suppression of false targets for the problem of self-cancellation in the absence of a priori information. Finally, the beampattern and performance curves of different methods are compared. The simulation results show that the methods can be effectively applied to the suppression of deceptive jamming in VHF-FDA-MIMO radar under the multipath effect.

Slow-Time FDA-MIMO Technique With Application to STAP Radar

Unlike the conventional phased array, the frequency-diverse array (FDA) employs a tiny frequency increment across the array elements, which is capable of providing range–angle–time-dependent beampattern, and thereby offers potential benefits in target localization and interference mitigation. Reported literature on FDA mostly focuses on its intrapulse (fast-time) property and ignores the interpulse (slow-time) feature induced by frequency offset. In this article, incorporating the neglected inherent slow-time coding feature, a novel slow-time FDA multiple-input multiple-output (FDA-MIMO) technique is proposed for the space-time adaptive processing (STAP) radar. The new coding scheme can separate transmitting (Tx) signals via slow-time Doppler filtering, and the problem of signal aliasing is tackled by appropriately designing the slow-time codes. At the receiving (Rx) side, two Rx schemes are devised for recovering range-dependent Tx degrees-of-freedom. Moreover, the relevant clutter rank and the rule for code design are derived in detail. The outstanding merits of the proposed slow-time FDA-MIMO STAP radar consist of the following: There is no specific restriction on the probing waveform; the negative effect of time-variant pattern is perfectly eliminated; and both the target localization accuracy and clutter suppression performance are superior over the state-of-the-art FDA radar systems. Numerical results corroborate the superiorities of the proposed waveform strategy for STAP application.

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).

DOA and Range Estimation for FDA-MIMO Radar with Sparse Bayesian Learning

Due to grid division, the existing target localization algorithms based on sparse signal recovery for the frequency diverse array multiple-input multiple-output (FDA-MIMO) radar not only suffer from high computational complexity but also encounter significant estimation performance degradation caused by off-grid gaps. To tackle the aforementioned problems, an effective off-grid Sparse Bayesian Learning (SBL) method is proposed in this paper, which enables the calculation the direction of arrival (DOA) and range estimates. First of all, the angle-dependent component is split by reconstructing the received data and contributes to immediately extract rough DOA estimates with the root SBL algorithm, which, subsequently, are utilized to obtain the paired rough range estimates. Furthermore, a discrete grid is constructed by the rough DOA and range estimates, and the 2D-SBL model is proposed to optimize the rough DOA and range estimates. Moreover, the expectation-maximization (EM) algorithm is utilized to update the grid points iteratively to further eliminate the errors caused by the off-grid model. Finally, theoretical analyses and numerical simulations illustrate the effectiveness and superiority of the proposed method.

Single-Snapshot Angle and Incremental Range Estimation for FDA-MIMO Radar

This article deals with the problem of angle and incremental range (i.e., the target range offset with respect to the center of the cell under test) estimation with a frequency diverse array multiple-input multiple-output (FDA-MIMO) radar exploiting a single data snapshot as observable. Starting from the observation that the maximum likelihood (ML) estimation entails a 2-D grid search over the parameters of interest, three approximated ML techniques are designed resorting to the coordinate descent algorithm and the adaptive monopulse criterion (employing either real or complex slope/bias corrections). At the analysis stage, the estimation performance of the proposed methods, including the tapered and double-step monopulse versions, is also assessed in comparison with the Cramér–Rao lower bound. Numerical results corroborate the effectiveness of the considered estimation strategies in some diverse simulated scenarios.

Detection performance of airborne FDA-MIMO radar under non-IID RCS scenario

ABSTRACT This paper studies the incoherent square-law detector in the Neyman–Pearson sense for airborne frequency diverse array multiple-input multiple-output (FDA-MIMO) radar system under a non-independent and identically distributed radar cross section model. The presented incoherent square-law detector is suitable for airborne FDA-MIMO radar with arbitrary frequency increments and correlation coefficients and achieves the optimal detection performance. The superiority of FDA-MIMO radar over traditional phased array and MIMO radars in target detection is validated by both theoretical analysis and numerical results.

FDA-MIMO radar for 3D localization: Virtual coprime planar array with unfolded coprime frequency offset framework and TRD-MUSIC algorithm

The frequency diverse array multiple-input multiple-output (FDA-MIMO) radar can detect target range by exploiting a small frequency offset across the transmit sensors, which can be utilized to jointly estimate angle and range. Nevertheless, the detection performance is basically restricted by the array aperture and signal bandwidth. In this paper, we propose a joint optimization design scheme for FDA-MIMO radar, i.e., the virtual coprime planar array with ‘unfolded’ coprime frequency offsets (VCPA-UCFO) framework, for 3D localization without ambiguity. The VCPA-UCFO framework can significantly save sensors and physical space while remarkably extend array aperture and signal bandwidth, which brings about remarkably enhanced economic benefits and estimation performance. Additionally, we construct the 3D localization problem as 3D-MUSIC spatial spectrum function and transform the 3D total spectrum search of the conventional 3D-MUSIC algorithm into 1D local spectrum search by cooperating ESPRIT algorithm and twice reduce dimension MUSIC (TRD-MUSIC) algorithm. The TRD-MUSIC algorithm can significantly relieve computational burden but with no performance degradation. The CRBs are given as performance benchmark. The analysis and simulations have verified the effectiveness and advantages of VCPA-UCFO framework and TRD-MUSIC algorithm in system cost, localization accuracy, resolution and computational complexity.

Transmit beamspace design for FDA–MIMO radar with alternating direction method of multipliers

Hybridization of a frequency diverse array (FDA) generated range-angle-time dependent beampattern with multiple input multiple output (MIMO) radar waveform diversity, namely, FDA-MIMO radar, provides more degrees-of-freedom to improve overall system performance. As the beampattern optimization needs an efficient method to approximate the desired beampattern and simultaneously minimize the cross-correlation sidelobes, we optimize the transmit beampattern over the beamspace matrix in this paper. That is, the transmit FDA antennas are divided into multiple overlapping subarrays and each subarray transmits an orthogonal waveform towards the target, whereas the weight vectors of all subarrays jointly form a beamspace matrix. Since the optimization problem turns to be a non-convex problem with a constant energy constraint, we propose an efficient algorithm based on alternating direction method of multipliers (ADMM) to solve it, which has a very fast convergence speed. The effectiveness and superiorities of the proposed method over existing methods are verified by extensive simulation results.

Target Localization With Jammer Removal Using Frequency Diverse Array

A foremost task in frequency diverse array multiple-input multiple-output (FDA-MIMO) radar is to efficiently obtain the target signal in the presence of interferences. In this paper, we employ a novel "low-rank + low-rank + sparse" decomposition model to extract the low-rank desired signal and suppress the jamming signals from both barrage and burst jammers. In the literature, the barrage jamming signals, which are intentionally interfered by enemy jammer radar, are usually assumed Gaussian distributed. However, such assumption is oversimplified to hold in practice as the interferences often exhibit non-Gaussian properties. Those non-Gaussian jamming signals, known as impulsive noise or burst jamming, are involuntarily deviated from friendly radar or other working radio equipment including amplifier saturation and sensor failures, thunderstorms and man-made noise. The estimation performance of the existing estimators, relied crucially on the Gaussian noise assumption, may degrade substantially since the probability density function (PDF) of burst jamming has heavier tails that exceed a few standard deviations than the Gaussian distribution. To capture a more general signal model with burst jamming in practice, both barrage jamming and burst jamming are included and a two-step "Go Decomposition" (GoDec) method via alternating minimization is devised for such mixed jamming signal model, where the $a$ $priori$ rank information is exploited to suppress two kinds of jammers and estimate the desired target. Simulation results verify the robust performance of the devised scheme.

Tensor-Based Angle and Range Estimation Method in Monostatic FDA-MIMO Radar

In the paper, joint angle and range estimation issue for monostatic frequency diverse array multiple-input multiple-output (FDA-MIMO) is proposed, and a tensor-based framework is addressed to solve it. The proposed method exploits the multidimensional structure of matched filters in FDA-MIMO radar. Firstly, stack the received data to form a third-order tensor so that the multidimensional structure information of the received data can be acquired. Then, the steering matrices contain the angle and rang information are estimated by using the parallel factor (PARAFAC) decomposition. Finally, the angle and range are achieved by utilizing the phase characteristic of the steering matrices. Due to exploiting the multidimensional structure of the received data to further suppress the effect of noise, the proposed method performs better in angle and range estimation than the existing algorithms based on ESPRIT, simulation results can prove the proposed method’s effectiveness.

FDA‐MIMO for joint angle and range estimation: unfolded coprime framework and parameter estimation algorithm

The frequency diverse array multiple-input multiple-output (FDA-MIMO) radar provides range estimation capability by exploiting a small frequency offset across the transmit sensors, which has been utilised in numerous applications. However, the estimation performance is basically limited by the array geometry and signal bandwidth. In this study, the authors propose a new FDA-MIMO framework, i.e. the unfolded coprime array with ‘unfolded’ coprime frequency offsets (UCA-UCFO) framework, for joint angle and range estimation without ambiguity. The array aperture and signal bandwidth are obviously expanded by employing UCA in the spatial domain and frequency domain, which results in significantly enhanced estimation accuracy and resolution. In addition, we construct the joint angle and range estimation problem as a two-dimensional (2D)-multiple signal classification spatial spectrum and transform 2D total spectrum search into a 1D local spectrum search by introducing a successive iteration (SUIT) algorithm. The SUIT algorithm can significantly relieve the computational burden but without performance degradation. The Cramér–Rao bounds of angle and range are provided as a performance benchmark. The analysis and simulations have validated the superiority and advantages of the UCA-UCFO framework and SUIT algorithm with respect to location accuracy, resolution, and computational complexity.

Range-Angle Decoupling and Estimation for FDA-MIMO Radar via Atomic Norm Minimization and Accelerated Proximal Gradient

Frequency diverse array multiple-input multiple-output (FDA-MIMO) radar can offer the capability of range-angle-dependent beampattern and enjoy the advantage of effectively resolving the targets closely spaced in the same angle cell but different range cells. However, traditional subspace methods for range-angle estimation fail to efficiently work in a limited number of snapshots and coherent targets. In addition, the coupling between range and angle may lead to the degradation of estimation accuracy with ambiguity problem. In this letter, a gridless compressed sensing-based algorithm is proposed to joint estimate range-angle for FDA-MIMO radar. First, a decoupling model is presented to separate the range and angle from each other. Then, a 2D atomic norm minimization (ANM) problem for range-angle estimation is formulated and transformed into a semi-definite programming (SDP) problem with convex relaxation. Finally, a computationally efficient estimation algorithm via accelerated proximal gradient (APG) is developed to solve the SDP problem. Numerical simulations are conducted to illustrate the superior performance of the proposed algorithm.

Cognitive FDA-MIMO With Channel Uncertainty Information for Target Tracking

In this paper, we propose a cognitive frequency diverse array multiple input multiple output (FDA-MIMO) design by utilizing channel uncertainty information. Time-variant non-uniform frequency offsets are utilized to decouple frequency diverse array (FDA) range-angle dependent beampattern and a design strategy is proposed to maximize the transmit energy toward the desired range-angle region by steering the beam to match the channel uncertainty for enhanced target detect and tracking performance. To unambiguously estimate target parameters, we divide the FDA elements into multiple fully overlapped subarrays using orthogonal waveforms. Furthermore, we adaptively update the transmit beamspace matrix with two optimization criterions, namely, signal-to-noise ratio maximization and Cramer–Rao bound minimization. All proposed approaches are verified by numerical results.

Range-ambiguous clutter characteristics in airborne FDA radar

Frequency diverse array (FDA) has received much attention in recent years. Different from classic phased-array (PA) that uses the same carrier frequency for all array elements, FDA adopts a small frequency increment across its array elements to produce angle, range and even time dependent transmit beampattern, which provides many promising applications, but it may result in time- and spatial-variant clutter characteristics. Since the impacts of FDA on radar clutter structures and characteristics still have not been systematically investigated, this paper studies range-ambiguous clutter characteristics for airborne FDA radar including FDA multiple-input multiple-output (FDA-MIMO) radar and coherent FDA radar systems. The corresponding receiver filtered signal models are formulated, and the clutter rank in different scenarios are analyzed. Moreover, by exploiting FDA range-dependent beampattern, we propose a method to distinguish range-ambiguous clutter in airborne FDA radar. Both theoretical analysis and simulation results validate the superiority of FDA radar over traditional PA and MIMO radars in suppressing range-ambiguous clutter and FDA-MIMO radar achieves better suppression performance than coherent FDA radar.