Frequency Diverse Array Radar Research Articles

Time-modulated planar frequency diverse array for multi-target detection

The frequency diverse array (FDA) is a very interesting technique in wireless communications. Many research papers are introduced in this field. A lot of them is concerned with linear point sources array. In this paper, a design of a time-modulated planar frequency diverse array architecture is proposed for tracking single or multi-target for the first time. The time-modulation array (TMA) and FDA are combined for detecting single and multi-target. The effectiveness of this combined scheme is demonstrated through simulation results that compared with a point source case to show its superior performance. Authors introduce planar FDA array instead of linear FDA array and realize the planar array using cylindrical dielectric resonator antenna array (CDRA). A planar array consists of 8 × 8 CDRA is used to enable the detection of single target/multi-target. The operating frequency of the antenna is set at 10 GHz, aligning with its applications in the FDA radar. The radiation characteristics of the CDRA antenna element are introduced. High maximum gain of 6 dBi is achieved with a remarkably high efficiency. A set of representative results is reported and analyzed to assess the effectiveness of the proposed approach.

Multi-scale moving target detection with FDA-MIMO radar

The recently developed frequency diverse array (FDA) radar applies a small frequency increment across the array elements, which provides advantages in clutter suppression, jamming suppression, and target detection for existing radar systems. In this paper, the frequency increment is enlarged to guarantee that the transmit waveforms are orthogonal in frequency domain for multiple-input multiple-output (MIMO) radar. A multi-scale moving target detection method of FDA-MIMO radar is proposed. The FDA radar with a large frequency increment suffers from the deteriorated decorrelation of scatterers within the same range bin and causes the inner-bin range dependence (IRD) property in transmit spatial domain. By taking additional space–time snapshots in transmit domain as training samples, the space–time adaptive processing (STAP) is applied in joint receive and Doppler domain for clutter suppression, which alleviates the requirement of insufficient training samples in non-stationary clutter environment. In the sequel, a set of beamformers within the whole angular domain of interest is utilized for target detection, which achieves target detection under the condition of random target locations and sizes. Numerical simulation results are provided to verify the effectiveness of the proposed method.

Adaptive FDA Radar Transmit Power Allocation for Target Detection Enhancement in Clutter Environment

The detection of static targets in clutter environments has been an active topic in radar community, which is also a difficult problem, since there is no Doppler information that can be used to distinguish the target from clutter. Aiming at this problem, in this article, we develop an adaptive approach based on frequency diverse array (FDA) radar to enhance the detection performance. First, a parametric measurement model that incorporates the practical dependence of the clutter responses on transmit frequencies is introduced. Then, based on the generalized likelihood ratio (GLR) test, an adaptive detector that requires no training data is developed to determine the existence of a target in a specific cell under test, where the scattering features of the target and clutter are assumed unknown. In addition, the detector has the property of constant false alarm rate (CFAR) with respect to the clutter. Moreover, under the criterion of maximizing the detection probability, we propose an adaptive scheme in which the collected data are utilized to select the transmit weights for power allocation to improve the detection. Numerical simulations are conducted to illustrate the effectiveness of the proposed detector and demonstrate the performance improvement owing to the adaptive power allocation design.

Designing FDA Radars Robust to Contaminated Shared Spectra

This paper considers the problem of jointly designing the transmit waveforms and weights for a frequency diverse array (FDA) in a spectrally congested environment in which unintentional spectral interferences exist. Exploiting the properties of the interference signal induced by the processing of the multi-channel mixing and low-pass filtering FDA receiver, the interference covariance matrix structure is derived. With this, the receive weights are formed using the minimum variance distortionless response (MVDR) method for interference cancellation. Owing to the fact that the resulting output signal-to-interference-plus-noise ratio (SINR) is a function of the transmit waveforms and weights, as well as due to the ever-greater competition for the finite available spectrum, a joint design scheme for the FDA transmit weights and the spectrally compatible waveforms is proposed to efficiently use the available spectrum while maintaining a sufficient receive SINR. The performance of the proposed technique is verified using numerical simulations in terms of the achievable SINR, spectral compatiblity, as well as several aspects of the synthesized waveforms.

Joint optimization of FDA-MIMO antenna selection and frequency offset to maximize SINR

The structured sparse multiple-input multiple-output frequency diverse array (FDA-MIMO) radar has range, angle estimation, and resolution advantages. However, the structured sparse array is not the optimal array structure with the max output signal-to-interference-noise ratio (SINR). In order to obtain the optimal FDA-MIMO structure, this paper maximizes the output SINR of the array by optimizing the array antenna selection and frequency offset. Because there is a coupling relationship between frequency offset and array antenna selection, and it is difficult to optimize them simultaneously, we divide the problem into two subproblems. According to the spatial separation coefficient (SCC), we propose the array antenna selection method using the angle of target and interference subspace and the frequency offset optimization approach using the constant modulus beamforming idea and particle swarm optimization algorithm. Then we join the two approaches to conduct alternate iterative optimization. By comparing the optimum FDA-MIMO with other structures of FDA-MIMO, we confirm the effectiveness and superiority of the optimum FDA-MIMO.

Reply to Comments on “Correction Analysis of ‘Frequency Diverse Array Radar About Time”’

Similar to the analysis method of dividing the actual time into “fast time” and “slow time” introduced in the signal processing community, dividing the actual time into “the transmit delay” and “the time index within pulse” is a new analysis method from a new perspective to facilitate the analysis of the time-varying property of frequency diverse array (FDA) radar. It does not break the nature of the unity of time. In this reply, the importance of our new findings and contributions are presented again in a more concisely way.

Comments on “Correction Analysis of ‘Frequency Diverse Array Radar About Time’”

In recent years, frequency diverse arrays (FDAs) have been receiving much attention due to their high degrees of freedom for beamforming <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> . Essentially, the beampatterns of FDA are related to angle, time, and range <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> , <xref ref-type="bibr" rid="ref2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[2]</xref> , <xref ref-type="bibr" rid="ref3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[3]</xref> , <xref ref-type="bibr" rid="ref4" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[4]</xref> . However, the time-varying property has limited the practical application of FDAs. Thus, there has been a lot of discussion about the time-varying property of FDAs <xref ref-type="bibr" rid="ref3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[3]</xref> , <xref ref-type="bibr" rid="ref4" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[4]</xref> , <xref ref-type="bibr" rid="ref5" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[5]</xref> , <xref ref-type="bibr" rid="ref6" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[6]</xref> , <xref ref-type="bibr" rid="ref7" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[7]</xref> , <xref ref-type="bibr" rid="ref8" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[8]</xref> .

Radar Cross Section Characterization of Frequency Diverse Array Radar

In this article, we develop a frequency diverse array (FDA) radar echo signal model for general complex targets including dumbbell and multiple scatterers. Moreover, we expose the reflectivity characterization, i.e., the radar cross section (RCS) for an FDA radar as a function of fast time, frequency offset, and angle. Note that, previously the RCS is not time dependent for the conventional radars including phased-array radar. Since statistical analysis is not, merely, enough for a fair FDA radar RCS investigations, we further derive the probability distribution function (PDF) of an FDA radar-based RCS by exploiting the statistical distribution characterization with randomly distributed scatterers. Finally, it has been proved that the PDF of an FDA radar RCS is related to both time and frequency offsets. All conclusions are validated by numerical results.

Moving target detection in range-ambiguous clutter scenario with PA-FDA dual-mode radar

Range-ambiguous clutter suppression is challenging for airborne radar in non-sidelooking geometry. The target detection performance might degrade severely due to range ambiguity and range dependence problems. It is proved that the frequency diverse array (FDA) is capable of resolving the range ambiguity and is beneficial for range ambiguous clutter suppression. However, FDA uses wide coverage transmit beampattern, which causes somewhat gain loss compared to the phased array (PA). In this paper, we establish a PA-FDA dual-mode radar to maximize the advantages of PA and FDA radars to improve target detection performance in range-ambiguous clutter scenario. Firstly, the range ambiguous resolvability of FDA is utilized, where range ambiguous clutters are separated by using pre-filtering before space-time adaptive processing. Therefore, the range dependence compensation algorithms can be performed independently to further address the range dependence problem of non-sidelooking array radar. In this case, the clutter covariance matrix (CCM) is reconstructed by using linear combination of distinguishable CCMs corresponding to different range regions, resulting in improved accuracy of CCM estimation. Secondly, the enhanced CCM is applied in PA counterpart, which maximizes the high beampattern gain of PA and range ambiguity resolvability of FDA. It is verified that the PA-FDA dual-mode radar outperforms the PA or FDA single-mode in simultaneously narrow-beam detection and wide-angle coverage. Thus, the proposed PA-FDA dual-mode radar can greatly contribute to searching and tracking tasks. Simulation examples demonstrate the effectiveness of the proposed method.

Iterative multi-target detection for PA-FDA dual-mode radar

In this paper, the multi-target detection for joint phased array (PA) and frequency diverse array (FDA) radars, referred to as PA-FDA dual-mode radar, is investigated by exploiting the high transmit power efficiency of PA as well as wide spatial coverage of FDA. The PA-FDA dual-mode radar is formulated in a signal-level fusion manner by combining the PA and the FDA, which enables us to exploit the joint information in the PA-FDA dual-mode radar. In the sequel, an iterative multi-target detection method is devised with two main steps: i) the generalized likelihood ratio test (GLRT) is performed, which provides the knowledge of target parameters, and ii) the conditional-cancelation-before-detection GLRT (CCBD-GLRT) detector is carried out, which detects other targets based on the previous detection knowledge. At the analysis stage, the optimal detector is provided for the signal-level fusion of PA and FDA radars. Moreover, the corresponding analytical expressions of the probabilities of detection as well as the probabilities of false alarm with respect to both the developed GLRT and CCBD-GLRT detectors are derived for multi-target detection. Simulation results demonstrate that the proposed multi-target detection method is effective and the PA-FDA dual-mode radar outperforms the PA and the FDA radars.

Range-angle-dependent beamforming for FDA radar with Hamming interelement spacing and sinusoidal multicarrier approach

By employing a tiny frequency offset across the array elements, a frequency diverse array (FDA) produces a beampattern with the property of being range-angle-dependent. However, the beampattern of a traditional FDA has many maxima at undesired range-angle couples, which is unfavorable for target localization and jamming suppression. In this paper, a novel FDA scheme with Hamming interelement spacing, namely, the HIS-FDA, is proposed. By adopting Hamming window weighted interelement spacing and frequency offsets optimized by the genetic algorithm, the HIS-FDA produces a dot-shaped well-performed beampattern, which has superior performance over the existing FDA systems, especially in the angle dimension. The multiple input multiple output technique and multiple matched filters are employed at the receiver to solve the time-varying problem. A new multicarrier (MC) technique termed the sinusoidal MC approach is also presented to improve the beampattern performance, especially in the range dimension. Our proposed scheme outperforms the existing FDA systems in terms of the mainlobe width in the range and angle profiles, the sidelobe level, and the range-angle spatial region of the mainlobe. Comparison results are provided to validate the superiority of the proposed scheme.

A Robust Beamforming Suppressing Deceptive Jamming Method Based On FDA-MIMO Radar

In comparison to phased array (PA) radar that just transmits a beampattern with angle-dependent, frequency diverse array (FDA) radar with adding a feature of distance dimension performs well in main-beam deceptive jamming suppression domain. However, in practical conditions, estimating an inaccuracy of the covariance matrix(CM) has a significant negative impact on algorithm performance, also as a mismatch of target SV has. Hence, a robust adaptive beamforming technique comes up in this article that selects the principal eigenvector to get accurate signal steering vectors (SV), further gets the reconstruction interference-plus-noise CM (IPNCM). According to experiments, the proposed algorithm keeps a robust and good performance under non-ideal circumstances.

Waveform optimization with SINR criteria for FDA radar in the presence of signal-dependent mainlobe interference

In this paper, we focus on the design of the transmit waveforms of a frequency diverse array (FDA) in order to improve the output signal-to-interference-plus-noise ratio (SINR) in the presence of signal-dependent mainlobe interference. Since the classical multi-carrier matched filtering-based FDA receiver cannot effectively utilize the waveform diversity of FDA, a novel FDA receiver framework based on multi-channel mixing and low pass filtering is developed to keep the separation of the transmit waveform at the receiver side, while preserving the FDA range-controllable degrees of freedom. Furthermore, a range-angle minimum variance distortionless response beamforming technique is introduced to synthesize receiver filter weights with the ability to suppress a possible signal-dependent mainlobe interference. The resulting FDA transmit waveform design problem is initially formulated as an optimization problem consisting of a non-convex objective function and multiple non-convex constraints. To efficiently solve this, we introduce two algorithms, one based on a signal relaxation technique, and the other based on the majorization minimization technique. The preferable performance of the proposed multi-channel low pass filtering receiver and the optimized transmit waveforms is illustrated using numerical simulations, indicating that the resulting FDA system is not only able to effectively suppress mainlobe interference, but also to yield estimates with a higher SINR than the FDA system without waveform optimization.

Joint design of the transmit and receive weights for coherent FDA radar

Frequency diverse array (FDA) differs from conventional array techniques in that it imposes an additional frequency offset (FO) across the array elements. The use of FO provides the FDA with the controllable degree of freedom in range dimension, offering preferable performance in joint angle and range localization, range-ambiguous clutter suppression, and low probability of intercept, as compared to its phased-array or multiple-input multiple-output (MIMO) counterparts. In particular, the FO of the coherent FDA is much smaller than the bandwidth of the baseband waveform, capable of obtaining higher transmit gain and output signal-to-interference-plus-noise ratio (SINR). In this paper, we investigate the problem of joint design of the transmit and receive weights for coherent FDA radar systems. The design problem is formulated as the maximization of the ratio of the power in the desired two-dimensional range-angle space to the power in the entire area, subject to an energy constraint that limits the emitted energy of each transmit antenna and a similarity constraint such that a good transmit beampattern can be guaranteed. Due to the resultant problem is NP-hard, therefore, a sequential optimization method based on semidefinite relaxation (SDR) technique is developed. Numerical simulations are provided to demonstrate the effectiveness of the proposed scheme.

Coherent receiver design and aperture expansion beamforming for frequency diverse array radar

Frequency diverse array (FDA) radar has attracted considerable attention in interference suppression due to its range-angle dependent beampattern property. However, the full-band coherent receiver design is sophisticated and expensive. Furthermore, prior research on FDA radar adaptive beamforming failed to suppress adjacent-target interference because of insufficient beam resolution. This paper aims to develop a receiver architecture based on fractional domain signal separation and to investigate aperture expansion adaptive beamforming based on interference-noise covariance matrix reconstruction and signal of interest steering vector estimation. The proposed receiver design not only simplifies the structure and saves resources, but it can also effectively separate the received signals, particularly for the FDA radar's overlapping linear frequency modulated baseband emission waveforms. The proposed aperture expansion beamforming approach improves beam resolution of beamforming and effectiveness in adjacent-target interference suppression.

Multiple‐input multiple‐output with frequency diverse array radar transmit beamforming design for low‐probability‐of‐intercept in cluttered environments

Multiple-input multiple-output with frequency diverse array (FDA-MIMO) radar has drawn great attention due to providing the range-angle beampattern via designing the transmit beamforming matrix. In this work, the authors investigate the transmit beamforming matrix optimization for Low-Probability-of-Intercept (LPI) of FDA-MIMO radar, which can accurately control the transmit beam energy to meet the LPI requirements and the clutter suppression. The idea of the transmit beamforming matrix design is to minimise the transmit power in a specific direction and simultaneously maximise the signal-to-interference-plus-noise ratio under the power constraint on each array element. To this end, a constrained multiple-ratio fractional programming model with concerning the transmit beam matrix and the receive filter is first constructed, and then, it is transformed into two suboptimisation problems using a circular iterative approach. Moreover, the specific solution of the transmit beamforming matrix is obtained using the quadratic transformation method and the alternating direction method of multipliers algorithm. In addition, the computational complexity is also analysed in this paper. The simulation results demonstrate the correctness and effectiveness of the proposed method.

Analysis of multicarrier frequency diverse array radar over time

The frequency diverse array (FDA) can provide degrees of freedom in both the range and angle domains by controlling the frequency offset across adjacent elements. Nevertheless, the time-variant problem affects the analysis and application of FDA, and there is a notable lack of research on the receivers of multicarrier FDA. In this paper, a novel perspective to understand the factor of time parameter is proposed. Furthermore, combined with the multiple input and multiple output scheme, two multicarrier FDA radar receivers are proposed to obtain the time-invariant and dot-shaped beampattern. Numerical simulations demonstrate the validity of theoretical results.

Frequency diverse array radar with non-uniform array spacing based on sigmoid function

Abstract As a widely recognized electronic beam steering concept, frequency diverse array (FDA) radar is an effective and feasible solution to provide beam scanning ability in both angle as well as range dimension as a function of time. However, the conventional FDA radar employing progressive incremental frequency offsets across the array elements generates an S-shaped and range-angle coupled beampattern. As such, the FDA beampattern can be decoupled into range-angle dimensions by employing non-linear frequency offsets or using non-uniform arrays. Frequency offsets design has been extensively researched in recent years, whereas non-uniform arrays were given little attention so far. In this paper, we propose a novel FDA radar with a unified configuration of non-uniform linear array, and non-linear frequency offsets to achieve a high-resolution dot-shaped range-angle dependent beampattern. More specifically, the non-uniform inter-element spacing is calculated using the sigmoid function, and non-linear frequency offsets are generated by logistic map, and triangular window function. Simulation results clearly demonstrate the performance advantages of the proposed FDA radar in terms of beam width and side lobe levels.

Adaptive Transmit Beamspace Optimization Design based on RD-log-FDA Radar

Because of the range-angle dependency in random log frequency diverse array (RD-log-FDA) radar, a method for designing beamspace transformation matrix in angle and range based on the receive signal has been proposed. It is demonstrated that the designed beamspace transformation matrix basically meets the requirements of beam gain. However, there are some problems in the transformation matrix designed, such as unstable beam gain and high sidelobe. Hence, we propose an optimization method by adjusting array element spacing and random number in frequency offset to get the optimum beam gain. Therefore, particle swarm optimization (PSO) is used to find the optimal solution. The beam gain comparison before and after the optimization is obtained by simulation, and the results show that the optimized array after beamspace preprocessing has more stable beam gain, lower sidelobe, and higher resolution in parameter estimation. In conclusion, the RD-log-FDA is capable of forming desired beam gain in angle and distance through beamspace preprocessing, and suppressing interference signals in other areas.

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.