Linear Frequency Diverse Array Research Articles

Design and Implementation of a Binary Phase-Shift Keying Frequency Diverse Array: Considerations and Challenges.

The frequency diverse array (FDA) is an architecture capable of beamforming in both range and angle, improving upon the traditional phased array (PA) which can only achieve beamforming in angle. The FDA employing directional modulation (DM) for secure directional communications (SDC) can reduce bit error rates (BERs) in both range and angle, again improving upon the traditional PA which can only reduce BER in angle. In this paper, we document the challenges involved in the design and implementation of a two-element linear FDA employing fast-time binary phase-shift keying (BPSK) modulations. We also show that the experimentally collected field data match well with the results of simulations based on our analytical model.

Ultrasonic nonlinear frequency diverse array: principle and applications

In ultrasonic testing, omnidirectional wave propagation presents challenges of nonfocus energy loss and interface interference. Traditional phased array (PA) methods, despite their focusing capabilities, suffer from limitations in energy utilization and target detection accuracy. Frequency diverse array (FDA) technology, initially developed for radar, has demonstrated potential for improved range-angle-dependent ultrasonic beampatterns but still exhibits limitations due to S-shaped coupling. This study proposes an ultrasonic nonlinear frequency diverse array (ultrasonic-NFDA) with nonuniform frequency offsets to address these issues. The ultrasonic-NFDA employs modulated frequency offsets by introducing nonlinear carrying functions and incorporating additional parameters to manipulate beamforming and enhances energy concentration at focal points. Furthermore, the multi-objective differential evolution algorithm is used for parameter optimization. The proposed method decouples the range-angle beampattern and improves the signal-to-interference-plus-noise ratio. Numerical evaluations and simulations demonstrate that ultrasonic-NFDA outperforms the ultrasonic linear FDA and PA series, achieving better peak sidelobe level and half-power beam width. Experimental validations confirm the effectiveness of ultrasonic-NFDA in practical ultrasonic testing scenarios, showing significant improvements in defect detection and imaging clarity. The optimized beampatterns effectively reduce artifacts and enhance the precision of defect localization. The proposed integration of nonlinear frequency offsets and parameter optimization in array testing offers a robust solution for more accurate and efficient ultrasonic inspection methodologies.

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.

Beampattern Synthesis and Optimization Method Based on Circular Frequency Diverse Array Engineering Model

The frequency diverse array (FDA) is capable of generating range-angle-dependent beampatterns by introducing a tiny frequency offset to the transmit carrier frequency of each array element. However, the beam-scanning potential of conventional linear FDA applications is limited, notably in their incapacity for 360° omnidirectional scanning. This paper introduces a method that leverages the geometric configuration of circular frequency diverse arrays (CFDAs) for synthesizing and optimizing beampatterns through a practical engineering approach. Initially, we compute the structural parameters and configurations of CFDA. Subsequently, the isophase plane is utilized to adjust the phase of each array element. Ultimately, the CFDA structure is used to optimize the non-uniform frequency offset, and the beampattern, which is capable of 360° omnidirectional scanning, is realized by low sidelobe optimization. Simulation results affirm that the CFDA antenna, as per the actual engineering model, possesses precise dot-shaped beampattern scanning abilities across both range and angle dimensions.

Transmit–Receive Sparse Synthesis of Linear Frequency Diverse Array in Range-Angle Space Using Genetic Algorithm

Unlike conventional phased array (PA), frequency diversity array (FDA) can perform the beampattern synthesis not only in an angle dimension but also in a range dimension by introducing an additional frequency offset (FO) across the array aperture, thus greatly enhancing the beamforming flexibility of an array antenna. Nevertheless, an FDA with uniform inter-element spacing that consists of a huge number of elements is required when a high resolution is needed, which results in a high cost. To substantially reduce the cost while almost maintaining the antenna resolution, it is important to conduct a sparse synthesis of FDA. Under these circumstances, this paper investigated the transmit-receive beamforming of a sparse-fda in range and angle dimensions. In particular, the joint transmit-receive signal formula was first derived and analyzed to resolve the inherent time-varying characteristics of FDA based on a cost-effective signal processing diagram. In the sequel, the GA-based low sidelobe level (SLL) transmit-receive beamforming of the sparse-fda was proposed to generate a focused main lobe in a range-angle space, where the array element positions were incorporated into the optimization problem. Numerical results showed that 50% of the elements can be saved for the two linear FDAs with sinusoidally and logarithmically varying frequency offsets, respectively termed as sin-FO linear-FDA and log-FO linear-FDA, with only a less than 1 dB increment in SLL. The resultant SLLs are below -9.6 dB, and -12.9 dB for these two linear FDAs, respectively.

The DOA location deception effect of frequency diverse array on interferometer

With advances in radar localisation, especially the emergence and development of passive localisation, there is an urgent demand for countermeasure technology. To counteract the passive direction-of-arrival (DOA) location, this article studies the DOA location deception effect of a frequency diverse array (FDA) on an interferometer. By analysing the phase distribution model of the uniform linear FDA (ULFDA) signal and the DOA location principle of the one-dimensional phase interferometer, it was found that the phase difference the FDA produces does not conform to the direction-finding law of the interferometer, which provides a potential capability for the FDA to achieve localisation deception for the interferometer. Based on the proposed DOA location deception model and the instantaneous signal-to-noise-ratio (ISNR), the CRLB and RMSE of the angle and x-intercept deviation are investigated. The results show that, compared with conventional phased array signals, the FDA signal can achieve DOA location deception on the interferometer, and by properly configuring the frequency increment sequence, the FDA can perform better DOA location deception on the interferometer, which means that the FDA provides promising potential for radar security.

Analysis of beampattern dwell time for planar frequency diverse array

Frequency diverse array (FDA) has received much attention due to its both range–angle-dependent beampattern. However, most of the existing works focus on the linear FDA, and time-varying characteristics of its beampattern only give a rough qualitative analysis. To further study the spatial beampattern dwell time issues, the pulsed-planar FDA measurement model is first given, and then, the quantitative analysis of beam dwell time which can be affected by observation point location (azimuth, elevation, and range) and array antenna frequency offset coding method for a given pulse transmitting signal is presented. Finally, the theoretical analysis is proved to be consistent with the simulations.

A cognitive active anti-jamming method based on frequency diverse array radar phase center

With the advances in electronic countermeasures (ECMS), especially the emergence and development of active jammers, there is an urgent demand for anti-jamming techniques. In this paper, we proposed a cognitive active anti-jamming method based on frequency diverse array (FDA) radar phase center. For the uniform linear FDA (ULFDA) radar, we derive the closed form of phase center, based on which the regulation effect of frequency increments is explored through Monte Carlo test. Based on the closed form of phase center, an optimization model considering the frequency increments regulation at the fixed time is established and solved by the improved swarm-immune optimization (PSO-IMMU) algorithm to realize active anti-jamming. Finally, for the jammers that implement jamming by determining the position of target, we propose a cognitive active anti-jamming method making the radar difficult for a jammer to detect or locate during the normal operation, and for the case of moving target and fixed jamming source, the Bayesian filter is applied to realize cognitive beamforming, while for the case of fixed target and moving jamming source, the auxiliary radar is applied to predict and estimate jamming source state along with the Bayesian filter. All proposed methods are verified by numerical simulation results.

Frequency Diverse Array Beampattern Synthesis With Taylor Windowed Frequency Offsets

Frequency diverse array (FDA) is capable of generating a range-angle-dependent beampattern via adjusting the frequency offset across array elements. The classical linear FDA generates an S-shaped beampattern due to the range-angle-dependent coupling. In order to remove the coupling, and obtain a well-focused dot-shaped beampattern, several FDA frameworks are proposed via adjusting frequency offsets. It seems that the window based tapering frequency offsets are able to form a single maximum with a satisfactory mainbeam sharpness. However, most window-based FDA schemes are focused on classical fixed windows. In this letter, an FDA framework with Taylor windowed frequency offsets is first proposed. Considering that adjustable tapering windows allow adjustments by parameter manipulation, the optimized parameters of the window function are determined. The FDA beamforming results with all kinds of frequency offsets are measured, and compared. Numerical results validate the superiority of proposed FDA in terms of mainlobe width, and sidelobe level.

Frequency Diverse Array Beampattern Synthesis Using Symmetrical Logarithmic Frequency Offsets for Target Indication

Although phased arrays have been widely used in various applications, their beams can only be steered to an angle for all range bins. In contrast, the frequency diverse array (FDA) introduces a tiny frequency offset across its array elements to form a range-angle-dependent beampattern. Nevertheless, the standard linear FDA can only provide an S-shaped beampattern, which is a disadvantage for target indication. In this communication, we propose a new FDA framework, which adopts symmetrical and logarithmic frequency offsets together with multicarrier technique, to produce a dot-shaped beampattern for target indication. The superiority of the proposed scheme is verified by both numerical results and comparisons with existing FDA frameworks.

Uni-Antenna Spatial Energy Compression Based on Unsteady Coherent Interference

In this work, the unique spatial energy compression phenomenon of uni-antenna frequency diverse system based on the unsteady coherent interference is explored comprehensively. By compressing the element spacing of linear frequency diverse array (FDA) to near-zero, the decoupling of angle dimension is significantly achieved from the conventional range-angle-dependent beampattern. Inspired by the ever-shrinking element spacing, the concept of uni-antenna frequency diverse system is firstly proposed. The relations between a series of parameters (i.e. the number of diversity, frequency offset values) and spatial energy distributions is investigated in-depth. The uni-antenna frequency diverse synthesizing method allows the focusing intensity and focusing period of transmitted energy to be flexibly adjustable. The electric intensity of the proposed uni-antenna frequency diverse system has at least 4dB more compared with that in conventional phased array at each special focusing ribbon, which brings a great improvement of SNR in radar detection. This system provides a very promising and potential research and development direction on collaborative detection scheme while integrating phased array technology. With energy compression and focusing in both angle and range dimensions achieved, illustrating that such interference fringes phenomenon of frequency diverse antenna system is more promising and suitable for high performance detection and ranging applications.

Generalized Linear Frequency Diverse Array Manifold Curve Analysis

Different from traditional phased-array, frequency diverse array (FDA) generates both angle and range dependent beampattern by the use of a small frequency offset across its array elements. Particularly, FDA range-dependent beampattern provides many new properties and potential applications. As array manifold curve plays an essential role in various array applications, this letter analyzes the generalized linear FDA manifold curve characteristics including arc length and its rate-of-change. It is proved that the arc length of FDA manifold curve is longer (implies better performance) than that of a phased-array for symmetric linear array configuration. Moreover, the derived Cramer-Rao lower bound also verifies that symmetric FDA outperforms phased array in direction-of-arrival estimation. All theoretical analyses are validated by numerical results.

Identifying unambiguous frequency pattern for target localisation using frequency diverse array

The beampattern of a conventional frequency diverse array (FDA) with linear frequency pattern (i.e. the centre frequency of each antenna element is linearly increasing) is coupled in range and angle. FDA with random frequency pattern can decouple the range and angle with high probability only when the number of elements is sufficiently large. The ambiguity of frequency patterns that are random permutations of a linear FDA is examined. An eigenvector-based criterion to identify possible ambiguity in target localisation using such arrays is proposed. Numerous results are presented to verify the effectiveness of the proposed ambiguity identification criterion.

Frequency Diverse Array Antenna Using Time-Modulated Optimized Frequency Offset to Obtain Time-Invariant Spatial Fine Focusing Beampattern

For a frequency diverse array (FDA) antenna, the combination of time-modulated and nonlinear distributed frequency offset is proposed to realize time-invariant spatial fine focusing beampatterns. The distribution of the nonlinear function is optimized by using artificial bee colony algorithm, and the resultant frequency offset is termed as time-modulated optimized frequency offset (TMOFO). In addition to design a TMOFO-FDA in realistic situations, the interval-based tolerance analysis is introduced to predict the impact of frequency-offset uncertainties or errors on the time-invariant spatial focusing beampattern. The spatial focusing performance of the TMOFO-FDA is compared with an analytical FDA scheme based on a time-modulated logarithmically increasing frequency offset (TMLFO). Numerical examples of a ten-element linear FDA with $\lambda _{0} / 2$ element spacing in the presence of mutual coupling effects based on the TMOFO and the TMLFO are reported and compared. The comparative results between the ideal TMLFO and TMOFO show that, in range-angle plane the size of the focal spot for TMOFO-FDA is reduced by about 70% compared to that for TMLFO-FDA. The side lobe level is reduced about 49%. The comparative results from IA-based beampattern tolerance analysis also reveal the superiority of the TMOFO-FDA scheme.

Decoupled frequency diverse array range–angle‐dependent beampattern synthesis using non‐linearly increasing frequency offsets

The frequency diverse array (FDA) using linearly increasing frequency offsets has received much attention, but it has a range and angle coupled beampattern. This study proposes a new uniform linear FDA with non-linearly increasing frequency offsets to decouple the range–angle-dependent beampattern. Square increasing and cubic increasing frequency offsets are suggested for the FDA. In doing so, the range and angle of targets are solely estimated without ambiguities by the multiple signal classification algorithm. Numerical results show that the proposed approach outperforms the existing approach using logarithmically increasing frequency offsets in both focusing transmit energy and target localisation performance, especially in the range dimension.

Linear Frequency Diverse Array Manifold Geometry and Ambiguity Analysis

Different from phased-array, frequency diverse array (FDA) offers range-dependent beampattern and thus provides new application potentials. But, there is a fundamental question: what is the FDA manifold geometric and ambiguity properties? In this paper, the FDA manifold geometric and ambiguity properties are investigated via manifold geometry analysis; the FDA resolution and detection capabilities are derived as a function of the manifold length and first curvature for the sources with unequal powers. The ambiguities inherent in a linear FDA manifold is investigated. Under the same conditions, FDA has better detection and resolution capabilities than conventional phased array. Since FDA offers a range-dependent beampattern, some of the manifold vectors that are linearly dependent in phased array, will became linearly independent in FDA. For these reasons, when compared to a phased-array radar, FDA radar can resolve more sources. All the derived expressions are validated by the extensive simulation results.

Beampattern analysis of planar frequency diverse array

Compared with conventional phased array, frequency diverse array (FDA) can provide range-angle-dependent beampattern. However, most of reported investigations on this concept focus on linear frequency diverse array, referred as Linear-FDA in this article. Compared with linear array, planar array can provide better directionality and higher gain. In this article, we focus on the beampattern characteristic analysis of planar frequency diverse array (Planar-FDA) and study the auto-scanning feature of its beampattern. The variation of the mainbeam with respect to time is analyzed and the constraint to guarantee the auto-scanning characteristic of the beampattern is derived. The signal transmitted from each element is designed under the constraint and the radiation characteristics of the beampattern of Planar-FDA are examined via three-dimensional electromagnetic field simulation software. © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:436–444, 2015.

Range-Angle Dependent Transmit Beampattern Synthesis for Linear Frequency Diverse Arrays

Phased-array is widely used in communication and radar systems, but the beam steering is fixed in an angle for all the ranges. In this paper, we propose a range-angle dependent beampattern synthesis scheme for linear frequency diverse array (FDA) using the discrete spheroidal sequence, with an aim to focus the transmit energy in a desired two-dimensional spatial section. Different from conventional phased-arrays, FDA employs a small frequency increment, compared to the carrier frequency across the array elements. The range-angle dependent beampattern synthesis method allows the FDA to transmit energy over a desired range or angle sector. This provides a potential to suppress range-dependent clutter and interference, which is not accessible for conventional phased-arrays. The system performance of the proposed FDA is evaluated by the output signal-to-interference-plus-noise ratio (SINR). The effectiveness is verified by comprehensive numerical simulation results.

Forward-looking radar GMTI benefits using a linear frequency diverse array

The ability to suppress range ambiguous clutter is difficult for forward-looking arrays in GHTI processing. Use of linear frequency diverse array (FDA) is proposed, whereby each array channel operates at a different frequency and produces a range dependent pattern. The FDA significantly increases output signal-to-interference plus noise ratio (SINR) at the range ambiguous clutter Doppler, suggesting detection improvement. Output SINR is shown to increase by as much as 40 dB when compared to a constant frequency array.