Frequency Diverse Array Radar Research Articles

A robust STAP approach for airborne FDA radar with multiple possible prior information constraints

In frequency diverse array (FDA) space–time adaptive processing (STAP) system, the spectrum of fast-moving target is non-well focused in the spatial–temporal plane, which causes a large mismatch between the actual and presumed target steering vector and dramatically degrades the performance of FDA-STAP system. In this paper, we propose a robust FDA-STAP approach based on multiple possible prior information constraints to resolve this issue and improve the performance of FDA-STAP system. In the proposed approach, multiple possible prior information, i.e., multiple large uncertainty regions, where the actual target possibly locate in spatial–temporal domains, are utilized to cover and constraint the estimated steering vector. The multiple uncertainty regions constraints make it possible to accurately estimate the fast-moving target steering vector. Moreover, to mitigate the influence of non-focused spatial–temporal spectrum of fast-moving target, a non-focused constraints is developed using the squared norm of space–time steering vector to avoid the estimated steering vector converge to the non-focused region of fast-moving target. Finally, the proposed robust FDA-STAP is converted into a non-convex quadratically constrained quadratic programming problem, and the semidefinite relaxation technique is employed to obtain the estimated target steering vector. Numerical results indicate that the proposed method has superior performance than other methods, including well-maintained main beam direction and significant performance improvement.

Multi-dimensional Ambiguity Function for Coherent Pulsed-LFM FDA Radar

Frequency diverse array (FDA) which employs a small frequency increment between adjacent elements can provide a range-angle-dependent beampattern with new application potentials. In this paper, the proposed coherent pulsed-LFM FDA scheme enables full spatial coverage with a single transmit waveform, wherein the transmit beamforming can be performed at the receiver with flexible signal processing means. In the coherent pulsed-LFM FDA radar configuration, the range sidelobe level (SLL) can be reduced significantly. Analyses of the multi-dimensional ambiguity function in terms of the low sidelobe characteristics, spatial coverage capability, and resolution properties in range, angle and Doppler domains are given by ambiguity function profiles. Comparisons with conventional phased array and MIMO (Multiple-Input Multiple-Output) radar are presented in the simulation. Results demonstrate the superiority of the proposed approach in angular coverage and sidelobe level with simplicity in engineering.

Analysis of Necessity of FDA Selecting Optimal Frequency Interval

The relationship between the output signal to jamming and noise ratio (SJNR) of frequency diverse array (FDA) and the correlation coefficient between the jamming and signal steering vector are deduced. The influence of the change of signal and jamming position on the output SINR is obtained. When jamming is located in mainlobe, the improper frequency interval will sharply reduce the output SINR and form a null. The detection ability of the FDA radar will also drop sharply and the null will change periodically with the selection of frequency interval. Both the theories and simulations verified this periodic null and demonstrated the necessity for selecting FDA’s optimal frequency interval.

Target Detection Performance Analysis of FDA-MIMO Radar

Inspired by recent advances in frequency diverse array (FDA) and multiple-input-multiple-output (MIMO) radars, this paper investigates the target detection performance of FDA-MIMO radar, which jointly utilizes the advantages of FDA radar and MIMO radar, for single- and multiple- coherent pulses, respectively. Firstly, the signal models in target detection are formulated for FDA-MIMO, standard FDA, phased-array and MIMO radars, respectively. We present a unified framework detector to comparatively analyze their target detection performance in the Neyman-Pearson sense. Furthermore, the deflection coefficient and signal-to-interference-plus-noise ratio (SINR) are also adopted as a performance metric to compare their performance. Numerical results show that FDA-MIMO radar achieves better target detection performance as compared to other conventional radar systems, specially when multiple coherent pulses are utilized.

A Novel Transmit–Receive System of Frequency Diverse Array Radar for Multitarget Localization

The frequency diverse array (FDA) has drawn substantial attention because it provides a new degree of freedom. However, the multitarget localization is fundamentally limited by the range-angle-coupled and range-periodic beampattern of the basic FDA. It has been suggested to design a special FDA configuration to localize targets, but seldom of the existing works consider the design both in transmitting and receiving. In this paper, a transmit–receive system of FDA radar is proposed for the multitarget localization. In order to decouple the beampattern in the range and angle domains, the configurations of subarray-based FDA (SB-FDA) and full-band FDA (FB-FDA) are chosen as transmitter and receiver, respectively. In such a system framework, the receive beamwidth in range domain is only a quarter of the transmission. Then, two typical multitarget scenarios, sparse targets and unresolved targets, are both considered in the multitarget localization. For sparse targets, a proper frequency increment is selected to control the range-periodic transmit and receive mainlobes to focus on a single target, besides being staggered with others. In this way, multitarget localization is achieved in different pulses with monopulse processing. For unresolved targets, a method of intra-pulse beam scanning is proposed to localize each target with little interference from others. We also analyze the system performance in Cramér-Rao lower bound (CRLB) of localization and output signal to interference-plus-noise ratio (SINR). Several simulation results demonstrate the effectiveness of the proposed transmit–receive system in multitarget localization.

Localization Performance Analysis of FDA Radar Receiver With Two-Stage Estimator

Frequency diverse array (FDA) has received much attention, but little work about FDA receiver architectures and receiver processing algorithms have been reported. In this paper, we analyze the localization performance of FDA radar with a two-stage estimator. Three FDA receive architectures are discussed and compared with the phased-array (PA). In order to overcome disadvantages of the monochromatic FDA radar signal model adopted in the literature that ignores the coherent transmit gain in FDA radar, we formulate a bandwidth model for a general FDA radar received signals including both nonoverlapping and overlapping spectra. The localization performance are assessed by the Cramer–Rao bound (CRB) and receive signal noise ratio. The proposed model provides more accurate representation of FDA radar received signals and more reasonable comparisons between FDA and PA radars. Additionally, a fast two-stage estimator is proposed to reduce the two-dimensional multiple signal classification computation complexity. All proposed methods are verified by both theoretical analysis and numerical results.

Multiple-Frequency CW Radar and the Array Structure for Uncoupled Angle-Range Indication

The frequency diverse array (FDA) radar has drawn great attention due to its range-, angle-, and time-dependent beampattern. However, the FDA radar suffers ambiguities in determining target locations, i.e., angle and range of targets are coupled. In this letter, we find that the key to decoupling the target location lies in destroying the mutual dependence of angle and range. Hence, the multiple-frequency continuous wave (MFCW) radar is proposed. The range measurement is obtained by transmitting continuous waves with multiple frequencies and separating the multiple echoes by digital mixer in the receiving end. The range information exists in the phase difference among the multiple echoes, and this process can be seen as sampling in range by multiple frequencies. Then, if a receiving array is used for spatial sampling, an angle measurement is obtained and the target location is decoupled. Four modes of the MFCW radar are derived and the reason for the uncoupled angle-range indication in the beampattern is analyzed in detail. The effectiveness of the proposed scheme is verified by simulation results.

Time-Invariant Joint Transmit and Receive Beampattern Optimization for Polarization-Subarray Based Frequency Diverse Array Radar

We propose a polarization-subarray based frequency diverse array (FDA) radar with the subarray-based FDA as the transmit (Tx) array and the polarization-sensitive subarray-based FDA (PSFDA) as the receive (Rx) array. The subarray-based FDA has the capability to achieve a single maximum beampattern at the target location, while the PSFDA can provide an extra degree of freedom to further suppress the interference and, thus, to improve the radar's signal-to-interference-plus-noise ratio (SINR). The time-dependent frequency offsets are designed for the proposed radar to realize the time-invariant beampattern at the desired target location over the whole pulse duration. To further improve the target detection performance, the time-invariant joint Tx–Rx beampattern design is considered based on the output SINR maximization. To effectively solve the nonconvex output SINR maximization problem, a suboptimal alternating optimization algorithm is proposed to iteratively optimize the FDA Tx beamforming, the PSFDA spatial pointings, and the PSFDA Rx beamforming. Numerical experiments illustrate that the time-invariant and single-maximum joint Tx–Rx beampattern at the target location is achieved. Moreover, compared to the basic FDA and logarithmic frequency offset FDA as well as conventional phased array radars, the proposed polarization-subarray based FDA radar achieves a significant SINR improvement, particularly when the desired target and the interferences are spatially indistinguishable.

Stepped Frequency Pulse Frequency Diverse Array Radar for Target Localization in Angle and Range Domains

Unlike phased array bringing angle-dependent and range-independent beamforming, a new kind of radar system called frequency diverse array (FDA) has been widely used for its ability to generate angle-range-dependent beampattern, which provides a broad prospect of radar application. Nevertheless, FDA beampattern is coupling in the angle and range responses, which results in the difficulty for FDA to differentiate the target in two domains simultaneously. In this paper, a stepped frequency pulse FDA (SFP-FDA) radar is proposed to wipe off the angle-range coupling in FDA and improve the target’s angle and range localization accuracy. Compared to the double-pulse FDA, the proposed system can achieve a better performance in range resolution and multitarget identification. The Cramér-Rao lower bound (CRLB) is derived and used to analyze the performance of the proposed system and double-pulse FDA radar. Numerical results are implemented to verify the validity of the proposed scheme.

Frequency diverse array radar signal and data processing

The frequency diverse array (FDA) radar is re-explored with a special focus on how the FDA data should be correctly and efficiently processed to maximise its full potential and capacity of search and detection. Some features, such as its extraordinary Doppler tolerance and ability of resolving range ambiguity without using multiple pulse repetition frequencies, are first demonstrated. The extension of non-linear and random frequency increments is proposed in order to suppress range sidelobes and increase range resolution. Wide-area search and detection is achieved by processing the same received data set without a need of electronic scan and repeat pulse transmission and reception. This not only greatly simplifies the radar design and operation but also makes radar quieter and stealth. The limitation of the FDA radar is its sacrificed detection range. Therefore, in comparison with the conventional phased-array radar, the detection area is fan-area-like for the former and pencil-beam-like for the latter, making two radars (or radar operation modes) complementary.

FDA Radar Ambiguity Function Characteristics Analysis and Optimization

Frequency diverse array (FDA) radar provides new application capabilities and potentials due to its range-dependent transmit array beampattern. As radar ambiguity function (AF) is an effective tool to analyze the range (time delay) and Doppler resolution characteristics of various radar systems, this paper derives and analyzes the FDA radar AF characteristics in a general way. These characteristics provide some insights into optimal FDA parameters design and are helpful for comparing delay-Doppler performance of the FDA radar with conventional phased-array radar. Furthermore, this paper optimally designs the frequency increments for better FDA radar AF with the simulated annealing algorithm. The optimization object is to minimize undesired range-angle-dependent sidelobes, so that we can focus the transmit beampattern to desired range-angle sections and simultaneously null undesired interferences. All the derived expressions and methods are verified by numerical results. The results also validate that the FDA indeed offers advantages over traditional phased array in delay-Doppler radar applications.

Beampattern Synthesis for Frequency Diverse Array via Reweighted $\ell _1$ Iterative Phase Compensation

This paper addresses the issue of beampattern synthesis with flexible magnitude response and low sidelobe in a frequency diverse array radar. It is formulated as an optimization problem in terms of $\ell _1$ -norm minimization, which encourages the sparsity of array pattern. An $\ell _1$ iterative phase compensation (IPC) technique is employed to transform the nonconvex constraint to phase compensation form. Then, to further reduce the sidelobe level, a reweighted $\ell _1$ -IPC algorithm is devised, in which a sparsity-enhanced scheme is utilized to convert the $\ell _1$ -norm to a new cost function that more closely resembles $\ell _0$ -norm. Numerical results are presented to demonstrate the effectiveness of the proposed approach in different scenarios.

Cognitive Target Tracking via Angle-Range-Doppler Estimation With Transmit Subaperturing FDA Radar

Cognitive radar is an intelligent active sensing technique, which can learn the interactions between radar and its surrounding environment and adaptively adjust the transmit waveforms or parameters for improved performance. In this paper, we propose a cognitive target tracking scheme via angle-range-Doppler estimation with transmit subaperturing frequency diverse array (TS-FDA) radar. FDA is an emerging array technique that employs a small frequency increment across its array elements to produce a range-angle-dependent beampattern, which provides promising applications for joint angle-range-Doppler estimation of targets. In order to jointly enjoy the advantages of FDA localization in angle-range dimension and phased-array in coherent gain, we divide the FDA elements into multiple subarrays and propose two optimization criteria, respectively, based on signal-to-noise ratio and Cramer–Rao bound, to adaptively design the transmit weight matrix according to the prior knowledge extracted from the cognitive observation data at each transmission updating for improved tracking performance. All proposed approaches are verified by numerical results.

Transmit Beampattern Synthesis for the FDA Radar

The frequency diverse array (FDA) radar has drawn great attention due to the periodicity of the beampattern in range, angle, and time. In this letter, we restudy the recent work that designed a time-invariant beampattern of the FDA radar, which can focus the transmit energy in a desired position. We reanalyze the derivation of the FDA beampattern synthesis and point out the neglected constraint condition, which leads the research of the FDA beampattern synthesis to an impractical direction. By comparing the replication of one of the prior works with our result, we draw a conclusion that it is impossible to obtain a beampattern merely focusing on some specific spatial positions and lasting for some specific time.

Sparsity-aware transmit beamspace design for FDA-MIMO radar

Frequency diverse array (FDA) can produce a range-angle-dependent beampattern due to the employment of a small frequency increment across the array elements. By utilizing this characteristic, this letter devises an FDA and multiple-input multiple-output hybrid radar to jointly estimate the ranges and angles of multiple targets via optimal transmit beamspace design. A uniform elemental power constraint is adopted as the optimization criterion is to minimize the mutual coherence of the sensing matrix using a sparse model and to achieve high-resolution estimation in both range and angle dimensions. A cyclic optimization approach based on power method-like is further developed to solve the non-convex design problem. The excellent performance of the proposed approach is demonstrated via computer simulations.

MIMO-Frequency Diverse Array Radar with Unequal Subarrays for Improved Range-Angle Dependent Beamforming

Frequency diverse array (FDA) radar has been proposed in last decade for joint range and angle beamforming of a target. Multiple input multiple output-frequency diverse array (MIMO-FDA) radar has also been presented recently in literature to steer multiple beams by creating subarrays in transmit array. These beams help to localize the target in range as well as angle dimension. Due to same subarray size, all the beams have same beamwidth and thus exhibit same response for a given target. In this paper, we have proposed an unequal size subarrays structure for the FDA radar (US-MIMO-FDA), which allow us more focusing of the target in range and angle dimension by using beams of variable width. As a result the echoes received at the receiver help in better estimation of target parameters. The effectiveness of proposed scheme has been shown by comparing transmit and received beam patterns of proposed scheme with MIMO-FDA with equal subarrays Performance analysis of proposed scheme has also been done in terms of output signal to interference plus noise ratio, detection probability and cramer-rao lower bound. Simulation and results have verified better focusing of target by proposed design as compared to existing subarrays schemes for MIMO-FDA.

Performance Analysis of Phased Array and Frequency Diverse Array Radar Ambiguity Functions

Performance Analysis of Phased Array and Frequency Diverse Array Radar Ambiguity Functions

Frequency Diverse Coprime Arrays With Coprime Frequency Offsets for Multitarget Localization

Different from conventional phased-array radars, the frequency diverse array (FDA) radar offers a range-dependent beampattern capability that is attractive in various applications. The spatial and range resolutions of an FDA radar are fundamentally limited by the array geometry and the frequency offset. In this paper, we overcome this limitation by introducing a novel sparsity-based multitarget localization approach incorporating both coprime arrays and coprime frequency offsets. The covariance matrix of the received signals corresponding to all sensors and employed frequencies is formulated to generate a space-frequency virtual difference coarrays. By using $\mathcal {O}(M+N)$ antennas and $\mathcal {O}(M+N)$ frequencies, the proposed coprime arrays with coprime frequency offsets enables the localization of up to $\mathcal {O}(M^2N^2)$ targets with a resolution of $\mathcal {O}(1/(MN))$ in angle and range domains, where $M$ and $N$ are coprime integers. The joint direction-of-arrival (DOA) and range estimation is cast as a two-dimensional sparse reconstruction problem and is solved within the Bayesian compressive sensing framework. We also develop a fast algorithm with a lower computational complexity based on the multitask Bayesian compressive sensing approach. Simulations results demonstrate the superiority of the proposed approach in terms of DOA-range resolution, localization accuracy, and the number of resolvable targets.

Elliptical frequency diverse array radars: uniform and non-uniform frequency offsets

ABSTRACTIn this paper a new configuration of Frequency Diverse Array (FDA) i.e. Elliptical Frequency Diverse Array (EFDA) has been proposed. The foresaid geometry has been analyzed with a uniform and non-uniform frequency offset. Analysis reveals highly range selective beampatterns with decreasing average side lobe levels (SLL). The paper further investigates tangent hyperbolic function for non-uniform frequency offset scheme in EFDA. Investigation reveals a 3D single maximum beampattern. Furthermore by utilizing the properties of tangent hyperbolic function, a highly configurable type array system is achieved, where beampatterns of three different configurations of FDA can be generated, by just adjusting a single function parameter.

Time-Invariant Range-Angle-Dependent Beampattern Synthesis for FDA Radar Targets Tracking

The frequency-diverse array (FDA) radar has drawn substantial attention in recent years because of its particular range-angle-dependent beampattern. However, with the linear incremental frequency offset, the basic FDA radar's beampattern is time-variant, range-periodic, and coupled in range and angle dimensions, which limits FDA radar's practical application seriously. In this letter, we propose a novel transmit beampattern synthesis method using the multicarrier FDA architecture and nonlinear time-dependent frequency offset. As a result, a pencil-shaped time-invariant and range-angle-dependent beampattern can be synthesized for target tracking. Furthermore, a time division method is utilized to form multiple narrow pencil-shaped beampatterns for tracking multiple targets within one pulse duration. Simulation results show the effectiveness of the proposed scheme and demonstrate its outperformance via comparison to other existing methods.