Adaptive Array Theory Research Articles

Beampattern Synthesis Based on Novel Receive Delay Array for Mainlobe Interference Mitigation

This paper investigates beampattern synthesis methods based on a novel Receive Delay Array (RDA) to mitigate interferences located in the mainlobe of the beampattern. In our system design, the RDA is developed by transmitting a stepped frequency linear frequency modulation waveform and delaying the received echo with a small time offset between adjacent receive antenna elements. In doing so, a range-angle-dependent beampattern is obtained in the joint transmit-receive spatial domain. A two-stage beamforming scheme, including the equivalent data-independent transmit beamforming and dimension-reduced data-dependent receive beamforming, is then proposed to mitigate mainlobe interferences. Furthermore, according to the adaptive array theory, by designing a transmit weight vector dependent of the interference steering vector, two beampattern synthesis algorithms are developed respectively based on the maximum gain and minimum deviation to adjust multiple responses of the transmit beampattern precisely. The mainlobe of the receive beampattern is also broadened with the use of the derivative constraint. By combining the devised transmit and receive weight vectors, a two-dimensional joint transmit-receive beampattern with a flat-top mainlobe and broadened nulls can be formed, where the interferences are mitigated against the direction-of-arrival (DOA) mismatch. Theoretical and practical analysis as well as parametric studies are provided to demonstrate the effectiveness of the proposed beampattern synthesis methods in mitigating mainlobe interferences.

Design of Real-Valued Wideband Beamformers Using an Adaptive-Array-Theory-Inspired WLS: Theory and Algorithm

The weighted least squares (WLS)-based beamformer design can achieve flexible beampattern control via adjusting the WLS weighting function inspired by the adaptive array theory (AAT). Nevertheless, the weighting function is conventionally adjusted in an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ad hoc</i> way, and precise beampattern control cannot be guaranteed. Although an analytical solution for the weighting function adjustment was proposed very recently, it is only applicable to complex-valued narrowband beamformers. In some applications such as acoustic/seismic array processing, however, real-valued wideband beamformers are required, since acoustic/seismic signals are usually unmodulated, real-valued and wideband. This paper studies the theory and design of real-valued wideband beamformers using an AAT-inspired WLS, which can achieve precise wideband beampattern control. The main contributions of this paper include: i) we theoretically prove the existence of the WLS weighting function for the real-valued wideband beamformers to achieve precise control of wideband beampatterns, and derive the corresponding analytical solutions; ii) we provide the insights into the impact of the weighting function on the cost function, which is useful to find the optimum solution for the weighting function among multiple feasible solutions; and iii) we propose an algorithm for the design of real-valued wideband beamformers using the proposed AAT-inspired WLS, which does not require to fine-tune any user parameters, and can guarantee precise control of wideband beampatterns as demonstrated by the simulation results.

MPARC: A fast beampattern synthesis algorithm based on adaptive array theory

This paper presents a multi-point array response control (MPARC) algorithm to realize fast beampattern synthesis. The MPARC algorithm stems from adaptive array theory, and it can adjust the array response at multiple angles, either simultaneously or individually. The designed weights are constructed as a linear combination of an initial weight vector and multiple steering vectors multiplied by different complex factors. Since the update of the designed weights would change the beampattern in the entire spatial domain, the minimum pattern distortion criterion is established to design the complex factors, and a closed-form weight vector is obtained. Moreover, a pattern synthesis scheme based on the MPARC algorithm is presented to synthesize focused and shaped beampatterns efficiently. The comparison with the existing oblique projection-based algorithms shows that the presented MPARC algorithm can achieve multi-point response adjustment with much lower computational complexity, and the angle omission problem is addressed in this paper. Numerical results are provided to demonstrate the performance of the MPARC algorithm in array response control and the efficiency in pattern synthesis.

An Analytical Solution for Weighted Least-Squares Beampattern Synthesis Using Adaptive Array Theory

The adaptive array theory has been successfully employed to the weighted least-squares (WLS)-based beampattern synthesis of arbitrary arrays for adjusting the weighting coefficients of WLS cost function, which enables flexible control of both mainlobe and sidelobe responses. However, the problem with the existing WLS beampattern synthesis approach is that the weighting coefficients, interpreted as “artificial interferers,” are adjusted in an ad hoc way since some key user parameters used therein need to be chosen via a tedious trial-and-error process. Moreover, it may not guarantee that the desired beampattern control objective can be met. To deal with the problem, this communication establishes theoretically the relationship between the weighting coefficients of WLS cost function and the desired array response and proposes an analytical solution for the WLS beampattern synthesis, which can guarantee the objective of desired beampattern control without fine-tuning of any user parameters. The effectiveness of the proposed solution is further verified by several numerical examples of beampattern synthesis for linear and planar arrays.

Flexible Array Response Control via Oblique Projection

This paper presents a flexible array response control algorithm via oblique projection, abbreviated as FARCOP, and its application to array pattern synthesis. The proposed FARCOP algorithm stems from the adaptive array theory, and it can flexibly, precisely and simultaneously adjust the array response levels at multiple angles based on an arbitrarily given weight vector. Different from the existing approaches, the proposed FARCOP algorithm controls multi-point responses by linearly transferring the given weight vector, with a transformation matrix containing a set of parameters, each of which can be very easily determined by the desired response level (at the control angle). Owing to the fact that those parameters are independent of each other, the response levels at the control angles can be either individually or jointly and, therefore, flexibly adjusted. Since the parameter phases can be arbitrary, we take the beampattern into account and propose to uniquely choose the optimal parameters under the typical criterion of maximum white noise gain (WNG). Accordingly, a gradient projection (GP) algorithm is devised to achieve the optimal solution. Moreover, a closed-form solution is derived for the centro-symmetric array. In addition, the application of the FARCOP algorithm to pattern synthesis is discussed. Comparing to the state-of-the-art methods like multi-point accurate array response control (MA <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> RC), the proposed FARCOP algorithm controls the array responses more flexibly with lower computational complexity. Representative examples are presented to demonstrate the effectiveness and superiority of the FARCOP algorithm under various situations.

OPARC: Optimal and Precise Array Response Control Algorithm—Part I: Fundamentals

In this paper, the problem of how to optimally and precisely control array response levels is addressed. By using the concept of the optimal weight vector from the adaptive array theory and adding virtual interferences one by one, the change rule of the optimal weight vector is found and a new formulation of the weight vector update is thus devised. Then, the issue of how to precisely control the response level of one single direction is investigated. More specifically, we assign a virtual interference to a direction such that the response level can be precisely controlled. Moreover, the parameters, such as the interference-to-noise ratio, can be figured out according to the desired level. Additionally, the parameter optimization is carried out to obtain the maximal array gain. The resulting scheme is called optimal and precise array response control (OPARC) in this paper. To understand it better, its properties are given, and its comparison with the existing accurate array response control algorithm is provided. Finally, simulation results are presented to verify the effectiveness and superiority of the proposed OPARC.

Pattern Synthesis for Arbitrary Arrays via Weight Vector Orthogonal Decomposition

This paper presents a new scheme based on Weight vector ORthogonal Decomposition (WORD) to control the array response at a given direction and a novel WORD-based approach to pattern synthesis for arbitrary arrays. The central concept of the proposed methods stems from the adaptive array theory. More precisely, it is found that the inverse of the noise-plus-interference covariance matrix in adaptive beamforming can be regarded as a linear combination of two orthogonal projection matrices, and, accordingly, the optimal weight vector is a linear combination of two orthogonal vectors. With such an observation, the WORD scheme is developed to design the desired weight vector. It is shown that the array response at a given direction can be precisely adjusted to an arbitrary level, by simply determining appropriate combination coefficients for those two orthogonal vectors. Furthermore, a closed-form expression of the weight vector can be achieved by introducing a new cost function that measures pattern variation. By employing the WORD scheme successively, a novel approach to pattern synthesis for arbitrary arrays is devised. At each implementation step of this approach, the array pattern is adjusted in a point-by-point manner by successively modifying the weight vector. As such, both the sidelobe and mainlobe regions can be flexibly synthesized. Numerical examples are provided to demonstrate the effectiveness and flexibility of the WORD scheme in array response control at a single direction as well as pattern synthesis.

$\text {A}^\text {2}\text {RC}$: An Accurate Array Response Control Algorithm for Pattern Synthesis

This paper presents a novel accurate array response control algorithm, abbreviated as A 2 RC, and its application to array pattern synthesis. The proposed A 2 RC algorithm deals with the problem of how to accurately control the array response at a given direction. Starting from the adaptive array theory, a deep analysis of the optimal weight vector is carried out. It is found that the normalized response at a given direction can be accurately adjusted to an arbitrary level, by means of making some simple modification to the initial weight vector. On this basis, all possible weight vectors, which have a specific form and can make the normalized response at the given direction equal to the prescribed value, are first figured out. Then, an effective approach to selecting the most appropriate one, which would cause the least pattern distortion, is devised. By applying the A 2 RC algorithm, a new pattern synthesis approach for arbitrary arrays is developed. In this approach, the array pattern is adjusted in a point-by-point manner by successively modifying the weight vector. Contrary to the conventional approaches that assign artificial interferences in an ad hoc way, our approach is able to obtain the weight vector without iteratively determining the powers of the artificial interferences. Extensive simulation results are provided to demonstrate the performance of the A 2 RC algorithm in array response control and the effectiveness of this algorithm in pattern synthesis under various situations.

Generalized 2-D Numerical Pattern Synthesis Algorithm for Low Cross Polarization and Low Sidelobe Synthesis

Numerical pattern synthesis (NPS) algorithm based on adaptive array theory is an effective spatial power pattern synthesis method for antenna arrays. In this letter, instead of using the artificial interferences weighted on the total power pattern in the conventional NPS algorithm, a generalized two-dimensional (2-D) NPS algorithm is proposed in which two weighting functions are assigned to control the copolarization and cross-polarization patterns, respectively. The weighting functions are iteratively updated until both the sidelobe and cross-polarization levels reach their prescribed ones. Two numerical examples for synthesizing the patterns of a linearly polarized planar array and a circularly polarized cylindrical array are provided to validate effectiveness and advantages of the proposed generalized 2-D NPS algorithm.

CR-Calculus and adaptive array theory applied to MIMO random vibration control tests

Performing Multiple-Input Multiple-Output (MIMO) tests to reproduce the vibration environment in a user-defined number of control points of a unit under test is necessary in applications where a realistic environment replication has to be achieved. MIMO tests require vibration control strategies to calculate the required drive signal vector that gives an acceptable replication of the target. This target is a (complex) vector with magnitude and phase information at the control points for MIMO Sine Control tests while in MIMO Random Control tests, in the most general case, the target is a complete spectral density matrix. The idea behind this work is to tailor a MIMO random vibration control approach that can be generalized to other MIMO tests, e.g. MIMO Sine and MIMO Time Waveform Replication. In this work the approach is to use gradient-based procedures over the complex space, applying the so called CR-Calculus and the adaptive array theory. With this approach it is possible to better control the process performances allowing the step-by-step Jacobian Matrix update. The theoretical bases behind the work are followed by an application of the developed method to a two-exciter two-axis system and by performance comparisons with standard methods.

Synthesis of Conformal Arrays With Optimized Polarization

Adaptive array theory is applied to a conformal antenna array to synthesize a main beam with optimized polarization employing dual polarized patch antennas as radiators. The required polarization in the main beam region of the array is realized by combining the weighted individual feeding ports of the patch antennas before the beam forming optimization is performed. This significantly reduces the number of unknowns in the beam forming optimization problem compared to previous optimization schemes for conformal arrays with optimized polarization properties. A numerical example for an array of dual fed linear patch antennas conformal to a spherical surface is presented. Measured pattern data for the patches are used to synthesize a main beam with specific linear polarization.

An Innovative Computational Approach Based on a Particle Swarm Strategy for Adaptive Phased-Arrays Control

In this paper a new approach to the control of phased arrays is presented and assessed. Starting from the adaptive array theory, a particle swarm strategy is used to tune the phase coefficients of the array in order to adaptively minimize/avoid the effects of interfering signals at the receiver. To show the effectiveness of the proposed approach, a selected set of numerical examples, concerned with linear as well as planar arrays, is presented. Furthermore, to evaluate the advantages of the particle swarm optimizer (PSO)-based strategy over state-of-art methods, a comparative study is carried out by analyzing the performance of the method in terms of both the signal-to-interference-plus-noise-ratio and resulting beam pattern. The achieved results, even though preliminary, seem to confirm that the PSO-based approach satisfactorily works and it generally outperforms previously proposed/state-of-art phase-only adaptive control strategies

Electronically steerable parasitic array radiator antenna

AbstractThe electronically steerable parasitic array radiator antenna consists of one feed radiating element and parasitic radiating elements placed in the near field of the active radiator. A beam is formed due to spatial electromagnetic field coupling among radiating elements. The radiation pattern is electronically controlled by means of the variable capacitance devices (varactors) loading the parasitic elements. Unlike a conventional phased array, only one transmitter and receiver are needed for system configuration. Therefore, adaptive beamforming of low dissipation power and low fabrication cost can be achieved. On the other hand, there is only one output port to observe the signal and the weights can be controlled indirectly via reactors instead of direct control. In addition, due to interelement mutual coupling and the parasitic element being directly connected to the reactive device, the linear adaptive array theory developed to date cannot be applied straightforward. In this paper, the configuration of this antenna, its operating principle and formulation, and its measurement method, control scheme, and applications to signal processing are presented. We describe a mathematical model to simulate the radio frequency behavior of the antenna, the equivalent weight vector used for formulation of the characteristics, the admittance matrix including varactors, the effective element length, the equivalent steering vector method, the method for effectively extending the variable range of the capacitance of the varactor, the reactance circuit to cancel nonlinear distortions, the method for calibration of varactors and radiation pattern by measurement of near field of the radiating element, the learning criteria used to control radiation patterns autonomously in adaptation to the electromagnetic environment, the reactance optimization algorithm, the concept of the reactance domain signal processing and the direction of arrival estimation based on such a process, and diversity reception and spatial correlation. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 87(10): 25–45, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20081

相互結合を考慮したアダプティブアレー理論による指向性合成

相互結合を考慮したアダプティブアレー理論による指向性合成

Pattern synthesis for arbitrary arrays using an adaptive array method

This paper presents a new pattern synthesis algorithm for arbitrary arrays based on adaptive array theory. With this algorithm, the designer can efficiently control both mainlobe shaping and sidelobe levels. The element weights optimize a weighted L/sub 2/ norm between desired and achieved patterns. The values of the weighting function in the L/sub 2/ norm, interpreted as imaginary jammers as in Olen and Compton's (1990) method, are iterated to minimize exceedance of the desired sidelobe levels and minimize the absolute difference between desired and achieved mainlobe patterns. The sidelobe control can be achieved by iteration only on sidelobe peaks. In comparison to Olen and Compton's method, the new algorithm provides a great improvement in mainlobe shaping control. Example simulations, including both nonuniform linear and planar arrays, are shown to illustrate the effectiveness of this algorithm.

Pattern synthesis of array antennas with arbitrary elements by simulated annealing and adaptive array theory

A method to carry out the pattern synthesis of arbitrary array antennas is presented. This method uses the simulated annealing technique to calculate the power interferences described in the Olen–Compton method. Its application to a linear array of 16 unequally spaced nonidentical elements and to a circular arc array of 25 axial dipoles is shown in order to illustrate its efficiency and accuracy. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 20: 48–50, 1999.

Pattern synthesis of array antennas with arbitrary elements by simulated annealing and adaptive array theory

A method to carry out the pattern synthesis of arbitrary array antennas is presented. This method uses the simulated annealing technique to calculate the power interferences described in the Olen–Compton method. Its application to a linear array of 16 unequally spaced nonidentical elements and to a circular arc array of 25 axial dipoles is shown in order to illustrate its efficiency and accuracy. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 20: 48–50, 1999.

Pattern synthesis in small phased arrays using adaptive array theory

A pattern synthesis technique for low sidelobe difference and scanned beams in small phased arrays is presented. The approach is based on adaptive array theory and is a development of a technique used for beam synthesis in an ideal, λ/2 spaced, isotropic array. The method has been applied to measured element pattern data from a five element linear array, which includes the effects of pattern corruption by mutual coupling. The successful synthesis of low sidelobe sum and difference beams are demonstrated, with the look direction on and scanned off boresight.

Numerical pattern synthesis of difference beams in conformal arrays

A numerical pattern synthesis technique for low and shaped sidelobe difference beams is described. The approach is based on adaptive array theory and is a modification of a technique developed for sum beam synthesis. The method has been applied to a conformal array and the results of synthesising low sidelobe ( –40 and –50 dB) difference beams are presented.

A numerical pattern synthesis algorithm for arrays

A numerical technique for pattern synthesis in arrays is presented. For a given set of elements, the technique allows one to find a set of array coefficients that steer the main beam in a given direction and yield sidelobes meeting a specified criterion, if such a set of array coefficients exists. If the pattern specifications cannot be met with the given elements, the algorithm finds the best attainable pattern. The advantage of this technique is that it can be used with an arbitrary set of array elements. Different elements in the array can have different element patterns, and the array can have arbitrary nonuniform spacing between elements. The synthesis technique is based on adaptive array theory. The given array elements are assumed to be used as the elements of an adaptive array. The main beam is pointed in the proper direction by choosing the steering vector for that direction, and the sidelobes are controlled by introducing a large number of interfering signals at many angles throughout the sidelobe region. The algorithm iterates on the interference powers until a suitable pattern is obtained.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>