Two-dimensional array beam scanning via externally and mutuallyinjection-locked coupled oscillators

The use of arrays of injection-locked voltage-controlled oscillators coupled to nearest neighbors has been proposed as a means of controlling the aperture phase of one and two-dimensional (2-D) phased-array antennas. It has been demonstrated both theoretically and experimentally that one may achieve linear distributions of phase across a linear array aperture by injection locking to an external oscillator the end oscillators of an array of a mutually injection-locked oscillators. These linear distributions cause steering of the radiated beam. It is demonstrated theoretically here that one may achieve beamsteering in a similar manner in two dimensions by injecting appropriately phased signals into the perimeter oscillators of a 2-D array. The analysis is based on a continuum representation of the phase previously developed in the context of beamsteering via tuning of the perimeter oscillators     

A continuum model of the dynamics of coupled oscillator arrays forphase-shifterless beam scanning

The behavior of arrays of coupled oscillators has been previously studied by computational solution of a set of nonlinear differential equations describing the time dependence of each oscillator in the presence of signals coupled from neighboring oscillators. The equations are sufficiently complicated in that intuitive understanding of the phenomena which arise is exceedingly difficult. We propose a simplified theory of such arrays in which the relative phases of the oscillator signals are represented by a continuous function defined over the array. This function satisfies a linear partial differential equation of diffusion type, which may be solved via the Laplace transform. This theory is used to study the dynamic behavior of a linear array of oscillators, which results when the end oscillators are detuned to achieve the phase distribution required for steering a beam radiated by such an array     

On a simple method of obtaining sidelobe reduction over a wideangular range in one and two dimensions

A patented technique for suppressing the sidelobes of an array antenna is considered. This technique involves the addition of two elements, one at each end of the array, which together produce an interferometer pattern used for the cancellation of sidelobes. It is shown here that the technique is most effective for uniform illumination and that there then exists an optimum fixed position for the added elements. The amplitude of the excitation of the auxiliary elements determines the angular location of the region of sidelobe reduction while the phase of the excitation tracks the beamsteering phase of the array. Thus, this technique is seen to be easily implemented in an array controlled by coupled oscillators. The technique generalizes in a straightforward manner to two-dimensional (2-D) arrays in which case a set of auxiliary elements on the perimeter of the array is required. A 2-D oscillator controlled array of this type is described here with which one can produce a main beam and a sidelobe suppression region that can be independently positioned anywhere in a hemisphere provided they do not coincide     

Continuum modeling of the dynamics of externally injection-lockedcoupled oscillator arrays

Mutually injection-locked arrays of electronic oscillators provide a novel means of controlling the aperture phase of a phased-array antenna, thus achieving the advantages of spatial power combining while retaining the ability to steer the radiated beam. In a number of design concepts, one or more of the oscillators are injection locked to a signal from an external master oscillator. The behavior of such a system has been analyzed by numerical solution of a system of nonlinear differential equations which, due to its complexity, yields limited insight into the relationship between the injection signals and the aperture phase. In this paper, we develop a continuum model, which results in a single partial differential equation for the aperture phase as a function of time. Solution of the equation is effected by means of the Laplace transform and yields detailed information concerning the dynamics of the array under the influence of the external injection signals     

A NOVEL PHASE CONTROL TECHNIQUE FOR INJECTION LOCKED OSCILLATORS

A novel technique to obtain injection locked oscillators phase tuning beyond 180° is demonstrated. The idea is to cascade injection locked oscillators together for phase change accumulation. A two stage injection locked oscillators can theoretically provide a maximum of 360?phase change within the locking range. This is particularly useful for phased array antenna applications.     

Steered coupled-cavity-backed Hertzian dipole array

This paper presents the operating characteristics of a coupled-cavity-backed Hertzian dipole resonator array excited with mutually injection-locked voltage-controlled oscillators (VCOs). It is demonstrated that microwave spatial power-combined inter-injection locking through mutual coupling of individual antenna oscillators can be obtained with an auxiliary coupling network formed by a cavity iris configuration introduced within a reduced-height waveguide arrangement. As a result, strong mutual-coupling control can be realized and exploited in conjunction with self-injection-locked oscillators in order to achieve direct phase modulation of the locked oscillators. Beam scanning up to 10° off the broadside through locked VCO phase modification has been demonstrated in a three-element array occupying a space of only 0.6 λ₀×0.027 λ_o at 998 MHz     

Injection Locking in Concurrent Dual-Frequency Oscillators

In a separate paper, the authors show that a nonlinear active core with a fourth-order resonator can generate two stable independent frequencies simultaneously. In this paper, the effect of injecting two frequencies into such a concurrent dual-frequency oscillator is analyzed and experimentally verified. It is shown that, for weak injection, the effect of injection at one frequency is decoupled from the effect of injection at the other frequency. The differential equation describing the effect of injection at either of the two frequencies is similar to the Adler's injection-locking equation for single-frequency oscillators. A theoretical analysis for a linear array of coupled concurrent dual-frequency oscillators is provided. It is shown that a linear phase progression at both frequencies can be achieved independently by detuning the array's end elements. Dual-frequency quadrature signal generation using two coupled concurrent dual-frequency oscillators is also demonstrated. To verify the theoretical derivations, an integrated circuit in a 0.18-$mu$m SiGe BiCMOS process is designed and fabricated. Measurement results closely match the theoretical predictions. The application of concurrent coupled oscillator array in dual-frequency beam forming with steering capability is also demonstrated.      

基于MIMO技术的二维波达方向估计

传统的L型阵相比面阵精简了阵列结构,以较少的阵元实现二维波达方向估计,但是波达方向估计性能受到物理孔径限制。本文将MIMO技术和L型阵结合,提出一种基于MIMO技术的L型阵二维波达方向估计方法。该方法通过MIMO等效虚拟阵列原理,将L型阵等效为一矩形平面阵列,然后在等效矩形阵列的基础上,采用MUSIC进行二维波达方向估计,以L型阵的物理孔径实现矩形平面阵列的估计性能。本文推导了二维波达方向估计的CRB,计算机仿真实验证实了所提方法的有效性。      

Influence of noise intensity on the spectrum of an oscillator

This paper investigates the influence of high-intensity noise on the correlation spectrum of a two-dimensional (2-D) nonlinear oscillator. An exact analytical solution for the correlation spectrum of this 2-D oscillator is provided. The analytical derivations are well suited for oscillators with white noise of any intensity, but computational constraints on the solution of the partial differential equation may make it impractical for cases where the number of state variables exceeds three. The spectral results predicted by our analytical method are verified by numerical simulations of the noisy oscillator in the time domain. We find that the peak of the oscillator spectrum shifts toward higher frequencies as the noise intensity is increased, as opposed to the fixed oscillation frequency predicted in the existing literature. This phenomenon does not appear to have been reported previously in the context of phase noise in oscillators.     

Fixed-Beam Frequency-Tunable Phase-Reversal Coplanar Stripline Antenna Array

A fixed-beam frequency-tunable coplanar stripline (CPS) antenna array using the phase reversal technique and varactor diodes tuning is presented. The antenna array is composed of plurality of half-wavelength CPS sections interconnected by phase reversing crossovers. These crossovers have two functions: they serve as the radiators (small dipoles) of the array and also provide their own required in-phase excitations for broadside radiation. Two microstrip-to-CPS transitions for excitation of the balanced input/output antenna array are implemented and compared. A six-element array is demonstrated theoretically and experimentally, with 9.3 dBi of gain for bidirectional radiation and 12.5 dBi of gain for unidirectional radiation using a back reflector. Moreover, shunt varactor diodes are incorporated along the CPS structure to achieve frequency tuning through a bias voltage control while broadside radiation patterns remain fixed. The return loss and the radiation patterns at several frequencies are presented, and up to 50% tuning range is obtained. The proposed antenna array is simple and uniplanar with small lateral size, high radiation efficiency and high directivity. In addition, it uses a very simple biasing circuit with high DC-RF isolation. Its balanced input/output makes it suitable for RF system integration and active integrated antenna design.     

A demonstration of the coupled oscillator based agile beam receiver concept

The Cao-York concept of using a linear array of mutually injection locked oscillators to provide local oscillator signals for an agile beam receiver is demonstrated using a 15 circuit array of L-band voltage controlled oscillators coupled to nearest neighbors. The concept involves mixing each 1.265 GHz local oscillator (l-o) signal with a corresponding 1.950 GHz signal received by an element in an antenna aperture and combining the resulting 685 MHz intermediate frequency (i-f) signals. A normally incident wave is simulated using a power divider to provide 15 equal in-phase signals to the r-f ports of the mixers and the i-f combining is accomplished using a similar power divider in reverse. The "antenna beam" is steered through this "normally incident wave" by antisymmetrically detuning the end oscillators of the array and a plot of the i-f combiner output represents the receive beam shape. Finally, this system is used to demonstrate the Kott sidelobe suppression technique.     

Sidelobes control of solid-state array antennas

An aperture design is described for two-dimensional (2-D) solid-state phased arrays that transmits low sidelobes. A five-step amplitude distribution for the aperture was optimized by a gradient search method to achieve -36-dB peak sidelobes. The optimized configuration was applied to a sample array of 36 columns by 14 rows, with 400 modules divided into five groups of power levels. The array performance with the actual module lattice structure taken into account is discussed. Gain drop and sidelobe degradations due to random amplitude and phase errors are also studied     

Radiation Pattern Analysis of Uniform Rectangular Planar Arrays for Millimeter Wave Communications: Comparative Study with Uniform Linear Arrays

Radiation patterns of a Uniform Rectangular Planar Array deployed for millimeter wave communications are analyzed. Millimeter wave, as the name suggests, works on very high frequency bands i.e. 28, 38 and 72 GHz bands resulting in reduced antenna size. The size of these antennas are in the range of millimeters and therefore they are integrated on-chip. They can also be steered to achieve very high directivity and channel capacity. Directional antennas are implemented using beamsteering in millimeter wave communications to achieve very high data rates and also high capacity. The data rates are reported to increase by around 40 times as compared to off-chip or external antennas. In this paper, beam patterns for a uniform linear array and a uniform rectangular planar array with beamsteering are analyzed and compared.

     

Discretized Gabor-based beam algorithm for time-harmonic radiation from two-dimensional truncated planar aperture distributions .I. Formulation and solution

In this first part of a two-paper sequence, we develop a Gabor-based Gaussian beam (GB) method for the representation of three-dimensional (3-D) time-harmonic vector electromagnetic fields excited by two-dimensional (2-D) truncated arbitrarily polarized planar aperture field distributions. The biorthogonal Gabor basis is tied to a lattice in the discretized four-dimensional (4-D) [configuration (space)]-[spectrum (wavenumber)] phase space which spans the 2-D aperture plane. This study generalizes previous investigations of the simpler corresponding procedure for 2-D fields excited by one-dimensional (1-D) apertures. By subsequent specialization, in the 1-D aperture case, to narrow-waisted 2-D ray-like GBs, we have shown that tracking such beams through interactions with complex environments and recombining them to synthesize the total 2-D field produces robust, efficient and accurate algorithms that are useful for a variety of forward and inverse scattering scenarios. Extension to the time domain via narrow-waisted pulsed GBs has likewise been considered. These potential applications have motivated the extension here to general 3-D EM fields excited by time-harmonic 2-D truncated apertures. The presentation relates each step in the analytic development to a corresponding step in the 1-D aperture case, thereby highlighting the complications (in the parameterizing phase space) associated with the 2-D aperture problem. The outcome is the formal exact solution of the problem under consideration.     

Phased array antenna analysis with the hybrid finite element method

A new analysis technique for infinite phased array antennas was developed and demonstrated. It consists of the finite element method (FEM) in combination with integral equation radiation conditions and a novel periodic boundary condition for 3-D FEM grids. Accurate modeling of rectangular, circular and circular-coaxial feeds is accomplished by enforcing continuity between the FEM solution and several waveguide modes across an aperture in the array's ground plane. The radiation condition above the array is enforced by a periodic integral equation in the form of a Floquet mode summation, thus reducing the solution to that of a single array unit cell. The periodic boundary condition at unit cell side walls is enforced through a matrix transformation. That mathematically “folds” opposing side walls onto each other with a phase shift appropriate to the array lattice and scan angle. The unit cell electric field is expanded in vector finite elements. Galerkin's method is used to cast the problem as a matrix equation, which is solved by the conjugate gradient method. A general-purpose computer code was developed and validated for cases of open-ended waveguides, microstrip patches, clad monopoles and printed flared notches, showing that the analysis method is accurate and versatile     

The unifying role of the coarray in aperture synthesis for coherentand incoherent imaging

Systems of two-dimensional (2-D) imaging arrays and apertures are considered from the point of view of their performance in the imaging of spatially incoherent as well as coherent source distributions. Such systems find applications in radar, sonar, and ultrasound imaging, as well as in applications such as seismology and radio astronomy. For linear imaging techniques related to beamforming and based on the Fourier transform relationship between the source distribution and the aperture plane measurements, the point spread function of the system completely characterizes its performance. This function is determined by the geometry of the physical aperture or array as well as the weighting that can be applied to measurements. It is shown that the introduction of the concept of coarray, both for receive apertures in incoherent imaging and for transmit/receive systems in reflection-mode coherent imaging, provides a convenient and elegant framework within which many apparently isolated techniques for point-spread function or aperture synthesis can be understood. In addition to this unifying role, coarray concept gives new insight into the aperture synthesis process, which allows interesting new imaging techniques to be developed, especially in coherent imaging     

基于近场测试的相控阵天线自动化校准 与阵面监测方法

相控阵天线装配好之后,由于各组成部件机械加工误差、装配误差、部件老化更换和环境温度改变等因素,各 单元通道的初始幅相产生差异,因此必须对天线的所有系统进行校准。本文针对小型化相控阵平台,通过硬连接将相控 阵天线的波控系统与测试设备相结合,提出一种简便的自动化近场逐点校准方法。同时,本文还提出一种简单的外监测 方法。当相控阵天线工作期间,可对阵面的幅相分布进行监测。可在相控阵天线工作期间,对近场幅相校准数据进行修 正,达到阵面自身校准的目的。经对一个16阵元的相控阵天线进行实验测量可知,该自动化校准与阵面自身校准方法可 以准确、快捷测试出天线阵面的幅相分布。非常适合一维、二维相控阵天线,尤其是小型化相控阵天线的幅相校准与监 测。     

Precise delay generation using coupled oscillators

A new delay generator based on a series of coupled ring oscillators has been developed; it produces precise delays with subgate delay resolution for chip testing applications. It achieves a delay resolution equal to a buffer delay divided by the number of rings. The coupling employed forces the outputs of a linear array of ring oscillators oscillating at the same frequency to be uniformly offset in phase by a precise fraction of a buffer delay. The buffer stage used in the ring oscillators is based on a source-coupled pair and achieves high supply noise rejection while operating at low supply voltages. Experimental results from a 2-μm N-well CMOS implementation of the delay generator demonstrate that it can achieve an output delay resolution of 101 ps while operating at 141 MHz with a peak error of 58 ps     

Analysis and development of a signal injection technique usingtransmission lines embedded at phased array aperture

In a performance monitoring/fault isolation and correction (PM/FIC) system of a phased array antenna, a built-in transmission line embedded in the array aperture is used for signal injection to check the signal flow. The authors present an analysis of electromagnetic coupling between a twin-lead transmission line and a dipole element. An analysis of the coupling between a transmission line and a linear array of dipole elements over a ground plane has also been developed. The calculated data compared with the measured data favorably. A development of microstrip-line signal injectors embedded in an aperture of a 2D array of monopole excited parallel-plate waveguides has also been made. Measurements of the feed and aperture distributions have been made and the measured distributions follow the designed feed distribution closely     

Phase scanning of one-dimensional pattern

A method of determination of phase function required for scanning a one-dimensional pattern is presented. Analysis reveals that the one-dimensional pattern is produced in the meridian plane of a two-dimensional aperture by application of nonlinear phase in the directions along and parallel to this plane. Scanning is produced by application of a linear phase progression in the perpendicular direction. The slope of the linear phase progression is different for different positions along the direction of nonlinear phase distribution. Expressions giving the variation of this slope along the length of the array for various amplitude distributions and desired radiation patterns are derived.