Two-Dimensional Beamforming with Nonsinusoidal Signals

A two-dimensional beamforming technique is presented for two-dimensional arrays of (N × N) sensors receiving plane wavefronts with nonsinusoidal time variations in the form of a single rectangular pulse of duration T or in the form of a coded sequence of rectangular pulses with nominal time duration T. The three-dimensional energy pattern has a main beam for small angles of incidence and a number of sidelobes for large angles of incidence. For wavefronts with rectangular time variations, the maximum sidelobe has the magnitude 1/N and, for coded time variations, the maximum sidelobe exceeds 1/N. The magnitude of the sidelobes of the energy pattern can be decreased by increasing the number of sensors in the array. The resolution angle can be decreased by the ratio (N1/N2) when the number of sensors is increased from (N1 × N1) to (N2 × N2) and it can be decreased by the ratio (T1/T2) when the nominal time duration is decreased from T2 to T1. Waveform distortion results in a degradation of the resolution angle.     

A self-steering array for nonsinusoidal waves based on arrayimpulse response measurement

An array antenna consisting of identical distortion-free sensors used for the reception of nonsinusoidal waves with finite bandwidth is modeled as a linear time-invariant causal system. It is shown that the impulse response of the array sensors is a function of the angle of incidence of the received wavefront. Based on this model, a self-steering array system for beam forming with noise-free rectangular pulses is developed. Its beam-forming mechanism determines the array impulse response to point a main beam in the direction of the source from which the waves are arriving. The array system is advanced further so that nonsinusoidal waves that suffer distortions due to scattering from a large scatterer, and/or dispersive propagation, can be processed to form a main beam in the direction of the scatterer, and to achieve classification and identification of the unknown scatterer     

智能天线中一种新的三维波束形成方法

提出了用分布于 x?y?z 三轴上的三个阵元估计扩频信号各条多径的来波方向(DOA)的方法,以及用由 x?y 均匀平面圆阵和 z 轴直线阵组成的阵列天线形成 3 维波束的方法。根据 CDMA 信号模型和多径信道模型,用 最大似然(ML)法分别估计出信号到达 3 个阵元的复信道响应,并利用复信道响应的幅角来估计各条多径信号 的 DOA;然后在已有最小均方误差(MMSE)法和最小二乘(LS)法的基础上生成带限制条件的扩展 MMSE(EMMSE)法形成 3 维波束。模拟表明,给出的 DOA 估计方法具有很高的精度,而 EMMSE 方法形成的波束主 瓣窄,旁瓣被抑制,有很高的输出信干噪比。     

Synthetic-Aperture Radar Based on Nonsinusoidal Functions: IX ?Array Beam Forming

For sinusoidal waves with bandwidth zero, one obtains the classical formula ? = ? ?/ L = ?c/fL for the resolution angle of a sensor array, where L is the length of the array, ? the wavelength, f the frequency, and c the phase velocity of the wave, while ? is a constant whose value is usually chosen to be 1. Waves with the time variation of a rectangular pulse of duration ?T yield the resolution angle e = 2?cf?P/PN, where P/PN is the signal-to-noise ratio and ?f = 1/2?T the nominal bandwidth of the pulse; the same result holds for coded pulse sequences, such as Barker codes or complementary codes, if the main lobe of their auto-correlation function has the shape of a triangle with rise time ?T. Hence, the resolution angle e can be reduced by increasing the signal power, as well as by increasing the array length L or the bandwidth ?f. For sinusoidal waves, an increase of the signal power brings no reduction of the resolution angle. The trade between signal power and frequency bandwidth is of interest whenever the attenuation increases rapidly with frequency, e.g., in high-resolution all-weather radar or in underwater acoustic beam forming.     

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     

一种空间谱估计测向中的低旁瓣电平波束合成算法

基于低旁瓣电平波束合成技术,是在旁瓣区域利用大量的干扰信号控制波束合成,通过迭代形成最优化权向量,主波束指向期望信号方向,旁瓣达到设计要求,使得空间谱估计测向的性能大大提高。该技术不仅适用于园阵也同样适用于线阵。计算机仿真结果证明了这种方法的正确性和有效性。     

Performance analysis and advancement of self-steering arrays fornonsinusoidal waves. I

The principle of a self-steering array system which has been developed in theory for beam forming with nonsinusoidal waves is analyzed and computer-simulated. A tradeoff between the maximum-scan angle of the array system, the array length, the operating frequency bandwidth, and the signal power for a small-resolution angle is established. Such a tradeoff is desirable in practice, but is not applicable to the conventional method of beam forming with zero-bandwidth sinusoidal waves. A design criterion for the optimal reception of nonsinusoidal waves by a linear array of sensors is established. The simulation results of the signal processor of the self-steering array system show that the beam-steering mechanism based on slope processing is efficient in the absence of thermal noise. The principle of the signal processor is slightly modified to enhance its performance in practice. The design of a variable-delay circuit that uses a charge-transfer device is presented. A novel mechanism of delay-time adjustment is developed for the self-steering array system to improve its response time     

Synthetic-Aperture Radar Based on Nonsinusoidal Functions: X-Array Gain, Planar Arrays, Multiple Signals

Beam forming based on a line array of sensors and radio signals with a triangular autocorrelation function was discussed in Part IX of this series. The resolution angle e was shown to vary like 1/?P/PN with the signal-to-noise ratio P/PN, which puts a premium on getting the best possible signal-to-noise ratio. This paper shows that the signal-to-noise ratio holding for one sensor can be replaced by the signal-to-noise ratio holding for the whole array, which usually is referred to as making use of the array gain. The result is generalized from the one-dimensional line array to the two-dimensional planar array. Furthermore, the method of beam forming is extended from signals returned by point-like scatterers or reflectors to structures composed of several point-like scatterers; the utilization of the array gain has not yet been investigated for this case.     

A Self-Steering Array for Nonsinusoidal Waves

A self-steering array system is described for beam forming with nonsinusoidal waves. The array system electronically steers a main beam in the direction of the source from which the wavefront is arriving without prior knowledge of the source locatiora. The principle of monopulse tracking radar is applied to the array system so that the angular coordinate of tihe source can be determiined with respect to the array axis. If the source is in rmotion, it can be tracked on pulse-to-pulse bases. Finally, the self-steering array system is advanced further to suppress the additive thermal noise presenit with the incoming signals, and to achieve good angular resolution and accuracy.     

Three-Dimensional Antenna Patterns for Nonsinusoidal Waves

Array beam forming with nonsinusoidal waves allows a trade-off between signal power, frequency bandwidth, and array size for a small resolution angle. In addition, one can derive various antenna patterns with desiralble features for achieving good angular resolution. Such patterns are peak-amplitude, peak-power, ramp-duration, flat-duration, energy, and slope patterns that have been derived for linear arrays. In this paper, the principle of beam forming with noise-free nonsinusoidal waves received by rectangular planar arrays is discussed. Three-dimensional peak-amplitude, energy, and slope patterns are derived for planar arrays with 4 × 4, 8 × 8, 16 × 16, and 32 × 32 sensor elements.     

On the Effect of Absorbing Materials on Electromagnetic Waves with Large Relative Bandwidth

Coats of absorbing material over metallic surfaces can substantially reduce the energy of a returned radar signal. This paper analyzes the effect of such coatings on radar signals with large relative bandwidths close to 1, rather than the conventional relative band- widths in the order of 0.01 or less. Normal incidence of the wave, and absorption due to ohmic losses are assumed. The purpose of the paper is strictly to draw attention to the significance of a change from small to large relative bandwidths, since the decades of work on the reflection of sinusoidal waves with various angles of incidence by targets with various shapes, constructed with a variety of materials, cannot be duplicated for nonsinusoidal waves with less than corresponding decades of effort.     

Scanning capabilities of large parabolic cylinder reflector antennas with phased-array feeds

Two methods of scanning large parabolic cylinder antennas are examined: one method moves a small array across the focal plane to form a scanning beam; the other method employs a larger stationary array which is capable of electronically scanning the beam. With conventional single-element feeds, the maximum possible scan angle decreases with increasing reflector size. With array feeds, however, the scan limits are shown to be independent of reflector size and antenna gain. Antennas with movable array feeds are found to have high performance (high gain and low sidelobes) even when scanned more than ten degrees off axis; antennas with stationary array feeds degrade rapidly beyond about one degree of scan because of aperture blockage. Off-axis designs which eliminate the aperture blockage are shown to extend the coverage of antennas with stationary feeds to aboutpm 5degrees.     

Target Detection and Localization Using MIMO Radars and Sonars

In this paper, we propose a new space-time coding configuration for target detection and localization by radar or sonar systems. In common active array systems, the transmitted signal is usually coherent between the different elements of the array. This configuration does not allow array processing in the transmit mode. However, space-time coding of the transmitted signals allows to digitally steer the beam pattern in the transmit in addition to the received signal. The ability to steer the transmitted beam pattern, helps to avoid beam shape loss. We show that the configuration with spatially orthogonal signal transmission is equivalent to additional virtual sensors which extend the array aperture with virtual spatial tapering. These virtual sensors can be used to form narrower beams with lower sidelobes and, therefore, provide higher performance in target detection, angular estimation accuracy, and angular resolution. The generalized likelihood ratio test for target detection and the maximum likelihood and CramÉr–Rao bound for target direction estimation are derived for an arbitrary signal coherence matrix. It is shown that the optimal performance is achieved for orthogonal transmitted signals. Target detection and localization performances are evaluated and studied theoretically and via simulations.     

Isophoric arrays-massively thinned phased arrays withwell-controlled sidelobes

Traditional filled phased arrays have an element placed in every location of a uniform lattice with half-wavelength spacing between the lattice points. Massively thinned arrays have fewer than half the elements of their filled counterparts. Such drastic thinning is normally accompanied by loss of sidelobe control. This paper describes a class of massively thinned linear and planar arrays that show well-behaved sidelobes in spite of the thinning. The term isophoric is derived from Greek roots to denote uniform weight. In isophoric arrays, element placement based on difference sets forces uniformly weighted spatial coverage. This constraint forces the array power pattern to pass through V uniformly spaced, equal, and constant values that are less than 1/K times the main beam peak, where V is the aperture size in half-wavelengths and K is the number of elements in the array. The net result is reduced peak sidelobes, especially when compared to cut-and-try random-placement approaches. An isophoric array will exhibit this sidelobe control even when the array has been thinned to the extent that K is approximately the square root of V. Where more than one beam must be generated at a time, isophoric array designs may be used to advantage even within a traditional filled array. By “interweaving” two isophoric subarrays within a filled array and by appropriate cyclic shifting of the element assignments over time, two independent antenna power patterns can be generated, each with a sidelobe region that is approximately a constant value of 1/(2K) relative to the main beam, where K is the number of elements in the subarray     

非正弦时域正交编码调制及其功率谱分析

针对传统非正弦时域正交调制(Nonsinusoidal Orthogonal Modulation in Time Domain,NOTDM)系统多址复用容量有限的问题,提出一种基于正交或准正交序列的非正弦时域正交编码调制方法。给出了系统的调制模型和数学表达式,理论推导了调制信号的功率谱表达式并仿真分析了采用不同编码的调制信号的功率谱。理论和结果表明,与非正弦时域正交调制信号相比,编码调制后的信号功率谱能保持原有包络,但是会产生离散谱,提高功率谱旁瓣值.采用自相关性能好的序列进行编码可以降低离散谱的谱线。     

Antenna patterns of nonsinusoidal waves with the time variation ofa Gaussian pulse II

For pt.I see ibid., vol.30, no.4, p.504 (1988). In Part I of this series of papers, antenna patterns for nonsinusoidal waves with the time variation of a Gaussian pulse, received (or radiated) by a linear array of sensors (or radiators) were derived. Computer plots of the peak-amplitude pattern, peak-power pattern, energy pattern, and slope pattern were presented. In this paper, the above antenna patterns are derived for a planar array of sensors (or radiators) receiving (or radiating) Gaussian pulses. Based on the characteristics of the Gaussian pulse, which are presented in Part I, the principle of frequency-domain array beam forming with Gaussian pulses is described. An expression for the antenna energy pattern based on the frequency-domain analysis is derived and plotted for comparison to the one obtained in Part I from the time-domain analysis     

大型阵列天线子阵划分及栅瓣抑制方法

利用遗传算法(genetic algorithm, GA)将大型阵列划分为非均匀邻接子阵,以主旁瓣比作为适应度函数,并对遗传操作增加约束条件,得到具有栅瓣抑制能力的子阵结构。提出了基于子阵级的波束扫描方法,在每个扫描分区内无需改变阵元权值,仅通过子阵级数字波束形成即可完成阵列的波束扫描,并分析了不同扫描角对阵列方向图的影响。为了抑制大扫描角带来的高旁瓣,运用自适应原理使子阵级方向图在高旁瓣位置形成凹陷。分析与仿真结果表明,该方法能够进一步提高阵列方向图的主旁瓣比,增加扫描分区的范围。      

Analysis of transmit beamforming performance on multiple-transmit binary ZCZ waveforms

The Transmit BeamForming (TBF) technology, applied in a multiple-transmit radar system, is studied in this paper, where multiple elements of antenna array transmit binary Zero Correlation Zones Orthogonal Signals (ZCZ-OS) independently. For each Direction Of Arrival (DOA) with respect to the transmitting array, the analysis on the gain and sidelobe level of TBF output is presented. This paper focuses on the range sidelobes performance within the main beam (in angle domain). For the normal direction, due to the inherent phase property of ZCZ-OS, the TBF output has part zero sidelobes area, of which the distribution is discussed. For the other directions, a systematic search algorithm to optimize the transmission order of signals is proposed for an optimal relationship chart of DOA and transmission order. The range sidelobe performance within the main beam can be improved as the optimal transmission order is adopted.     

Conformal microstrip phased array for aircraft tests with ATS-6

The development of a novelL-band microstrip phased array for aircraft is described. The array is electronically steerable in elevation, conformal to the surface of an aircraft, 0.14-in thick, low cost in production quantities, installed without cutting large holes in the aircraft, and capable of 12-dB gain relative to right hand circular isotrope. The microstrip radiating element is described, and its operation is explained. The array design is considered in relation to ground plane curvature, grating lobes, sidelobes, beam shape and gain. A technique for obtaining30degphase resolution from 3-bit phase shifters is presented. The design of simple loaded line and switched line phase shifters is reported.     

A Self-Steering Two-Dimensional Planar Array for Nonsinusoidal Waves

The principle of a one-dimensional self-steering array system for beam forming with nonsinusoidal waves has been developed previously. In this paper, an adaptive antenna system consisting of a two-dimensional planar array of sensor elements and a real-time adaptive receiver processor is described. The sensor elements of the planar array are arranged into rows and columns so that the steering commands for the azimuth ald elevation directions can be generated separately. The array system electronically steers a beam in the direction of the source from which the waves are arriving without prior knowledge of the source location.