On grating nulls in adaptive arrays

The effect of element patterns on grating nulls in adaptive arrays is considered. Two simple array models, a two-element and a three-element array with dipole element patterns, are used to study this question. The element patterns are assumed unequal (i.e., the beam maxima point in different directions). It is shown that element patterns greatly affect the occurrence of grating nulls in the array. Unequal element patterns cause extra grating nulls ("sign reversal grating nulls") to occur, in addition to conventional grating nulls. These sign reversal grating nulls can occur even with element spacing less than a half-wavelength. For a two-element array with dipole element patterns, it turns out that grating nulls cannot be avoided if the spacing is greater than a half-wavelength. However, with more than two elements, the situation is not so bleak. An example is given of a three-element array with dipole patterns and one-wavelength spacing in which all grating nulls are eliminated.     

Null steering in linear arrays by using amplitude control of signals in the feeder network

A method of steering nulls in linear arrays by using amplitude control, rather than phase shifters, is described. The system is extended to steer all of the independent nulls in an array of any size. The problem of grating nulls is briefly discussed, and it is shown how an automatic null-steering array can be designed.     

Null steering using the minimax approximation by controlling only the current amplitudes

A linear programming technique using the minimax approximation to steer the nulls of an array by controlling the current amplitudes is presented. The technique determines the current amplitudes that produce the minimum sidelobe level for a given beam width and prescribed nulls in arbitrary directions. The results show the ability of this technique to steer the nulls in the sidelobe region while maintaining the main beam directed towards the desired signal. This technique also allows the number of controlled nulls to attain the full degrees of freedom for the array.     

Phase-only synthesis of nulls in the sum and difference radiation patterns of the phased array antenna of a coordinate meter

Two approaches to the phase-only synthesis of nulls in radiation patterns (RPs) of the phased array antenna (PAA) of a coordinate meter are considered. The approaches use the specificity of the structure of the sheet of the measuring PAA. Such a PAA forms the sum RP and two difference RPs, which ensure measuring of the angular coordinates of an object. The problem of the phase-only synthesis of pattern nulls in prescribed directions in one or several PAA RPs with the angular orientation of the nulls of difference RPs kept in the RP scanning direction is solved. Design relationships are derived and a RP synthesis method, which is based on iterative univariate minimization of a nonlinear functional and includes analytic determination of the minimum of this functional at each iteration, is described. Examples of the array pattern synthesis are presented. The effect the phasing increment on the depth of formed nulls is analyzed and the dependence of the value of the PAA RP in the scanning direction on the position of the formed null is investigated. The effect of synthesized nulls on the shape of the PAA direction-finding characteristic is analyzed.     

The convex geometry of subchannel attenuation coefficients inlinearly precoded OFDM systems

Channels with spectral nulls are sometimes dubbed bad channels because they can cause poor performance in communication systems. This article investigates the validity of this intuition by studying the geometry of an orthogonal frequency-division multiplex (OFDM) system. It is shown that the subchannel attenuation coefficients form a natural coordinate system for describing finite-impulse response (FIR) channels in an OFDM framework. It is also shown that channels with spectral nulls are geometrically significant; they form the faces of the convex set of all subchannel attenuation coefficients. This novel perspective makes it immediately clear why the worst performance of a linearly precoded OFDM system is achieved over a channel having the greatest number of spectral nulls. The practical implications of these results are discussed     

Synthesis of antenna patterns with prescribed nulls

The least mean square pattern synthesis method is extended to include constraints such as pattern nulls or pattern-derivative nulls at a given set of angles. The problem is formulated as a constrained approximation problem which is solved exactly, and a clear geometrical interpretation of the solution in a multidimensional vector space is given. The relation of the present method to those of constrained gain maximization and signal-to-noise ratio (SNR) maximization is discussed and conditions for their equivalence stated. For a linear uniformN-element array it is shown that, whenMsingle nulls are imposed on a given "quiescent" pattern, the optimum solution for the constrained pattern is the initial pattern and a set ofM-weighted(sin Nx)/sin x-beams. Each beam is centered exactly at the corresponding pattern null, irrespective of its relative location. For the case of higher order nulls, thenth pattern derivative is similarly canceled by thenth derivative of a(sin Nx)/sin x-beam. In addition, simple quantitative expressions are derived for the pattern change and gain cost associated with the forced pattern nulls. Several illustrative examples are included.     

Development of target null theory

In a co- or cross-polarized channel, the polarization states of the transmitting and receiving antennas are the same or orthogonal, and the corresponding target nulls (i.e., the co-pol nulls or x-pol nulls) are defined as the polarization states of the transmitting antenna such that the received power equals zero. However, no systematic studies have been carried out to solve the problem of the corresponding target nulls if the polarization states of the transmitting and receiving antennas are independent. In this paper, the target null theory is extended to the case of two independent polarization states. For two arbitrary independent symmetric scattering matrices, it is proved that there exists only one pair of polarization states such that both of the received powers equal zero. This polarization states' pair is called the co-null of the two targets, which can easily be obtained by solving an eigenvalue problem. Based on this concept and algebraic theory, the concept of the co-null space is introduced for the symmetric scattering matrix case, and many important results are presented, e.g., the relations between the co-null and the co-pol/x-pol nulls, the properties of the co-null space, and the relation between the co-null and target decomposition. Finally, the co-null for the asymmetric scattering matrix case is studied. The concepts of the mono-co-null space and the bi-co-null space are introduced, and the relations between both spaces are presented     

Synthesis of random antenna array patterns with prescribed nulls

Under study is a method devised to reduce sidelobes of thinned random antenna arrays over specified angular sectors. The thinned array is assumed random in the sense that the nominal location of the elements is known, but their actual position may vary randomly. It is shown that by imposing adequately dense pattern nulls, it is possible to reduce the sidelobes effectively in the region of the nulls. The problem is formulated as a set of points in the radiation pattern, which are constrained to specified values. The unknowns are the excitations, or weights, applied to the array elements. In the general case, the linear system of equations is consistent and has an infinite number of solutions. The solution selected optimizes the pattern in a minimum variance sense. Quantitative relations are derived for the pattern change and the gain cost associated with the imposed pattern nulls. Several examples are included to illustrate the results.     

Experimental verification of null steering by element positionperturbations

Null steering in an adaptive array is realized by element position perturbations. Small position perturbations are assumed, which is valid when the number of imposed nulls is small compared to the number of array elements. The null steering has been achieved for an eight-element monopole array over a ground plane. The array illumination function is used solely for pattern formation and can also be used for main beam steering. Single and double nulls are realized in the sidelobe region. The experimental results prove the validity of null steering by controlling the element positions     

Aerial Design in Inductive Loop Telemetry

Two problems are considered which concern circular loop receiving aerials used in inductive loop telemetry. The first is that certain transmitter orientations give rise to signal nulls. The second is the optimum aerial size. By inverting the roles of the transmitting and receiving aerials, a simple way of describing the orientations which give rise to signal nulls is found. The factors which limit the range of an aerial are discussed and a simple method for deciding whether or not it is advantageous to enlarge or reduce the aerial radius is given.     

一种干扰零陷加宽的静态波束控制方法

基于静态波束控制技术(Quiescent Pattern Control),提出了一种新的适用于天线零陷加宽的新方法,该方法通过对得到的最优权值按照最小均方误差准则进行二次约束计算出新的权值,从而获得在干扰方向较宽零陷的静态方向图.理论分析和计算机仿真表明,该方法能够很好地克服干扰运动和接收天线平台运动或者震动时对输出信噪比造成的不良影响,具有很好的稳健性.     

Bees algorithm for interference suppression of linear antenna arrays by controlling the positions of selected elements

An efficient method based on bees algorithm (BA) for the pattern synthesis of linear antenna arrays with the prescribed nulls is presented. Nulling of the pattern is achieved by controlling only the positions of selected elements. The BA is an optimization algorithm inspired by the natural foraging behavior of honey bees to find the optimal solution. Simulation results for Chebyshev patterns with the imposed single and multiple nulls are given to show the effectiveness of the proposed method.     

Removal of surface-wave induced radiation nulls for patch antennasintegrated with vehicle windscreens

A solution to the problem of radiation nulls for patch antennas integrated with vehicle windscreens is presented. The nulls, attributable to surface waves within the windscreen superstrate, are removed by the addition of a thin resistive film to the windscreen surface. Analysis of the surface-wave modes at 5.8 GHz within two typical laminated windscreen structures coated with a resistive film shows a sheet resistance value of 50 Ω/sq to be appropriate. Polar-pattern results demonstrate the effectiveness of the technique in removing the radiation nulls without significantly reducing the forward gain     

A New Method of Generating Spectral Nulls at the Transmitter in Cognitive Radio

In cognitive radio (CR), cognitive users can sense the wholes and white spectrum and generate spectrum notch in the spectrum bands occupied by primary users (PUs) or interference. Thus, the key technology in CR is to control the spectrum shape of the transmitted signal to avoid PUs and interference. In this paper, a new method of shaping the transmitted signal spectrum envelope by spectrum-spread technology is proposed. The proposed method can generate spectral nulls at the band of PUs or interference in the CR environment. Compared to the existing methods generating spectrum nulls, the proposed method can effectively generate spectral nulls to avoid interference or PUs only by designing the pseudo-random code waveform (PCW) based on direct sequence spread spectrum technology. The condition of electromagnetic spectrum occupation is detected by CR technology so as to construct an ideal spectrum template. Based on the spectrum template, we study the design of the baseband waveform. The bit error rate (BER) performance of the proposed method in different sorts of interferences, and the relation between the BER and the spectrum overlap degree (SOD) are derived, of which the concept of SOD is proposed. The expression between BER and SOD shows that BER is proportional to SOD, which shows the criterion to design the PCW. The signal spectrograms in the receiver in presence of tone jamming and BPSK jamming indicate that the proposed scheme can effectively generate spectrum nulls in the frequency band occupied by PUs or interference. Furthermore, the BER versus SNR and BER versus SIR simulation results both in presence of tone jamming and BPSK jamming show that the proposed method has a significantly improved the BER performance by generating spectral nulls to avoid PUs or interferences. Simulation results are carried out to corroborate our theoretical analysis.     

Performance of trellis codes for a class of equalized ISI channels

The performance of trellis codes is examined for a class of intersymbol interference (ISI) channels that occur in high-frequency radio systems. The channels considered are characterized by in-band spectral nulls and by a rapid time variation. The baseline modulation technique is 4QAM (four-point quadrature amplitude modulation). When spectral nulls are absent, performance of fractionally spaced linear equalizers and trellis decoders is found to be near ideal and to be better than using symbol-spacing in the equalizer. However, error propagation in the feedback path, resulting from equalizer-based decisions, ruins the performance of the combination of decision-feedback equalizers and trellis decoders when spectral nulls are present. Their performance can be improved by using fractionally spaced feedforward equalizer sections and by designing the decoder to compensate for ISI. Rate 2/3 codes are found to outperform rate 1/2 codes in error performance     

零陷优化的稳健波束形成算法

传统的自适应波束形成算法在干扰方向出现扰动且期望信号导向矢量失配时,不仅无法持续有效地抑制干扰,而且会在期望信号方向产生零陷致使期望信号相消,算法性能严重下降。针对该问题,本文提出了一种零陷优化的稳健波束形成算法。该算法首先通过干扰导向矢量的左右旋转来展宽零陷,接着将采样数据向干扰子空间投影,并对干扰分量进行加权处理以增强采样数据中的干扰强度,加深干扰零陷,最后采用导向矢量不确定集约束算法保证期望信号的接收增益。计算机仿真结果表明:该算法能够有效展宽干扰零陷,并能够保证期望信号增益,具有较好的稳健性。      

基于一种新的遗传算法的天线方向图综合技术

给出了一种基于实数编码遗传算法的天线方向图综合方法.在遗传算法模型中采用了向下、向上外推和非一致杂交算子等交叉技术,并结合内插、交换等多种技术形成综合交叉方式.该算法克服了已有算法早熟、对初始群体依赖性等缺陷的同时,较大幅度地提高了算法的收敛速度和可靠性;通过在目标函数中加入零陷方差项克服了现有算法零陷不均衡的缺陷.计算机仿真结果表明,与现有算法相比,该方法用于天线方向图综合具有收敛速度快、零陷均衡、可靠等优势.     

基于零空间的宽零陷发射波束形成技术

文中提出了一种适合于MIMO技术联合使用的零空间波束形成算法，该算法采用MIMO技术中常用的奇异分解方法，同时引入Gershman导数约束法来展宽波束零陷，既实现了增强期望，又能在干扰方向上形成较宽的零陷，增强了系统的鲁棒性。     

一种利用幅值抖动形成阵列零陷的方法

该文提出了一种在阵元关于阵列中心对称的线阵中利用幅值抖动形成零陷的方法,该方法能够在多个强干扰源方向或在较宽的范围形成深度零陷, 而不影响主瓣, 同时克服了传统幅值抖动方法零陷深度不足、旁瓣水平高的缺陷。该方法使得移相器只需用来控制主瓣方向, 加快了响应速度。仿真表明,该算法实现简单,且其性能可与复权值控制方法的性能相比。同时由于幅度抖动的对称性, 在中心对称的线阵中只需要天线数目一半的衰减器, 成本较低。     

Optimal polarizations for partially polarized backscatter

Optimal polarizations are those which produce nulls in the co-polarized (CO-POL) and cross-polarized (X-POL) components of backscattered radiation. The discussion of optimal polarizations is here extended to the partially polarized case where nulls are replaced by minima. The width of the minima is related to the degree of polarization of the received radiation and, experimentally, to the correlation of orthogonal components. Formulas are presented for the location and width of these minima.