The Effect of Random Steering Vector Errors in the Applebaum Adaptive Array

The effect of random errors in the steering vector of an Applebaum adaptive array is examined. Each component of the steering vector is assumed to have a random error component uncorrelated between elements. The array output signal-to-interferenceplus-noise ratio (SINR) is computed as a function of the error variance. It is shown that the array output SINR becomes more sensitive to steering vector errors as more elements are added to the array and as the received desired signal power becomes larger. The variance of the steering vector error that may be tolerated depends on the required desired signal dynamic range. The larger the dynamic range that must be accommodated, the smaller the error variance must be.     

Adaptive Arrays for Multiple Simultaneous Desired Signals

Steered beam adaptive arrays for multiple simultaneous desired signals are discussed. It is shown that the performance of a steered beam adaptive array depends upon the range of input signal strengths and the choice of the steering vector. Optimum steering vectors for various input signal strengths are given. All choices of steering vectors are equally effective in the rejection of jammers.     

Steered Beam and LMS Interference Canceler Comparison

The performance of two kinds of interference cancelers is compared, namely, a constrained steered beam interference canceler (CSBIC) and a least mean square interference canceler (LMSIC). For simplicity, this is done for a two-element array. In our comparison we use the array output desired signal-to-interference power ratio (SIR) and the desired signal-to-noise ratio (SNR). These power ratios are obtained for the CSBIC and LMSIC under two sets of conditions: 1) The error in the assumed angle of incidence for the CSBIC is small, and the LMSIC operates in a codetracking mode. 2) The error in the assumed angle of incidence for the CSBIC is large, and the LMSIC operates in a code-acquisition mode. Comparison of the corresponding power ratios obtained under these two sets of conditions then establishes the condition under which it is more desirable to use a CBSIC as compared with an LMSIC.     

Performance of a Modified Applebaum Adaptive Array

The performance of a modified Applebaum adaptive array is studied. The new array is obtained by removing the desired signal component from the output signal fed back to the correlator of an Applebaum type adaptive array. Various signal scenarios, including single desired signals or multiple simultaneous desired signals are examined. The new array is less sensitive to beam pointing errors and does not cause power inversion of desired signals. In the case of multiple simultaneous desired signals, the new array does not degrade the SNRs of strong desired signals.     

An Adaptive Interference Canceling Array Utilizing Hybrid Techniques

The steady state properties of an adaptive array utilizing prior knowledge of both approximate signal arrival direction and signal characteristics are presented. The method combines the features of a directionally constrained array and an array with a self-generated reference signal. Explicit results are obtained for output signal, interference, and noise powers assuming a single interferer is present. The inclusion of a self-generated reference circuit is shown to reduce the sensitivity to pointing error typical of arrays utilizing a zero order directional constraint, the improvement being a consequence of the reduction of the desired signal component fed back to the sidelobe canceling circuit. A relationship between the degree of sensitivity reduction and the quality of the reference signal is developed. Results of computations of signal to interference plus noise ratios for a 7-element 10-wavelength nonuniformly spaced array as a function of pointing error are presented. These results show the behavior with one interferer inside and outside the beamwidth of the quiescent array and with multiple interferers for various degrees of perfection of the reference generating circuit. In all cases the computations confirm that the otherwise severe effects of small pointing errors are substantially reduced.     

Beam-pointing error compensation method of phased array radar seeker with phantom-bit technology

A phased array radar seeker (PARS) must be able to effectively decouple body motion and accurately extract the line-of-sight (LOS) rate for target missile tracking.In this study,the real time two-channel beam pointing error (BPE) compensation method of PARS for LOS rate extraction is designed.The PARS discrete beam motion principium is analyzed,and the mathematical model of beam scanning control is finished.According to the principle of the antenna element shift phase,both the antenna element shift phase law and the causes of beam-pointing error under phantom-bit conditions are analyzed,and the effect of BPE caused by phantom-bit technology (PBT) on the extraction accuracy of the LOS rate is examined.A compensation method is given,which includes coordinate transforms,beam angle margin compensation,and detector dislocation angle calculation.When the method is used,the beam angle margin in the pitch and yaw directions is calculated to reduce the effect of the missile body disturbance and to improve LOS rate extraction precision by compensating for the detector dislocation angle.The simulation results validate the proposed method.     

The Performance of an LMS Adaptive Array with Frequency Hopped Signals

The performance of an LMS adaptive array with a frequency hopped, spread spectrum desired signal and a CW interference signal is examined. It is shown that frequency hopping has several effects on an adaptive array. It causes the array to modulate both the amplitude and the phase of the received signal. Also, it causes the array output SINR (signal-to-interference-plus-noise ratio) to vary with time and thus increases the bit error probability for the received signal. Typical curves of the desired signal modulation and the time-varying SINR at the array output are presented. It is shown how the array performance depends on hopping frequency, frequency jump size, interference frequency, signal arrival angles, and signal powers.     

The Effect of a Pulsed Interference Signal on an Adaptive Array

The performance of a least mean square (LMS) adaptive array in the presence of a pulsed interference signal is examined. It is shown that a pulsed interference signal has two effects. First, it causes the array to modulate the desired signal envelope (but not its phase). Second, it causes the array output signal-to-interferenceplus-noise ratio (SINR) to vary with time. The desired signal modulation is evaluated as a function of signal arrival angles, powers and interference pulse-repetition frequency (PRF) and pulsewidth. It is shown that the signal modulation is small except when the interference arrives close to the desired signal. To evaluate the effect of the time-varying SINR, it is assumed that the array is used in a differential phase-shift keyed (DPSK) communication system. It is shown that the SINR variation causes a noticeable but not disastrous increase in the bit error probability.     

Angle measurement in the presence of mainbeam interference

The problem of reducing interference impinging on an antenna array when the sources lie in the main beam is addressed. Adaptive antenna arrays are incorporated to form adapted sum and difference beams in which the interference signals are suppressed. Monopulse error curves are then obtained, providing the necessary distortion correction curves across the entire mainbeam tracking angle region. New Cramer-Rao (C-R) bounds on the angle estimation error are derived with generalized assumptions on the signal amplitude and phase. The bounds previously derived by others are valid under different conditions. With these generalized assumptions on the signal characteristics, a Monte Carlo simulation is performed, based on the estimation procedure presented, to determine the angle estimation error. These errors are compared with the C-R bounds. Good performance is shown for sufficient S/N₀ and angular separation between the target and the interference sources     

Adaptive Array Behavior with Periodic Phase Modulated Interference

We consider a least mean square (LMS) adaptive array [1] receiving a phase modulated interference signal. The phase modulation is assumed to be periodic and to have finite bandwidth. Under these assumptions, we determine the time-varying array weights, the modulation on the array output desired signal, and the time-varying output interference-to-noise ratio (INR) and SINR (signal-to-interference-plus-noise ratio). We present numerical results describing the behavior of a 2-element adaptive array that receives an interference signal with sinusoidal phase modulation. We show how each signal parameter (arrival angle, power, modulation index, and modulation frequency) affects the performance of the array.     

Adaptive Array Behavior with Periodic Envelope Modulated Interference

A method is presented for determining the effects of envelope modulated interference on a least mean square (LMS) adaptive array. The interference is assumed to have periodic envelope modulation with a bandwidth that is small compared with the carrier frequency. For such interference, the method allows one to calculate the periodic steady-state behavior of the array weights and the resulting array performance. As an example, we compute the effects of an ordinary amplitude modulated (AM) interference signal on the array. It is shown that such interference causes the array to modulate the desired signal envelope but not its phase. With a differential phase-shift-keyed (DPSK) desired signal, AM interference is found to have about the same effect on bit error probability as CW interference.     

Some properties of retrodirective beam of multiple sidelobecanceler

The retrodirective or perturbation beam concept is often used to aid in explaining the nulling of interference sources. The classical explanation for cancellation of a single-zero-bandwidth source is that of a perturbation beam steered to and peaking at that interferer angle. The subtraction of this perturbation beam from the main beam causes the nulling. It is shown that, for discrete point main and auxiliary antennas, this explanation can be generalized to non-zero bandwidth sources. It is demonstrated that if the main and auxiliary antennas are spatial points, then the retrodirective beam is nonuniformly weighted, steered to the interference source, and peaks at the interferer angle. For the more realistic assumption of a nonpoint main antenna, the retrodirective beam does not peak at the interferer angle for any bandwidth     

二维耦合振荡器有源天线阵相位误差特性及其对天线方向图的影响

分析了二维耦合振荡器有源天线阵的相位误差特性及其对天线方向图的影响。分析结果表明,二维耦合振荡器有源天线阵的相位误差具有积累特性;阵元自由振荡频率的误差越小,阵元锁相带宽越大,波束指向误差越小;随着阵元自由振荡频率误差的增大,天线阵增益降低,副瓣电平抬高。     

An Lms Adaptive Array Using a Pilot Signal

A least mean square (LMS) adaptive array requires a reference signal. When the desired signal contains a pilot signal, it may be used as the reference signal. In this paper the steady-state performance of an LMS adaptive array in which the pilot signal is used as the reference signal is examined. It is shown that the LMS adaptive array occasionally suppresses the desired signal. The loop gain, which is an important parameter, is also considered.     

Robust algorithm for combating look direction error problems

A simple and fast zero tracking algorithm for adaptive arrays with large look direction errors is presented and investigated. Basically, the algorithm is based on adjusting the complex zeroes of a power inversion array in a time-multiplexed manner to track all the sources in the environment. To preserve the desired signal which is supposed to be closest to the look direction of 0°, the algorithm removes the zero with the shortest distance to e^j0 so that the directional response consists of only nulls steered at the jammers. When compared with the least mean square (LMS) algorithm employing zeroth and first-order look direction constraints, the new algorithm has about the same implementation complexity, is considerably faster, and possesses a much better signal-to-noise ratio (SNR) performance when the look direction is erroneous     

Adaptive Array Behavior with Sinusoidal Envelope Modulated Interference

The behavior of a LMS (least mean square) adaptive array with modulated interference is described. An interference signal with sinusoidal, double-sideband, suppressed-carrier modulation is assumed. It is shown that such interference causes the array to modulate the desired signal envelope but not its phase. The amount of the desired signal modulation is determined as a function of signal arrival angles and powers and the modulation frequency of the interference. Such interference also causes the array output signal-to-interference-plus-noise ratio (SINR) to vary with time. However, it is shown that when the desired signal is a digital communication signal, the averaged bit error probability is essentially the same as for continuous wave (CW) interference.     

Optimum transmitter optics aperture for satellite opticalcommunication

An important aspect in satellite optical communication is to obtain minimum bit error rate (BER) using minimum power. This aim can be achieved with very small transmitter beam divergence angles. The disadvantages of too narrow divergence angle is that the transmitter beam may sometimes miss the receiver satellite, due to pointing vibrations. A mathematical model of communication and tracking systems that optimize the BER as function of the transmitter gain is derived     

相控阵雷达捷联波束稳定方法

针对相控阵雷达系统中平台扰动引起的波束指向变化问题,提出一种捷联波束稳定方法。该方法作为独立模块实现,由角速度传感器和信号处理机组成,无需精确的初始姿态。角速度传感器感知平台扰动造成的天线转动角速度,信号处理机完成补偿角的迭代求解和波束的控制。通过算法仿真和利用单轴转台模拟平台扰动验证可得,采用捷联波束稳定方法后,雷达测量角误差明显减小,隔离度指标有了极大改善。因此,该方法能够有效地减小平台扰动对波束指向的影响,易于工程实现,适用于小型化的无人机等平台。     

基于正交基变换的旁瓣对消算法研究

针对广义旁瓣对消算法中阻塞矩阵难以构造的问题,提出了一种基于正交基变换的广义旁瓣对消算法。该算法在任意布阵形式下都可以方便地计算出阻塞矩阵,可以大大提高算法适应性。该方法易于在硬件上实现,通过正交基变换数据预处理,可以使波束指向期望方向,通过旁瓣对消算法实现对干扰的抑制。最后,通过理论推导并结合计算机仿真验证了该方法的有效性。     

Adaptive processing at the subarray level

This paper describes a class of partially adaptive arrays with adaptive processing applied to the outputs of steered subarrays. The problem is to detect a signal or estimate its direction of arrival in the presence of jammers. The advantage of applying adaptive processing to subarrays is that it requires much less CPU time than the corresponding fully adaptive processing. The subarray processing equations for the two kinds of problem are described. In this paper, we compare partially adaptive processing performance with fully adaptive processing performance in the case of the following antenna and signal sources:

• •- array with regularly spaced sensors ;
• •- between 20 and 100 elements ;
• •- between 3 and 20 subarrays ;
• •- a single jammer ;
• •- desired signal from the antenna zenith.

We suggest a method for determining the optimal subarray configurations in this case. An example is given to show that the performance of an antenna with five subarrays is comparable to that of a fully adaptive thirty-element array for eliminating a single jammer with a target at the zenith.