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.     

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.     

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.     

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 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.     

A sampling-based approach to wideband interference cancellation

Classical adaptive array schemes which use only complex spatial weights are inherently narrowband and consequently perform poorly when attempting to suppress wideband interference. The common solution to this problem is the use of tapped delay line filters in each spatial channel to facilitate space-time adaptive processing (STAP). The higher performance provided by the STAP architecture comes at the cost of a considerable increase in complexity. This paper presents a simpler technique based on programmable time adjustable sampling (TAS) that provides a limited number of wideband degrees of freedom. Two TAS methods are introduced: TAS-sidelobe canceler (TAS-SLC) is based on the sidelobe canceler, while TAS-minimum variance beamformer (TAS-MVB) is derived from the minimum variance beamformer. TAS is implemented by adjusting the sampling instant at selected array channels. TAS-SLC consists of controlling the sampling in the main channel of the sidelobe canceler With TAS-MVB array complex weights are substituted with TAS time delays. The performance of TAS methods with wideband interference is compared to the conventional sidelobe canceler and minimum variance beamformers. It is shown that TAS-SLC provides better performance than the sidelobe canceler, while TAS-MVB outperforms the minimum variance beamformer     

Canceler Performance Degradation Due to Estimation Noise

The multiple sidelobe canceler (MSLC) configured using the gradient descent algorithm converges to an approximation to the optimum weight vector. Since the weight vector estimate is obtained from a finite data set, there is a random error that increases the steady state residue power. An exact analysis of the steady state residue power for a digital implementation is performed. The analysis predicts that as the algorithm's gain (step size) is increased, the steady state residue power tends towards infinity. The gain that causes infinite power is smaller than the gain that causes instability for the average weight vector analysis. It is shown that the steady state residue power is equal to the minimum residue power multiplied by a factor that depends upon ratios of the eigenvalues. The steady state residue power is evaluated for some special cases. It is shown that the value of the factor is greatest when the interference is due to a single jammer.     

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     

Multicomponent receiver architectures for GPS interference suppression

The global positioning system (GPS) is a one-way satellite-based navigation system employing spread-spectrum techniques that is widely used for commercial and military applications. Although the very low signal-to-noise ratio (SNR) is handled by the large spreading gain, GPS is susceptible to high-power interference signals and various types of jammers. We propose multicomponent receiver architectures for GPS interference suppression. A conventional antenna system is first considered which utilizes a minimum-variance distortionless-response (MVDR) beam former and assumes that the GPS signal angle of arrival (AOA) and the antenna model are known at the receiver. However, this receiver is sensitive to AOA estimation errors and can have a high computational complexity. This sensitivity problem is eliminated by a multicomponent system based on a multistage matched filter (MF). Since this MF receiver also has a high computational complexity because the jammer AOAs must be estimated, we introduce a blind interference canceler based on the constant modulus (CM) array that is insensitive to AOA estimation errors and has a low computational complexity. Computer simulations are provided to illustrate the performance of the various systems for interference suppression in example signal scenarios.     

Adaptive canceler and pulse compressor interactions

Performance results for the sidelobe level of a compressed pulse that has been preprocessed through an adaptive canceler are obtained. The adaptive canceler is implemented using the sampled matrix inversion algorithm. Because of finite sampling, the quiescent compressed pulse sidelobe levels are degraded due to the preprocessing of the main channel input data stream (the uncompressed pulse) through an adaptive canceler. It is shown that if N is the number of input canceler channels (main and auxiliaries) and K is the number of independent samples per channel, then K/N can be significantly greater than one in order to retain sidelobes that are close to the original quiescent sidelobe level (with no adaptive canceler). Also it is shown that the maximum level of degradation is independent of whether pulse compression occurs before or after the adaptive canceler if the uncompressed pulse is completely contained within the K samples that are used to calculate the canceler weights. This same analysis can be used to predict the canceler noise power level that is induced by having the desired signal present in the canceler weight calculation     

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.     

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.     

A new CFAR sidelobe canceler algorithm for radar

Signal or target detection is sometimes complicated by the presence of strong interference. When this interference occurs mainly in the sidelobes of the antenna pattern, a solution to this problem is realized through a sidelobe canceler (SLC) implementation. Since the false-alarm probability is a system parameter of special importance in radar, an interference-canceling technique for radar application should maintain the false-alarm probability constant over a wide range of incident interference power. With the requirements of sidelobe interference cancellation and constant false alarm rate (CFAR), a new algorithm for radar detection in the presence of sidelobe interference is developed from the generalized likelihood ratio test of Neyman-Pearson. In this development, the received interference is modeled as a nonstationary but slowly varying Gaussian random process. Cancellation of the sidelobe interference is based upon a `synchronous' estimate of the spatial covariance of the interference for the range gate being tested. This algorithm provides a fixed false-alarm rate and a fixed threshold which depend only upon the parameters of the algorithm     

Pointing Accuracy and Dynamic Range in a Steered Beam Adaptive Array

The performance of a steered beam adaptive array as a function of the beam pointing error is examined. The purpose is to determine how close the steered beam has to be to the actual desired signal arrival angle for good performance. It is shown that the beam pointing error that can be tolerated is essentially a question of dynamic range. The greater the desired signal dynamic range that must be accommodated by the array, the more accurate the beam pointing angle must be.     

重力姿轨耦合效应引起的太阳能电站轨道共振

以任意相控阵天线式空间太阳能电站为研究对象,主要研究了其在轨运行过程中受到的重力姿轨耦合效应对其轨道运动的影响。首先,通过Hamilton原理建立起考虑重力姿轨耦合效应时的姿态运动和轨道运动的方程。其中,任意相控阵天线式空间太阳能电站被简化成刚体,它的重力势能以其结构尺寸和其轨道半径的比值为小量进行泰勒展开,并保留至二阶项。之后,采用解析的方法对方程进行分析,并发现当电站的姿态运动满足一定条件时,其轨道运动将会出现共振现象。此外,重力姿轨耦合效应还会引起空间太阳能电站轨道运动长期的漂移,通过选择合适的轨道运动初始条件可以消除漂移;而且,在一定条件下,重力姿轨耦合效应还会引起轨道运动的发散。最后,数值仿真结果验证了分析的正确性。     

Effects of CW Interference on Narrow-Band Second-Order Phase-Lock Loops

This paper describes an experimental study of the effect of continuous wave (CW) interference and white noise on a second-order phase-lock loop. The reciprocal of the loop mean-square phase error is used as an index of performance, and the effect of interference levels that do not cause cycle skipping or loss of lock is described in terms of this index. Loop thresholds are determined by measurement of cycle-skipping rates. Stationary or slowly-sweeping CW interference caused a degradation in loop threshold of roughly 3 dB for every 6 dB of interference power above the noise power level. The effective loop signal-to-noise ratio was decreased approximately 1 dB at interference-to-noise power ratios of -3 dB. Interference levels equal to the signal level consistently caused loss of lock, regardless of the loop signal-to-noise ratio.     

Results from a Four-Element Adaptive Antenna Experiment

Experimental results from a four-element, linear, half-wavelength spacing, adaptive-array antenna under the control of the least mean square (LMS) algorithm are presented. The array is found to be capable of nulling a 70-MHz signal to -35 dB below a desired signal over a 5-MHz bandwidth. The antenna processing gain is constant over a desired signal-to-jammer signal power ratio range from -20 dB to 5 dB. A sharp reduction in processing gain is observed for angular separations between jammer and desired signal of less than 10°. Antenna patterns taken with weights set in 300 iterations of the LMS algorithm show that the one strong, one weak jammer combination has a longer weight convergence time and reduced processing gain compared with a two strong jammers combination. Contours of constant desired signal-to-jammer signal power ratio, after adaptive antenna processing, reveal a complex shape for communication between air and ground due to the finite angular resolution of the adaptive antenna.     

阵列旋转对功率倒置算法性能的影响分析

针对卫星导航抗干扰中,功率倒置算法下导航信号载噪比受干扰来波方向的影响,通过理论推导和数值计算的方法研究了天线阵列旋转与功率倒置算法抗干扰性能的关系。分析结果表明:天线阵列旋转会使功率倒置算法下的阵列增益在最大值和最小值之间呈现连续的、周期性的变化。相比固定天线阵不变的载噪比,阵列旋转能够使信号在一段时间内获得更大的载噪比,对于四阵元Y型阵列,阵列旋转理论上对载噪比的最大提升程度可以达到14dB左右。仿真结果验证了理论推导的正确性。     

Power Inversion Array in a Rotating Source Environment

The steady state performance of the Frost power inversion array is evaluated, assuming constant rotational velocity of the external noise environment in the sin ? domain. The weight vector is solved implicitly in terms of a linear matrix equation. Approximate criteria are derived for weight vector and output power deviation from optimal values, which are then applied to determine the maximum scan rate of a radar sidelobe canceler.     

Interference between FM Carriers and a Digitally Modulated SCPC Circuit

The interference from the digital single channel per carrier (SCPC) circuits into frequency-modulated carrier systems has been calculated by convolving the desired and the interfering spectra extending the previously published works. Resulting interference noise power in FDM/FM systems covering a wide range of modulation indices and basebands has been presnted. Also plots of interference noise power as a function of the number of SCPC circuits have been presented for various values of carrier power to interference power ratios.