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 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.     

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.     

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.     

Median cascaded canceller for robust adaptive array processing

A median cascaded canceller (MCC) is introduced as a robust multichannel adaptive array processor. Compared with sample matrix inversion (SMI) methods, it is shown to significantly reduce the deleterious effects of impulsive noise spikes (outliers) on convergence performance of metrics; such as (normalized) output residue power and signal to interference-plus-noise ratio (SINR). For the case of no outliers, the MCC convergence performance remains commensurate with SMI methods for several practical interference scenarios. It is shown that the MCC offers natural protection against desired signal (target) cancellation when weight training data contains strong target components. In addition, results are shown for a high-fidelity, simulated, barrage jamming and nonhomogenous clutter environment. Here the MCC is used in a space-time adaptive processing (STAP) configuration for airborne radar interference mitigation. Results indicate the MCC produces a marked SINR performance improvement over SMI methods.     

Interference in Frequency-Locked Doppler Tracking Loops

The effects of interference on frequency-locked Doppler tracking loops are investigated. Conditions for jump from locking on the desired signal to locking on the interfering signal are established. Parasitic frequency modulation of the desired signal results when the other signal interferes with it. The index of this parasitic modulation as a function of the interference-to-desired signal amplitude ratio is computed. Both critical amplitude ratio and critical parasitic modulation index at the occurrence of jump are derived. Comparing frequency-locked loops with phase-locked loops with phase-locked loops in the presence of interference shows the former performs better for most cases of practical importance in Doppler tracking systems.     

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.     

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.     

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.     

The Effects of Gaussian Interference on Communication Systemswith Adaptive Arrays

The performance of a bandlimited binary phase-shift-keyed (BPSK) communication system is examined when the received BPSK signal is corrupted by both thermal noise and a directional Gaussian noise interfering signal. The system uses an LMS adaptive array to suppress this interference. The effects of signal power levels, arrival angles, bandwidths, and the array bandwidth are examined. The performance of a system that uses tapped delay lines for the array weights is also examined. It is shown that the performance of a system with tapped delay lines is not affected by the interference bandwidth for a single interferer.     

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.     

Distortion Generated in Angle-Modulation Systems by Phased Arrays

The case of linear, uniformly weighted phased arrays is examined via time and frequency domain analyses. Bounds that must be placed on array length, modulation frequency, modulation index ?, and scan angle relationships if excessive distortion is to be avoided in wideband angle-modulated communication systems are established. Distortion is shown to consist of odd harmonic terms. It is also shown that, for one class of equivalent RF signals, phased arrays produce approximately three times as much distortion in frequency-modulation (FM) systems as in phase-modulation (PM) systems. Graphs of distortion plotted as functions of signal and array parameters show that, for practical array sizes, distortion is a monotonically increasing function of the product of L and sin ? where L is the length of the array expressed in modulation wavelengths ?m and ? is the scan angle. In PM systems, distortion also increases monotonically with the modulation index ?. Plots of distortion versus L sin ? show that even relatively small arrays can produce intolerable distortion levels in wideband systems; e.g., an FM system having ? = 3,L = 0.35?m, and ? = 60 degrees exhibits approximately 20 percent distortion.     

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.     

Reference Loop Phase Shift in an N-Element Adaptive Array

Adaptive arrays based on the LMS algorithm require the generation of a reference signal which is usually derived from the array output. A particular problem associated with this technique is that of a phase shift in the reference signal loop. The effects of this phase shift on the performance of an N-element adaptive array are discussed. It is shown that a reference loop phase shift causes the array weights to cycle, thereby frequency translating the signals at the output. The weight-cycling frequency is related to various system parameters of an N-element array. In particular, it is observed that the cycling frequency increases as the number of antennas (N) increases.     

The Steady-State Antenna Patterns of Adaptive Arrays

The antenna pattern of a receiving adaptive array of arbitrary three-dimensional geometry operating in an environment of K sources, one desired signal and (K - 1) jammers, is considered. It is shown that the adapted (voltage) antenna pattern of the array is a linear combination of K (or less) basis patterns, each of which is a function of one source only. We find that these basis patterns have a simple physical meaning, namely, the kth basis pattern is the pattern realized by the array when the transmission of source k is considered a desired signal and all other sources are turned off. When the array elements are isotropic, these basis patterns are retrodirective (that is, the mainlobe of the kth basis pattern points at source k). It had been shown that this property is also exhibited by a different decomposition of the adapted pattern in the special case of a single jammer (K = 2). In contrast, our decomposition which is simpler than the earlier one, yields retrodirective beams for all K. The simple, physically meaningful, pattern decomposition developed here is quite significant in the insight it provides regarding the basic underlying principles of adaptive arrays. It is also instrumental in elucidating their capabilities and limitations.     

Analysis of an adaptive CFAR detector in non-Gaussian interference

Coherent signal detection in non-Gaussian interference is presently of interest in adaptive array applications. Conventional array detection algorithms inherently model the interference with a multivariate Gaussian random vector. However, non-Gaussian interference models are also under investigation for applications where the Gaussian assumption may not be appropriate. We analyze the performance of an adaptive array receiver for signal detection in interference modeled with a non-Gaussian distribution referred to as a spherically invariant random vector (SIRV). We first motivate this interference model with results from radar clutter measurements collected in the Mountain Top Program. Then we develop analytical expressions for the probability of false alarm and the probability of detection for the adaptive array receiver. Our analysis shows that the receiver has constant false alarm rate (CFAR) performance with respect to all the interference parameters. Some illustrative examples are included that compare the detection performance of this CFAR receiver with a receiver that has prior knowledge of the interference parameters     

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.     

Reference Loop Phase Shift in Adaptive Arrays

Adaptive arrays for use in communication systems require the generation of a so-called reference signal, which is usually derived from the array output. A particular problem associated with this technique, the problem of reference loop phase shift, is discussed. It is shown that phase shift in the reference loop causes the array weights to cycle, and also causes the array to frequency-modulate the signal. In spite of this frequency change, the array maintains a maximum SNR at the output.     

基于Kalman滤波的GPS/INS接收机自适应干扰抑制方法

 考虑到惯导信息辅助GPS(GPS/INS)接收机对干扰抑制实时性的要求,提出一种基于Kalman滤波的GPS/INS接收机自适应干扰抑制方法。自适应广义旁瓣相消(GSC)多采用低复杂度最小均方(LMS)算法更新权矢量,收敛速率较低,严重时会导致接收机定位中断。首先利用Householder变换构建GSC下支路的阻塞矩阵,用于阻塞任意二维阵型阵列接收的期望信号;再用Kalman滤波自适应更新下支路权矢量,从而有效提高阵列输出信干噪比(SINR)。理论分析和仿真结果说明本文方法可有效抑制干扰对接收机的影响,且具有实时性高的特点。