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.     

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.     

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 Effect of Differential Time Delays in the LMS Feedback Loop

The effect of differential time delay in the feedback loops of an LMS adaptive array is examined. Differential time delay is shown to have two effects on array performance. First, it causes the weights to oscillate during weight transients. Second, it degrades the output signal-to-interference-plus-noise ratio (SINR) from the array. Weight oscillation occurs when the phase shifts in the LMS loop are not matched at the signal carrier frequency. SINR degradation depends on signal bandwidth: the wider the bandwidth, the larger the degradation.     

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.     

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。     

Prediction of Adaptive Array Performance

A direct relationship between the conventional properties of an array and the array performance in an adaptive mode is given. Expressions are provided to obtain the output signal-to-interference-plus-noise ratio (SINR) of an adaptive array in terms of its conventinal pattern and the locations of the desired signal and jammers. These expressions permit one to evaluate the performance of an adaptive array without an exhaustive search for all possible scenarios and parametric values to ascertain that the required performance levels be met. In fact, one can predict the jammer locations for which the array will provide its best and worst performance by observing the conventional pattern. Several examples are provided to demonstrate the relationship between the conventional pattern and the adaptive array performance. The examples include both linear and planar arrays.     

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 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.     

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.     

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 anticipative adaptive array for frequency-hopping communications

To fully utilize the theoretical processing gain achievable when an adaptive array and frequency hopping are combined, frequency compensation is required. Improved versions of an anticipative adaptive array are examined that provide efficient compensation by adapting the complex weights at each antenna element to the appropriate values for a carrier frequency before that frequency is received. The underlying adaptive algorithm used is the maximum algorithm. Computer simulation results are used to compare the different versions of anticipative processing. These results show that an appropriate version ensures the rapid convergence of weights to values that provide wideband nulling of the interference and noise     

The Effect of Integrator Pole Position on the Performance of an Adaptive Array

The LMS adaptive array requires an integrator in each weight feedback control loop. In practice the integrator is often replaced by a low-pass filter, i.e., by a filter with a single pole at s = - ? (where s is complex frequency). The effect of this pole position on array performance is examined. It is shown that to obtain optimal performance from the array, ? must be less than k?2, where k is the loop gain and ?2 is the thermal noise power per element. When at exceeds k?2, the output signal-to-inter ference-plus-noise ratio from the array is degraded for intermediate values of interference power.     

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.     

圆台阵列杂波模型及空时二维自适应处理

针对圆台共形阵列,建立了空时二维自适应处理(STAP)的杂波模型,给出了圆台阵列杂波抑制最优权值的计算方法。在此基础之上,为了实现可应用到实际环境中的自适应处理方法,进一步讨论了将局部联合域(JDL)降维算法推广至圆台阵列中的问题。得出了圆台阵列JDL算法降维变换矩阵的表达形式,研究了参考波束的数目选取、波束指向等因素对降维损失的影响。理论分析以及仿真结果表明,通过合理选择通道数、波束方位向指向间隔等参数,该算法能够减少自适应波束形成的计算量,而且可以用较少的训练样本获得较好的处理性能。     

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.     

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.     

Equivalent transformation for a partially adaptive array

A partially adaptive array is one in which elements of a phased array are controlled or adaptively weighted in groups or in which certain elements, called auxiliary elements, are made controllable. Mathematically, this type of array is formed by transforming all of the elements of an array by a nonsquare matrix such that the resulting output vector has a length less than the number of array elements. It is shown that there is an equivalent matrix transform that can effectively be utilized in analyzing the partially adaptive array's performance when a small number of external jammers are present. Processor implementation and convergence rate considerations lead to the desirability of reducing the dimensionality of the cancellation processor while maintaining good sidelobe interference protection. A meaningful measure of canceller performance is to compute the optimal output signal-to-noise ratio. This expression is a function of the jammer, direction-of-arrival vectors (DOAVs), jammer powers, the array steering vector, and internal noise. It is shown that if this expression is computed for the fully adaptive array then it is easily computed for the partially adaptive array by transforming the jammer DOAVs and the steering vector by the orthogonal projection matrix defined by the rows of the subarray transformation matrix and substituting these vectors back into the original expression for the fully adaptive array