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.     

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.     

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.     

Interference Canceler Array with Reference Generating Loop

Adaptive arrays utilizing an internally generated reference signal to drive least mean square (LMS) weight determining loops have experienced difficulty arising from phase shifts induced by the reference generating circuits. The phenomenon observed is that the expected value of the weights oscillate in the steady state modulating the incoming signal. A scheme is reported which avoids this problem. It differs from earlier methods in that the reference generator has no infinite limiter so that the amplitude of the reference is not constant and in that one element is left unweighted. Alternative schemes were considered wherein the reference signal is drawn from all the array elements or from the weighted elements only. Only the latter is fully reported here, and is found superior. It is shown that in the presence of a desired signal and independent element noise, the processing scheme proposed produces weights whose expected values converge to a constant nonoscillatory state provided certain mild constraints are satisfied. In particular, if a cos ? ? 1, a being the gain and ? the phase shift of the filter in the reference generator, the weights converge. In addition, the steady state signal-to-noise power ratio (SNR) is determined. It is found that with a cos ? close to unity the SNR is that of an (N-1) element array coherently combined, where N is the number of elements. The SNR falls off with departures of a and ? from 1 and 0, respectively, but not drastically.     

Rapid convergence by cascading Applebaum adaptive arrays

An adaptive array architecture is described which has improved convergence speed over the conventional Applebaum array when the eigenvalue spread of the input signal covariance matrix is large. The architecture uses N+1 Applebaum adaptive arrays in a two-layer cascaded configuration. The gain constants in the first layer are set so that large interfering sources are quickly nulled, but small interfering sources are suppressed more slowly. Since the first layer removes the large interfering signals, the gain constant for the second layer can be set to a large value to quickly null the smaller interferers. The adaptation time is examined for several combinations of signal levels and array sizes. It is shown that, in many signal environments, the computational requirements for the cascaded array compare favorably with those of conventional sample matrix inversion (SMI) methods for large arrays     

An LMS Adaptive Array for Multipath Fading Reduction

Multipath fading often poses a serious hindrance in radiocommunication. The application of a least-mean-square (LMS)adaptive array to the problem of multipath fading reduction is discussed. However, it is known that multipath components are in general correlated with one another. We examine the effect of the correlation on the performance of the LMS adaptive array. When the correlation coefficient does not equal or approximate 1, the LMS adaptive array suppresses the multipath signals significantly by nulling. On the other hand, when the correlation coefficient nearly equals 1, the LMS adaptive array prevents the output signalpower from decreasing. Therefore, the LMS adaptive array mayreduce the multipath fading effectively for any correlation coefficient value. A reference signal in the LMS adaptive array is also discussed. It is shown that synchronization in the referencesignal generation must be extremely accurate. Moreover, aprocessor configuration is proposed which may generate thereference signal with the required accuracy.     

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.     

Matched-Filter Response to a Linear FM Signal Transmitted Through a Phased Array

The response of a linear phased array with a matched filter connected at its output is investigated when a linear FM signal is incident on the array at an arbitrary angle. The filter is assumed to be matched to the linear FM signal. The dispersion produced by the array results in a mismatch at the receiver which depends on the scan angle and on the type of feed system used with the array. The distortion of the compressed pulse is studied for the series end-fed arrays, the series     

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.     

Multiplier Offset Voltages in Adaptive Arrays

The effects of multiplier offset voltages in adaptive arrays are examined. Multiplier offset voltages arise when active circuits are used to implement the error-by-signal multipliers required in an array based on the LMS algorithm. These offset voltages are known from experimental work to have a strong effect on array performance. It is first shown how multiplier offset voltages may be included in the differential equations for the array weights. Then their effect on weight behavior is studied. It is found that the offset voltages affect the final values of the weights, but not the time constants. Furthermore, the effect they have is influenced by the amount of element noise in the array. An adequate amount of noise is necessary to minimize weight errors due to offset voltages. An example is treated to show the effect of offset voltages on the final array weights and the output signal-to-noise ratio (SNR). With offset voltages present, it is found that there is a maximum SNR that can be obtained from the array. A specific input SNR is required to obtain this maximum output SNR. Finally, it is shown that a finite operating range for the weights places a further restriction on the acceptable values of offset voltages and noise.     

Adaptive Array Bandwidth with Tapped Delay-Line Processing

The bandwidth of adaptive arrays with tapped delay lines behind the elements is examined. Such processing offers improved bandw over that attainable with quadrature hybrid processing. The performance of a two-element array with four types of processing (equarature hybrids, single delay lines, 3-tap delay lines, and 5-tap delay lines) is compared. It is shown that with half-wavelength element spacing, a quadrature hybrid and single delay-line processor are inadequate at 10-percent bandwidth. A 3-tap processor is adeq however, up to 40-percent bandwidth.     

A fast adaptive null-steering algorithm based on output powermeasurements

Presented and investigated here is a simple and fast adaptive algorithm for linear power inversion arrays whose nulls can be accurately steered by controlling the element weights. Based on measurements of the powers of the three signals derived from the array output and the output of an auxiliary beamformer, the algorithm tracks unknown jammers in the environment by steering the nulls of the array one by one in a cyclical time-multiplexed manner. When compared with the least mean square (LMS) algorithm, the proposed algorithm has about the same implementation complexity, a better convergence behavior and the advantage that nulls are directly available     

Postfiltering in Digital Beamformers

Assuming a sinusoidal signal superimposed on a narrow-band Gaussian noise as the input to a receiving array, the output power and signal-to-noise ratio of a digital beamformer with postfiltering were formulated so that subsequent calculations could be made without an analysis in the frequency domain. The formulation utilized the quantizer functions previously given by the author and certain spectral power distribution factors originally attributed to Davenport but more rigorously derived and discussed in the present work. A numerical study based on this formulation for a DIMUS array in a correlated noise field reveals that except for certain rare circumstances, postfiltering generally improves the output SNR or array gain. It is demonstrated that the amount of postfiltering gain not only varies with array input SNR but also depends strongly upon the spacing-to-wavelength ratio, and its meaningful interpretation can only be made in conjunction with both the clipping and noise correlation losses. In particular, balancing postfiltering gain against the two losses suggests that receiving arrays with element spacings smaller than one-half of the operating wavelength may be used to the advantage of system design under certain conditions.     

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 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.     

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.     

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.     

基于旋转轴向阵列的风扇宽频噪声实验

航空发动机降噪研究迫切需要一种叶轮机械管道内宽频噪声测量方法来指导降噪设计。本文通过对阵列测量的声压信号进行互相关分析,得到管道内顺流和逆流传播的模态声功率结果。安装在风扇实验台进口段的传声器阵列由2排周向间隔180°的轴向阵列组成,每排阵列有14个等间距的传声器。阵列安装在可周向旋转的测量段上,实验中测量段每隔6°旋转一次,共获得840个测点位置的声场信号。结果表明入射波与反射波最大可相差10dB。模态分解结果表明,转静干涉模态是转子通过频率及其谐频处的主导模态。利用不同参考信号计算出的声场结果相同,说明该实验测试方法对参考信号位置没有特殊要求,进一步说明该方法有很好的适用性。     

Control-Loop Noise in Adaptive Array Antennas

Adaptive array receiving antennas can be designed to sense the external noise field and to optimize the array illumination function. A substantial improvement in signal-to-noise ratio can be obtained with adaptive arrays when the external noise field is nonuniformly distributed in angle. The external noise process may be time varying and contain both discrete sources and continuously distributed sources. Two adaptive array implementations which maximize the signal-to-noise ratio are described in this paper. Expressions are derived for control-loop noise, i.e., the variance of the array element weights, and for the additional noise in the array output due to this element weight noise. It is shown that both the element weight noise and the array convergence rate are determined by the eigenvalues of the noise covariance matrix.