Error Analysis of the Optimal Antenna Array Processors

The optimal weights of an antenna array processor, which maximizes the output signal-to-noise ratio (SNR) in the absence of errors, are computed using the noise-alone matrix inverse (NAMI) and the steering vector in the look direction or the signal-plus-noise matrix inverse (SPNMI) and the steering vector. In practice the estimated steering vector as well as the estimated optimal weights are corrupted by random errors. This paper has analyzed the effects of these errors on the performance of the NAMI processor and the SPNMI processor by deriving analytic expressions for the output signal power, output noise power, output SNR, and the array gain as a function of the error variance. The treatment is for a general array configuration and no assumption about a particular array geometry is made.     

Effect of Sampling Time Jitter on Array Performance

The effect on array SNR of errors in sampling times (jitter) isan analyzed for the "Bryn processor." Jitter is modeled as a discrete-paramter er random process, and expressions for array SNR are determined as a function of signal and noise spectra and jitter characteristics. For a plane wave signal, it is found that jitter in the data used to design the processor has no effect on output SNR if the noise is independent between channels. However, jitter in the input (evaluation) n) data can cause a substantial loss in peak array SNR and in the array's frequency selectivity. These losses can be expected to increase as the high-frequency content of the data increases. The Bryn processor also loses its interpretation as a likelihood ratio processor in the presence of jitter. The effect of jitter can be reduced in many cases by increasing the sampling rate.     

Noise factor and antenna gains in the signal/noise equation for over-the-horizon radar

A recommended form of the signal-to-noise equation that includes both internal and external system noise and signal/noise processing losses is discussed. The recommended form conforms to the internationally accepted definition of system operating noise factor but is extended to include signal/noise processing. The predetection signal-to-noise ratio (SNR) of a radar or communication system is proportional to the power gain of the transmit antenna and the directive gain of the receive antenna, and is inversely proportional to the operating noise factor of the receiving system. The operating noise factor is approximately equal to the product of the external noise factor and the signal/noise processing factor when the system is external noise limited, as is usually the case for over-the-horizon (OTH) radar.<>     

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.     

Signal-to-Noise Ratios in Self-Biased-Pwer-Law Amplifiers with Saturation

The relation between the output signal-to-noise ratio (SNR) and the input SNR is presented for the bandpass self-biased third-law amplifier with saturation, when the input is composed of sinusoidal carrier and zero-mean stationary narrowband Gaussian noise. It is found that significant improvement in the output SNR at low input SNR's can be achieved by the self-biased third-law amplifier with saturation operated in class A. The results obtained are also verified experimentally.     

Detection of Known Signals in Nonstationary Noise

The basic design of a nonlinear, time-invariant filter is postulated for detecting signal pulses of known shape imbedded in nonstationary noise. The noise is a sample function of a Gaussian random process whose statistics are approximately constant during the length of a signal pulse. The parameters of the filter are optimized to maximize the output signal-to-noise ratio (SNR). The resulting nonlinear filter has the interesting property of approximating the performance of an adaptive filter in that it weights each frequency band of each input pulse by a factor that depends on the instantaneous noise power spectrum present at that time. The SNR at the output of the nonlinear filter is compared to that at the output of a matched filter. The relative performance of the nonlinear system is good when the signal pulses have large time-bandwidth products and the instantaneous noise power spectrum is colored in the signal pass band.     

DOA estimation using one-bit quantized measurements

The effects 1-bit quantization of the input samples has on the direction-of-arrival (DOA) estimation accuracy are considered. The signal model assumes a single stochastic Gaussian point source that is embedded in white Gaussian noise (WGN). The inherent limitations governed by the extreme clipping of the input data are analyzed using the Cramer-Rao bound (CRB) that is derived for a two-sensor array. In addition, several estimators for the I-bit estimation are discussed. Numerical and analytical analyses of the estimation error reveal weak dependency on signal-to-noise ratio (SNR) with singular behavior of the estimation error in certain DOA angles.     

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.     

Transmission Characteristics of an FM Signal Through a Hard Limiting Repeater

The response of an FM detector to an FM signal which is passed through a hard limiting repeater together with additive Gaussian noise is described. A general expression of the output SNR is derived that enables the determination of the threshold behavior. To clarify the feature of a transmission characteristic, a comparison with a linear repeater is also made. The output SNR is found to be larger than that of the linear system for all practical values of input CNR's.     

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.     

Radiometric detection of spread-spectrum signals in noise ofuncertain power

The standard analysis of the radiometric detectability of a spread-spectrum signal assumes a background of stationary, white Gaussian noise whose power spectral density can be measured very accurately. This assumption yields a fairly high probability of interception, even for signals of short duration. By explicitly considering the effect of uncertain knowledge of the noise power density, it is demonstrated that detection of these signals by a wideband radiometer can be considerably more difficult in practice than is indicated by the standard result. Worst-case performance bounds are provided as a function of input signal-to-noise ratio (SNR), time-bandwidth (TW) product and peak-to-peak noise uncertainty. The results are illustrated graphically for a number of situations of interest. It is also shown that asymptotically, as the TW product becomes large, the SNR required for detection becomes a function of noise uncertainty only and is independent of the detection parameters and the observation interval     

Signal-to-Noise Ratio of Arbitrary Power-Series Nonlinear Amplifier

A general analysis of the effect of an arbitrary power-series nonlinear amplifier followed by a coherent mixing device on signal-to-noise ratio (SNR) is performed. An expression is derived for the improvement factor which is defined as the logarithm of the ratio of the output SNR to the input SNR. This expression is applicable to the coherent amplitude detector and phase locked loop as well as noncoherent amplifier by appropriate selections of the detection angle. Moreover, the improvement factor can be obtained for noise with an arbitrary amplitude distribution. To demonstrate the applicability of this analysis, the improvement factors of the nonlinear amplifiers such as a power-law amplifier and a power-series amplifier with positive and negative discriminations are numerically calculated for the cases where the input noise amplitude distributions are Rician and triangular.     

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.     

星载DBF接收天线误差校正算法

 提出了一种改进的基于子空间的星载数字波束形成（DBF）接收天线的误差校正方法。根据阵列互耦效应主要取决于阵元间的几何距离这一特点,利用阵元空间排布的对称性简化了天线的互耦模型,将天线的互耦效应及射频(RF)通道失配统一为通道间的幅相不一致。通过在基带注入特定的阵内相位差降低了子空间算法的计算复杂度。在建立7单元正六边形平面阵仿真模型的基础上,分析不同信噪比(SNR)环境下校正算法的性能,经比较得出可以通过提高发射信号功率改善误差估计的精度,验证了算法的有效性。仿真分析结果表明该算法在卫星通信系统中有一定的工程应用价值。     

宽带信号角跟踪和四通道单脉冲方案

分析了宽带信号角跟踪的特殊问题及其实现方案。基于互相关函数的角误差检测方法,推导出了在非相关噪声及相关噪声背景下差路信号的输出信噪比及其角度随机误差的数学表达式,进而给出了带宽增益和最佳带宽的概念,以及提高输出信噪比的方法。为了在低载噪比（C/N）时获得角捕获所需要的和路信号以及差路的归一化信号,提出了四通道单脉冲方案。最后归纳出了低C/N时宽带信号角捕获和角跟踪的几种方法并提出了建议。     

使用电场传感器阵列的水下运动目标检测与参数估计

研究了基于电场传感器阵列的水下运动目标检测与参数估计方法。在背景噪声为高斯白噪声和目标作匀速直线运动的假设下,利用电场传感器阵列获取的船舶水下准静态电场空时特征,通过广义似然比检测和随机搜索寻优算法,可实现对海水中运动船舶的目标检测和参数估计。仿真试验结果表明:在信噪比大于0 dB时能够取得较好的估计精度;在信噪比低至10 dB时仍能有效检测目标。     

Output Signal-to-Noise Ratio for Amplitude and Intensity Modulated Laser

General expressions are obtained for output SNR for both amplitude- and intensity-modulated lasers, where bandlimited Gaussian noise has been chosen as a modulating signal, and in the presence of background light. Two types of modulating signals are considered: the baseband and bandpass modulating signals. Detailed calculations are made for output SNR when an ideal narrowband optical filter is used. The dependence of output SNR on several parameters, such as the center frequency of the modulating signal, the effective average quantum rate, and input SNR, are discussed. In addition, the difference in performance between amplitude and intensity modulation is discussed. The detection characteristics of the homodyne system are also considered.     

Theory of LDV Tracking Systems

The application of frequency-tracking systems to the analysis of laser doppler velocimeter (LDV) signals degraded by background noise has been studied both theoretically and experimentally. Expressions are derived for both the correlation function and the expected value of the phase derivative in the general case of noise off center from the Doppler frequency, and these results are specialized to specific cases of practical interest. Laboratory measurements of output signal-to-noise ratio (SNR) and dc error, for varying input SNR and noise center frequency offset, show good agreement with the theoretical predictions.     

On the Mean Frequency Measurement System Using Correlation Detection

This paper is concerned with the problem of measuring the mean frequency of the power spectrum of a zero-mean, stationary, narrowband Gaussian random signal in the presence of additive Gaussian noise. Signal-to-noise ratios at the output of the mean frequency measurement system using correlation detection are analyzed in terms of input signal-to-noise ratio, input signal and noise bandwidths, and integration time. The results obtained are verified experimentally, and a comparison with a conventional zero-crossing detector is also made.     

常规闭口风洞相阵列气动声学试验

传统气动声学研究观点认为,精确的声学测量要求风洞背景噪声和洞壁反射足够低,传声器测量结果有足够高的信噪比,这是大多数风洞无法达到的要求。近些年,基于声纳和雷达技术发展起来的麦克风相阵列技术可以通过增加阵列的传声器数目从而大幅提高声学测量的信噪比,具有噪声源研究和定位能力,并被成功地应用于非声学固壁风洞噪声源测量和噪声物理机制研究。作者基于相阵列波束生成频域算法研制出常规闭口风洞相阵列系统及相关技术,在FD-09风洞尝试进行了相阵列校准试验和某民机噪声测量试验。结果表明：相阵列技术能够准确捕捉到真实的校准声源,并从技术上验证了相阵列系统在常规闭口风洞测量气动噪声是有效的。