Hard Limiting and Sequential Detection Applied to Loran-C

The combination of an antenna, a 100 kHz bandpass filter, a hard limiter, and a sequential detector can supply highly accurate Loran-C data to a digital processor, even under low signal-to-noise-ratio conditions. For such a simple, low-cost receiver, calculations are given for the accuracy of the envelope and phase tracking of the Loran-C signal as a function of the signal-to-noise (Gaussian and atmospheric) ratio, averaging time, and radian speed of the observer with respect to the transmitter. Mentioned are the quasi-noise censoring effects of the hard limiter. Besides the Loran-C application, the hard limiter-sequential detector system can in general be applied for low-cost, synchronous signal detection under poor signal-to-noise ratio.     

Hard-Limiter Output Autocorrelation Function: Gaussian & Sinusoidal Input

An expression is derived for the autocorrelation function of the output of a hard limiter whose input is stationary Gaussian noise with zero mean plus independent random-phase sinusoidal signal. The output spectrum may then be evaluated. This spectrum is extremely useful in understanding the properties of a filter-limit-filter-detect signal processor whose signal input is an actual sinusoid, or when a sinusoid is used as a test signal.     

Hard-Limiting an Offset Signal

Expressions are derived for the output autocorrelation function of a hard limiter driven by the sum of signal, noise, and an offset term. Two signal types are considered: a random-phase sinusoid and a stationary, zero-mean Gaussian process. For each signal the offset at the sampling times is modeled first as a constant, and second, as a sequence of binary-valued random variables.     

Carrier and intermodulation performance of limiters excited bymulticarriers

A general formula, using a Fourier-series representation, is derived for the input-output characteristic of ideal hard limiters, biased hard limiters and biased soft limiters. Using this formula one can obtain an expression, involving Bessel functions for calculating the amplitudes of the output products of a limiter excited by a multicarrier signal plus Gaussian noise. In contrast with previously published results, the implementation of the present expression requires the computation of functions that are available in most mathematical-library subroutines and can even be implemented by using programmable pocket calculators. Results obtained by using the present expression are in excellent agreement with the previously published results. Additionally, the expression is used to generate a soft- and a hard-limiter signal-suppression database for the case in which a single large carrier and a number of equal-power small carriers exist in a noisy environment     

Interference Due to Limiting and Demodulation of Two Angle Modulated Signals

Two angle modulated signals (FM or PM) passing through a limiter and then a demodulator are analyzed. The analysis considers the problem of adjacent carrier interference, direct adjacent channel interference (DACI) or cross talk, and adjacent channel interference (ACI). The analysis of adjacent carrier interference shows that if the 3rd order IM is not to overlap the signal spectra, the carrier frequencies must be separated by 2B where B is the bandwidth of each carrier. The ACI analysis shows that the carrier frequencies must be separated by B+2?m for no ACI, since the demodulator reduces the bandwidth of the 3rd order IM from 3B to 2B+2?m where ?m is the maximum frequency of each baseband. The DACI analysis shows that DACI does not exist in a PM system and is -52 dB for an ideal hard limiter with no bandpass filter. But the DACI is -58 dB for an ideal hard limiter with a more realistic bandpass filter.     

应答机测距转发性能分析

分析了采用视频AGC（自动增益控制）、射频AGC和限幅器等3种测距转发模式的应答机性能,分析结果表明：视频AGC模式下,应答机测距通道的输出功率恒定,测距转发性能不随上行信号强度变化而变化;射频AGC模式下,应答机测距通道的输出功率不恒定,测距转发性能随着上行信号强度变化而变化;而限幅器模式可看作射频AGC的一种特殊情况。仿真分析了我国研制的限幅器和射频AGC两种模式应答机的性能,结果表明理论计算的性能与实测结果一致,理论分析正确且理论分析结果可作为链路计算的依据。     

The Effect of Hard Limiting in the Presence of Large Out-of-Band Interfering Signals

The effect of hard limiting on the phase of a test signal was investigated when large out-of-band interfering signals are present at the input to the limiter. First a single and then two discrete interfering signals were considered. The interfering signals and the test signal are restricted to narrow but separated bands. The test signal is recovered after limiting by narrowband filtering. The analysis of the single interfering signal is essentially the same as that performed by Cahn.1 In this correspondence experimental evidence is presented to verify the analysis and, in addition, the case of two interfering signals is considered.     

The Effect of Hard Limiting an Angle-Modulated Signal Plus Noise

The effect of hard limiting an angle-modulated signal plus narrow-band Gaussian noise is analyzed. Several examples are considered?sinusoidal angle modulation, Gaussian angle modulation, and biphase angle modulation. The general conclusion is that when a zonal band-pass filter is used, which rejects dc and second harmonics, an angle-modulated signal plus Gaussian noise provides the same output signal-to-noise ratio as shown by Davenport for a CW signal plus Gaussian noise. However, when a narrow bandpass filter is used, which has a bandwidth approximately equal to the input angle-modulated signal, an angle-modulated signal plus Gaussian noise has a better output signal-to-noise ratio than a CW signal plus Gaussian noise.     

Analysis and Design Considerations of Hard Limiters for LF and VLF Navaid Receivers

Hard limiters, followed by a D-type flip-flop as a digital-signal-polarity detector, are very effective receiver/phase detectors for low frequency (LF) and very low frequency (VLF) navigation receivers. However the performance not only depends on the signal quality, but also on the specifications of the hard limiter and the flip-flop. Analysis of the tracking accuracy is given as a function of the dc offsets of the limiter and the flip-flop, the linear gain of the limiter, the signal-to-noise ratios of one or more input signals, and the power consumption of the limiter. The results are presented in formulas and graphs for application by circuit designers. A design example of a low-power, high-gain limiter is given.     

Spurious Target Generation Due to Hard Limiting in Pulse Compression Radars

A method is presented to calculate the output of a hard limiter if the input consists of a superposition of three phase-coded signals. A detailed investigation is made of the case where the limiter input signals are phase reversal modulated according to a maximum length linear code. It is shown in this case that a false target signal is generated at the limiter output. The amplitude distribution of the false target signal is investigated along with the distribution of the captured true target signals. A digital computer simulation confirms the theoretically predicted effects.     

基于中值滤波和小波变换的混合滤波方法在推进剂监测中的应用

目前,监测传感器传出信号中混有很多噪声,为提高信号可信度,需要一种有效的信号处理方法。文章基于Matlab仿真环境,完成了信号仿真和滤波算法的设计,重点对单传感器仿真信号的去噪和多传感器信息融合进行了研究,提出了基于中值滤波和小波阈值滤波的混合滤波方案和基于Kalman滤波的信号融合方案。研究工作有:基于高斯白噪声和脉冲噪声的数学特性,合理假设出5种基本信号形式;依据实际数据,完成单传感器和多传感器信号仿真,确定信噪比和均方根误差作为去噪评定指标;综合分析现有的滤波算法的滤波特性,利用不同长度滑动窗口的中值滤波处理实验信号,选取合适长度的滑动窗口。设置对比实验确定小波阈值滤波中的小波基函数选取、阈值计算和分解尺度等参数;融合中值滤波和小波阈值滤波优势,设计混合滤波方案,去除单传感器仿真信号中的噪声;研究信息融合理论在泄漏监测系统中的应用,设置不同融合方式下的对比实验,确立最佳融合方式下的Kalman滤波方案,实现多传感器信息融合。     

Bounds on Probability of Error in Decision Feedback Equalizers

Evaluation of the probability of error in decision feedback equalizers is difficult due to the presence of a hard limiter in the feedback path. This paper derives the upper and lower bounds on the probability of a single error and multiple error patterns. The bounds are fairly tight. The bounds can also be used to select proper tap gains of the equalizer.     

The Effect of Limiting a Biphase or Quadriphase Signal Plus Interference

This paper analyzes the case of limiting an incoherent or coherent interference signal at the frequency of a biphase or quadriphase digital signal. The results give the IM products, interference, and attenuation of the digital signal, plus interference through a hard limiter.     

The Detection Performance of the Siebert and Dicke-Fix CFAR Radar Detectors

The Siebert and the Dicke-fix CFAR radar detectors, used to maintain a constant false alarm rate (CFAR) in radar receivers under very similar circumstances, are considered. The Siebert detector represents the maximum-likelihood detection procedure for a signal in Gaussian noise of unknown power level, whereas the Dicke-fix makes use of a bandpass limiter to normalize the input and thus ensure a constant false alarm rate. The detection performance of the two detectors is determined and a comparison shows that over a wide range of parameters, the Dicke-fix introduces a loss which is approximately 1 B larger than for the Siebert detector.     

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.     

An Analysis of the Performance of the Oscillating Limiter Driven by FM Signals Corrupted by Noise

The behavior of the oscillating limiter (OL) driven by FM signals is surveyed, and its performance with signal corrupted by noise is investigated. For high values of the carrier-to-noise ratio (CNR), if the frequency deviation of the signal is small in comparison with the locking range of the OL, it is calculated, and experimentally verified, that a system OL discriminator is equivalent to a system bandpass limiter discriminator followed by a linear network whose frequency response has been specified. When the frequency deviation is not so small, the baseband noise power increases with it; a formula is given that allows the calculation of this power when the signal is such that the circuit operates in quasistationary fashion. For low values of the CNR, a mathematical analysis presents unsurmountable difficulties. However, heuristic argumentation leads to an interpretation of the operation of the OL in the threshold region, which is substantiated by an experimental investigation. The results of this paper enable a comparative evaluation of a system OL discriminator and a system bandpass limiter discriminator, to which the former reduces when the feedback path in the OL is open.     

低频信号的混沌高斯化检测方法

大气天电噪声是干扰低频信号的主要噪声源。文章主要针对大气噪声的高斯化方法进行研究,提出了基于混沌方程快速求解、混沌相变判别等技术的噪声高斯化方法,以非线性信号处理技术为依据,通过实验室模拟信道环境,完成低频弱信号的混沌高斯化及检测,2PSK弱信号检测的理论实验验证了其有效性,可为低频接收技术的发展提供依据。     

Sequential track extraction

Sensors like radar or sonar usually produce data on the basis of a single frame of observation: target detections. The detection performance is described by quantities like detection probability Pd and false alarm density f. A different task of detection is formation of tracks of targets unknown in number from data of multiple consecutive frames of observation. This leads to quantities which are of a higher level of abstraction: extracted tracks. This again is a detection process. Under benign conditions (high Pd, low f and well separated targets) conventional methods of track initiation are recommended to solve a simple task. However, under hard conditions the process of track extraction is known to be difficult. We here concentrate on the case of well separated targets and derive an optimal combinatorial method which can be used under hard operating conditions. The method relates to MHT (multiple hypothesis tracking), uses a sequential likelihood ratio test and derives benefit from processing signal strength information. The performance of the track extraction method is described by parameters such as detection probability and false detection rate on track level, while Pd and f are input parameters which relate to the signal-to-noise interference ratio (SNIR), the clutter density, and the threshold set for target detection. In particular the average test lengths are analyzed parametrically as they are relevant for a user to estimate the time delay for track formation under hard conditions     

Experiments in Adaptive Estimation of Unknown Binary Waveforms

A special-purpose adaptive machine is described which carries out estimation in real time of an unknown binary waveform which is perturbed with additive Gaussian noise. Unknown waveforms of over 103 samples in duration can be recovered. The unknown waveforms are of unknown epoch and can reappear at either random or periodic time intervals. The observed signal is received at moderate or low signal-to-noise ratios so that a single observation of the received data (even if one knew the precise signal arrival time) is not sufficient to provide a good estimate of the signal waveshape. Experimental results are described which show transient behavior waveform estimate. The transient behavior is expressed as the number of errors in the current estimate of the signal plotted vs. time. In a noisy environment, each ``learning' transient is a random time function. These learning transients are shown for several different signal-to-noise ratios and indicate the threshold noise levels for various types of initial states of the machine memory.     

轴流风扇宽频噪声声功率实验研究

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。为了研究管道内宽频噪声,利用沿管道内壁面布置的环形麦克风阵列对单级轴流风扇进行了噪声测量,通过测量信号与参考信号互相关以及奇异值分解(SVD)方法成功地得到管道内宽频噪声结果。结果表明:该方法不仅可以计算出管道内主要单音,而且可以计算宽广频率范围内的宽频噪声;并能有效分辨出管道内向前和向后传播的声功率。宽频噪声结果证实该方法可以应用到高背景噪声和硬壁反射下的管道内声场研究。