Calculating the performance of linear and square-law detectors

A method is presented for calculating the performance of linear and square-law detectors in detection schemes that employ noncoherent integration. The method consists of transforming the coherent characteristic function, which is usually easy to obtain to a noncoherent moment generating function describing the test statistic of a linear or square-law detector. The method provides a single mathematical framework for many signal models (both classical and new) and can be implemented using standard numerical routines. Although the method is not always optimum in terms of computing speed for specific classical models, its common approach for all signal models makes it very efficient in term of learning and implementation times. Classical results as well as results for an extended set of target models consisting of an arbitrary number of constant amplitude random phase returns are presented to demonstrate the technique. It is shown for the signal parameters considered that the performance difference between the linear and square-law detectors is relatively insignificant     

An adaptive array detector with mismatched signal rejection

An adaptive detection algorithm with a sensibility parameter for rejecting unwanted signals is presented. This algorithm is a simple modification of the generalized likelihood ratio (GLR) detector (or test) for detecting a signal in zero mean Gaussian noise with unknown correlation matrix. Specifically, the adaptive detection algorithm is obtained by introducing an arbitrary positive scalar, which is called the sensitivity parameter, into the GLR detector as a multiplier of an already existing quadratic term. The GLR detector then becomes a special case of this detector for the unity sensitivity parameter. It is shown that the sensitivity parameter controls the degree to which unwanted signals are rejected. From numerical examples, it is demonstrated how the sensitivity parameter can be chosen such that unwanted signals, can be rejected while maintaining acceptable detection loss for slightly mismatched signals. Further insight into previous work on adaptive detection is also given     

Optimum detection and location estimation of target lines in the range-time space of a search radar

The average likelihood ratio detector is derived as the optimum detector for detecting a target line with unknown normal parameters in the range-time data space of a search radar, which is corrupted by Gaussian noise. The receiver operation characteristics of this optimum detector is derived to evaluate its performance improvement in comparison with the Hough detector, which uses the return signal of several successive scans to achieve a non-coherent integration improvement and get a better performance than the conventional detector. This comparison, which is done through analytic derivations and also through simulation results, shows that the average likelihood ratio detector has a better performance for different SNR values. This result is justified by showing the disadvantages of the Hough method, which are eliminated by the optimum detector. To have an estimate for the location of the detected target line in the optimum detection method as the Hough method, which detects and localizes the target lines simultaneously, we present the maximum a posteriori probability estimator. The estimation performance of the two methods is then compared and it is shown that the maximum a posteriori probability estimator localizes the detected target lines with a better performance in comparison with the Hough method.     

Detection of random signals via spectrum matching

Using a priori knowledge of the signal power spectral density (PSD), a spectrum matching approach which effectively utilizes the available signal spectral shape is developed for random signal detection. Two spectrum matching detector (SMD) structures, which are implemented by correlogram and periodogram, respectively, are examined. Theoretical calculation of their false alarm rates is derived and confirmed by simulations. It is also demonstrated that the proposed detectors outperform the standard periodogram, Bartlett method, and energy detector under constant false alarm rate (CFAR) condition for two different random signals.     

Spectral Analysis and Subtraction of Noise in Radar Signals

A new method of maximum entropy spectral estimation called the revised maximum entropy method (MEM) is formulated and is applied to the spectral analysis of the echo signals from atmospheric turbulence observed by an incoherent scatter radar. The revised MEM is shown free from many demerits of the other methods for spectral analysis. Further it makes it possible to subtract the white noise usually contained in the data during the processing. Some examples of spectral estimation are shown for the actual radar signals and the simulated data. Another application of the revised MEM is the subtraction of the clutter component which is difficult to do by linear filtering. The method is successfully applied to several data abounding with the clutter to obtain the spectra of the echo signals with less clutter distortion.     

Mean-Level Detection of Nonfluctuating Signals

Analysis of the performance of a mean-level threshold in the detection of nonfluctuating signals is performed. Formulas for the probability of detection are derived and a simple recursive method that can be used for computations is described. Binary integration is discussed, and it is shown that the loss in sensitivity due to the use of an adaptive threshold followed by binary integration is only a fraction of a decibel when compared with optimum binary integration. Binary integration results are given for both fluctuating and nonfluctuating signals.     

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     

On detection using filter banks and higher order statistics

We suggest a method, based on the use of filter bank and higher order statistics (cumulants), for detection of transient signals. The method first uses a bandpass filter bank, which separates the spectrum of the observed signal into narrow frequency bands. Each subfilter of the filter bank is then followed by a cumulant estimator, and thereby suppressing colored noise. By selecting those subfilters that have large output energies, the filter bank can approximate the behavior of a matched filter. Moreover, no a priori information about the waveform of the signal is needed. The performance of the detector is evaluated by using a simulated signal as well as a measured signal. The presented detector is compared with the optimal matched filter detector.     

Multiple-Tone Signals and Detection Probabillities

An analysis technique is presented for multiple-tone signals insystems employing noncoherent integration of a square-law detectoroutput. It is shown how the characteristic function for the teststatistic can be found from the easily determined "coherent"characteristic function defined in the two-dimensional signal space.This result is applied to two detection problems, the detection of multiple-tone signals in Gaussian noise and the detection of a Gaussian signal in multiple-tone plus Gaussian noise interference.The detection curves are compared to an approximation that is often used in practice to estimate performance. It is found that detection performance in the presence of multiple-tone interferences can be significantly different from that in the presence of Gaussian noise alone.     

Waveform Design for Multistatic Radar Detection

We derive the optimal Neyman-Pearson (NP) detector and its performance, and then present a methodology for the design of the transmit signal for a multistatic radar receiver. The detector assumes a Swerling I extended target model as well as signal-dependent noise, i.e., clutter. It is shown that the NP detection performance does not immediately lead to an obvious signal design criterion so that as an alternative, a divergence criterion is proposed for signal design. A simple method for maximizing the divergence, termed the maximum marginal allocation algorithm, is presented and is guaranteed to find the global maximum. The overall approach is a generalization of previous work that determined the optimal detector and transmit signal for a monostatic radar.     

基于CPLD的多路脉冲序列信号检测器设计

用VHDL语言在CPLD器件上实现了一种多路脉冲序列信号检测器,能够用七段数码管实时显示各路已检测出序列信号数目,电路各摸块用VHDL语言来描述。文章介绍了仿真信号的形成原理和电路设计方法,并给出了部分电路和仿真波形。整个多路脉冲序列信号检测器设计在一块CPLD芯片上,与其他方法设计的序列信号检测器相比,具有体积小、可靠性高、功牦低的特点。由于采用模块化的设计,对功能的修改和增加只要修改VHDL源程序,而不必更改硬件电路,从而实现数字系统硬件的软件化。     

Detection probabilities for correlated Rayleigh fading signals

Both the method of saddlepoint integration and its associated saddlepoint approximation are applied to calculating the probability of detecting correlated Rayleigh-fading signals in Gaussian noise by means of a detector that integrates M samples of the output of a quadratic rectifier. The quadrature components of the signal samples are modeled as an autoregressive moving-average process, and specific results are exhibited for a first-order Markov process. By these methods the fluctuation loss can be computed for much larger values of M and for larger values of the detection probability than previously. Values calculated by the saddlepoint approximation prove to be close enough to the exact values to be useful over a broad range of signal parameters     

Detectability of signals in Laplace noise

Closed-form expressions for the false-alarm and detection probabilities attained by the optimum and the linear detectors of a positive signal in n independent samples of noise having a bilateral exponential or Laplace distribution require lengthy computation when n is large, and those for the optimum detector suffer from round-off error because their terms alternate in sign. It is shown how the method of saddlepoint integration can be conveniently applied to compute these probabilities, and numerical comparisons of the accuracies of the methods are presented. The relative efficiency of the two detectors is calculated as a function of n and found to approach the asymptotic value of 2 very slowly     

The Detection Performance of a Modified Moving Window Detector

The modified moving window detector for binary integration has a shorter window length compared with the ordinary moving window detector because of the addition of a third threshold. When the second threshold is reached, a counter begins to count until the third threshold is reached. A graphical method using a probability chain is developed here to analyze and to calculate the detection performance of this type detector. The detection performances for some practical cases are calculated by computer and are compared with the ordinary moving window detector.     

用N2O-C2H2火焰原子吸收光谱法测定不锈钢材料中硅含量

运用N2O-C2H2火焰原子吸收光谱法测定不锈钢材料中的硅含量。介绍硅的最佳测定条件以及线性范围的浓度，在样品测定中对干扰因素进行了综合考虑。实验表明：N2O-C2H2火焰原子吸收光谱法灵敏度高、干扰小、选择性和重现性好，步骤简单、操作容易、分析周期短。测定样品含硅量10μg/mL～60μg/mL(n=6)时，其相对标准偏差均小于1．0％，标准加入回收率均为97．0％～103．0％(n=6)，适用于不锈钢材料中硅含量的测试，达到了实验室分析质量控制的要求。     

Search radar detection and track with the Hough transform. III.Detection performance with binary integration

For pt.II see ibid., vol. 30, no 1, (Jan. 1994). This paper considers how well a Hough transform detector with binary integration improves the performance of a typical surveillance radar. For Hough transform detection, binary integration offers some advantages over noncoherent integration when multiple targets appear in range-time space or when the detector receives signals with a wide range of power. We derive expressions for P_F and P_D for a Hough transform binary integrator and apply the expressions to a typical surveillance radar. The results show that for the case considered, the binary Hough integrator improves the power budget of the radar by about 3 dB for a nonfluctuating target and 1 dB for a highly fluctuating target     

亚音速升力面气动敏感性导数计算

具有任意曲线前缘的亚音速升力面的气动敏感性导数由核函数法给出。用自适应积分法计算弦向积分,用Multhopp法结合抽去奇点,计算Mangler积分主值。将积分核展成Chebyshef多项式的渐近展开式以保证结果的收敛性。最后将广义力系数及其敏感性导数表示成简单形式,对椭圆、矩形和后掠机翼作了计算,所得结果在升力面理论精度范围内与直接由核函数法得到的结果一致;而且所得到的偏导数可在飞机设计中分析综合用于多学科优化。     

Comparison of various periodograms for sinusoid detection andfrequency estimation

With the advent of the fast Fourier transform (FFT) algorithm, the periodogram and its variants such as the Bartlett's procedure and Welch method, have become very popular for spectral analysis. However, there has not been a thorough comparison of the detection and estimation performances of these methods. Different forms of the periodogram are studied here for single real tone detection and frequency estimation in the presence of white Gaussian noise. The threshold effect in frequency estimation, that is, when the estimation errors become several orders of magnitude greater than the Cramer-Rao lower bound (CRLB), is also investigated. It is shown that the standard periodogram gives the optimum detection performance for a pure tone while the Welch method is the best detector when there is phase instability in the sinusoid. As expected, since the conventional periodogram is a maximum likelihood estimator of frequency, it generally provides the minimum mean square frequency estimation errors     

Monopulse Radar Angle Tracking Accuracy with Sum Channel Limiting

The variance of angle tracking error is found for an amplitude-comparison form of monopulse radar when the sum channel contains a limiter prior to the angle error detector. The error expression is valid for any shape of transmitted pulse and any duration of range tracking gate but does assume matched filters in signal processing channels. The procedures used are rigorous and an example of results is worked out for the special case of a rectangular transmitted pulse envelope. It is shown, for rectangular pulses, that achievable angle tracking error variance with sum channel limiting is not more than 2.22 dB larger than the theoretical minimum for any processor and not more than 1.29 dB larger than a similar signal processor that uses a "linear" angle error detector. Results apply for large single-pulse signal-to-noise ratio.     

Performance of a Two-Sample Mann-Whitney Nonparametric Detector in a Radar Application

The detection of signals in an unknown, typically non-Gaussian noise environment, while attempting to maintain a constant false-alarm rate, is a common problem in radar and sonar. The raw receiver data is commonly processed initially by a bank of frequency filters. The further processing of the outputs from the filter bank by a two-sample Mann-Whitney detector is considered. When the noise statistics in all filters are identical, the Mann-Whitney detector is distribution free, i. e., the false-alarm probability may be prescribed in advance regardless of the precise form of the noise statistics. The primary purpose of this paper is to demonstrate the potential advantage of nonparametric detectors over conventional detectors. The signal detection performance of the Mann-Whitney detector is compared to that of an ordinary linear envelope detector plus integrator in the presence of Gaussian and several hypothetical forms of non-Gaussian noise. This comparison is made for both uniform and nonuniform distributions of noise power across the filter bank. Besides providing a much more constant false-alarm rate than the conventional detector, the Mann-Whitney detector's signal detection performance is found also to be much less sensitive to the form of the noise statistics. In one case, its detection sensitivity is found to be 11 dB better than that of the conventional detector. Even when the noise power density is made moderately nonuniform across the filter bank, the detection performance of the Mann-Whitney detector is found not to be significantly affected.