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.     

Some Matched Filter Configurations for Infrared Systems

An analysis of the output of three alternative matched filter configurations in an infrared scanning system model is presented. The sensor is corrupted by thermal noise, generation-recombination noise, photon noise, and modulation noise, the latter providing an extreme discoloration in the signal passband. Expressions for the signal voltage density spectrum, signal pulse shape, noise power spectrum, and average noise power at the matched filter output are derived where the integral evaluations attendant to these derivations do not appear elsewhere in the literature. The paper also provides graphical displays of the signal-to-noise power ratio at the filter output versus various system parameters, noise power spectrum out of the matched filter versus ?, and the signal pulse shape out of the filter versus time. Also included are discussions of practically realizable approximations to the matched filters and curve fitting techniques for the signal pulse shape function.     

On suboptimal detection of 3-dimensional moving targets

The author designates matched filters that are completely characterized by the velocity of the target as assumed velocity filters (AVFs). Like most matched filtering techniques where the signal parameters range in a continuum, the AVF must be implemented suboptimally by partitioning the velocity space. The author investigates the possibility of using a signal-to-noise ratio (SNR) loss factor as the criterion for the partition. The loss factor is a measurement of the loss of SNR at the output of the matched filter due to mismatch of filter parameters. In the scenario of detecting a moving satellite from a ground-based sensor, because of the vast sky the sensor has to search, it is important to keep the number of filters minimal. The author shows that, with a fixed loss factor, the number of filters required for coverage increases linearly as the span of the two-dimensional velocity space increases quadratically. The rate of increase is further reduced when the loss factor is made proportional to expected target angular speed     

Remarks on ?Comments on 'Signal Resolution via Digital Inverse Filtering'?

Published comments on a recent paper criticized the use of inverse filtering as applied to resolution of overlapping radar signal returns. It is shown that an inadequate model of the inverse filter was assumed by the critic, which lead him to predict excessive time sidelobes at the filter output. It is demonstrated, by computer simulation, that the time sidelobes at the output of the true inverse filter are down 30 dB or more.     

Mismatched Filtering of Sonar Signals

A replica correlator (matched filter) is an optimum processor for a receiver employing a pulse of continuous wave (CW) signal in a white Gaussian noise background. In an active sonar, however, when the target of interest has low Doppler shift and is embedded in a high reverberation background, this is not so. High sidelobes of the correlator frequency response pass a significant portion of the signal contained in the mainlobe of the reverberation spectrum. In order to reduce the sidelobes of the correlator output spectrum and at the same time keep the increase in its 3 dB bandwidth to a small amount, we propose lengthening of the replica of the transmitted signal and weighting it by a Kaiser window. It is demonstrated that by extending the weighted replica by 50 percent compared with the transmitted signal, it is possible to reduce the sidelobe levels to at least 40 dB below the mainlobe peak, with the concomitant increase of the 3 dB band-width by less than 5 percent. The degradation in signal-to-noise ratio (SNR) performance for such a ?mismatched? filter receiver with respect to the matched filter is less than 1.5 dB.     

Proportional Tracking with Clipped-input Matched Filters

A proportional boresight-error measurement is described for tracking systems that is applicable to envelope-producing matched filters with hard-limited inputs. The error response is derived as a function of input SNR and the filter output SNR is estimated.     

GPS多径信号的自适应滤波估计方法

 研究全球定位系统(GPS)多径信号估计的问题。通过分析自适应滤波器的原理,建立了数字中频信号处理的数学模型,提出一种用自适应滤波实现GPS多径幅度、码相位和载波相位估计的方法。该方法采用不同延迟的伪随机序列对信号进行解扩、解调和累加,得到了作为期望信号的系列自适应滤波相关值。对该方法与其他3种方法进行了理论上的分析比较,得出本方法具有信噪比高、自适应滤波性能好、带有码相位信息和不存在载波模糊度问题等优点。根据各种滤波器算法的特点和本应用的需求,给出了选用递归最小二乘算法实现的方法。通过计算机仿真,验证了提出的方法能够在14 dB的信噪比下,以1个采样间隔的时间延迟分辨率和0.005周的载波相位估计精度估计出GPS L1的多径信号。     

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.     

Improved Range Resolution Filters for Rectangular-Pulse Radar Systems

The performance of several new clutter-reduction filters suitable for rectangular-pulse radar systems is investigated. The new filters consist of various approximations and modifications of two filters known to be optimal for certain criteria: the well-known Urkowitz filter which optiizes the clutter improvement ratio, and the newer sidelobe reduction filter which minimizes output noise power subject to peak sidelobe constaints. The new filters are compared usig five basic criteria: clutter improvement ratio, signal-to-noise ratio, sidelobe peak ratio, pulse compression ratio, and filter complexity. The results are summarized in tabular and graphical form.     

Signal-to-Noise Ratio Calculations in Pulse and Pulse Doppler Radars

In low pulse-repetition frequency (PRF) pulse radars, signal-to-noise ratio (SNR) is usually calculated on a per pulse basis and this value is then multiplied by the number of pulses integrated to obtain the SNR for a given duration of target illumination. In high PRF pulse Doppler radars, SNR is usually calculated by using the centerline power of the transmitted signal spectrum as the target return power because the centerline is kept in the receiver and returns of the PRF lines are notched out [1]. We show here that both methods of SNR calculations are entirely equivalent for matched transmit-receive radar systems.     

Poly-phase codes and optimal filters for multiple user ranging

A technique is introduced to select poly-phase codes and optimal filters of a pulse compression system that have specific temporal and frequency characteristics. In the particular problem under study, multiple vehicles are assigned unique codes and receiver filters that have nearly orthogonal signatures. Narrowband users, that act as interference, are also present within the system. A code selection algorithm is used to select codes which have low autocorrelation sidelobes and low cross correlation peaks. Optimal mismatched filters are designed for these codes which minimize the peak values in the autocorrelation and the cross correlation functions. An adjustment to the filter design technique produces filters with nulls in their frequency response, in addition to having low correlation peaks. The method produces good codes and filters for a four-user system with length 34 four-phase codes. There is considerable improvement in cross and autocorrelation sidelobe levels over the matched filter case with only a slight decrease in the signal-to-noise ratio (SNR) of the system. The mismatched filter design also allows the design of frequency nulls at any frequency with arbitrary null attenuation, null width, and sidelobe level, at the cost of a slight decrease in processing gain     

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.     

基于独立成分分析的混合LFM信号检测

混合LFM信号广泛存在于实际信号环境巾,对其检测极其重要。对有严重交叉项的混合LFM信号的检测十分困难,因此提出了一种基于独立成分分析的混合LFM信号检测法。通过盲源分离提取各独立成分,利用时频分布矩阵的联合对角化法抑制交叉项,再由各成分信号自项求和重构Wigner-Ville分布,采用Wigner-Hough检测各LFM成分。分析了Wigner-Hough变换输入信噪比和输出信噪比的关系,仿真验证了算法的有效性,得出随着样本点数的增加,在低信噪比条件下,能获得好的检测性能的结论：     

Missing radar pulse clutter processing

The degradation of conventional clutter processing filters due to missing pulses resulting from RF interference blanking, ambiguous range returns when no filter pulses are used, or eclipsing is described. The effects of a missing pulse on uncompensated and optimum clutter filters are investigated. The maximum improvement factor method and other methods are compared to the optimum filtering. New methods and results using a minimax log energy search method are described and are shown to provide performance and/or implementation complexity advantages     

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。     

Energy Detection of a Random Process in Colored Gaussian Noise

A likelihood receiver for a Gaussian random signal process in colored Gaussian noise is realized with a quadratic form of a finite-duration sample of the input process. Such a receiver may be called a "filtered energy detector." The output statistic is compared with a threshold and if the threshold is exceeded, a signal is said to be present. False alarm and detection probabilities may be estimated if tabulated distributions can be fitted to the actual distributions of the test statistic which are unknown. Gamma distributions were fitted to the conditional probability densities of the output statistic by equating means and variances, formulas for which are derived assuming a large observation interval. A numerical example is given for the case in which the noise and signal processes have spectral densities of the same shape or are flat. The optimum filter turns out to be a band-limited noise whitener. The factors governing false alarm and detection probabilities are the filter bandwidth, the sample duration, and the signal level compared to the noise. Two sets of receiver operating characteristic curves are presented to complete the example.     

Comments on "Optimum Bandwidth of a Low-Pass Filter for Detection of a Pulse in Nonstationary Noise"

In a recent correspondence1 a calculation of the optimum bandwidth of a low-pass RC filter for the detection of a pulse signal in nonstationary noise was presented. The purpose of this correspondence is: 1) to point out additional references to the work which has been conducted in the stationary noise case, and 2) to present an interesting alternate derivation of the expected output noise power for the nonstationary noise case.     

Optimum Signal and Filter Design in Underwater Acoustic Echo Ranging Systems

Optimization of the filter, the signal, and the signal and filter jointly are studied in the sonar environment under noise and reverberation limited conditions. The maximization of the receiver output signal-to-interference ratio is used as a performance criterion with unit energy constraint on both signal and filter. In the filter design problem, the optimum filter function is the solution of a linear integral equation. The kernel of the integral equation is a function of the target and medium scattering functions and the reverberation distribution. In the signal design problem, a similar type of integral equation is obtained as in the filter optimization problem. In the joint signal and filter design problem, it is shown that the optimum signal and filter functions are the solutions to a pair of linear integral equations with the largest (SIR)O. Several examples are investigated for different mediums and reverberation distributions with the finite matrix approximation method. An interative technique is used to compute the joint optimization of signal and filter.     

Probability Densities and Characteristic Functions for Fluctuating Targets

Probability density functions and characteristic functions for the projected area of a tumbling target object are derived together with the densities and characteristic functions for the corresponding signal-plus-noise voltage output of an infrared sensor. Several cases are considered in which the signal pulse arrival time is either known or unknown, a matched filter or a suboptimum filter is used; the signal pulse shape is either Gaussian or is unspecified; and the target orientation angles are either uniformly or nonuniformly distributed.     

低通滤波器的阶跃响应及其对动态校准的影响

动态测试系统在利用阶跃信号进行动态校准时,系统中的低通滤波器环节所产生的衰减振荡可能会误导测试人员,特别是对于带传压管道的动态压力测试系统。仿真与测试结果表明,各种模拟低通滤波器和IIR数字低通滤波器的阶跃响应都会出现一定的衰减振荡。针对带低通滤波器的系统以及其他系统的阶跃激励校准,通过对简单FFT频响分析方法、矩形单脉冲法、冲激响应法三种方法的比较,发现矩形单脉冲法能更正确地对阶跃校准数据进行频响分析。