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.     

Likelihood-ratio detection of frequency-hopped signals

The optimum system for intercepting frequency-hopped signals uses a channelized receiver and a likelihood-ratio test (LRT). Previous results on the performance of the optimum system have been based on Gaussian assumptions, which are generally valid for transmissions having large time-bandwidth areas. Results, obtained by Monte Carlo simulation, for relatively small time-bandwidth transmissions are given here. The signal model is a simple one known as “pure frequency hopping.” Comparisons with the LRT show that energy detection loss increases when the time-bandwidth product of the transmission is increased by increasing the number of frequencies, even when the number of pulses is also increased. The loss decreases when only the number of pulses is increased. Over the parameter range observed, binary detection loss tends to increase with the number of pulses and decrease with the number of frequencies. Results are included for a moving-window version of the LRT. A parameter of the LRT is the signal-to-noise ratio (SNR). The effect of using a design value not equal to the true SNR is shown     

Some Properties and Effects of Reverberation in Acoustic Surveillance

Following the work of Van Trees,[1] the effect of wide-sense stationary clutter on signal detectability with a matched filter is determined. The improvement to be gained by a high time-bandwidth product in the transmitted waveform for the detection of low-velocity targets is clearly shown. The additional noise contributed by the clutter is reduced by a factor equal to the time-bandwidth product. This reducing effect occurs provided that the transmitted waveform is adjusted properly. The optimum transmitted waveform for detection of low-velocity targets turns out to be one whose energy density spectrum is flat over the bandwidth of interest. This derivation is made by a simple application of Schwarz's inequality rather than the application of the calculus of variations that was done by Manasse.[14] Computations were made of the loss encountered by a narrow-band single-frequency waveform and by a wide-band linear FM waveform, each used in a matched-filter detector. The contrast is especially marked for very low target speeds where the narrow-band waveform is very bad. Its loss drops off sharply with target speed while the loss of the wide-band waveform drops off very slowly in comparison. Beyond a certain small target speed, the narrow-band loss is negligible. However, with enough bandwidth, the wide-band waveform can be made to have acceptable loss at all target speeds.     

A Time Sidelobe Reduction Technique for Small Time-Bandwidth Chirp

A filtering technique is described which permits time sidelobe suppression of small time-bandwidth product shirp. Signal-to-noise loss and time sidelobe level sensitivity to Doppler shift are presented for a filtered chirp waveform whose time-bandwidth product is 10.     

Statistical Analysis of Wide-Band Pseudorandom Matched Filter Sonars

A stochastic model of pseudorandom (PR) signals is adopted and a statistical analysis carried out of the velocity (i. e., Doppler) and acceleration tolerances of wide-band PR matched filter sonar systems. The reference functions for these correlation detection systems are considered to be time-compressed or time-expanded replicas of the transmitted signal. Results are derived for the case of a PR signal having a flat power spectral density over a finite bandwidth. It is shown that the velocity and acceleration tolerances are essentially independent of the signal bandwidth and that therefore the radar-derived expressions for the narrow-band tolerances can be extended to the wide-band sonar case. An interesting result is that the derived acceleration tolerance is approximately three times the widely used estimate that is based on the target remaining in the same Doppler channel over the integration time.     

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     

Chirp Waveform Generation Using Digital Samples

This paper describes two methods of generating an analog frequency-modulated waveform by the use of a small number of digital samples of the ?chirp? waveform. The number of digital samples required is a function of the time-bandwidth product. For certain values of time-bandwidth product, this type of signal generation becomes extremely efficient. Several proofs are offered which show how to select ?optimum? values of time-bandwidth products. Two hardware implementations are suggested. One is based on the use of modulo arithmetic and a small stored memory table. The second method utilizes the inherent signal symmetries available if ?optimum? time-bandwidth products are selected. The symmetrical signal patterns are stored in recirculating reversible shift registers which can be read out at high speeds.     

Linear FM Signal Formats for Beacon and Communication Systems

This paper examines the capabilities of the class of linear FM spread-spectrum signals within the context of potential communications systems usage in order to establish some performance criteria and bounds that permit comparison with other spread-spectrum formats. A systematic basis is provided for parameter selection for this class of signals by examining the interaction a mong the frequency-modulation indices, time-bandwidth product, and cross-talk criteria that determine the number of effective linear FM signals (or channels) that can be used within the constraints of a bounded time-frequency region. A general expression is derived relating N, the number of useful signals, R2, a cross-talk parameter, ToWo, the mean time-bandwidth product, and ?max and ?min, the maximum and minimum FM rates of the signal set. Canonic signal processor structures are described for ensembles of linear FM signals that have either constant duration or constant bandwidth. It is then shown that the signal modulation format can be modified in accordance with classical paired-echo theory to expand the utility of this class of signals in both synchronous and nonsynchronous operations to yield the equivalent of time-division and code multiplexing. Possible applications for this signal format are discussed.     

Degradation of Probability of Error Due to IF Filtering

The probability of error P(e) is computed in a binary communication system with a single-pole IF filter. The effect of time-bandwidth product foT and IF frequency to band width ratio f1/Ifo on P(e) is shown. The sampling time is optimized and the effect of nonoptimal sampling time on P(e) is calculated.     

一种高动态低信噪比卫星导航信号捕获方法

为提升高动态低信噪比环境下卫星导航信号的捕获性能,提出了一种基于分数阶傅里叶变换(FrFT)及部分匹配滤波(PMF)的捕获方法。在该方法中,接收机首先利用PMF对接收信号做分段相干积分,随后借助快速傅里叶变换(FFT)对分段积分结果做离散快速FrFT,最后通过检测FrFT输出的峰值完成信号的捕获。由于具有多普勒频率变化率的卫星导航信号在FrFT后呈现能量聚焦特性,所提方法能够显著提高信号的长时间相干积分增益。同时对所提算法的捕获概率、平均捕获时间以及算法复杂度等性能指标进行了理论分析及计算机仿真验证。仿真表明,与传统的PMF-FFT方法相比,所提方法能够通过延长相干积分时间的方式有效提升高动态低信噪比卫星导航信号的捕获概率、降低捕获时间。     

Self-Clutter Cancellation and Ambiguity Properties of Subcomplementary Sequences

In radar signal design it is well known that a fixed volume under the ambiguity surface representing signal energy can only be shifted but not eliminated in the delay-Doppler plane because of the constraint imposed by Woodward's total volume invariance. Rihaczek has shown that periodic signal repetition, though appealing to increased energy, increases the time-bandwidth product at the expense of introducing pronounced ambiguities in the delay-Doppler plane, and thus self-clutter is generated when signals are repeated in the time domain to increase energy. The undesirable self-clutter has a masking effect on targets in different resolution cells thereby limiting performance. An analysis is presented to show that a class of waveforms described in an earlier paper as the subcomplementary set of sequences which are basically repetitive and Hadamard coded, exhibit the property of cancelling self-clutter completely in the delay-Doppler plane if their ambiguity functions are combined. By this technique it is possible to repeat contiguously a basic waveform N times in a prescribed manner to increase signal energy and to cancel totally the resulting self-clutter by combining the ambiguity functions of N different repetitive waveforms which are Hadamard coded. A convenient matrix method to combine the ambiguity functions of subcomplementary sequences, which is an extension of known methods to derive the ambiguity function of repetitive waveforms, is presented. Radar implementation considerations and comparison of performance with various forms of linear frequency modulation (FM) are also discussed.     

Stretch: A Time-Transformation Technique

Stretch is a passive, linear, time-variant technique for performing temporal operations on many classes of signals. The technique employs three dispersive networks and a mixer. Signal slowdown, speedup, or time reversal can be attained by choice of network slopes. These temporal operations are performed within a signal "window," and the duration of the window is determined by the network time-bandwidth products. Both heuristic argumentation and rigorous analysis are presented, as are the results of a simple laboratory experiment.     

Phase-Coded Interrupted CW Signals and Processors

High resolution radars require signals with large time-bandwidth product such as CW signal and coherent pulse train (CPT). We discuss a phase-coded interrupted CW (ICW) signal which is the combination of CW signal and CPT. Phase codes used here are with perfect periodic autocorrelation. The periodic ambiguity function of ICW signals is studied including single-carrier signal and multi-carrier signal. It is interesting that the gate function has different effects on two signals and contributes to a multi-carrier ICW signal which yields nearly perfect autocorrelation. Meanwhile we also suggest an efficient receiver approach to ICW signals, which can reduce the computational burden of the processor and utilize the good properties of P3 and P4 codes.     

Time-Frequency HOP Signals Part II: Coding Based upon Quadratic Congruences

High-efficiency multicomponent signals for maximization of signalto-noise ratio are investigated. Maximization of signal-to-noise ratio in colored noise requires control of volume distribution of the signal ambiguity function and transmission of unity efficiency signals. Signal efficiency is defined as the ratio of average power to the peak power. It is concluded that the signals must be frequency hop pulse trains. Quadratic congruences are chosen to place the components in time-frequency space. The number-theoretic properties of these signals provide bounds on the position and amplitude of the various peaks of the signal ambiguity function. The tradeoffs are shown between volume removal, number of component signals, and the time-bandwidth product.     

基于Kalman滤波的高频CW电报信号自动识别

针对强噪声背景下高频CW电报信号检测算法性能严重下降、误码率较高的问题,文章提出一种基于卡尔曼滤波的高频CW电报信号同步检测识别算法。利用自同步法对CW电报信号实现位同步,进而利用卡尔曼滤波针对时变干扰噪声设置自适应阈值,对信号能量进行软判决,实现CW电报信号的自适应跟踪检测,提取有效信号进行识别。通过短波信道仿真软件和实际短波通信测试表明,该算法能够在强噪声背景下有效检测识别CW电报信号,且算法可由迭代实现。     

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.     

Coherent detection in Laplace noise

The discrete-time detection of a time-varying, additive signal in independent Laplace noise is considered. Previous efforts in this area have been restricted to the constant signal, and identically distributed noise case. Theoretical (closed form) expressions for the false alarm and detection probabilities are developed for both the Neyman-Pearson optimal detector and the classical matched filter detector. Comparisons between the two detectors are made which illustrate the effects of signal-to-noise power ratio and sample size for certain false alarm and detection probability constraints. In view of the fact that the optimal Laplace detector is not UMP, we also investigate the effect of signal amplitude mismatch     

Adaptive resolution of mainlobe and sidelobe detections using model order determination

This work presents the development and performance evaluation of a methodology for distinguishing between mainlobe and sidelobe detections that arise in adaptive radar systems operating in adverse environments. Various adaptive detection test statistics such as the adaptive matched filter (AMF), the generalized likelihood ratio test (GLRT), and adaptive coherence estimate (ACE), and combinations of these, have been previously analyzed with respect to their sidelobe rejection capabilities. In contrast to these methods which are based on detecting a single target with known direction and Doppler, the present method uses model order determination techniques applied to the AMF or GLRT data observed over the range of unknown angle and Doppler parameters. The determination of model order, i.e., the number of signals present in the data, is made by using least-squares model fit error residuals and applying the Akaike Information Criterion (AIC). Comprehensive computer simulation results are presented which demonstrate substantial improvement in sidelobe rejection performance and detections of multiple sources compared with previous methods.     

Recent advances in analog signal processing

Analog signal processors which perform convolution, correlation, matched filtering, and Fourier transformation are considered. Specifically, the authors focus on one- and two-dimensional signal processors using charge-coupled-device, surface-acoustic-wave, acoustooptic, and superconductive components. The device performances are compared in terms of parameters such as signal bandwidth, time-bandwidth product, and dynamic range. These analog components are compared with existing and planned digital processor designs. Potential applications are highlighted in wideband spread-spectrum packet-radio communication, radar range-Doppler imaging, wideband compressive receivers, and low-bit-rate image-coding systems     

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.