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     

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     

Detectability of Spread-Spectrum Signals

Methods of detecting spread-sprectrum signals without knowledge of the pseudorandom code used to generate the signal are described. Exact and approximate methods of calculating relationships among detection probability, false alarm rate, and signal-to-noise ratio are given for radiometers and for channelized pulse-detection systems. The detection performance of the radiometer is compared graphically with that of pulse-detection systems, for two different kinds of pulse detection decision rules. Detection performance as a function of certain signal parameters is shown to be very different for a pulse-detection system than for a radiometer, and this difference in behavior provides a basis for selecting signal parameters that minimize the probability of detection. The reasoning that underlies the selection process is explained, and the process is outlined for each of several signal parameters.     

Cyclic code shift keying: a low probability of intercept communication technique

A low probability of intercept (LPI), or low probability of detection (LPD) communication technique known as cyclic code shift keying (CCSK) is described. We discuss the basic concepts of CCSK and describe a system based on the use of random or pseudorandom codes for biphase modulation. We use simulation to show that the bit error rate (BER) for CCSK can be closely estimated by using existing equations that apply to M-ary orthogonal signaling (MOS). Also, we show that significantly fewer computations are required for CCSK than for MOS when the number of bits per symbol is the same. We show that using biphase modulation results in waveforms that have a large time-bandwidth product and very low input signal-to-noise ratio (SNR) and thus inherently have an LPI by a radiometer. We evaluate detection by a radiometer and show that LPI can be achieved by using codes of lengths greater than about 2/sup 12/ (i.e., by transmitting more than about 12 bits per symbol). Results illustrate the effect that the CCSK symbol length and error probability, and the radiometer integration time and probability of false alarm (PFA), have on detection by a radiometer. We describe a variation of CCSK called truncated CCSK (TCCSK). In this system, the code of length 2/sup k/ is cyclically shifted, then truncated and transmitted. Although shortened, the truncated code still represents k bits of information, thus leading to an increased data rate. We evaluate radiometer detection of TCCSK and it is shown that the probability of detection is increased compared with the detection of CCSK.     

Novel wideband multimode hybrid interferometer system

In this paper, a novel hybrid of a three-element interferometer comprised of multimode antennas is analyzed. The phase ambiguities associated with the long baselines of the interferometer are resolved using the "coarse" angle estimates provided by the multimode antenna. This results in the elimination of the short baseline interferometers of the conventional five-element interferometer. It is shown here that the signal-to-noise ratio (SNR) must be above a threshold value to resolve the phase ambiguities with a high degree of probability. An expression that shows the dependence of this threshold SNR on the interferometer spacing and the variance of the angle estimates provided by the multimode antenna is derived. A single three-element wideband multimode antenna interferometer can replace several five-element conventional interferometers, each covering a separate frequency band.     

一种信道系数服从高斯分布的8PSK信号信噪比盲估计算法

信噪比（SNR,Signalto Noise Ratio）是衡量通信系统性能的重要指标。针对传统信噪比估计算法要求利用训练序列或一帧数据范周内信道系数恒定等问题,提出了一种8PSK信号在信道系数服从高斯分布的衰落信道下肯信噪比估计算法。该算法取接收信号实部或虚部数值运算构成中间观测量,理论分析8PSK信号经过衰落信道后...     

Analysis of multiframe target detection using pixel statistics

Current track-before-detect (TBD) algorithms are developed and analyzed using a path statistic for each potential object trajectory. However this path statistic does not characterize overall performance gain. We propose a pixel-based statistic. This allows the TBD approach to be characterized as an image enhancement algorithm with detection gains compared with single frame detections. It is shown that for the TBD approach to have superior detection over single frame detection the target signal-to-noise ratio (SNR) must be greater than a threshold SNR in order to overcome the uncertainty in the target path. Tradeoffs are made for a class of velocity constrained target paths in terms of the detection gain with respect to the maximum target velocity and number of frames integrated     

一种瞬时大带宽DRFM系统的信道化设计

为实现宽带雷达回波信号的模拟生成,通常采用基于信道化技术的射频存储(DRFM)系统。在信道化DRFM系统中,不合理的信道划分方案和多相滤波器设计会导致频谱混叠、频谱分量缺失和幅度失真。文章提出了一种相邻信道频谱有50%交叠的信道划分方法,并对信道化滤波器组进行了优化设计。在此基础上,给出了一种瞬时大带宽DRFM系统的实现方案。仿真结果表明,文章提出的设计方案可以实现Nyquist采样带宽内雷达信号的射频存储和模拟转发,且具有较小的幅度失真,可以满足瞬时大带宽雷达回波信号的模拟需求。     

一种基于DRFM和数字信道化技术的 宽带雷达目标干扰模拟器设计

提出了一种DRFM和数字信道化技术的宽带雷达目标干扰模拟器设计方案,详细讨论了宽带雷达信号的数字信道化接收算法和基于DRFM的扩展目标/干扰生成方法。仿真分析结果表明,该方案可以实现1 GHz带宽的雷达导引头目标干扰信号模拟,并可推广用于宽带雷达导引头干扰机和宽带雷达导引头数据采集系统设计。     

从探测概率的角度评价飞机的隐身性能

采用雷达散射截面(RCS)均值来衡量飞机的隐身性能并不能给出足够充分的信息,从信号检测概率的角度来衡量飞机的可探测性可以提供更完整的信息。本文从探测概率的角度详细分析了4种典型隐身飞机RCS起伏数据与虚警概率、探测概率、探测距离、信噪比(SNR)等参数间的关系,并给出了完整的推导过程,采用此方法可以对任意飞机目标在给定雷达参数下的可探测性进行准确计算。一般在雷达性能评估中需要用到RCS起伏模型,本文对飞机目标回波信号进行检测分析时采用数值计算方法,信号的概率密度函数(PDF)直接来源于原始回波起伏信号,避免了模型拟合带来的回波特性失真,且不会产生大的计算误差。通过对比分析计算结果发现:单脉冲检测下回波信号均值中值比越大,回波取值范围越小,则信号的检测概率越小,其中均值中值比一般相差3倍以上时可以得到明显不同的检测概率;在快起伏假设下,非相参积累检测的积累脉冲数Nin即便较小,也能得到较大的信噪比增益,此增益可能大于Nin。     

Interference Effects of Pseudo-Random Frequency-Hopping Signals

When a pseudo-random frequency-hopping signal is intercepted by a conventional receiver operating within the same frequency band, the interfering signal has the form of a pulse-amplitude modulated signal. Each pulse amplitude is dependent upon the hopping frequency and the selectivity characteristic of the victim receiver. The probability density function for the interfering pulse amplitude prior to demodulation is determined when the probability density function for the hopping frequency is uniform and the victim-receiver characteristic is 1) ideal flat bandpass, 2) single tuned, and 3) Gaussian shaped. It is shown that the average interfering pulse amplitude and interference power decrease as the frequency-hopping bandwidth increases with respect to the victim-receiver bandwidth. Fast Fourier transform computer techniques are used to obtain the probability density function of the interference amplitude in a Gaussian receiver when several (from 2 to 10) pseudo-random frequency-hopping systems are simultaneously using the same frequency band. The probability that the interference exceeds a prescribed threshold value is computed from the derived probability density functions. This probability may be used in signal-to-interference ratio calculations, to describe the capture effect, or to compute the expected number of clicks produced in an FM discriminator.     

Digital channelized receiver based on time-frequency analysis for signal interception

A digital channelized receiver is presented for the interception of a wide variety of signals of complex structure, including those with low probability of interception. The receiver is designed from the perspective of the time-frequency analysis. It uses an extended time-frequency representation based on the noncoherent integration of the short-time Fourier transform (STFT) on which the detection system and the encoder work. The encoder includes robust frequency estimation, automatic modulation recognition, and clustering, to handle broadband and simultaneous signals and to prevent out-of-channel detections (a typical phenomenon in channelized receivers). The receiver has been evaluated for a wide range of signals and shows a good performance in terms of detection, estimation, and processing of simultaneous signals. Signals collected from real-life systems and synthetic signals have been utilized.     

Limitations of radiometer performance in spherically invariantnoise

The radiometer is a common method for detection of unknown signals in noise. Most analyses of radiometer performance are based on assumptions of stationary Gaussian noise with known marginal statistics. In this note, we use a spherically invariant noise model to derive simple expressions for radiometer performance degradation in noise variance uncertainty. Numerical examples are provided to show that channel uncertainty imposes a substantial penalty in detection performance     

An Upper Bound on Detection Probability for Fluctuating Signals

In the theory of signal detectability, the signal-to-noise ratio (SNR), defined as the quotient of the average received signal energy and the spectral density of the white Gaussian noise, is a fundamental parameter. For a signal which is exactly known, or known except for a random phase, this ratio uniquely defines the detection performance which can be achieved with a matched filter receiver. However, when the signal amplitude is a random parameter, the detection performance is changed and must be determined from the probability density function (pdf) of the amplitude. Relative to the case of a constant signal amplitude, such signal amplitude fluctuation usually degrades performance when a high probability of detection (Pd) is required, but improves performance at low values of Pd; the corresponding change in the required SNR is the so-called signal fluctuation loss Lf. Thus, since Lf in some cases represents an improvement in performance for low values of Pd, a question of at least theoretical interest is: how large might this improvement be, when the class of all signal amplitude pdf's is considered. The solution, presented here, results in a lower bound on the signal fluctuation loss Lf as a function of Pd, or equivalently an upper bound on Pd as a function of SNR. The corresponding most favorable pdf was determined using the Lagrange multiplier technique and results of a numerical maximization are included to provide insight into the general properties of the solution.     

Probablity of Detection for ICW Radars

Eclipsing of received signals is analyzed for Interrupted Continuous Wave (ICW) radars. A probability density for the Signal to Noise Ratio (SNR) at the Doppler filter output is derived which incorporates eclipsing effects and a fluctuating target cross section model. The probability of detection as a function of SNR is calculated for typical ICW parameters and the magnitude of the detection loss due to eclipsing is assessed     

Radio Interferometry of Random Terrestrial Backgrounds

When relative motion exists between the antenna of a microwave radiometer and a random background, the variance of the radiometer output can, in many cases, be primarily determined by the spatial variance of the background. The result is a decrease in signal-to-noise ratio for small target detection. In this paper an interferometer is examined as a potential means of suppressing this background variance until the limiting variance imposed by the receiver is more nearly realized. A bivariate normal distribution in conjunction with three different correlation functions is assumed for the background apparent temperature field. The elements of the interferometer are assumed to possess a very narrow "pencil" power pattern. With relative motion between antenna and background, the audio power density spectrum at the output of the interferometer is exanmned. The background variance suppression achieved by an interferometer is shown to be a function of element spacing, wavelength, correlation distance for the background, range to the background, and form of the correlation function of the background. The result is that a radiometer may be designed which is receiver-limited rather than background-limited.     

Satellite Tracking Simultaneous-Lobing Monopulse Receiving System with Polarization Diversity Capability

A 136-MHz to 10-GHz simultaneous-lobing monopulse receiving system, utilizing polarization diversity in both coherent (phase-lock) and noncoherent (nonphase-lock) operational modes, has been developed for the National Aeronautics and Space Administration (NASA) Space Tracking and Data Acquisition Network (STADAN). This sum-and-difference monopulse system, called APDAR (Advanced Polarization Diversity Autotrack Receiver), utilizes a maximalratio polarization diversity combining technique that matches the receiving antenna polarization to the incoming variable polarization from a spin-stabilized or tumbling satellite. Autotrack performance becomes independent of the incoming polarization orientation by continuous in-phase addition of the carrier-signal components from orthogonal antenna elements. This technique relies upon the principle that fading does not occur simultaneously on oppositely polarized receiving channels. APDAR results in improved autotrack performance by eliminating adverse effects of severe (over 30-dB) cross-polarization fading. The predetection diversity combining technique employed provides an average 3-dB signal-to-noise (SNR) improvement. This paper describes a series of 136-MHz satellite tracking tests and analyzes a maximal-ratio predetection diversity combiner, a three-loop phase-lock loop system, and a frequency-switched radiometer.     

一种变信噪比条件下的恒虚警野值检测方法

野值检测又称异常值检测,是模式识别、机器智能和知识发现等领域经常面临的一个问题。当出现环境失配,数据信噪比（SNR）发生变化时,测试样本和训练样本所含噪声会有不同方差,以往的野值检测方法在虚警控制方面将会失效。针对这一问题,提出一种基于归一化残差（NR）的野值检测方法。该方法首先根据所需虚警概率和噪声方差变化情况确定野值检测门限,其次基于训练样本计算待考查模式的NR值,再比较NR值与检测门限的相对大小,从而判断待考查模式是否为野值。这一方法所依赖的检测门限对所需虚警率和噪声方差变化具有适应能力,因此可以在变信噪比条件下实现恒虚警（CFAR）野值检测。仿真实验验证了所提方法在虚警控制和野值检测方面的优越性能。     

Effect of a Few Dominant Specular Reflectors Target Model Upon Target Detection

Some data indicate that aircraft targets viewed from certain aspects are well modeled as consisting of a few specular reflectors. The effect of a simplified form of this target model upon radar detection performance for two different waveforms has been analyzed. The signal-to-noise ratio (SNR) required for detection as a function of waveform bandwidth for a conventional-single-channel waveform and for a four-channel frequency diversity waveform is evaluated. It is shown that for either waveform there is an optimum bandwidth to minimize the SNR required for detection. In addition, the single-channel minimum is less than the four-channel minimum. The best performance occurs for the single-channel waveform when the waveform bandwidth just resolves the individual reflectors. For typical targets, this bandwidth is of the order of 35 to 75 MHz. It is also shown that only a 0.8-dB loss relative to this minimum is incurred when using a four-channel narrow bandwidth waveform.     

Peformance of dynamic programming techniques forTrack-Before-Detect

“Track-Before-Detect” (TBD) is a target tracking technique where no threshold is applied at each measurement frame. Instead, data are processed over a number of frames before decisions on target existence are made. The track is returned simultaneously with the detection. A simple algorithm is presented and demonstrated via simulations. A detailed analysis enables detection and tracking performance to be predicted for particular algorithm parameters. Good performance is observed at low signal-to-noise ratio (SNR), with rapid degradation as SNR is reduced further. For some cases the detection performance does not improve regardless of how many frames of data are processed. Tracking performance may also be poor even though detection performance is good