Frequency-hopping signal detection using partial band coverage

The performance of a channelized radiometer in detecting a frequency-hopping signal is analyzed for a variable number of parallel radiometers not necessarily covering the entire hopping band. The full band may not be covered because of an attempt to avoid interfering signals, limited radiometer resources, lack of knowledge of the band frequency location, or combinations of these factors. The analysis provides for calculation of the value of the signal-to-noise ratio (SNR) required to achieve a given probability of detection for a specified false-alarm rate, assuming an observation interval equivalent to N hops using either a fixed or a moving observation window. The dependence of the probability of detection on a misalignment of the detector observation intervals with the hop transitions is also analyzed. Numerical results are presented and discussed. Applied to a typical slow-hopping VHF radio, the results imply that a 150-hop transmission can be detected by a channelized radiometer covering half the hopping band when the SNR is about 2 dB     

一种组合型的探干一体化信号设计分析

针对雷达信号资源利用率有待提升、低截获性能不足的问题,提出 1种复合调制的创新型探干一体化信号波形。线性调频信号本身具有良好的低截获性能,伪随机码序列分量具有较好的干扰性,同时又能一定程度上扩展信号带宽,两者的复合调制信号具有良好的探测和干扰性能。对基于 LFM的探干一体化信号波形进行了调制原理分析,并分别从时域、频域、功率谱、模糊函数、自相关特性等角度分析其探测、干扰特性。仿真实验证明,相较于单一调制的线性调频信号,一体化信号具有更宽的频带、更优良的干扰特性和探测性能,同时,有更高效的雷达资源利用率。     

Adjacent Channel Interference in a Binary Bandpass Communication System

The effect of adjacent channel interference on the probability of error in a binary bandpass communication system with an integrating and dumping detector is investigated. Narrowband filters are assumed in the receiver of the main signal and transmitters of both main and interfering signals. Plots of the probability of error as a function of signal to noise ratio in the main channel or as a function of carrier frequency difference between the main and interfering signals are presented, assuming that the filters are of the Butterworth type. These figures are helpful in the selection of minimal frequency spacing of adjacent channels.     

The Performance of an LMS Adaptive Array with Frequency Hopped Signals

The performance of an LMS adaptive array with a frequency hopped, spread spectrum desired signal and a CW interference signal is examined. It is shown that frequency hopping has several effects on an adaptive array. It causes the array to modulate both the amplitude and the phase of the received signal. Also, it causes the array output SINR (signal-to-interference-plus-noise ratio) to vary with time and thus increases the bit error probability for the received signal. Typical curves of the desired signal modulation and the time-varying SINR at the array output are presented. It is shown how the array performance depends on hopping frequency, frequency jump size, interference frequency, signal arrival angles, and signal powers.     

On Signal and Noise Level Estimation in a Coherent PCM Channel

Joint maximum likelihood estimators are presented for the signal amplitude and noise power density in a coherent PCM channel with white Gaussian noise and a correlation receiver. The estimates are based upon the correlation coefficient outputs of the receiver. From these estimators, an estimator for the quantity (received signal energy)/bit/,(noise power)/(unit bandwidth) upon which the error probabilities depend, is derived. This estimator is shown to be useful as 1) a point estimator for the signal-to-noise ratio for the higher values of this ratio (about 4 dB or greater), and 2) an easily calculated statistic upon which to base data acceptance or rejection criteria. The acceptance or rejection levels are obtained by the use of confidence interval curves in conjunction with word error probability data.     

Adaptive Array Behavior with Periodic Envelope Modulated Interference

A method is presented for determining the effects of envelope modulated interference on a least mean square (LMS) adaptive array. The interference is assumed to have periodic envelope modulation with a bandwidth that is small compared with the carrier frequency. For such interference, the method allows one to calculate the periodic steady-state behavior of the array weights and the resulting array performance. As an example, we compute the effects of an ordinary amplitude modulated (AM) interference signal on the array. It is shown that such interference causes the array to modulate the desired signal envelope but not its phase. With a differential phase-shift-keyed (DPSK) desired signal, AM interference is found to have about the same effect on bit error probability as CW interference.     

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.     

Analysis of an adaptive CFAR detector in non-Gaussian interference

Coherent signal detection in non-Gaussian interference is presently of interest in adaptive array applications. Conventional array detection algorithms inherently model the interference with a multivariate Gaussian random vector. However, non-Gaussian interference models are also under investigation for applications where the Gaussian assumption may not be appropriate. We analyze the performance of an adaptive array receiver for signal detection in interference modeled with a non-Gaussian distribution referred to as a spherically invariant random vector (SIRV). We first motivate this interference model with results from radar clutter measurements collected in the Mountain Top Program. Then we develop analytical expressions for the probability of false alarm and the probability of detection for the adaptive array receiver. Our analysis shows that the receiver has constant false alarm rate (CFAR) performance with respect to all the interference parameters. Some illustrative examples are included that compare the detection performance of this CFAR receiver with a receiver that has prior knowledge of the interference parameters     

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.     

The Effects of Gaussian Interference on Communication Systemswith Adaptive Arrays

The performance of a bandlimited binary phase-shift-keyed (BPSK) communication system is examined when the received BPSK signal is corrupted by both thermal noise and a directional Gaussian noise interfering signal. The system uses an LMS adaptive array to suppress this interference. The effects of signal power levels, arrival angles, bandwidths, and the array bandwidth are examined. The performance of a system that uses tapped delay lines for the array weights is also examined. It is shown that the performance of a system with tapped delay lines is not affected by the interference bandwidth for a single interferer.     

基于STFRFT的LFM引信抗欺骗干扰方法

针对线性调频脉冲压缩引信易受转发式假目标欺骗干扰问题,提出了基于短时分数阶傅立叶变换(STFRFT)的抗欺骗干扰方法。首先,通过分数阶傅立叶变换将回波信号与欺骗干扰各分量信号进行分离;再利用相同调频率的LFM信号经短时分数阶傅立叶变换后最大幅值与窗函数宽度成线性关系,而不同调频率的最大幅值不随窗函数宽度变化的特点,有效分辨假目标欺骗干扰,正确检测目标回波信号;最后,通过仿真证明了方法的正确性,并验证所提方法具有良好的抗欺骗干扰效果。     

Noncoherent Detection of Sinusoidal Signals in Sinusoidal Clutter

Probability density expressions associated with the noncoherent detection of a sinusoidal signal have been obtained. The signal is assumed to be imbedded in sinusoidal clutter at the same frequency and narrow-band Gaussian noise. The density expressions are shown to be a function of the signal-to-noise power ratio and the clutter-to-noise power ratio. The expressions have been numerically evaluated for a number of conditions, and the results under each reception hypothesis are presented graphically. Under large-sample conditions, the probability density for a multisample test statistic is shown to be Gaussian, and the probability of detection expression is written such that commonly available tabulated data can be utilized to determine the probabilities.     

Receiver operating characteristics for the coherent UWB randomnoise radar

An ultrawideband (UWB) random-noise radar operating in the 1-2 GHz frequency band has been developed and held-tested at a 200 m range at the University of Nebraska. A unique heterodyne correlation technique based on a delayed transmitted waveform using a photonic delay line has been used to inject coherence within this system. The performance of this radar, assuming a point target, has been investigated from a statistical point of view by developing the theoretical basis for the system's receiver operating characteristics (ROC). Explicit analytical expressions for the joint probability density function (pdf) of the in-phase (I) and quadrature (Q) components of the receiver output have been derived under the assumption that the input signals are partially correlated Gaussian processes. The pdf and the complementary cumulative distribution function (cdf) for the envelope of the receiver output are also derived. These expressions are used to relate the probability of detection (P_d) to the probability of false alarm (P_f ) for different numbers of integrated samples, and the results are analyzed     

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.     

Leading Edge Estimation Errors

The leading edge estimator (LEE) of a pulse signal is defined as the instant at which a filtered version of the received noisy signal passes a preset threshold. A rigorous analysis for a rectangular pulse model of the signal results in an exact probability density function for the LEE, valid within the time interval of the leading edge of the filtered pulse. Possible occurrence of the threshold crossing outside of this interval is considered to be an anomalous estimate, since it leads to a gross error in comparison with the regular cases. It is found that the density function of the LEE error is asymmetrical and therefore biased, that the probability PA of anomalous estimation increases with the filter bandwidth, thus setting a well definable limit to the latter and that, for prespecified PA, the minimum bias and variance are proportional, respectively, to R-1 and R-2, minima being obtained by allowing for the largest bandwidth compatible with PA. On the other hand, for given bandwidth the variance decreases only as R-1. Here R is the signal-to-noise energy ratio. Results are presented in form of parameterized graphs.     

GNSS干扰信号检测方法研究

研究了GNSS导航接收机在干扰源条件下的干扰检测和识别技术。除常见的卫星干扰如脉冲干扰、扫频干扰、BPSK干扰、宽带高斯白噪声干扰外,还添加了QPSK和8PSK干扰进行建模分析,并提取了常见的特征参数,如信号3dB带宽和频谱峰度等。通过研究,高阶累积量被提取作为MPSK干扰类内识别的特征参数。研究了基于决策树和BP神经网络等分类器算法的干扰盲识别,并分析比较了这些分类算法的识别准确率,为抗干扰领域的研究提供了重要参考。     

An Analysis of Helicopter Rotor Modulation Interference

In satellite-to-helicopter communications, interference exists on the incoming signal when the receiving antenna is located below the rotor blades. A bound is established for the performance of a coherent fixed-tone ranging system operating at L band in this interference environment. The scalar diffracted field beneath the rotating blades, at L band and above, is found to satisfy the criterion of Fresnel diffraction, and is computed using the techniques of Fourier optics. The diffracted field is expressed in terms of a narrow-band signal. The amplitude and phase components are calculated from a Fourier Series expansion using the FFT algorithm. The significant harmonics of the phase component of the interference combine with the baseband of the narrow-band, phase-modulated ranging signal. This results in CW interference, and in rearrangement of the first-order, sideband, ranging-tone channel powers. The degradation in ranging accuracy is evaluated by computing the signal-to-interference (SIR) ratio for a set of ranging tones. The post-detection (SIR)PD at the output of the correlator is shown to be a function of the amplitude of the phase harmonics of the interference, the relative difference between the ranging tone and interference center frequencies (a function of rotor speed), the rangetone modulation indices, and the post-detection filter noise bandwidth.     

Potential interference sources to GPS and solutions appropriate forapplications to civil aviation

When the GPS (Global Positioning System) is subjected to interference, the system performance gradually deteriorates as the interfering levels increase. Two modes of interference are discussed in detail, namely, that from transmissions at frequencies close to the GPS frequencies and that from transmissions with a harmonic in the GPS band. It is argued that the former requires RF filtering in the receiver with a quality better than that generally specified. The latter cannot be dealt with in such a way. Measurements carried out on the harmonic levels transmitted by one UK TV transmitter and several hundred aircraft VHF transmitters are reported. The measurements show there is a measurable level of harmonics in the GPS band. The UK TV transmitter does not, however, represent a threat to aviation unless the aircraft is so close as to represent a physical danger. The probability that one aircraft's VHF transmitter will interfere with the GPS receiver on another aircraft is tolerably small, but there is a significant probability that a GPS receiver can suffer when there is a VHF transmission from the same aircraft. Several recommendations are made, including an international effort to ensure that spurious emissions are both quantified and kept at a level significantly lower than that achieved today     

Noncoherent Detection of Split-Phase FSK by Multiple Predetection Filtering

When the cumulative drift in the center frequency of a binary split-phase FSK signal exceeds the peak deviation of the signal, a conventional noncoherent receiver (i.e., one provided with only two IF filters) may be unable to achieve the probability of error per bit which the designer desires. This limitation may be overcome if the receiver is provided with a bank of more than two contiguous filters (each followed by an envelope detector) tospan the total IF band the instantaneous IF signal might occupy. It is shown that the probability of error per bit for such a receiver is a function of 1) the ratio F of peak frequency deviation to peak frequency drift, 2) the number M of IF filter/detectors, and 3) the signal-to-noise ratio ? in the output of the filter containing the signal. It is further shown thatfor a given value of F an increase in M reduces the amount of transmitter power the communication system designer must provide to yield a given probability of error per bit.     

An Optimum Phase Synchronizer in a Partially Coherent Receiver

The derivation and the statistical properties of the maximum a posteriori probability phase estimator of a sinusoidal signal in white Gaussian noise are considered. The probability density function of the phase estimate is developed. The estimator efficiency and performance as a phase synchronizer in a partially coherent receiver are calculated and compared with a first-order phase-locked loop phase estimator.