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.     

High-Resolution Frequency Measurement by Linear Prediction

The efficacy of linear prediction spectrum analysis (LPSA) (also called autoregressive or maximum entrophy spectrum analysis) for problems concerning narrowband signals in noise is examined by means of Monte Carlo simulation. For the case of pure tones (sinusoids) in white noise, both frequency estimation accuracy and resolution of two closely spaced tones with the linear prediction approach are discussed. In addition, estimation of the carrier frequency of a narrowband random (fading) Gaussian signal in noise is considered. The results are compared with standard fast Fourier transform (FFT) methods. These comparisons indicate that there is no significant advantage to using the linear prediction approach with real (bandpass) data. It is concluded that these experiments should be repeated with complex (baseband) data before a complete assessment of the LPS approach can be made.     

Instantaneous Frequency Estimation Using Adaptive Linear Predictor Weights

A computationally efficient scheme for estimating the digital instantaneous frequencies of narrowband inputs is introduced. The frequency estimates are obtained by searching for minima of the inverse input power spectrum. This spectrum is estimated at each input sample from the weights of an adaptive linear predictor which uses the LMS (least mean square) algorithm to update its weights. The related minima are sought via an iterative search algorithm, referred to as the iterative frequency estimator. This algorithm is computationally more efficient than available methods, and also provides a higher resolution. Simulation results are included; these include tracking of random message sequences in FM signals, and the formant frequency estimation of speech.     

Output Signal-to-Noise Ratios for Amplitude-Modulated Noise-Like Lasers

A general expression of the output SNR of a photodetector is derived for a noise-like laser amplitude-modulated by a stationary Gaussian random modulating signal in the presence of a background light. The electric field Vx(t) of the noise-like laser is assumed to be a stationary narrowband Gaussian random process with zero mean. Two types of modulating signal are considered, the baseband and bandpass modulating signals. More specifically, the effects of the center frequency of the modulating signal, the modulating degree, the bandwidth ration of the noise-like laser to the modulating signal, the effective average quantum rate, and input CNR on output SNR are studied. The detection characteristics of the noise-like laser are also made clear by comparison with the case of a coherent laser.     

A Logarithmic Frequency Allocation Algorithm for Wideband Discrete Frequency Pulse Trains

It is shown that signal waveforms utilizing discrete frequency modulation (DFM) which are generated using a narrowband or frequency shift algorithm have ambiguity sidelobe distortion which is caused by the approximation of time compression by frequency shift. A logarithmic frequency allocation algorithm is presented which couches the signal design problem in terms of band and step ratios, rather than in terms of bandwidth and frequency steps, and is consistent with the wideband formulation of the ambiguity function. The algorithm makes use of the same basic code generating sequence used for narrowband frequency allocation, but the resulting signal will have invariant ambiguity sidelobe positions for any receiver realization in the delay-time compression plane.     

A new and robust CFAR detection algorithm

A constant false alarm rate (CFAR) detection method which is based on a combination of median and morphological filters (MEMO) is proposed. The MEMO algorithm has robust performance with small CFAR loss, very good behavior at clutter edges and high detection performance in the case of closely spaced narrowband signals (targets). The proposed MEMO method is favourably compared with cell averaging (CA) and ordered statistics (OS) CFAR detectors. The Monte Carlo method is employed to analyze the MEMO-CFAR detector     

The Effect of Hard Limiting in the Presence of Large Out-of-Band Interfering Signals

The effect of hard limiting on the phase of a test signal was investigated when large out-of-band interfering signals are present at the input to the limiter. First a single and then two discrete interfering signals were considered. The interfering signals and the test signal are restricted to narrow but separated bands. The test signal is recovered after limiting by narrowband filtering. The analysis of the single interfering signal is essentially the same as that performed by Cahn.1 In this correspondence experimental evidence is presented to verify the analysis and, in addition, the case of two interfering signals is considered.     

Evaluating the Detectability of Gaussian Stochastic Signals by Steepest Descent Integration

It is shown how to compute the detection probability of certain signals by numerical integration of the Laplace inversion integral involving the characteristic function or the moment-generating function of the detection statistic. The contour of integration is taken as the path of steepest descent of the integrand and is determined numerically as the integration proceeds. The method is applied to calculating the performance of the optimum detector of a Gaussian stochastic signal in white noise when the signals actually present have a different average s.n.r. from that assumed in the design. Results are presented for narrowband signals with Lorentz and rectangular spectral densities. The detectability of the former is shown to be more sensitive than that of the latter to the value of the design s.n.r. The relative disadvantage of the threshold detector, also assessed by this method, is smaller for signals with a rectangular than for those with a Lorentz spectral density.     

Broadband focusing for partially adaptive beamforming

A broadband adaptive beamforming approach based on the concept of signal-subspace alignment is formulated and contrasted with the conventional approach. The proposed method involves a preprocessor that focuses the signal spaces at different frequencies to a common one and a narrowband beamformer following the preprocessor. The merits that result as a consequence are partial adaptivity due to single frequency weights and decorrelation of coherent signals thus combating signal cancellation. The latter effect is studied by deriving expressions for the desired-signal distortion in a minimum variance distortionless response (MVDR) beamformer and analyzing them. Implementation issues of the preprocessor are addressed. Simulation results confirm the utility of the focusing preprocessor     

On Optimal Minimax Jamming and Detection of Radar Signals

A game between an intelligent jammer J and decision maker DM is considered. DM seeks to detect a coherent slowly fading narrowband signal under a Neyman-Pearson criterion. His observations are corrupted with additive narrowband noise, the source of which is J's jamming with a power constraint, but otherwise almost arbitrary statistics. DM knows J's action but the converse is not true. When the number of samples increases asymptotically, a minimax solution for the game exists where the jamming is Gaussian, independent of the desired signal amplitude level and probability distribution. The same result also holds for detection of a nonrandom baseband signal.     

Detection of moving targets in wideband SAR

A likelihood ratio is proposed for moving target detection in a wideband (WB) synthetic aperture radar (SAR) system. WB is defined here as any systems having a large fractional bandwidth, i.e., an ultra wide frequency band combined with a wide antenna beam. The developed method combines time-domain fast backprojection SAR processing methods with moving target detection using space-time processing. The proposed method reduces computational load when sets of relative speeds can be tested using the same clutter-suppressed subaperture beams. The proposed method is tested on narrowband radar data.     

On the Mean Frequency Measurement System Using Correlation Detection

This paper is concerned with the problem of measuring the mean frequency of the power spectrum of a zero-mean, stationary, narrowband Gaussian random signal in the presence of additive Gaussian noise. Signal-to-noise ratios at the output of the mean frequency measurement system using correlation detection are analyzed in terms of input signal-to-noise ratio, input signal and noise bandwidths, and integration time. The results obtained are verified experimentally, and a comparison with a conventional zero-crossing detector is also made.     

Hybrid discriminative/class-specific classifiers for narrowband signals

The class-specific (CS) method of signal classification operates by computing low-dimensional feature sets defined for each signal class of interest. By computing separate feature sets tailored to each class, i.e., CS features, the CS method avoids estimating probability distributions in a high-dimension feature space common to all classes. Building a CS classifier amounts to designing feature extraction modules for each class of interest. In this paper we present the design of three CS modules used to form a CS classifier for narrowband signals of finite duration. A general module for narrowband signals based on a narrowband tracker is described. The only assumptions this module makes regarding the time evolution of the signal spectrum are: (1) one or more narrowband lines are present, and (2) the lines wandered either not at all, e.g., CW signal, or with a purpose, e.g., swept FM signal. The other two modules are suited for specific classes of waveforms and assume some a priori knowledge of the signal is available from training data. For in situ training, the tracker-based module can be used to detect as yet unobserved waveforms and classify them into general categories, for example short CW, long CW, fast FM, slow FM, etc. Waveform-specific class-models can then be designed using these waveforms for training. Classification results are presented comparing the performance of a probabilistic conventional classifier with that of a CS classifier built from general modules and a CS classifier built from waveform-specific modules. Results are also presented for hybrid discriminative/generative versions of the classifiers to illustrate the performance gains attainable in using a hybrid over a generative classifier alone.     

一种宽带阵列幅相与互耦误差联合校正算法

宽带数字阵列雷达接收通道中存在随频率变化的幅相误差和互耦误差,会严重影响雷达性能。针对这一问题,提出了一种宽带数字阵列幅相与互耦误差联合校正算法。首先选取通带内多个离散频点,对于每个频点,将幅相误差和互耦误差作为一个整体,采用基于子空间原理的窄带校正算法估计其阵列失真参数,并计算校正矩阵;然后将其组合起来,构成频域离散校正矩阵;最后基于最小二乘准则,设计了宽带有限长脉冲响应(FIR)校正滤波器矩阵。利用该矩阵,可实现通带范围内任意带宽入射信号的校正。计算机仿真实验验证了该算法的有效性。对实测数据的处理结果表明该算法在宽带数字阵列雷达系统中具有实用价值。     

Detection Probabilities for Log-Normally Distributed Signals

The amplitude and power of a large family of radio signals are observed to have log-normal probability density functions. Among these are signals propagated through random inhomogeneous media, a notable example being low frequency atmospheric radio noise. Of greater importance are certain radar targets that have been observed to have essentially log-normal density functions. Both ships and space vehicles may fall into this category. Curves of probability of detection vs. signal-to-noise ratio for the case of log-normal signals in Gaussian noise have been computed and are presented in this paper. The curves apply for square-law detection with varying degrees of postdetection linear integration. Both fully correlated and completely uncorrelated fluctuating signals are considered. It is shown that for log-normal signal distributions having large variances, the probability of detection differs significantly from that obtained using curves based on an assumed Rayleigh signal distribution.     

基于周期FRFT的多分量LFMCW雷达信号分离

 多分量线性调频连续波(LFMCW)信号的截获和特征提取是雷达情报侦察的难点,为了实现对多分量LFMCW信号的快速检测和有效分离,提出了一种基于周期分数阶Fourier变换(PFRFT)的多分量LFMCW雷达信号分离新方法。首先介绍了PFRFT,分析了PFRFT和FRFT之间的关系,讨论了LFMCW信号的PFRFT特征。然后给出了一种离散PFRFT的计算方法,结合周期分数阶Fourier域(PFRFD)的窄带滤波和CLEAN算法实现了多分量LFMCW信号的分离。仿真结果表明:①PFRFT的计算效率较周期Wigner-Hough变换(PWHT)具有明显优势;②LFMCW信号分量在特定PFRFD中具有能量峰值,分离后能较好保留时频特征;③当两个LFMCW信号分量的功率相差较大时,适合在PFRFD分离,反之适合在时域分离;④当信噪比(SNR)为0 dB时,两个具有相同功率的LFMCW信号分量分离后,与初始信号分量的相关系数都达到了0.9以上。     

Adaptive Arrays Can Be Used to Separate Communication Signals

Using eigentheory, it is shown how up to n unknown independent narrowband signals arriving from different directions at an array of n antenna elements can be separated into n channels where each channel contains primarily one signal. An expression for the signal-to-interference ratio (SIR) on eachoutput channel is determined analytically and evaluated for many illustrative cases. The results show that in most cases the SIR is + 10 dB or greater; only when two signals arrive within a few degrees of each other does the SIR fall substantially below 0 dB.     

Eigenstructure-based algorithms for direction finding withtime-varying arrays

This paper considers the problem of finding the directions of narrowband signals using a time-varying array whose elements move during the observation interval in an arbitrary but known way. We derive two eigenstructure-based algorithms for this problem, which are modifications of techniques developed originally for time-invariant arrays. The first uses array interpolation, and the second uses focusing matrices. Like other eigenstructure-based methods, these algorithms require a modest amount of computations in comparison with the maximum likelihood (ML) estimator. The performance of the algorithms is evaluated by Monte-Carlo simulations, and is compared with the Cramer Rao Bound (CRB). Although both techniques were successful for wideband array processing with time-invariant arrays, we found that only the interpolated array algorithm is useful for direction finding (DF) with time-varying arrays     

Transformation of the Spectrum of a Signal in Communication between Relativistically Moving Inertial Frames

Future space exploration may involve communications between spacecraft moving at relativistic velocities. One of the significant problems associated with such communication is spectral distortion of signals which are propagated between relativistic frames. This distortion is generated by both changing propagation distances and purely relativistic electromagnetic field transformations. In this paper a linear integral transformation is formulated for relating the Fourier spectra of the source antenna excitation current and the resulting incident electric field at the receiving antenna. The kernel of the transformation is evaluated for the case of a steerable source antenna tracking on the advanced receiver position. The transformation is then applied to the case of an ideal thin-wire half-wave dipole source antenna excited by a narrowband, double-sideband modulated current. The specific distortions of spectral spreading and translation are then related to increased bandwidth and upper cutoff frequency requirements of receiving systems in relativistic applications.