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.     

SNR-based multipath error correction for GPS differential phase

Carrier phase multipath is currently the limiting error source for high precision Global Positioning System (GPS) applications such as attitude determination and short baseline surveying. Multipath is the corruption of the direct GPS signal by one or more signals reflected from the local surroundings. Multipath reflections affect both the carrier phase measured by the receiver and signal-to-noise ratio (SNR). A technique is described which uses the SNR information to correct multipath errors in differential phase observations. The potential of the technique to reduce multipath to almost the level of receiver noise was demonstrated in simulations. The effectiveness on real data was demonstrated with controlled static experiments. Small errors remained, predominantly from high frequency multipath. The low frequency multipath was virtually eliminated. The remaining high frequency receiver noise can be easily removed by smoothing or Kalman filtering     

Effect of Sampling Time Jitter on Array Performance

The effect on array SNR of errors in sampling times (jitter) isan analyzed for the "Bryn processor." Jitter is modeled as a discrete-paramter er random process, and expressions for array SNR are determined as a function of signal and noise spectra and jitter characteristics. For a plane wave signal, it is found that jitter in the data used to design the processor has no effect on output SNR if the noise is independent between channels. However, jitter in the input (evaluation) n) data can cause a substantial loss in peak array SNR and in the array's frequency selectivity. These losses can be expected to increase as the high-frequency content of the data increases. The Bryn processor also loses its interpretation as a likelihood ratio processor in the presence of jitter. The effect of jitter can be reduced in many cases by increasing the sampling rate.     

基于混合体制雷达网的弹道目标微特征及外形参数提取

针对弹道中段目标微特征难以识别与分辨的问题,提出了一种基于低分辨雷达和高分辨雷达相结合的混合体制雷达网的有翼弹道目标微特征及外形参数提取方法。依据非线性信号参量可分离模型,利用非线性最小二乘估计方法解算出有翼弹道目标群各散射中心的幅相参数,结合不同雷达提取的微特征的关联性,利用散射中心关联处理实现了各类散射中心的分离。在此基础上,利用弹道目标的微特征,结合弹道目标各散射中心的相对位置关系,重构出各目标的三维微特征及各散射中心的三维位置矢量,进而估计出目标的进动特征和结构参数。仿真结果表明:当信噪比(SNR)为5 dB时,该方法的重构精度保持在92%左右。     

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.     

Fast Maximnurm Likelihood Joint Estimation of Frequency and Frequency Rate

A fast maximum likelihood algorithm is presented that jointly estimates the frequency and frequency rate of a sinusoid corrupted by additive Gaussian white noise. It consists of a coarse search and a fine search. First the two-dimensional frequency-frequency rate plane is subdivided into parallelograms whose size depends on the region of convergence of Newton's method used in maximizing the log-likelihood function (LLF). The size of the parallelogram is explicitly computed and is optimal for the method used. The coarse search consists of maximizing the LLF over the vertices of the parallelograms. Then starting at the vertex where the LLF attained its maximum, a two-dimensional Newton's method to find the absolute maximum of the LLF is implemented. This last step consists of the fine search. The rate of convergence of Newton's method is cubic, and is extremely fast. Furthermore Newton's method will converge after two iterations when the starting point used in the method lies within 75 percent of the distances defined by the parallelogram of convergence whose center coincides with the true values of frequency and frequency rate. In this case, the root mean square error (RMSEs) for frequency and frequency rate are practically equal to the Cramer-Rao bound at all signal-to-noise ratio (SNR)?15 dB. The frequency-frequency rate ambiguity function is shown to be even and its periodicities are extracted.     

Quantitative SNR analysis for ISAR imaging using jointtime-frequency analysis-Short time Fourier transform

V.C. Chen recently presented an inverse synthetic aperture radar (ISAR) imaging technique using the joint time-frequency analysis (JTFA), which has been shown having a better performance for maneuvering targets over the conventional Fourier transform method. The main reason is because the frequencies of the radar returns of the maneuvering targets are time varying and a JTFA is a technique that is suitable for such signals, in particular a JTFA may concentrate a wideband signal, such as a chirp, while it spreads noise. We quantitatively study the signal-to-noise ratio (SNR) in the ISAR imaging using one of the typical JTFA techniques, namely the short time Fourier transform (STFT). We show that the SNR increases in the joint time-frequency (TF) domain over the one in the time or the frequency domain alone both theoretically and numerically. This quantitatively shows the advantage of the JTFA technique for the ISAR imaging     

基于自适应分段混合系统的轴承故障诊断

针对强噪声背景下轴承早期故障的诊断问题,提出一种基于自适应分段混合随机共振（adaptive piecewise hybrid stochastic resonance,APHSR）系统的检测方法。采用经验模态分解法（EMD）进行信号预处理,分别采用能量密度法和相关系数法去除高、低频噪声,自动筛选最优固有模态函数,经尺度变换后输入分段混合随机共振系统模型,提取故障信号。工程实验显示:经过APHSR系统,轴承故障特征频率的频谱幅值、频谱幅值与周围最大噪声之差和最大信噪比（SNR）均高于经验模态分解和经典随机共振方法,其中齿轮箱故障轴承信噪比分别提高了9.579 dB和7.473 dB,转子故障轴承信噪比分别提升了8.597 dB和5.695 dB,对凯斯西储大学故障轴承数据处理后的信噪比分别提升了3.369 dB和17.043 dB。数据表明APHSR方法具有高效性,提高了轴承故障信号诊断能力。      

Postfiltering in Digital Beamformers

Assuming a sinusoidal signal superimposed on a narrow-band Gaussian noise as the input to a receiving array, the output power and signal-to-noise ratio of a digital beamformer with postfiltering were formulated so that subsequent calculations could be made without an analysis in the frequency domain. The formulation utilized the quantizer functions previously given by the author and certain spectral power distribution factors originally attributed to Davenport but more rigorously derived and discussed in the present work. A numerical study based on this formulation for a DIMUS array in a correlated noise field reveals that except for certain rare circumstances, postfiltering generally improves the output SNR or array gain. It is demonstrated that the amount of postfiltering gain not only varies with array input SNR but also depends strongly upon the spacing-to-wavelength ratio, and its meaningful interpretation can only be made in conjunction with both the clipping and noise correlation losses. In particular, balancing postfiltering gain against the two losses suggests that receiving arrays with element spacings smaller than one-half of the operating wavelength may be used to the advantage of system design under certain conditions.     

A noise insensitive solution to an ambiguity problem in spectralestimation

The instantaneous frequency measurement (IFM) receiver is capable of measuring the center frequency of single frequency pulses over a wide range (bandwidth) of center frequencies. Because of various constraints, the frequency resolution requirement results in long correlator delay times that reduce the single correlator bandwidth. A large bandwidth can be achieved only if two or more correlators are used. The problem of estimating frequency is then reduced to the simultaneous congruence problem of number theory. A design procedure is presented for solving the congruence problem for a given amount of noise protection, a stated frequency resolution, a minimum bandwidth, and a fixed level of precision (bits) in the IFM receiver     

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.     

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.     

Bounds on Time-Delay Estimation for Monochromatic Signals

Time-delay estimation (TDE) of monochromatic signals,observed by spatially separated sensors, is widely used for sourcelocalization in radar/sonar applications. We use lower bounds tostudy the accuracy of TDE as a function of signal to noise ratio(SNR), frequency, and sensor separation. We show that the Cramer-Rao bound, which is frequently used as a standard ofreference, yields optimistic predictions in many cases.     

一种航空噪声背景下的语音增强方法

依据航空噪声的频谱特性,提出将自适应滤波算法与改进的谱减法相级联的方法来增强语音。在强航空噪声背景下,处理后的语音不仅信噪比得到了很大提高,而且在有效抑制背景噪声和音乐噪声的同时,其清晰度和可懂度也得到了很大的改善。     

一种提高脉冲雷达多普勒相位精度的方法

针对低信噪比条件下脉冲雷达模糊多普勒相位精度较低,可能导致相位测距时不能正确解相位模糊问题,基于EMD（Empirical Mode Decomposition,经验模式分解）区间阈值去噪方法,提出了一种新的提高多普勒相位精度的方法：利用EMD分解后各层信号的频率特性和能量特性,选取合适的阈值,并对各层信号进行区间阈值化处理,在提高信号信噪比的同时保持了信号的连续性.分别在回波信号噪声为高斯白噪声和AR（2）相关噪声的情况下,以及不同信噪比条件下,对该方法进行验证.仿真结果表明：在低信噪比条件下,当回波信号噪声为白噪声和相关噪声时,EMD区间阈值去噪方法能将回波信号信噪比提高5 dB,去噪性能优于小波阈值去噪方法,其对应多普勒相位精度能提高1倍以上.     

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。     

Signal-to-Noise Ratio of Arbitrary Power-Series Nonlinear Amplifier

A general analysis of the effect of an arbitrary power-series nonlinear amplifier followed by a coherent mixing device on signal-to-noise ratio (SNR) is performed. An expression is derived for the improvement factor which is defined as the logarithm of the ratio of the output SNR to the input SNR. This expression is applicable to the coherent amplitude detector and phase locked loop as well as noncoherent amplifier by appropriate selections of the detection angle. Moreover, the improvement factor can be obtained for noise with an arbitrary amplitude distribution. To demonstrate the applicability of this analysis, the improvement factors of the nonlinear amplifiers such as a power-law amplifier and a power-series amplifier with positive and negative discriminations are numerically calculated for the cases where the input noise amplitude distributions are Rician and triangular.     

Frequency-Agile Radar Signal Processing

Modern radars may incorporate pulse-to-pulse carrier frequency modulation to increase probability of detection, to reduce Vulnerability to jamming, and to reduce probability of interception. However, if coherent processing is used for clutter rejection, the frequency of N consecutive pulses must be held constant for N-pulse clutter cancellation or Doppler filtering. If M pulses are transmitted during the time the antenna illuminates a target, there are M/N coherently integrated echoes available for noncoherent integration in the computer or the operator's display to further improve the signal-to-noise ratio (SNR). In this paper, analytical and simulation methods are employed to determine the balance between coherent and noncoherent integration that yields the greatest SNR improvement. Attention is focused upon a model using peak selection of fast Fourier transform (FFT) Doppler channels and is compared to a reference model involving only a single Doppler channel. Curves of detectable SNR as a function of M and N are presented for both models.     

频率直方图法在复合材料检测中的应用

飞行器中复合材料结构的无损检测大多采用超声波检测方法。在实际检测过程中，类似碳纤维复合材料这样的特殊材料组织的结构比较复杂，所得到的超声波回波信号经常受到较强的结构噪声的干扰，信噪比较低，影响缺陷信号的识别。利用分离谱技术中最小值法，考虑结构噪声幅度对频率变化的敏感性，应用频率统计直方图法，对窄带信号的采样点进行统计、比较，选择绝对值最小的采样点信号作为输出信号，得到最佳频率检测带，对这些频带采用带通滤波器进行滤波，从而较好地将目标回波和结构噪声区分开，更准确地对复合材料构件讲行无损检测。     

Noise factor and antenna gains in the signal/noise equation for over-the-horizon radar

A recommended form of the signal-to-noise equation that includes both internal and external system noise and signal/noise processing losses is discussed. The recommended form conforms to the internationally accepted definition of system operating noise factor but is extended to include signal/noise processing. The predetection signal-to-noise ratio (SNR) of a radar or communication system is proportional to the power gain of the transmit antenna and the directive gain of the receive antenna, and is inversely proportional to the operating noise factor of the receiving system. The operating noise factor is approximately equal to the product of the external noise factor and the signal/noise processing factor when the system is external noise limited, as is usually the case for over-the-horizon (OTH) radar.<>