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.     

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.     

Signal-to-Noise Ratios in Self-Biased-Pwer-Law Amplifiers with Saturation

The relation between the output signal-to-noise ratio (SNR) and the input SNR is presented for the bandpass self-biased third-law amplifier with saturation, when the input is composed of sinusoidal carrier and zero-mean stationary narrowband Gaussian noise. It is found that significant improvement in the output SNR at low input SNR's can be achieved by the self-biased third-law amplifier with saturation operated in class A. The results obtained are also verified experimentally.     

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.     

Hard-Limiting an Offset Signal

Expressions are derived for the output autocorrelation function of a hard limiter driven by the sum of signal, noise, and an offset term. Two signal types are considered: a random-phase sinusoid and a stationary, zero-mean Gaussian process. For each signal the offset at the sampling times is modeled first as a constant, and second, as a sequence of binary-valued random variables.     

Maximun Posterion Probability Demodulation of Angle-Modulated Signals

An algorithm is presented for maximum posterior probability (MPP) demodulation of angle-modulated signals. A sampled data version of the problem is considered, in which additive Gaussian noise and Gaussian modulating signal are assumed. The algorithm is a numerical method for solving the nonlinear equations which are necessary conditions for MPP estimation. Results of a simulation of the algorithm are presented and discussed. Improvements in performance with respect to a phaselocked loop appear to stem from use of data before and after the time position of a phase estimate and from optimization of performance at low signal-to-noise ratio (SNR) as well as at high SNR.     

Transmission Characteristics of an FM Signal Through a Hard Limiting Repeater

The response of an FM detector to an FM signal which is passed through a hard limiting repeater together with additive Gaussian noise is described. A general expression of the output SNR is derived that enables the determination of the threshold behavior. To clarify the feature of a transmission characteristic, a comparison with a linear repeater is also made. The output SNR is found to be larger than that of the linear system for all practical values of input CNR's.     

The Output Pdf of a Polarity Coincidence Correlation Detector

A general expression is derived for the probability density function of the output of a cross correlator, the inputs of which are assumed to consist of clipped sine waves of similar frequency plus uncorrelated, stationary Gaussian noise. The correlator output is shown to be a piecewise linear function of the random phase difference between the two input processes; hence, the density function for the correlator output is obtained by a relatively simple transformationfrom the probability density function of the random phase difference.     

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。     

Hard-Limiter Output Autocorrelation Function: Gaussian & Sinusoidal Input

An expression is derived for the autocorrelation function of the output of a hard limiter whose input is stationary Gaussian noise with zero mean plus independent random-phase sinusoidal signal. The output spectrum may then be evaluated. This spectrum is extremely useful in understanding the properties of a filter-limit-filter-detect signal processor whose signal input is an actual sinusoid, or when a sinusoid is used as a test signal.     

A Correlation Polarimeter for Noise-Like Signals

Optimum estimation (tracking) of the polarization plane of a linearly polarized electromagnetic wave is determined when the signal is a narrow-band Gaussian random process with a polarization plane angle which is also a Gaussian random process. This model is Compared to previous work and is applicable to space communication. The estimator performs a correlation operation similar to an amplitude -comparison monopulse angle tracker, giving the name correlation polarimeter. Under large signal-to-noise ratio (SNR), the estimator is causal. Performance of the causal correlation polarimeter is evaluated for arbitrary SNR. Optimum precorrelation filtering is determined. With low SNR, the performance of this system is far better than that of previously developed systems. Practical implementation is discussed. A scheme is given to reduce the effect of linearly polarized noise.     

Error Analysis of the Optimal Antenna Array Processors

The optimal weights of an antenna array processor, which maximizes the output signal-to-noise ratio (SNR) in the absence of errors, are computed using the noise-alone matrix inverse (NAMI) and the steering vector in the look direction or the signal-plus-noise matrix inverse (SPNMI) and the steering vector. In practice the estimated steering vector as well as the estimated optimal weights are corrupted by random errors. This paper has analyzed the effects of these errors on the performance of the NAMI processor and the SPNMI processor by deriving analytic expressions for the output signal power, output noise power, output SNR, and the array gain as a function of the error variance. The treatment is for a general array configuration and no assumption about a particular array geometry is made.     

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     

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.     

Probability Density Function at the Output of the Delay-Lock Discriminator

The first-order probability density at the output of the correlation network of the delay-lock discriminator is determined using the methods developed by Arthur, Kac, and Siegert. The analysis assumes that the input signal is stationary and Gaussian and that the discriminator is locked on. No restrictions are made on the bandpass filter characteristics in the channels.     

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.     

基于小波域维纳滤波的激光陀螺数据处理研究

针对激光陀螺随机漂移数据的非平稳特性,设计了小波滤波器,使经小波滤波后的数据近似成为平稳序列,并进行了相应的平稳性检验.在小波变换的基础上,结合维纳滤波器处理平稳信号能力强的特点,提出了一种小波域维纳滤波法.仿真试验表明,此方法更显有效性.     

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.     

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...     

The Effect of Hard Limiting an Angle-Modulated Signal Plus Noise

The effect of hard limiting an angle-modulated signal plus narrow-band Gaussian noise is analyzed. Several examples are considered?sinusoidal angle modulation, Gaussian angle modulation, and biphase angle modulation. The general conclusion is that when a zonal band-pass filter is used, which rejects dc and second harmonics, an angle-modulated signal plus Gaussian noise provides the same output signal-to-noise ratio as shown by Davenport for a CW signal plus Gaussian noise. However, when a narrow bandpass filter is used, which has a bandwidth approximately equal to the input angle-modulated signal, an angle-modulated signal plus Gaussian noise has a better output signal-to-noise ratio than a CW signal plus Gaussian noise.