Degradation of Signal-to-Noise Ratio Due to IF Filtering

A receiver for biphase modulated signals using an integrate-and-dump filter is optimum only if the IF filter bandwidth is infinite. Finite IF filter bandwidth results is a performance degradation. Using the predetection signal-to-noise ratio as the performance criterion, a lower bound on this quantity is determined as a function of the ratio (IF filter bandwidth)/(bit rate). The corresponding upper bound on the error probability is also presented.     

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.     

Logarithmic Detection with Postdetection Filtering

An analysis is presented of the performance of a logarithmic detector or followed by a low-pass filter, under the assumption of a large ratio of IF bandwidth to postdetection bandwidth. This allows for the probability of detection and similar quantities to be computed in a straightforward manner. The mean and variance of the filter output are found by first deriving the autocorrelation function of the logarithmic detector output and then obtaining the power spectral ral density. A useful engineering approximation is made for the variance which is valid for all signal-to-noise ratios.     

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.     

The Effects of Filtering and Limiting a Double-Binary PSK Signal

This paper describes a digital computer simulation of a double-binary phase-shift keying system. This simulation program is used to investigate the effects of limiting action and of the shape and bandwidth of the filter on the system performance, expressed in terms of error probability     

Binary Communication with Large Bandwidth to IF Frequency Ratios

The effect of I F filter bandwidth to I F frequency ratio on the probability of error in a binary bandpass communication system with nonreturn-to-zero (NRZ) and split-phase (SP) signals is investigated. ed. Explicit results are given for the case when the bandpas I F filter is transformed from a single-pole low-pass filter.     

卫星光通信APT控制系统H∞设计

 捕获瞄准跟踪(APT)控制系统的设计是影响整个星间光通信系统性能的重要因素。利用指向偏差的概率分布阐述了卫星光通信过程中捕获概率、跟踪误差及误码率受卫星平台振动和终端装置参数摄动的影响,通过功率谱分析了卫星平台振动在低频段、对象不确定性在高频段对指向偏差的影响,并对其进行了模型化分析。采用H_∞控制混合灵敏度设计方法同时抑制干扰和处理受控对象不确定性问题进行控制器设计。仿真验证表明该方法得到的控制器对平台干扰具有抑制力,对对象摄动具有鲁棒性。     

The Effect of Pulse Shape and Duty Cycle on Laser Binary Communication Systems

The result of an investigation of the effects of pulse shape and duty cycle on the probability of error are presented for a pulse-gated binary modulation (PGBM) laser communication system when the background irradiance has the important Lorentzian spectral shape.     

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.     

Limiter-Discriminator Detection Performance of Manchester and NRZ Coded FSK

The theory of limiter-discriminator detection of a frequency shift keyed (FSK) carrier is reviewed and this theory is used to predict the bit error probability performance of Manchester coded and nonreturn-to-zero (NRZ) coded data. A major result of the study is that the predetection time bandwidth product BT and the devia tion ratio h needed to give optimum performance for Manchester coding are seen to be larger than optimum NRZ FSK. Specifically, BT ~ 2 and h ~ 1 will result in Manchester performance about 2 dB worse than optimum NRZ.     

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.     

Optimal and Suboptimal Perfomance of a PCM/FM Communication System

Theoretical results are presented on probability of error in the detection of binary FM signals for various frequency deviations with fixed bit rate, restricted predetection filter bandwidth, ideal limiterdiscriminator reception, and integrate-and-dump postdetection filter decision. The results show that suboptimal system performance can be achieved by choosing the largest possible value of deviation index which lies approximately at 0.7 + 2n, where n = 0, 1,...,k. k is determined by the reconstructability of signal after the bandpass filter.     

Comments on "Bounds on Probability of Error in Decision Feedback Equalizers"

In the above paper1 a technique was proposed to derive an upper bound on the error probability of a decision feedback equalizer. It involves decomposition of the probability density function of residual intersymbol interference and derivation of Chebyshev-type bounds on the error functionals over the decomposed functions. In this correspondence, we demonstrate that the technique is not applicable in general. The result is not a bound in many cases.     

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。     

Determination of Failure Thresholds in Hybrid Navigation

A systematic approach for the determination of failure thresholds for hybrid navigation systems is described. Cost functions which reflect the importance assigned to the consequences of false and missed alarms are minimized. The false alarm probability is obtained as a function of the threshold magnitude by observing the statistical behavior of the instrument outputs in the normal operating mode. The missed alarm probability is obtained by determining the sensitivity of navigation error performance to instrument error sources. Two cost functions are considered. To illustrate this method, failure detection and identification (FDI) thresholds are determined for the Space Shuttle Approach and Landing Test flight.     

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.     

Third-Order Loop Filter Design for Acceleration-Rate Tracking

A perfect third-order loop filter design that can be implemented as a digital filter is obtained which minimizes the noiseless steady-state acceleration rate (jerk) error for a fixed loop noise bandwidth. Simulations were performed to obtain transient responses of the third-order loop plus a sample fourth-order loop under a jerk input. The results enable one to obtain a loop design that minimizes the loop noise bandwidth required for a given steady-state jerk error and thus obtain better noise jitter performance.     

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.     

Optimum Signals for Radar

The research reported herein deals with the general problem of the selection of radar waveforms. The investigation is specifically concerned with the synthesis of radar signals which are optimum in the sense that they are characterized by ambiguity surfaces minimized over certain predetermined regions of the ambiguity plane. The weighted ambiguity surface is utilized as the weighted error criterion. This error criterion is mathematically tractable and pertinent to radar system performance but is not unduly restrictive as some orientation parameters are left unspecified for subsequent cost or penalty function analysis. The signal optimization is approached by variational techniques augmented by equality and inequality constraints, for example, limiting the amount of bandwidth or frequency modulation to be less than some system requirement. Several examples are presented demonstrating the optimization techniques and providing a minimum error for the stated problem. It is shown that for any given type of amplitude modulation of the radar signal, the variance or dispersion of the ambiguity surface is not decreased for any type of phase modulation added. The optimum signal for an elliptical weighting function is derived for several cases. The minimum error is shown to depend upon the constraints and the unspecified orientation parameters and, for one case, on the second moment of the signal.     

Applications of level crossing theory to target intervisibility: to be seen or not to be seen?

Here we discuss intervisibility (the existence of an unobstructed line of sight (LOS) between two points) accounting for the vertical and horizontal errors in the estimated locations of both points as well as elevation errors in the database of the terrain that could obstruct the LOS between these points. The errors are first simply treated as a "white" noise sequence: we assume no correlation between the intervisibility at two different times, and the probability of an instantaneous intervisibility event is in this case developed. This is useful; but perhaps of greater concern is whether or not a target remains visible long enough and/or often enough that its motion can be tracked? Consequently, we present a second treatment in which the errors are stochastic processes of a certain bandwidth, and both the probability density function (pdf) of an intervisibility interval and the average number of intervisibility intervals over a certain time period are developed.