Probability Densities and Characteristic Functions for Fluctuating Targets

Probability density functions and characteristic functions for the projected area of a tumbling target object are derived together with the densities and characteristic functions for the corresponding signal-plus-noise voltage output of an infrared sensor. Several cases are considered in which the signal pulse arrival time is either known or unknown, a matched filter or a suboptimum filter is used; the signal pulse shape is either Gaussian or is unspecified; and the target orientation angles are either uniformly or nonuniformly distributed.     

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.     

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.     

基于概率统计的DS/FH系统干扰检测算法

基于时频分布的干扰检测算法是DS/FH（Direct Sequence/Frequency Hopping,直接序列扩频/跳频扩频）系统干扰检测的传统手段,针对其运算量大、实时性差,以及无法检测某些特殊干扰信号等问题,提出一种基于概率统计的干扰检测算法.通过统计DS/FH系统频谱图中各频率的幅值出现位置,以DS/FH信号与干扰信号频谱分布规律的差别为判决依据,完成DS/FH系统中干扰信号的检测.分析和仿真结果表明：该检测算法能够有效识别DS/FH系统中的典型干扰信号,与传统基于时频分布的检测算法相比,能够实现某些特殊干扰信号的有效检测;同时,由于该算法不需要进行复杂的时频联合分析,其运算复杂度大大降低,能够实现DS/FH系统干扰信号的快速检测.     

Detection Statistics for Laser Radar in Atmospheric Turbulence with Fluctuating Targets

The probability of detection and false-alarm rates are developed for laser radar systems perturbed by background radiation, fluctuating targets, and atmospheric turbulence. In particular, some results on the decibel loss due to atmospheric turbulence are presented.     

Adaptive Detection Probabilities for Fluctuating Target Models in Nonhomogeneous Gaussian Noise

Under the assumption that the average noise power may vary from cell to cell, new, more easily computed expressions are given for the probability of detecting a fluctuating target by means of a cell-averaging CFAR test. The generalized chi-square family of fluctuating targets is considered with the Swerling I and III models given as special cases.     

Probability of Detecting a Fluctuating Target Immersed in Both Noise and Clutter

The probability of detecting either a Swerling 1 or Swerling 2 target immersed in both Rayleigh-distributed noise and log-normally distributed clutter is calculated. Results are presented which demonstrate the effect of noise-to-clutter ratio, signal-to-noise ratio, and number of pulses integrated on the detection statistics.     

Exact Detection Probability for Partially Correlated Rayleigh Targets

The detection probability PD of a radar receiver which postdetection integrates N pulses of an expqnentially correlated signal from a Rayleigh target in thermal noise is determined. At the limiting correlation coefficients, p = 1 and p = 0, the analysis yields, respectively, the well known Swerling case 1 and case 2 formulas. The effect of partial (0 ? p ? 1) correlation is exhibited in a set of curves of PD versus signal-to-noise ratio, X, for various N and p. Additional curves compare the exact fluctuation loss determined from the above analysis with an approximate expression universally employed by radar system engineers.     

Analysis of Detection Probability for the Acoustooptic Receiver

A numerical method is described for analyzing the performance of an acoustooptic receiver. The method provides output waveforms, probability density functions for samples of the output, and detection probabilities for output samples. The approach is general in that input pulse envelope shapes, pulse offset frequencies, and output rilter magnitude responses are arbitrary. The basic analysis is also independent of the shape of the optical beam and of the photodiode windows.     

Multiple-Tone Signals and Detection Probabillities

An analysis technique is presented for multiple-tone signals insystems employing noncoherent integration of a square-law detectoroutput. It is shown how the characteristic function for the teststatistic can be found from the easily determined "coherent"characteristic function defined in the two-dimensional signal space.This result is applied to two detection problems, the detection of multiple-tone signals in Gaussian noise and the detection of a Gaussian signal in multiple-tone plus Gaussian noise interference.The detection curves are compared to an approximation that is often used in practice to estimate performance. It is found that detection performance in the presence of multiple-tone interferences can be significantly different from that in the presence of Gaussian noise alone.     

Mean-Level Detection of Nonfluctuating Signals

Analysis of the performance of a mean-level threshold in the detection of nonfluctuating signals is performed. Formulas for the probability of detection are derived and a simple recursive method that can be used for computations is described. Binary integration is discussed, and it is shown that the loss in sensitivity due to the use of an adaptive threshold followed by binary integration is only a fraction of a decibel when compared with optimum binary integration. Binary integration results are given for both fluctuating and nonfluctuating signals.     

Error Probability for Fading CPSK Signals in Gaussian and Impulsive Atmospheric Noise Environments

Recently the performance of digital communication systems in the presence of impulsive atmospheric noise has been evaluated assuming a noise model which is in excellent agreement with experimental results. We evaluate the bit error probability for coherent phase-shift keying (CPSK) signaling assuming the same atmospheric noise model but considering a more reasonable representation of the communication channel which accounts for the simultaneous presence of Gaussian (always present) atmospheric noise and signal fading.     

Approximation to Probability of Detection for Log-Normal Target Fluctuation

A relatively simple expression for the approximation to the probability of detection of a log-normally fluctuating target is provided. Absolute errors normally have a magnitude less than 0.01.     

基于检测前跟踪的超视距雷达微弱目标检测方法

天波超视距雷达（over-the-horizonradar,OTHR）通过快速傅立叶变换（FFr）实现相干积累,再利用常规的方法进行目标检测。但这种方法在弱目标、低信噪比的情况下效果并不好。本文提出了一种基于检测前跟踪（track-before-detect,TBD）的OTHR弱目标检测方法,利用数学形态学对每帧弱目标回波信号进行滤波,再通过动态规划方法进行检测。仿真结果表明,该方法能够有效地提高OTHR对弱目标的检测能力,运算效率高,实用性强。     

Fluctuating Target Detection in Clutter Using Sidelobe Blanking Logic

In an earlier paper, Maisel [6] considered two-channel detection systems using a sidelobe blanking logic when a nonfluctuating target was present. This paper is an extension of the earlier work to include fluctuating targets. The Swerling I, II, III, and IV models are considered when single-pulse detection is of interest. An adaptive threshold procedure is also briefly discussed whereby the probability of false alarm at any given resolution cell is maintained constant, even though the input clutter level may vary from cell to cell or from beam position to beam position. Useful data are presented for detection probabilities in the range 0.5 to 0.9, for false alarm probabilities in the range 104 to 10-8, and for a false detection probability of 0.1 for a sidelobe target yielding an apparent signal to total noise power density ratio of 13.0 dB in the main beam receiver.     

Detection of Slow Fluctuating Targets with Frequency Diversity Channels

In this paper an exact closed-form expression for the radar detection probability is derived and results are plotted for a frequency diversity radar receiver. The receiver model performs post-detection integration on all received pulses in all diversity channels. The target model assumed is the slow fluctuating Rayleigh-distributed (Swerling case I target) scatterer. Each of the M frequency diverse channels receives N amplitude-correlated returns to give a total of NM post square-law detection integrations. The tabulated data falls between the two extreme cases, that for which all the returns are amplitude-correlated and that for which each return is independent. The plotted results fall close to the figures obtained through simple empirical relationships.     

Detection Performance of Soft-Limited Phase-Coded Signals

General analytic expressions are developed for the soft-limited digital pulse compressor (matched filter). This theoretical development is then used for the hardware realization of a two-channel (I,Q), 3-bit-limited digital pulse compressor with a compression ratio of 255: 1. The realized hardware uses state of the art integrated circuit devices. An experimental laboratory setup is described. This setup is used to study hard-limited versus 3-bit-limited matched-filter performance characteristics with the data in the following areas: 1) constant false alarm rate (CFAR) characteristics as a function of threshold settings and noise levels; 2) single target detection characteristics as a function of input signal-to-noise ratio (SNR); and 3) two target performance characteristics: a) the amplitude of a weaker target as a function of target ratio and target overlap; and b) the detection characteristics of a weaker target as a function of weaker target SNR, strong target SNR, and target overlap.     

Detection Performance of Hard-Limited Phase-Coded Signals

The performance of a complex phase-coded waveform digital processor with hard-limiting constant false-alarm rate (CFAR) is presented. Processing losses relative to ideal matched-filter performance are computed and verified by hardware measurement. The losses considered include the consequences of hard limiting, envelope algorithm implementation, range cusping, and the associated effects of code length, IF filter bandwidth, and in-phase and quadrature channel phase offset. The range resolution properties of two closely spaced targets are also considered.     

Effects of Band Limiting on the Detection of Binary Signals

PCM/NRZ systems operating in the presenceof noise and in a band-limited channel areconsidered. Two types of bit detectors arestudied, integrate and dump, and sample. Theincreased signal power needed to give thesame performance as an optimum detectorand a broad-band channel is computed. Theresults depend on the bit pattern. The averageeffect of band-limiting over all bit patternsand two extreme cases are plotted for eachdetector. The results show that integrate anddump is always superior to sample and that ifthe sample detector is used, one should bandlimit before sampling at a frequency of 0.6times the bit rate.