Noise Injected into Coherent Carrier Signals by Random Phase Changes

The autocorrelation and power spectrum of spurii arising from periodic random phase injections into a coherent backscatter signal are found. Design considerations of appropriate filters to eliminate spurii noise is discussed.     

Limiting the Impulsive Noise in a PLL

This paper analyzes the operation of a phase-locked loop (PLL) preceded by a bandpass limiter (BPL) in the presence of impulsive noise. It is shown that the effect of the limiter consists essentially in a change of the statistics of the pulse strengths of the noise, so that the behavior of a BPL + PLL can be deduced from that of a simple PLL by suitable adjustment of the noise model. It is found that the limiter greatly enhances the PLL performance by reducing both the phase-error variance in the loop and the probability of cycle slippage. Finally, the design of the filter of the BPL is discussed, resulting in the conclusion that the best results are obtained by using a singletuned RLC circuit.     

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.     

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.     

The Nonparametric Detection of Signals Embedded in Log-Normal Noise

The nonparametric detection of signals embedded in log-normal noise is discussed. The generalized sign (GS), Mann-Whitney (MW), modified Savage (MS), and modified rank squared (MRS) non-parametic detectors are considered and are compared with the mean and trimmed mean (TM) detectors when envelope detection is used. The detection of both nonfluctuating and Rayleigh fluctuating signals is considered.     

Spectral Analysis and Subtraction of Noise in Radar Signals

A new method of maximum entropy spectral estimation called the revised maximum entropy method (MEM) is formulated and is applied to the spectral analysis of the echo signals from atmospheric turbulence observed by an incoherent scatter radar. The revised MEM is shown free from many demerits of the other methods for spectral analysis. Further it makes it possible to subtract the white noise usually contained in the data during the processing. Some examples of spectral estimation are shown for the actual radar signals and the simulated data. Another application of the revised MEM is the subtraction of the clutter component which is difficult to do by linear filtering. The method is successfully applied to several data abounding with the clutter to obtain the spectra of the echo signals with less clutter distortion.     

Interference Due to Limiting and Demodulation of Two Angle Modulated Signals

Two angle modulated signals (FM or PM) passing through a limiter and then a demodulator are analyzed. The analysis considers the problem of adjacent carrier interference, direct adjacent channel interference (DACI) or cross talk, and adjacent channel interference (ACI). The analysis of adjacent carrier interference shows that if the 3rd order IM is not to overlap the signal spectra, the carrier frequencies must be separated by 2B where B is the bandwidth of each carrier. The ACI analysis shows that the carrier frequencies must be separated by B+2?m for no ACI, since the demodulator reduces the bandwidth of the 3rd order IM from 3B to 2B+2?m where ?m is the maximum frequency of each baseband. The DACI analysis shows that DACI does not exist in a PM system and is -52 dB for an ideal hard limiter with no bandpass filter. But the DACI is -58 dB for an ideal hard limiter with a more realistic bandpass filter.     

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.     

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.     

On Transient and Periodic Signal Detection in Time-Varying Noise Power

Detectability of periodic and synchronously recurrent transient signals in a noisy environment in which the noise power is time varying is investigated. For at least one noise model, it is shown that the basic nonlinearity of the optimum detector is a limiter. Performance of this optimum detector is compared with analog cross-correlation and clipper cross-correlation (CCC) detectors. It is shown that the CCC performs nearly optimally, especially at low signal-to-noise ratios, and that its performance is significantly better than that of the analog cross correlator.     

Optimum Linear Estimation of Stochastic Signals in the Presence of Multiplicative Noise

This paper considers optimum (MMSE) linear recursive estimation of stochastic signals in the presence of multiplicative noise in addition to measurement noise. Often problems associated with phenomena such as fading or reflection of the transmitted signal at an ionospheric layer, and also situations involving sampling, gating, or amplitude modulation, can be cast into such formulation. The different kinds of estimation problems treated include one-stage prediction, filtering, and smoothing. Algorithms are presented for discrete time as well as for continuous time estimation.     

Sonar Array Detection of Gaussian Signals in Gaussian Noise of Unknown Power

A statistical test is postulated for detecting, with an M-element hydrophone array, a Gaussian signal in spatially independent Gaussian noise of unknown power. The test is an extension of the uniformly-most-powerful (UMP) unbiased test for a two-element array. The output signal-to-noise ratio of the test is calculated and, for a large number of independent space-time samples, is shown to be no better than a mean-level detector (MLD). Receiver operating characteristic curves (ROC) for the MLD are computed and compared to the ROC curves for the optimum (Bayes) parametric detector. The input signal-to-noise power ratios required to provide a detection probability of 0.5 differ by less than 0.2 dB for a fifty-element array with wide variation in false-alarm probability and time-bandwidth product. This result suggests that both the extended bivariate UMP unbiased test and the MLD perform close to the unknown UMP unbiased test for independence of a multivariate Gaussian distribution.     

On Clutter Modeling and the Spectra of Two-Dimensional Gauss-Markov Random Signals

The spectral properties of two-dimensional isotropic clutter signals are examined for the cases in which 1) the clutter has an exponential spatial autocorrelation function, and 2) the clutter is a two-dimensional Gauss-Markov random signal. The one- and twodimensional power spectral densities before and after antenna filtering are obtained, and some of the differences and similarities between these two models are discussed in the context of spectral analysis.     

Noise Due to Flutter and Skew in Recording of Pseudorandom Scanned TV Signals

The distortion of a pseudorandom scanned TV signal caused by flutter and skew introduced by the tape recording apparatus is analyzed theoretically. Specifically, the signal-to-noise ratio is computed for a typical system, under the assumption that the distortion can be considered to be additive random noise with a Gaussian amplitude distribution.     

Performance of an Ideal Quantum Receiver of a Coherent Signal of Random Phase

An ideal quantum receiver is to detect a coherent narrow-band optical signal in the presence of thermal background radiation. Curves are given both of the average probability of error in a binary communication system transmitting O's (blanks) and 1's (pulses) with equal probabilities, and of the probability of detection for various fixed values of the false-alarm probability.     

Effects of Random Implementation Errors in Matched Filters for Binary Phase Code Pulse Signals

The effects of implementation errors in tapped delay line filters on the peak-to-sidelobe ratio and the signal-to-noise ratio of binary PSK pulse compression codes are considered. As error model the delay elements and weighting factors of such filters are assumed to have an error distribution with known mean and variance.     

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.     

An Alternate Approach to the Prediction of Polynomial Signals in Noise from Discrete Data

When the problem of predicting the past, present, or future value of a polynomial signal or any of its derivatives is considered, where the signal is in white Gaussian noise, the standard approach has been to minimize mean-square-error with constraints by use of Lagrange multipliers. In this paper an alternate approach is described, using results of Rao and Bhattacharyya from the statistical literature, which reduce the specified prediction problem to a simple one requiring no formal minimizations and no use of Lagrange multipliers. It further has the advantage of yielding the covariances between estimates of the polynomial and its derivates. Useful engineering formulas for smoothing and prediction are developed in the main part of the paper. These include both filter and covariance expressions. A tutorial discussion of the theory is given in two appendixes.     

残缺齿轮限位机构

通过合理设置残缺齿和残缺齿槽的数量和位置,便可设计出不同活动范围的限位机构.本文论述了残缺齿轮限位机构的原理和设计、制造方法以及实际应用的范例.     

Hard Limiting in Synthetic Aperture Signal Processing

In synthetic aperture radar a large linear phased array is formed from the rapid movement of a single element through each position in the array. Storage and coherent combining of the successive radar echoes are central to the array-forming process. Optical processing is the most common technique because of the efficiency with which Fourier transformation may be accomplished with simple optics. Real-time operation, however, requires all-electronic processing, which is difficult to accomplish because of the huge quantity of data to be manipulated. Dynamic range compression by hard limiting may ease the problem by reducing the number of bits per frame. The effects of hard limiting are analyzed in this paper. It is shown that large targets simultaneously illuminated by the radar antenna will produce image targets or ghosts displaced in angle. Statistically homogeneous clutter will "linearize" the hard-limited receiver and suppress the ghosts without loss in contrast, as does thermal noise if it is larger than the target echoes. Pulse compression reduces the probability of images from prominent targets. Judicious choice of the pulse-compression waveform is a powerful tool for destroying coherent buildup of images from all large targets not in the same range resolution cell. Linear FM, the most common choice, unfortunately does not exhibit this desirable property.