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.     

Effects of CW Interference on Narrow-Band Second-Order Phase-Lock Loops

This paper describes an experimental study of the effect of continuous wave (CW) interference and white noise on a second-order phase-lock loop. The reciprocal of the loop mean-square phase error is used as an index of performance, and the effect of interference levels that do not cause cycle skipping or loss of lock is described in terms of this index. Loop thresholds are determined by measurement of cycle-skipping rates. Stationary or slowly-sweeping CW interference caused a degradation in loop threshold of roughly 3 dB for every 6 dB of interference power above the noise power level. The effective loop signal-to-noise ratio was decreased approximately 1 dB at interference-to-noise power ratios of -3 dB. Interference levels equal to the signal level consistently caused loss of lock, regardless of the loop signal-to-noise ratio.     

Lock threshold deterioration induced by antenna vibration and signal coupling effects in hypersonic vehicle carrier tracking system of Ka band

The envelope of a hypersonic vehicle is affected by severe fluctuating pressure, which causes the airborne antenna to vibrate slightly. This vibration mixes with the transmitted signals and thus introduces additional multiplicative phase noise. Antenna vibration and signal coupling effects as well as their influence on the lock threshold of the hypersonic vehicle carrier tracking system of the Ka band are investigated in this study. A vibration model is initially established to obtain phase noise in consideration of the inherent relationship between vibration displacement and electromagnetic wavelength. An analytical model of the Phase-Locked Loop(PLL), which is widely used in carrier tracking systems, is established. The coupling effects on carrier tracking performance are investigated and quantitatively analyzed by imposing the multiplicative phase noise on the PLL model. Simulation results show that the phase noise presents a Gaussian distribution and is similar to vibration displacement variation. A large standard deviation in vibration displacement exerts a significant effect on the lock threshold. A critical standard deviation is observed in the PLL of Binary Phase Shift Keying(BPSK) and Quadrature Phase Shift Keying(QPSK) signals. The effect on QPSK signals is more severe than that on BPSK signals. The maximum tolerable standard deviations normalized by the wavelength of the carrier are 0.04 and 0.02 for BPSK and QPSK signals,respectively. With these critical standard deviations, lock thresholds are increased from à12 andà4 d B to 3 and à2 d B, respectively.     

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.     

Dynamics of the Phase-Locked Loop without a Limiter

The general (nth order) phase-locked loop is analyzed, of which the amplitude is not constant. The input carrier signal is amplitude-modulated by wide-band stationary Gaussian noise, and the signal, superposed with the additive white stationary Gaussian noise, enters the nonlimited phase-locked loop. Under the above assumptions the loop can be shown to constitute an n-dimensional vector Markov process, so that the process satisfies the n-dimensional Fokker-Plank equation. The probability density function depends on the effective loop signal-to-noise ratio and the effective modulation power.     

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.     

Some Matched Filter Configurations for Infrared Systems

An analysis of the output of three alternative matched filter configurations in an infrared scanning system model is presented. The sensor is corrupted by thermal noise, generation-recombination noise, photon noise, and modulation noise, the latter providing an extreme discoloration in the signal passband. Expressions for the signal voltage density spectrum, signal pulse shape, noise power spectrum, and average noise power at the matched filter output are derived where the integral evaluations attendant to these derivations do not appear elsewhere in the literature. The paper also provides graphical displays of the signal-to-noise power ratio at the filter output versus various system parameters, noise power spectrum out of the matched filter versus ?, and the signal pulse shape out of the filter versus time. Also included are discussions of practically realizable approximations to the matched filters and curve fitting techniques for the signal pulse shape function.     

PAM approach to weak CPM and its application to flight termination receivers

A method for computing the PAM representation for weak continuous phase modulation (CPM) is presented and applied to the modulation defined in the enhanced flight termination system (EFTS) standard. The pulse-amplitude modulation (PAM) representation was used to formulate a reduced-complexity detector whose performance is within 0.7 dB of maximum likelihood detection and 5.6 dB better than limiter-discriminator detection in the additive white Gaussian noise (AWGN) environment. The complexity of the reduced-complexity detector is less than 25% that of the maximum likelihood detector but, unlike the limiter-discriminator detector, requires a carrier phase PLL. In the presence of phase noise, the reduced-complexity detector outperforms limiter-discriminator detection when the RMS frequency deviation due to phase noise is less than 10% of the bit rate.     

Spectrum Distortion Due to Frequency Instabilities in a Two-Way Coherent Doppler Radar

The power spectral density of the intermediate frequency signal in a coherent Doppler navigation radar is derived. The effects of antenna parameters, periodic frequency instabilities, signal two-way transit time, and transmitter frequency modulation noise are considered Several examples based on the measured frequency modulation noise of a solid-state source transmitter are presented. The results indicate the degree of loss in signal-to-noise ratio, and spectrum broadening due to an increase in signal transit time and/or frequency modulation noise.     

Spectral Moment Estimates from Correlated Pulse Pairs

Estimates statistics of the first two power spectrum moments from the pulse pair covariance are analyzed. The input signal is assumed to be colored Gaussian and the noise, white Gaussian. Perturbation formulas for the standard deviation of both mean frequency and spectrum width are applied to a Gaussian shaped power spectrum, and so is a perturbation formula for the bias in the width estimate. Mean frequency estimation from interlaced pulse pairs is presented. Throughout this study, estimators from independent, spaced, and contiguous pulse pairs are compared to provide a continuum of statistics from equispaced tightly correlated to statistically independent pulse pairs.     

非参量量化秩检测器的性能研究

 许多作者讨论过非参量秩检测器在雷达信号处理中的应用。秩检测器首先把接收波形样本转换为秩。如果检验单元和参考单元的噪声样本独立和分布,则无信号时检验单元的秩具有离散均匀分布,与输入噪声的分布无关。所以秩检测器可能提供分布自由的恒虚警率性能。量化秩检测器（QRD）只对二进量化秩进行积累,所以它实现起来很经济。本文分析QRD的检测性能。证明QRD有一最佳秩量化门限（ORQT）。确定高斯和韦伯噪声中的ORQT。另外,把QRD同高斯噪声中的局部最佳秩检测器和最佳参量检测器进行比较。     

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.     

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     

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.     

Phase-Lock Loop Jump Phenomenon in the Presence of Two Signals

Jump phenomena are known to exist in many non-linear systems [I], [2], [3]. The non-linear analysis presented in this paper explains and predicts the conditions for the jump phenomenon that is observed in a phase-locked loop (PLL) preceded by an automatic gain control (AGC). The jump phenomenon occurs when the frequency separation AM of two sinusoids at the input to the AGC is greater than the bandwidth B of the linearized PLL. If the loop is initially locked to the stronger signal, the weaker signal will frequency-modulate the PLL voltage-controlled oscillator (VCO) with a modulation frequency AI. The amplitude S2 of the weaker signal al can be increased until it becomes greater than the amplitude Si of the signal being tracked, without causing the loop to lose lock; i. e., the VCO continues to track the original signal. However, if the ratio of the amplitudes S2 S1 = R is increased above some critical value RC > 1, the loop will lose lock on the original signal, and jump to track the interfering signal. If the frequency separation is at least twice the PLL bandwidth, a good approximation for this critical ratio is Rc ? ?w/B.     

Output of a Balanced Frequency Discriminator Driven by a Sine Wave and Gaussian Noise

The output of a realizable balanced frequency discriminator is calculated for an input consisting of a sine wave plus Gaussian noise. Explicit autocorrelation and power spectra are found for one practical embodiment of the discriminator for various input carrier-to-noise ratios, with the carrier tuned to center frequency and also off-center. The formulas also permit the calculation of the output for the case of a spectrum of noise slowly swept through the discriminator. Although qualitatively similar to results previously obtained with an ideal discriminator, substantial differences are also found. Measurements are made that closely verified the theoretical results. No limiting is assumed.     

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.     

The Performance of Analog Correlators for Several Integrator Functions

A measure of analog correlator performance is considered and interpreted reted as an output signl-to-noise ratio. This quantity is shown to depend on the fourth-order expectation of the input signals and the characteristics of the integrating system. Based on the output signal-to-noise ratio, figures of merit are established for correlators utilizing an ideal low-pass filter, an RC filter, and a finite time integrator. These figures of merit indicate to what degree the correlators reject noise components. For jointly Gaussian inputs, the variation of the output signal-to-noise ratio with the input signal-to-noise ratio is shown to be independent of the integrating system. Finally, a graphical comparison indicates the characteristics of the three systems for several different parameters. This comparison shows that the finite time integrator is superior to the other two systems considered.     

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.     

Mismatched Filtering of Sonar Signals

A replica correlator (matched filter) is an optimum processor for a receiver employing a pulse of continuous wave (CW) signal in a white Gaussian noise background. In an active sonar, however, when the target of interest has low Doppler shift and is embedded in a high reverberation background, this is not so. High sidelobes of the correlator frequency response pass a significant portion of the signal contained in the mainlobe of the reverberation spectrum. In order to reduce the sidelobes of the correlator output spectrum and at the same time keep the increase in its 3 dB bandwidth to a small amount, we propose lengthening of the replica of the transmitted signal and weighting it by a Kaiser window. It is demonstrated that by extending the weighted replica by 50 percent compared with the transmitted signal, it is possible to reduce the sidelobe levels to at least 40 dB below the mainlobe peak, with the concomitant increase of the 3 dB band-width by less than 5 percent. The degradation in signal-to-noise ratio (SNR) performance for such a ?mismatched? filter receiver with respect to the matched filter is less than 1.5 dB.