The Effect of Spectral Shape on the Probability of Error in Laser Binary Communication Systems

The effect of spectral bandwidth and spectral shape upon laser binary communication systems is investigated. The probability of error is plotted as a function of bandwidth for Lorentzian and Gaussian shaped spectra. The results show that even when the average noise power and the signal-to-noise ratio are held constant, the probability of error varies considerably as a function of spectral bandwidth.     

Influence of Bandwidth Restriction on the Signal-to-Noise Performance of a PCM/NRZ Signal

The influence of bandwidth restriction on the performance of a PCM transmission system is treated. In particular, the relationship is investigated between signal-to-noise, bandwidth, and bit-error probability of an NRZ (non-return-to-zero) signal. The detector used in the investigation contains a device that integrates the signal over the bit period. Theoretical results were obtained by a Fourier analysis of bandwidth-restricted signals and by an autocorrelation analysis of the bandwidth-restricted noise. Theoretical and experimental results are in good agreement.     

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.     

Effect of a Few Dominant Specular Reflectors Target Model Upon Target Detection

Some data indicate that aircraft targets viewed from certain aspects are well modeled as consisting of a few specular reflectors. The effect of a simplified form of this target model upon radar detection performance for two different waveforms has been analyzed. The signal-to-noise ratio (SNR) required for detection as a function of waveform bandwidth for a conventional-single-channel waveform and for a four-channel frequency diversity waveform is evaluated. It is shown that for either waveform there is an optimum bandwidth to minimize the SNR required for detection. In addition, the single-channel minimum is less than the four-channel minimum. The best performance occurs for the single-channel waveform when the waveform bandwidth just resolves the individual reflectors. For typical targets, this bandwidth is of the order of 35 to 75 MHz. It is also shown that only a 0.8-dB loss relative to this minimum is incurred when using a four-channel narrow bandwidth waveform.     

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.     

Computer Optimization of FM/FM Telemetry Systems

In this correspondence, the threshold carrier power of FM/FM systems and the receiver IF bandwidth are optimized through a computer program. For a typical set of IRIG (inter-range instrumentation group) channels, it is demonstrated that the required carrier signal-to-noise ratio can be as low as 5 dB (much less than the conventional 12 dB value) in order to maintain the subcarrier signal-to-noise ratio at 12 dB, the threshold level. comparison of the optimized and the conventional taper analysis is tabulated.     

Phase-Shift-Keyed Signal Detection with Noisy Reference Signals

This paper derives and graphically illustrates the performance characteristics of Phase-Shift-Keyed communication systems where the receiver's phase reference is noisy and derived from the observed waveform by means of a narrow-band tracking filter (a phase-locked loop). In particular, two phase measurement methods are considered. One method requires the transmission of an auxiliary carrier (in practice, this signal is usually referred to as the sync subcarrier). This carrier is tracked at the receiver by means of a phase-locked loop, and the output of this loop is used as a reference signal for performing a coherent detection. The second method is self-synchronizing in that the reference signal is derived from the modulated data signal by means of a squaring-loop. The statistics (and their properties) of the differenced-correlator outputs are derived and graphically illustrated as a function of the signal-to-noise ratio existing in the tracking filter's loop bandwidth and the signal-to-noise ratio in the data channel. Conclusions of these results as well as design trends are presented.     

SNR/bandwidth tradeoff in coherent radar sampling

It is shown that if the pulse-repetition frequency of a coherent pulse-Doppler radar is at least twice the Doppler bandwidth, one may, using appropriate downconversion, sample the radar signal at half the Nyquist rate with no loss in range resolution and no folding of Doppler frequencies. This results in a 3-dB loss of signal-to-noise ratio     

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.     

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.     

An Analysis and Comparison of Energy Direction Finding Systems

Direction finding systems that use knowledge of only the aporoximate center frequency and bandwidth of the arriving signal and perform the azimuth estimate using the signal energy azimuthal distribution are of widespread interest. In this paper, a variety of such systems are considered. Their performances are analyzed and compared to each other and to a baseline optimal system. Particular attention is given to systems that will perform well against wideband signals in a low signal-to-noise environment.     

Some Results on Digital Chirp

Generating chirp waveforms by means of phase coding yields a simple, cost-effective mechanization. The coding process, however, introduces phase errors whose effect must be included in the design. An approximate analysis is presented, valid for moderate to high compression ratios, which allows error effects on compressed pulse amplitude and sidelobes to be calculated in a simple manner. The anaylsis provides criteria for selecting the coding bit width (sample rate), weighting network bandwidth, and phase-coder quantization interval and transition times. Weighting functions for maximizing the signal-to-noise ratio (SNR) or for producing desired close-in sidelobe performance are derived, as is an exact expression for the transmitted spectrum. Numerical results are presented for Gaussian and the maximum-SNR weighting. The results indicate that performance will be satisfactory for many applications.     

Enhanced resolution in simple radars

Many simple radars use fact-risetime pulses, but wide bandwidth does not translate into corresponding high resolution since the spectrum is far from flat. A scheme for enhancing down- and cross-range resolution of multiple targets through a two-step partial equalization of the spectrum is illustrated by detailed computer simulation, with emphasis on the tradeoffs between resolution and signal-to-noise ratios. Three examples are treated: two equal scattering centers, two unequal scattering centers, and compound target     

Reconciling steady-state Kalman and alpha-beta filter design

The deterministic design of the alpha-beta filter and the stochastic design of its Kalman counterpart are placed on a common basis. The first step is to find the continuous-time filter architecture which transforms into the alpha-beta discrete filter via the method of impulse invariance. This yields relations between filter bandwidth and damping ratio and the coefficients, α and β. In the Kalman case, these same coefficients are related to a defined stochastic signal-to-noise ratio and to a defined normalized tracking error variance. These latter relations are obtained from a closed-form, unique, positive-definite solution to the matrix Riccati equation for the tracking error covariance. A nomograph is given that relates the stochastic and deterministic designs     

Maximizing the Usable Bandwidth of MTI Signal Processors

A technique is presented for maximizing the percentage of usable Doppler bandwidth throughout which a radar return can be detected while maintaining an acceptable clutter suppression. The technique employs the weighted Chebyshev approximation to the design of a transversal high-pass digital filter which has an optimal passband ripple for a given number of filter weights and associated integration gain consistent with the required increase in signal-to-noise ratio needed for acceptable probabilities of detection and false alarm. Conventional approaches to the design of a movingtarget arget indictor (MTI) filter which maximizes the improvement factor by clutter suppression typically improve the signal-to-background noise ratio over less than 50 percent of the range between dc and the pulse-repetition frequency fT. This technique can increase the usable bandwidth to 80 percent or more of fT. Two examples are included which utilize parameter values from the Army Missile Command's experimental radar and demonstrate the interactive influence of such filter parameters as the number of weights, passband ripple and bandedge, and stopband attenuation and cutoff.     

Detection of stochastic signals in the frequency domain

The optimum detector for a random signal, the estimator-correlator, is difficult to implement. If the power spectral density (PSD) of a continuous time signal is known, a locally optimum detector is available. It maximizes the deflection ratio (DR), a measure of the detector output signal-to-noise ratio (SNR). A discrete version of this detector is developed here, called the discrete-MDRD, which takes a weighted sum of the spectral components of the signal data as the detection statistic. Its derivation is applicable to nonwhite noise samples as well. A comparison of this new detector against three other common types, through their DR values and simulation results, reveals that the discrete-MDRD is near optimal at low SNRs. When the PSD of a signal is not known, a common test statistic is the peak of the PSD of the data. To reduce spectral variations, the PSD estimator first divides the data sequence into several segments and then forms the averaged PSD estimate. The segment length affects the DR values; the length that maximizes the DR is approximately the reciprocal of the signal bandwidth. Thus for unknown signal PSD, a detector that approaches the maximum DR is realizable from just the knowledge of the signal bandwidth, which is normally available. Examples and simulation results are provided to illustrate the properties and performance of the new detector     

Optical fiber wavelength division multiplexing

During flight, aircraft avionics transmit and receive RF signals to/from antennas over coaxial cables. As the density and complexity of onboard avionics increases, the electromagnetic interference (EMI) environment degrades proportionately, leading to decreasing signal-to-noise ratios (SNRs) and potential safety concerns. The coaxial cables are inherently lossy, limiting the RF signal bandwidth while adding considerable weight. To overcome these limitations, we have investigated a fiber optic communications link for aircraft that utilizes wavelength division multiplexing (WDM) to support the simultaneous transmission of multiple signals (including RF) over a single optical fiber. Optical fiber has many advantages over coaxial cable, particularly lower loss, greater bandwidth, and immunity to EMI. In this paper, we demonstrate that WDM can be successfully used to transmit multiple RF signals over a single optical fiber with no appreciable signal degradation. We investigate the transmission of FM and AM analog modulated signals, as well as FSK digital modulated signals, over a fiber optic link (FOL) employing WDM. We present measurements of power loss, delay, SNR, carrier-to-noise ratio (CNR), total harmonic distortion (THD), and bit error rate (BER). Our experimental results indicate that WDM is a fiber optic technology suitable for avionics applications.     

白天大气层内星敏感器观星能力分析

利用星敏感器进行白天大气层内观星,首先要解决的问题是强天空背景的干扰。通过对白天天空背景和不同光谱恒星的特点进行分析,提出了光谱滤波和偏振成像加形态学滤波和多帧图像累加的技术路线,综合利用光学方法和图像处理方法提高观测对比度和信噪比。给出了白天观星的信噪比模型,并在不同天空背景偏振度条件下,得出了G、K、M光谱恒星的0至5等星的单帧图像信噪比和对应的使CCD(Charge Coupled Device,电荷耦合器件)接近饱和的极限曝光时间。结果表明:星等值越低,天空背景偏振度越大,则信噪比越高;同等条件下,信噪比由小到大依次为G、K、M光谱恒星;而对于低信噪比的图像,通过多帧累加后可满足观测的要求。     

A Self Bit Synchronizer Matched to the Signal Shape

A suboptimum self bit synchronizer is considered that matches the signal shape, i. e., operates making a clever use of the knowledge of the signaling waveform. The noise performance of this system is analyzed for high signal-to-noise ratios, and an expression is obtained for the variance of the timing errors. This variance is compared with that of systems proposed by other authors on the basis of equal closed-loop noise bandwidth and equal signal shape. It is found that the use of this matched synchronizer enables appreciable timing jitter reductions.     

On the Accuracy And Resolution of Radar Signals

Information matrices are derived for estimates of the range parameters of moving targets as obtained by combining a priori information (if available) with reflected radar signals observed in the presence of additive white Gaussian noise. The inverse of the information matrix provides a lower bound on the covariance matrix of any unbiased parameter estimates. This bound can be approached with a high signal-to-noise ratio and optimum data processing (matched filters). Arbitrary frequency modulation, amplitude modulation, and target motion as well as various assumptions on processing the RF phase are considered. The multiple-target case makes possible investigation of a signal's resolution ability, as well as its accuracy potentials. Results for a carrier frequency much greater than the effective signal bandwidth are obtained as a special case. A main purpose of the paper is the reduction of the original radar problem to a linear model which is equivalent in the sense of having the same information matrix. These models provide valuable insight into the relative effects of multiple targets, choice of modulation, a priori information, and assumptions regarding RF phase and bandwidth. The linear equivalent model also leads to a valuable computational algorithm for investigations using digital or hybrid computers. The various special cases of interest are obtained by simple modifications of the general case, and thus the algorithm can provide a very versatile tool for evaluating and designing radar signals.