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.     

Estimation techniques for GMSK using linear detectors in satellite communications

This paper describes data-aided signal level and noise variance estimators for Gaussian minimum shift keying (GMSK) when the observations are limited to the output of a filter matched to the first pulse-amplitude modulation (PAM) pulse in the equivalent PAM representation. The estimators are based on the maximum likelihood (ML) principle and assume burst-mode transmission with known timing and a block of L₀ known bits. While it is well known that ML estimators are asymptotically unbiased and efficient, the analysis quantifies the rate at which the estimators approach these asymptotic properties. It is shown that the carrier phase, amplitude, and noise variance estimators are unbiased and can achieve their corresponding Cramer-Rao bounds with modest combinations of signal-to-noise ratio and observation length. The estimates are used to estimate the signal-to-noise ratio. It is shown that the mean squared error performance of the ratio increases with signal-to-noise ratio while the mean squared error performance of the ratio in decibels decreases with signal-to-noise ratio. Simulation results are provided to confirm the accuracy of the analytic results.     

双偏振干涉式光纤陀螺的多相位调制技术

在双偏振干涉式光纤陀螺的发展过程中，光纤环上的应力、扭转等会造成正交偏振态之间的交叉耦合，降低陀螺系统的稳定性。提出了一种基于双偏振干涉式光纤陀螺的六态方波调制技术并进行了理论推导。该技术与传统的方波和四态方波调制相比，降低了偏振交叉耦合误差，提高了信噪比，大大增加了信号解算精度。通过实验对比测试了干涉式光纤陀螺在不同调制技术下的偏置稳定性。实验结果表明六态方波调制技术的偏置稳定性达到了9.85×10-4（°）/h，验证了六态方波提高信号解算精度的效果。     

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.     

Effect of Fading on FM Reception with Cochannel Interference

The combined effect of cochannel interference and nonselective Rayleigh fading on the reception of analog FM signals in additive Gaussian noise is analyzed. Rice's click model for the breaking region is used. Analysis in the absence of interference is performed first and the effect of modulation on the click rate is found to be nearly negligible. For the case with cochannel interference the click rate is computed in the absence of modulation. Curves are given for detected signal-to-noise ratio (SNR) versus carrier-to-noise ratio (CNR) with signal-to-interference ratio (SIR) as a parameter and SNR versus SIR with CNR as a parameter. The results agree well with recently published results of a simulation study.     

A Class of Signals for Analog Telemetry over a Coherent Channel

This paper proposes and studies a class of signals which generalize frequency position modulation (FPM) and pulse position modulation (PPM). The generalization adds a degree of freedom analogous to a duty factor. Varying this quantity has an effect similar to that of varying the time-bandwidth occupancy in an FPM or PPM system, but it does not significantly increase the channel occupancy. The mean-square error is studied under large signal-to-noise ratio conditions and in the threshold region. We find that the additional degree of freedom allows us to trade between performance in these two ranges of signal-to-noise ratio. The nature of the signals, and their error behavior make them well suited to adaptive telemetry over a coherent channel. Small degrees of channel incoherence are considered and shown to produce only a small degradation in performance.     

A Semi-Empirical Approach to the PLL Threshold

This correspondence considers the response of the PLL near threshold to an input consisting of a modulated carrier and white, Gaussian noise. For high input signal-to-noise power ratios ?, the output noise power is Gaussian with a parabolic spectrum. As ? is decreased, the PLL tends to lose lock which gives rise to impulses or ?spikes? in the output with a resulting white power spectrum. The additional output noise due to these ?spikes? causes a threshold in the output signal-to-noise ratio. Unfortunately the loss of lock rate in the PLL depends on the modulation as well as the noise power. A semiempirical approximate expression for the loss of lock rate as a function of the noise and sinusoidal frequency modulation is presented and is used to determine the optimum design procedure for PLL's to demodulate FM signals of varying modulation indexes, ?.     

面向声源定位的改进广义互相关时延估计方法

面向以数字微机电系统(MEMS)麦克风作为声传感器的声源定位阵列,完成了前端麦克风阵列的电路设计和以现场可编程逻辑门阵列(FPGA)为核心的数据采集系统的开发,并对麦克风输出的脉冲密度调制信号进行了降采样处理.针对传统的广义互相关算法在低信噪比下时延估计误差较大的问题,提出了一种改进PHAT加权函数的方法.在同等条件下对基于不同加权函数的广义互相关算法进行了MATLAB仿真验证,实验结果表明,在低信噪比条件下该方法相较于传统的广义互相关算法,时延估计误差更小且抗噪性能更强.     

Studies of Logarithmic Radar Receiver Using Pulse-Length Discrimination

Using a logarithmic amplifier giving a detected output followed by a high-pass filter is a technique for reducing adverse effects of distributed clutter in radar receivers. A pulse-length discriminator (PLD) used as the high-pass filter is treated here. Theoretical and experimental results for the loss in detectability introduced by this receiver, as compared with a matched filter or a good approximation thereto, have been obtained. For the case of single-hit detection, losses of 4 to 8 dB are introduced by the logarithmic amplifier/pulse-length discriminator (LOG AMP/PLD) combination; for post-detection integration, the losses are reduced to 2 to 4 dB. The latter values would apply where the LOG AMP/PLD output is presented on a PPI (plan position indicator). Some experimental results of the ability of the LOG AMP/PLD receiver to reject signals of incorrect pulse length show that signals exceeding the design pulse length by more than 25 to 50 percent are effectively suppressed. No significant short-pulse discrimination is obtained from the receiver.     

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。     

Two Methods of Ambiguity Resolution in Pulse Doppler Weather Radars

A comparison is made of the performance of a weather Doppler radar with a staggered pulse repetition time and a radar with a random (but known) phase. As a standard for this comparison, the specifications of the forthcoming next generation weather radar (NEXRAD) are used. A statistical analysis of the spectral moment estimates for the staggered scheme is developed, and a theoretical expression for the signal-to-noise ratio due to recohering-filtering-recohering for the random phase radar is obtained. Algorithms for assignment of correct ranges to pertinent spectral moments for both techniques are presented.     

Feedback Transmission of Binary Data with Automaton Receiver

Feedback transmission of binary data over a discrete-time additive Gaussian white noise channel is considered. The effect of some specific finite memory structure at the receiver is investigated. The whole communication scheme is the discrete analog of the one previously analyzed by Khas'minskii. The resulting average transmission time is increased by only about 20 percent of the theoretical limit in the low signal-to-noise ratio region. Numerical results are also shown.     

The Response of Hard-Limiting Bandpass Limiters to PM Signals

The signal-to-noise ratio of the output of a hard-limiting bandpass limiter to a PM signal is calculated by using the probability density function of the random phase variable. The signal-to-noise ratio transfer characteristics are plotted for comparison.     

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.     

Closed-Form Expressions for Noncoherent Radar Integration Gain and Collapsing Loss

Closed-form formulas allow rapid determination of noncoherent integration gain and integration loss when the single-sample IF signal-to-noise ratio (SNR) is known. In addition, if the required SNR is known for any number of integrated pulses, the required SNR for any other number is easily determined. A closed-form expression is given for radar collapsing loss, expressed in terms of the equivalent integrated signal-to-noise ratio required to produce a given combination of false-alarm and detection probabilities. Alternatively, the single-sample signal-to-noise ratio of a set of samples may be used together with the closed-form expression for integration gain to get the equivalent integrated signal-to-noise ratio.     

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.     

Signal-to-Noise Ratio in the Bandpass Output of a Discriminator

A formula is derived for the output signal-to-noise power ratio from a limiter-discriminator that is followed by an ideal (rectangular) bandpass filter. This signal-to-noise ratio is shown to be inversely proportional to the difference between the cube of the upper cutoff frequency and the cube of the lower cutoff frequency. The formula commonly utilized by designers for the discriminator output signal-to-noise ratio was derived for the case of a lowpass filter on the discriminator output. The bandpass and low-pass formulas are compared to indicate 1) the advantage of bandpass filtering for the discriminator output, and 2) the error incurred if the designer employs the low-pass formula to evaluate the performance of a bandpass filter design. Finally, the accuracy of a narrow-band approximation for the bandpass formula is evaluated.     

Theory of LDV Tracking Systems

The application of frequency-tracking systems to the analysis of laser doppler velocimeter (LDV) signals degraded by background noise has been studied both theoretically and experimentally. Expressions are derived for both the correlation function and the expected value of the phase derivative in the general case of noise off center from the Doppler frequency, and these results are specialized to specific cases of practical interest. Laboratory measurements of output signal-to-noise ratio (SNR) and dc error, for varying input SNR and noise center frequency offset, show good agreement with the theoretical predictions.     

基于MED和LMD的自动倾斜器轴承广义Shannon熵谱分析

针对轴承信号微弱故障特征易被强背景噪声淹没的问题,提出采用最小熵反褶积,通过逆滤波器最优化设计,对目标信号进行降噪处理,其峭度值提高了约3.8倍,增强了信号的微弱故障特征;针对非平稳非线性信号频率成分复杂难以解调的问题,提出采用局部均值分解(LMD)和峭度-相关系数筛选准则,其可对非平稳非线性信号进行自适应分解和最优重构,提高了信号的信噪比;针对信号耦合调制及边频突出的问题,通过引入广义Shannon熵进行包络谱带内降噪处理,信号一阶故障特征调制频率与故障特征频率的幅度比降低了24%~43%。通过实验室信号及某型直升机自动倾斜器轴承故障诊断地面试验的分析结果验证了该方法的合理性和可行性。      

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.