Linear FM signal parameter estimation from discrete-timeobservations

The authors consider the problem of estimating the parameters of a complex linear FM signal from a finite number of noisy discrete-time observations. An estimation algorithm is proposed, and its asymptotic (large sample) performance is analyzed. The algorithm is computationally simple, consisting of two fast Fourier transforms (FFTs) accompanied by one-dimensional searches for maxima. The variance of the estimates is shown to be close to the Cramer-Rao lower bound when the signal-to-noise ratio is 0 dB and above. The authors applied the algorithm to the problem of estimating the kinematic parameters of an accelerating target by pulse-Doppler radar. A representative test case was used to exhibit the usefulness of the algorithm for this problem, and to verify the analytical results by Monte Carlo simulations     

Error Probabilities in PCM/FM with Phase-Lock Loop Discriminators

Previous literature has analyzed PCM/FM telemetry systems using idealized FM demodulators at the receiver. However, in many systems operating today, phase-lock loop demodulators are employed which depart noticeably from ideal operation as the loop falls ?out of lock.? In this paper an approximate expression for error probability is derived, which clearly indicates the effect of the loop on the previously published data using ideal discriminators. It is shown that the presence of the loop becomes apparent at input signal-to-noise ratios below approximately 3.5 dB, while the amount of error increase over the ideal case depends, to a large extent, upon the shape of IF filtering being used.     

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 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, ?.     

FM Threshold Performance of the Frequency Demodulator with Feedback

The FM threshold performance of the frequency demodulator with feedback (FMFB) is experimentally optimized. Rules of thumb for the practical design of the FMFB with limiter in the loop are proposed. Such design rules provide for optimum FMFB threshold performance given specifications of the received signal. Equivalences among the FMFB, phase-locked loop, and limiter- discriminator offer some additional physical insight into the threshold-extending mechanism of the FMFB not presented by previous investigators.     

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.     

Probability Density of the Click Duration in an Ideal FM Discriminator

The expression of the probability density function PClick(T) of the duration r of the clicks is determined as a function of 1) the expected number of clicks per second, Felick 2) the expected number of times per second that the noise component x(t) in phase with the carrier has instantaneous amplitude larger than that of the carrier itself 3) the probability density function peross(T) of the duration of the time intervals in which x(t) < -A 4) the probability that the values of the noise component in quadrature with the carrier will be of opposite sign at the extremes of time intervals of duration v. Using for Pcross(T) an approximate formula that holds fairly well in the range of the values of the signal-to-noise power ratio ? usually encountered, PIick(T) has been calculated for several values of a and for two shapes of the noise spectrum, Gaussian and rectangular. Finally, an expression is given for the mean value of T.     

Interference between FM Carriers and a Digitally Modulated SCPC Circuit

The interference from the digital single channel per carrier (SCPC) circuits into frequency-modulated carrier systems has been calculated by convolving the desired and the interfering spectra extending the previously published works. Resulting interference noise power in FDM/FM systems covering a wide range of modulation indices and basebands has been presnted. Also plots of interference noise power as a function of the number of SCPC circuits have been presented for various values of carrier power to interference power ratios.     

FM Laser Noise Effects on Optical Doppler Radar Systems

A detailed analytical study is made of the effect of FM noise on a laser carrier frequency which is used in a Doppler radar. Both long-term drift and short-term FM noise are considered. The case of high modulation index of the noise is permitted by the theory. Forward as well as slanted beams are examined. Curves have been calculated for each case to allow rapid estimates of the bandwidth requirements to accomodate the laser noise. This, in turn, will give the resolution limit of the radar caused by that noise. A summary of the results is given.     

Cancellation of Unwanted Spectral Components in an FM Multivibrator System

The performance of FM multivibrator systems for high quality communications applications is limited by the presence of unwanted spectral components. A theory is presented for an improved system in which unwanted spectral components are cancelled, achieved by generating a cancelling component in a square-law device. The cancelling component tracks the unwanted component in both frequency and amplitude over a wide bandwidth of signal frequencies. Reductions in magnitude of the unwanted components by at least 16 dB are predicted; reductions of better than 14 dB have been achieved in practice.     

New approach for suppression of FM jamming in GPS receivers

A new approach is proposed for the suppression of FM jammers in C/A code GPS receivers. This approach is based on the cascading of the augmented-state approximate conditional mean (ASACM) filter and the discrete wavelet transform (DWT) filter. An ASACM filter for single interference suppression in spread-spectrum systems has been reported in the recent literature. However, the formulation of the ASACM filter and its performance analysis is lacking in the case of suppression of multiple FM interferences. The ASACM filter is formulated here for the suppression of multiple FM jammers. Further, a DWT filter using biorthogonal wavelet is suggested for the suppression of FM jammers. Finally, these two filters are cascaded to get an optimum performance for higher jammer to signal ratio, which is of importance in the GPS, for the case of suppression of multiple FM jammers. The performance of the proposed filters is analyzed through simulation examples for the suppression of single and multiple FM jammers in GPS receivers     

Discriminator Detection of Wide-Band PCM/FM

The performance of discriminator detection of wide-band PCM/FM is investigated. Formulas are derived that allow one to predict system performance with the effects of both predetection and postdetection filtering accounted for. In particular, for a postdetection equivalent noise bandwidthbit time product b0T=2, it is shown that best results are obtained with a modulation index ?=0.6. Furthermore, it is shown that performance to within 1.5 dB of theoretical can be obtained.     

Detection Performance of a Mean-Level Threshold

The problem of detecting signals in nonstationary clutter is met by presenting a mean-level or adaptive threshold which adjusts to the changing background level. Such a threshold performs better than a fixed threshold that must be set for the highest amplitude clutter. However, the mean-level threshold does not perform as well for stationary noise as a fixed threshold set at the proper value. One measure of effectiveness of an adaptive threshold is its performance in stationary noise (compared to the optimum fixed threshold) for a specified speed of response. For the mean-level threshold, a simple mathematical solution is found for the detection probability when the noise is stationary and the signal scintillates rapidly. The performance is evaluated for a wide range of mean-level-threshold time constants and for several false-alarm probabilities. The results are presented graphically. As an example, the mean-level threshold suffers 3 dB in detectability (equivalent signal-to-noise ratio) in the presence of stationary noise as compared to the optimum fixed threshold for 50-percent probability of detection, false-alarm probability of 10-8, and an adjustment time of 15 times the signal duration.     

Transmission Characteristics of an FM Signal Through a Hard Limiting Repeater

The response of an FM detector to an FM signal which is passed through a hard limiting repeater together with additive Gaussian noise is described. A general expression of the output SNR is derived that enables the determination of the threshold behavior. To clarify the feature of a transmission characteristic, a comparison with a linear repeater is also made. The output SNR is found to be larger than that of the linear system for all practical values of input CNR's.     

Estimation and classification of FM signals using time frequency transforms

This work deals with electronic warfare: we have to process an intercepted radar-emitted signal assumed to be frequency-modulated (FM). A battery of parametric models being available, we face the two main problems: the parameter estimation, given a model, and the classification, given the battery. For the former, we propose the classical maximum likelihood estimator (MLE) and an original numerical scheme to reach it. For the latter, we construct a test based on the estimated variances cross-ratios. Both perform very efficiently with respect to (w.r.t.) the Cramer-Rao lower bound (CRLB) and the rate of correct classification, respectively, for low signal-to-noise ratios (SNRs).     

Principle and Design of a Vernier FM Radar System

This paper describes the principle and the signal design of a proposed new FM radar system. In order to measure the surface characteristics of a small target at a long distance, or to discriminate among multiple targets, very accurate range or Doppler resolutions are necessary [1]. The proposed system satisfies the range resolution requirement by detecting the target with two different resolutions: coarse resolution for measuring range, and fine resolution for measuring the target details. The principal advantage of the system is in the vernier scale for the measurement of a distance. The system is just as easily realizable as conventional FM radar, requires no special filters in the receiver, and represents a saving in the required bandwidth for the same range resolution.     

GPS多径信号的自适应滤波估计方法

 研究全球定位系统(GPS)多径信号估计的问题。通过分析自适应滤波器的原理,建立了数字中频信号处理的数学模型,提出一种用自适应滤波实现GPS多径幅度、码相位和载波相位估计的方法。该方法采用不同延迟的伪随机序列对信号进行解扩、解调和累加,得到了作为期望信号的系列自适应滤波相关值。对该方法与其他3种方法进行了理论上的分析比较,得出本方法具有信噪比高、自适应滤波性能好、带有码相位信息和不存在载波模糊度问题等优点。根据各种滤波器算法的特点和本应用的需求,给出了选用递归最小二乘算法实现的方法。通过计算机仿真,验证了提出的方法能够在14 dB的信噪比下,以1个采样间隔的时间延迟分辨率和0.005周的载波相位估计精度估计出GPS L1的多径信号。     

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.     

电容成像传感器优化设计及其试验研究

为了减小电容层析成像(Electrical Capacitance Tomography,ECT)传感器相邻极板间耦合电容引起电容测量时的噪声值,设计了差分电极传感器系统并对差分电极与测量电极距离进行参数优化。实验系统采用现场可编程门阵列(Field Programmable Gate Array,FPGA)直接数字频率生成模块生成数字量的正弦激励信号,通过D/A转化为正负交流信号分别对测量电极和差分电极进行激励。差分电极与测量电极到管道中点的距离比例约1:1.2时传感器灵敏度最佳,仿真图像误差降低至0.23,图像相关系数提升到0.84;实验中空场时的系统平均信噪比比普通传感器提升了5.10dB,满场时的系统平均信噪比提升了4.50dB,相邻电极对的静止电容减少至38%,而电容变化占用最多测量值,即62%。差分电极传感器系统经过电极之间距离的优化设计,传感器系统性能得到提升,通过实验验证其可行性,并且能够应用在滑油监测。     

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.