Phase-Locked Loop Behavior near Threshold

The phase-locked loop behavior is analyzed following the quasilinearization Booton's method. When the loop is locked on an unmodulated input signal with a static phase error, the phase detector nonlinearity produces an interaction between the static phase error and the voltage-controlled-oscillator (VCO) noise phase fluctuations. Formulas allowing one to compute the static phase error increase and the VCO phase variance increase are derived. When the input signal is phase modulated, there is an interaction between the static phase error, the VCO noise phase fluctuations, and the input signal phase modulation. Formulas are obtained that allow one to compute the loop loss of performances (static phase error increase and VCO phase variance increase) and the coherent phase demodulator output signal-to-noise ratio decrease. Finally, a slight modification to Booton's procedure is proposed, leading to results in better agreement with experimental data.     

Another Source of VOR Omni Error

In the vicinity of reflecting objects, a VOR receiver picks up both the direct and reflected signals. This summation adds both amplitude and phase modulation to the signal that were not present at the transmitter. The error due to this phase modulation is fairly evident since the desired directional information is transmitted as a relative phase. What is not so evident is the fact that the amplitude modulation can also produce a phase error. This happens when asymmetrical filters are used to process the amplitude-modulated signal. The asymmetrical filter converts some of the amplitude-modulated sidebands into phase modulation which is recorded as a direct phase error.     

Imperfect Carrier Recovery Effect on Filtered PSK Signals

Coherent demodulation of a PSK signal requires the generation of a local carrier phase reference. Methods are given to determine the detection loss caused by noisy phase recovery and its use in the coherent detection of filtered BPSK and QPSK signals. It is assumed that the phase noise can have a static part and a random component with a Tikhonov-type distribution. The static part is mostly due to offset frequency tracking of the PLL used to recover the carrier, while the random component is due to thermal noise present in the carrier recovery loop and is also due to the random nature of the phase modulation. It is shown that the probability of error of BPSK and QPSK can be expressed as a finite sum of a set of strictly alternating converging series when the number of ISI terms is finite. Upper and lower bounds on the probability of error have been derived when this number becomes infinite and we show how this error rate can be computed with any desired accuracy. Numerical results are presented for various values of static error and phase noise variance when the transmit and receive filters are 4-pole Butterworth filters. For filtered PSK signals and for a bit error rate of 10-6, our results show that the additional degradation in presentday receiver systems due to imperfect carrier recovery can be less than 0.1 dB for BPSK and less than 1 dB for QPSK.     

Interference in Frequency-Locked Doppler Tracking Loops

The effects of interference on frequency-locked Doppler tracking loops are investigated. Conditions for jump from locking on the desired signal to locking on the interfering signal are established. Parasitic frequency modulation of the desired signal results when the other signal interferes with it. The index of this parasitic modulation as a function of the interference-to-desired signal amplitude ratio is computed. Both critical amplitude ratio and critical parasitic modulation index at the occurrence of jump are derived. Comparing frequency-locked loops with phase-locked loops with phase-locked loops in the presence of interference shows the former performs better for most cases of practical importance in Doppler tracking systems.     

误差对同轴六分支分扭人字齿轮传动系统静均载性能影响

以同轴六分支分扭人字齿轮传动系统为研究对象,依据各齿轮受力状态建立该系统的静力平衡方程。考虑到制造误差和安装误差及输入输出轮浮动导致的错位,基于当量啮合误差理论,分析误差的存在性,最后根据系统功率闭环特征建立系统变形协调方程,形成了同轴六分支人字齿轮传动系统静均载分析方法,并结合实例求出系统各齿轮之间静均载系数及分支静均载系数。研究结果表明:在无误差或各齿轮误差均相同为常值时,第Ⅰ级各齿轮静态啮合力为1.773×105 N,第Ⅱ级各齿轮静态啮合力为3.673×105 N,系统具有很好静均载性能,系统分支静均载系数为1,该系统构成功率闭环误差可相互抵消;制造和安装误差幅值同时作用为50 μm时,求得制造误差下分支静均载系数变化幅度比安装误差下分支静均载系数要大,可知制造误差对系统静均载性能影响程度要大;分扭和并车误差幅值同时作用为50 μm时,并车级比分扭级静均载性能更容易受误差的影响,因此输出构件应该有浮动量。综上所述,随制造或安装误差增大或减少,都会对系统静均载性能造成不良的影响,其研究成果可为同轴减速器传动系统制造误差和安装误差精度确定,均载系数确定提供科学依据。      

基于提前停止判决的编码软信息辅助载波同步

 针对目前编码辅助载波同步算法中复杂度较高、延时大的问题,提出了引入辅助停止判决机制的编码辅助载波同步算法。在现有的编码辅助载波同步结构基础上,该算法能对环路信噪比(SNR)进行实时判定,在环路SNR满足限定条件后提前停止编码辅助载波同步迭代,而不影响译码性能。采用新的相位估计方式估计含相位噪声的载波相位,提升了该条件下的环路信噪比。仿真采用码率为1/2的低密度奇偶校验(LDPC)码作为编码方式,结果表明:在误码率为10^-5时,该算法减少了约50%的编码辅助载波同步迭代次数;在含相位噪声的信号条件下,与理想解调译码相比,性能损失不超过0.15 dB。     

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.     

基于功率复用的椭圆球面波函数非正交调制方法

围绕如何降低基于椭圆球面波函数的非正交调制（PSWF-NPSM）系统误码率，降低信号检测复杂度，引入调制信号功率复用思想，提出基于功率复用的椭圆球面波函数非正交调制（PD-PSWF-NPSM）方法。该方法对载波信号按子波带进行功率分配，增加了调制信号最小欧式距离，降低了系统误码率；在接收端，提出基于检测统计量的串行干扰相消信号检测方法，依据不同支路信号间功率差异，对信号进行分离、检测。理论与仿真分析表明，该方法在不降低系统频带利用率、调制信号功率谱、峰均功率比特性前提下，能够有效提高系统误码性能，降低调制信号检测复杂度；与原非正交调制方法相比，当误比特率（BER）为10^-5时，所提方法系统误码性能提升约1.7 dB。     

Optimum Signals for Radar

The research reported herein deals with the general problem of the selection of radar waveforms. The investigation is specifically concerned with the synthesis of radar signals which are optimum in the sense that they are characterized by ambiguity surfaces minimized over certain predetermined regions of the ambiguity plane. The weighted ambiguity surface is utilized as the weighted error criterion. This error criterion is mathematically tractable and pertinent to radar system performance but is not unduly restrictive as some orientation parameters are left unspecified for subsequent cost or penalty function analysis. The signal optimization is approached by variational techniques augmented by equality and inequality constraints, for example, limiting the amount of bandwidth or frequency modulation to be less than some system requirement. Several examples are presented demonstrating the optimization techniques and providing a minimum error for the stated problem. It is shown that for any given type of amplitude modulation of the radar signal, the variance or dispersion of the ambiguity surface is not decreased for any type of phase modulation added. The optimum signal for an elliptical weighting function is derived for several cases. The minimum error is shown to depend upon the constraints and the unspecified orientation parameters and, for one case, on the second moment of the signal.     

Carrier-Tracking Loop Performance for Quaternary and Binary PSK Signals

By expressing the open-loop response voltage as a Fourier series in terms of the phase-tracking error and then utilizing a very useful mean-value expression, we assess the performance of loops suited to recovering the carrier of four-phase (quaternary) and two-phase (binary) phase-shift-keyed (QPSK and BPSK) signals. At high signal to noise ratios (SNRs) they perform comparably, but at low SNRs the former's performance deteriorates much more rapidly. The loop's ability to maintain the carrier frequency despite the noise accompanying the PSK signal is measured by the mean and the variance of the oscillator's control voltage. In particular, Spilker's loop for QPSK and the Costas loop for BPSK signals are discussed.     

数字闭环光纤陀螺死区机理研究与抑制

在数字闭环光纤陀螺中,死区产生及其附近噪声特性恶化的主要因素可以归结于施加在相位调制器上信号的串扰。根据死区产生机理的不同,提出了偏置相位调制和阶梯波反馈调制两种死区串扰误差因素的观点。通过对这两种死区误差机理的分析和比较,提出了采用模拟相加反馈方案可以避免偏置相位调制死区误差的观点。采用速率转台法测试了光纤陀螺的死区特性,验证了理论仿真和计算的正确性。最后,通过采用三角波相位抖动抑制死区误差技术,将一种高精度光纤陀螺0.08(°)/h的死区误差抑制到0.001(°)/h以下。     

极弱信号环境下GPS位同步和载波跟踪技术

为解决环路未锁定、无法找出正确的导航数据位跳变点时极弱全球定位系统(GPS)信号跟踪问题,通过分析信号跟踪模型和相关器1 ms采样数据特性,将最优路径动态规划算法应用于GPS位同步,并提出基于平方根无迹卡尔曼滤波(SRUKF)和位同步结合的载波联合跟踪算法。建立了适合位同步的SRUKF载波环参数估计模型,针对位同步的实现条件和无相位频率先验信息的情况,将位同步模块提前,研究设计了环路未锁定时串行和并行两种弱信号跟踪方案。位同步跟踪完成后环路采用单独的SRUKF工作方式。实验结果证实该文提出的算法具有较高的数据位边缘检测概率(EDR)和参数估计性能,而无须关心环路是否处于锁定状态,能够对载噪比低至22 dB/Hz的弱信号实现跟踪。     

Spectral Analysis of ELT Signals for SARSAT

Search and rescue satellite-aided tracking (SARSAT) relays the emergency locator transmitter (ELT) signals of distressed aircraft to an earth station for spectral analysis. Of considerable importance are the characteristics of the spectrum of the ELT signal since the probability of locating the downed aircraft is closely related to the quality of the ELT signal spectrum itself. In this paper, it is shown that the spectrum can be adversely affected by a number of factors including the phase and frequency characteristics of the carrier and their interaction with the amplitude modulation. Two new models are proposed which greatly reduce the self-generated interference produced by ELT units presently being used.     

数字闭环光纤陀螺的调制串扰误差

 通过分析数字闭环光纤陀螺的阶梯波调制信号与输出死区、周期噪声干扰及小角速度漂移的关系,提出了调制串扰误差的概念。指出调制信号与探测器输出信号之间的电交叉耦合及调制信号产生的调制误差是产生调制串扰误差的干扰源。将调制串扰通道模型简化为比例环节和部分积分环节,并和光纤陀螺理想模型结合,建立了光纤陀螺调制串扰误差模型,利用该模型推导出了产生死区的条件及周期噪声干扰和小角速度漂移造成的输出偏差表达式,并对周期噪声的幅值、频率与陀螺输出量级、带宽之间的关系进行了定量分析。调制串扰误差的仿真和实验结果与理论分析结果基本一致,验证了调制串扰误差模型的正确性。     

一种基于非平稳信号分析的时相调制信号解调算法

基于非平稳信号分析方法,对时相调制(Time-Phase Modulation,TPM)信号的时频分布特性进行了详细分析,建立了TPM调制信号相位突变与时频分布幅度的映射关系,利用该映射提出了一种基于非平稳信号分析的TPM调制信号解调算法,并对该解调算法性能进行了理论分析,讨论了最佳判决门限选取方法,仿真结果验证了理论分析的正确性。理论分析及仿真表明,基于非平稳信号分析的TPM调制信号解调算法获得了优于传统的相关解调的调制系统差错性能。     

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.     

Uniform Sampling Analysis of a Hybrid Phase-Locked Loop with a Sample-and-Hold Phase Detector

Phase-locked-loop (PLL) bit synchronizers often employ integrate-and-dump type phase detectors that provide phase error information only at discrete points in time. Usually these phase detectors are followed by sample-and-hold circuits to produce a stairstep error voltage as the input to a standard analog circuit loop filter. When the loop is configured in this manner, it is referred to as a hybrid PLL. Sampled-data analysis methods (Z transforms) are used to determine the stability and transient response of this loop.     

基于导航姿态解算的光纤陀螺平台低频角振动测试方法研究CSCD

为准确评价光纤陀螺平台的低频角振动特性,提出了一种基于导航姿态解算的光纤陀螺平台低频角振动测试方法。首先,通过角振动台精确模拟载体的低频角振动状态,并通过光纤陀螺平台飞行导航过程中的断调平差分信号,实现平台框架角度信号与角振动台激励角度信号的数据同步;然后,利用平台式惯导系统的导航姿态解算方法,实时解算低频角振动过程中光纤陀螺平台的台体姿态,并通过坐标系转换得到平台基座系相对于地理系的实时姿态;最后,通过对光纤陀螺平台稳定回路的幅相特性分析,得到低频角振动激励下稳定回路的幅值和相位特性,实现对光纤陀螺平台角动态特性的准确评估。     

一种联合估计的有源校正高精度测向算法

针对存在系统误差的阵列模型,提出了一种有源标校下的联合估计测向算法。该算法把误差矩阵估计转化为误差系数估计,并采用到达角精确已知的源信号进行标校,在此基础上使用最小二乘法联合估计幅相不一致误差系数和互耦误差系数,最后使用结合误差矩阵的MUSIC算法测量信号的到达角。仿真表明,该算法仅需要3个标校源,其精度相比于无阵列误差情况下降0.05°,具有较好的工程可实现性。     

Ground-multi path mitigation via polarization steering of GPS signal

Multipath (MP) is the dominant error source in Global Positioning System (GPS) code-based position solutions requiring high accuracy. A technique is introduced here to mitigate error due to ground-reflected MP signals. The technique uses two orthogonal dipoles to capture the direct GPS signal and the ground-reflected GPS signal. Adjusting the amplitude and phase of the received voltage between the two dipoles can reduce the impact of MP error. Theoretical derivations of this technique are performed for a GPS signal upon reflection from dry soil, seawater, and fresh water. The theoretical results are verified with a real world experiment on the aforementioned surfaces. GPS pseudo-range (PR) and carrier-to-noise ratio (C/No) measurements for specific satellites are used to verify the predicted theoretical results.