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.     

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.     

On the Acquisition Time for an Apollo Ranging Code

An Apollo ranging system is considered whose phase reference is obtained by a phase-locked loop for bit synchronization. The bit phase reference is noisy, and the error probability for the ranging code is shown to depend on the input signal energy per bit to noise density ratio. The procedure of computing the acquisition time for the ranging code is then presented and the acquisition time for a lunar ranging code is plotted versus the input signal-to-noise density ratio.     

Noise analysis of a digital tanlock loop

The noise performance analysis of a nonuniform digital phase-locked loop (DPLL), called the digital tanlock loop (DTL), is investigated by both analytic and computer-simulation methods. The results are presented in terms of phase error probability mass function and mean time to skip cycle versus input signal-to-noise ratio (SNR). These results are compared to the ones obtained with the conventional sinusoidal DPLL loop (DPLL). It is found that, for low-to-moderate input SNR, the DTL has only a slight improvement over the DPLL. The DTL, however, has larger linear characteristics than the conventional DPLL, which makes it attractive for applications that require an increased tracking range or as a first stage in carrier tracking systems based on optimum estimation procedures such as a Kalman smoother     

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.     

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.     

Quasi-Optimal Demodulation of Pulse-Frequency Modulation Systems

Novel demodulator structures are derived using a theory for the quasi-optimal on-line demodulation of pulse-frequency modulated (PFM) signals in the presence of white Gaussian channel noise. The basic demodulator consists of a phase-locked loop with time-varying gain elements. Furthermore, its integrators are appropriately reset as each new pulse is received. This modulator may be augmented with additional integrators and gain elements to achieve quasi-optimal demodulation with delay. The quasi-optimal demodulation approaches optimal demodulation, in the minimum mean-square-error sense, as the signal-to-noise ratio increases. The various quasi-optimal receivers are derived by application of the extended Kalman filter theory to a state-space signal model.     

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。     

一种用于深空测距的数字化锁相环设计

在深空测距中,扩大锁相环捕获范围与提高锁相环对微弱信号检测能力是一对矛盾。为解决这一矛盾,本文提出一种基于频率引导与二次混频的数字化锁相环结构,并对其性能进行理论分析和计算机仿真。仿真结果表明,该锁相环可以很好地在较大范围内实现对微弱测距信号的捕获锁定。该结构已在实际测距接收机中使用。     

Digital accumulators in phase and frequency tracking loops

Results on the effects of digital accumulators in phase and frequency tracking loops are presented. Digital accumulators or summers are used extensively in digital signal processing to perform averaging or to reduce processing rates to acceptable levels. For tracking the Doppler of high-dynamic targets at low carrier-to-noise ratios, it is shown through simulation and experiment that digital accumulators can contribute an additional loss in operating threshold. This loss was not considered in any previous study and needs to be accounted for in performance prediction analysis. Simulation and measurement results are used to characterize the loss due to the digital summers for three different tracking loops: a digital phase-locked loop, a cross-product automatic frequency tracking loop, and an extended Kalman filter. The tracking algorithms are compared with respect to their frequency error performance and their ability to maintain lock during severe maneuvers at various carrier-to-noise ratios. It is shown that failure to account for the effect of accumulators can result in an inaccurate performance prediction, the extent of which depends highly on the algorithm used     

Interferences in Phase-Locked Loops

An analysis of the behavior of a second-order phase-locked loop is presented when an unwanted signal is added to the useful signal. Both signals are sinusoidal and unmodulated, and the analysis is made in the absence of additive noise. When the loop remains locked on the useful signal, a parasitic signal exists at the phase detector output. This signal produces a parasitic phase modulation of the VCO and a static phase error in the loop. The parasitic signal amplitude, the parasitic phase modulation index, and the static phase error are calculated. A necessary condition for the loop to remain in lock is derived. When the loop is initially unlocked, locking can occur either on the useful signal or on the unwanted signal, depending on the amplitude ratio and the frequency difference of the two signals. A formula allowing one to compute the pull-in time is obtained. When the loop locks on the useful signal, acquisition can be slower or faster than in the absence of an unwanted signal. The same phenomenon is observed when the loop locks on the unwanted signal.     

Noise Dynamics of the Phase-Locked Loop with Signal Clipping

Employing techniques similar to the averaging methods of Krylov and Bogoliubov, an approximate noise analysis of the phase-locked loop with signal clipping is presented. The validity of the method is demonstrated by comparing the stationary probability density function for the phase error, generated by a system simulation, with the derived theoretical results. The latter portion of the paper discusses the relation of the phase-locked loop to Kalman-Bucy filter theory and presents a demodulator design that illustrates the self-adaptive properties attainable in phase-locked loops with signal clipping.     

Switchless Control Strategies for Minimum Time Frequency Transitions in Phase-Locked Loops

The problem of minimum time frequency transitions in phase-locked loops with both phase and frequency controls applied is investigated using Pontryagin's maximum principle. Typically, a type II secondorder loop with a damping ratio of 0.707 subjected to a step change in the frequency of its input signal is considered and switchless control strategies that force the transients in the loop to settle down in minimum time are obtained.     

Performance analysis of GPS carrier phase observable

The accuracy analysis of Global Positioning System (GPS) carrier phase observable measured by a digital GPS receiver is presented. A digital phase-locked loop (DPLL) is modeled to extract the carrier phase of the received signal after a pseudorandom noise (PRN) code synchronization system despreads the received PRN coded signal. Based on phase noise characteristics of the input signal, the following performance of the first, second, and third-order DPLLs is analyzed mathematically: (1) loop stability and transient process; (2) steady-state probability density function (pdf), mean and variance of phase tracking error; (3) carrier phase acquisition performance; and (4) mean time to the first cycle-slipping. The theoretical analysis is verified by Monte Carlo computer simulations. The analysis of the dependency of the phase input noise and receiver design parameters provides with an important reference in designing the carrier phase synchronization system for high accuracy GPS positioning     

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.     

Random Characteristics of the Type II Phase-Locked Loop

The results of a study of the characteristics of the second-order Type II phase-locked loop with a Gaussian noise input, and obtained by digital computer simulation, are presented. The digital simulation is described and the random state variables are defined such that their characteristics can be interpreted in terms of existing phase portraits of autonomous phase-locked loops. The statistics associated with the state variables, which are phase error and a measure of frequency error, and those associated with the number of cycles skipped and the mean time to unlock, are given.     

S频段小数分频锁相环频率合成器实现与应用

传统的整数分频锁相环频率合成技术无法在单个环路实现高频率、低分辨率和低相噪的目标,小数分频锁相环在提高鉴相频率的同时减小分频计数值,从而降低相位噪声。针对USB统一测控系统的需要,本文提出基于单片小数分频锁相环的微波频率合成方法。实验结果表明,小数分频锁相环频率合成器具备良好的信号输出特性,可以为测控系统提供低成本频率合成方案。     

一种基于EPLL技术的自适应正交解调技术研究

针对过零检测实现的全数字锁相环不仅锁相速度慢, 而且过零点的扰动会 直接影响锁相精度以及适合模拟电路实现的相干解调技术,在数字电路中实现则需要设 计高阶数字低通滤波器,将占用大量数字电路资源并且会显著增加系统功耗等问题,在 设计一种新型全数字锁相环(All-digital Enhanced Phase-lock Loop,EPLL)的基础上,结合自 适应正交解调技术,提出了一种基于EPLL 技术的自适应正交解调技术方案,并对该方 案进行了研究与仿真。仿真得到了满意的结果,验证了基于EPLL 技术的自适应正交解 调技术方案的可行性,并研究验证了算法的参数变化对其性能的影响,为今后算法在数 字系统中的实现以及其在各领域的应用研究奠定了坚实的基础。     

Optimum Strategies for Minimum Time Frequency Transitions in Phase-Locked Loops

Pontryagin's maximum principle is applied to minimize the time for a phase-locked loop to lock to a step change in frequency. In particular, a Type II phase-locked loop is considered in detail. Phase control and frequency control of the input signal are analyzed with the nonlinearity of the phase detector taken into consideration. It is shown that application of Pontryagin's maximum principle offers a decided advantage in shortening this time by proper control.     

Flexible loop filter design for spacecraft phase-locked receivers

A flexible loop filter design for spacecraft phase-locked receivers is proposed. The loop filter is implemented as digital hardware with coefficients that are set by registers. Either a perfect or an imperfect integrating loop filter can be effected. This flexibility is important since not one type of loop filter is preferred for all circumstances. An imperfect integrator is preferred when, as is often the case for spacecraft receivers, it is important to minimize the best-lock frequency drift of an idling loop. A perfect integrator is preferred when the tracking performance of the loop is the most important consideration