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.     

Adaptive Array Behavior with Periodic Envelope Modulated Interference

A method is presented for determining the effects of envelope modulated interference on a least mean square (LMS) adaptive array. The interference is assumed to have periodic envelope modulation with a bandwidth that is small compared with the carrier frequency. For such interference, the method allows one to calculate the periodic steady-state behavior of the array weights and the resulting array performance. As an example, we compute the effects of an ordinary amplitude modulated (AM) interference signal on the array. It is shown that such interference causes the array to modulate the desired signal envelope but not its phase. With a differential phase-shift-keyed (DPSK) desired signal, AM interference is found to have about the same effect on bit error probability as CW interference.     

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.     

Adaptive Array Behavior with Sinusoidal Envelope Modulated Interference

The behavior of a LMS (least mean square) adaptive array with modulated interference is described. An interference signal with sinusoidal, double-sideband, suppressed-carrier modulation is assumed. It is shown that such interference causes the array to modulate the desired signal envelope but not its phase. The amount of the desired signal modulation is determined as a function of signal arrival angles and powers and the modulation frequency of the interference. Such interference also causes the array output signal-to-interference-plus-noise ratio (SINR) to vary with time. However, it is shown that when the desired signal is a digital communication signal, the averaged bit error probability is essentially the same as for continuous wave (CW) interference.     

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。     

The Effect of a Pulsed Interference Signal on an Adaptive Array

The performance of a least mean square (LMS) adaptive array in the presence of a pulsed interference signal is examined. It is shown that a pulsed interference signal has two effects. First, it causes the array to modulate the desired signal envelope (but not its phase). Second, it causes the array output signal-to-interferenceplus-noise ratio (SINR) to vary with time. The desired signal modulation is evaluated as a function of signal arrival angles, powers and interference pulse-repetition frequency (PRF) and pulsewidth. It is shown that the signal modulation is small except when the interference arrives close to the desired signal. To evaluate the effect of the time-varying SINR, it is assumed that the array is used in a differential phase-shift keyed (DPSK) communication system. It is shown that the SINR variation causes a noticeable but not disastrous increase in the bit error probability.     

Conical Scanning System for Pioneer Jupiter Spacecraft

The concept, operation, and predicted performance of an RF tracking control system used to point the Pioneer F/G spacecraft at the Earth is described. This system employs a modified conical scanning technique called Conscan. The signal processor, the most interesting unit of the system, is described in detail to show that it approximates a maximum likelihood estimator. The dynamic behavior of the spacecraft and the stability analysis of the system are presented, demonstrating that the system performance is basically determined by the open-loop phase and amplitude errors introduced by the antenna, receiver, and signal processor. A detailed error budget shows that the phase and amplitude errors are small. Finally, closed-loop simulation and test data are presented to verify the error budget.     

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.     

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.     

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。     

多径效应对GPS载波相位观测量的影响

推导了ＧＰＳ接收机中多径效应引入的最大载波相位跟踪误差的闭合形式。得到以下结论：当直达信号跟踪误差不超过１码片时,最大载波测相多径误差为１／４周,该值出现在测码伪距多径误差最小的情况下;当直达信号跟踪误差超过或等于１码片时,接收机跟踪多径信号,信号误检发生。     

Linear Minimum Variance Estimation with Complex Phase Errors

The linear minimum variance estimator of a random signal, received multiplied by a complex Gaussian phase error and added to random noise, is investigated. The results apply to the propagation of images through the turbulent atmosphere, fading channels, and synthetic-aperture radar. Among others, a result is that the multiplicative error can be replaced by an additive error, usually white. The best signal modulation is found in two important special cases.     

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.     

The Performance of an LMS Adaptive Array with Frequency Hopped Signals

The performance of an LMS adaptive array with a frequency hopped, spread spectrum desired signal and a CW interference signal is examined. It is shown that frequency hopping has several effects on an adaptive array. It causes the array to modulate both the amplitude and the phase of the received signal. Also, it causes the array output SINR (signal-to-interference-plus-noise ratio) to vary with time and thus increases the bit error probability for the received signal. Typical curves of the desired signal modulation and the time-varying SINR at the array output are presented. It is shown how the array performance depends on hopping frequency, frequency jump size, interference frequency, signal arrival angles, and signal powers.     

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.     

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。     

An Analysis of Helicopter Rotor Modulation Interference

In satellite-to-helicopter communications, interference exists on the incoming signal when the receiving antenna is located below the rotor blades. A bound is established for the performance of a coherent fixed-tone ranging system operating at L band in this interference environment. The scalar diffracted field beneath the rotating blades, at L band and above, is found to satisfy the criterion of Fresnel diffraction, and is computed using the techniques of Fourier optics. The diffracted field is expressed in terms of a narrow-band signal. The amplitude and phase components are calculated from a Fourier Series expansion using the FFT algorithm. The significant harmonics of the phase component of the interference combine with the baseband of the narrow-band, phase-modulated ranging signal. This results in CW interference, and in rearrangement of the first-order, sideband, ranging-tone channel powers. The degradation in ranging accuracy is evaluated by computing the signal-to-interference (SIR) ratio for a set of ranging tones. The post-detection (SIR)PD at the output of the correlator is shown to be a function of the amplitude of the phase harmonics of the interference, the relative difference between the ranging tone and interference center frequencies (a function of rotor speed), the rangetone modulation indices, and the post-detection filter noise bandwidth.     

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。