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.     

一种时间传递系统中调制器时延的数字标定算法

针对传统示波器观察法测量BPSK（Binary phase shift keying,二进制相移键控）调制器时延时存在整码元模糊、噪声敏感、载波初相要求苛刻及标定精度低的缺点,利用软件无线电的相关处理技术,提出一种精密的BPSK调制器时延标定算法.通过高速数字示波器对BPSK调制器的输入基带信号和输出载波调制信号进行双通道同步过采样,对输出信号与输入信号采样值进行循环相关,根据相关峰值对应的样本点序号以及连接电缆的校准时延,计算得到BPSK调制器时延.仿真和试验验证表明：提出的算法不受载波初始相位影响,时延标定上限可达1个伪随机码周期,而且低载噪比情况下也能得到准确结果.数字示波器的通道采样率为10 GSa/s时,采用提出的算法进行BPSK调制器时延标定,标定结果的不确定度可以达到0.2 ns.     

无人机高速DS/FH混合扩频通信系统关键模块设计

针对UAV(Unmanned Aerial Vehicle,无人机)测控链路高抗干扰需求,给出了实现跳频速率20 000次/s的扩跳混合无人机测控数据链系统实现方案.系统采用跳频频率并行捕获模式.跳频源设计采用直接频率合成、DDS(Direct Digital Synthesis,直接数字频率合成)和PLL (Phase-Locked Loop,锁相环)相结合的混合频率合成技术.利用相位响应滤波器,通过正交调制技术完成MSK(Minimum Shift Keying,最小频移键控)、GMSK (GaussianMinimum Shift Keying,高斯最小频移键控)调制.通过推导得出2 bit差分解调输出与载波频率选择有关,且为四分之数据率的整数倍关系.然后通过实例分析给出了跳频频率间隔选取方法,即跳频间隔应当将临近跳频的主瓣分开,同时跳频载波频率应当设在其他跳频频谱的零点处.最后总结了高速扩跳频系统参数设计一般步骤.     

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, ?.     

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.     

基于UKF准开环结构的高动态载波跟踪环路

 对高动态环境下的全球卫星导航系统（GNSS）载波信号跟踪方法进行了研究。在分析高动态载波信号模型的基础上,提出了一种基于无迹卡尔曼滤波（UKF）的准开环载波跟踪方法。此方法能够消除导航数据二进制相移键控(BPSK)调制的影响,并采用四维UKF相位估计模型提高跟踪精度,同时对估计值进行补偿以减少滤波器的滞后性。通过模拟接收机的高动态运动轨迹,从跟踪误差、跟踪结果和补偿效果3个方面,与基于卡尔曼滤波（KF）的锁频环(FLL)辅助锁相环(PLL)结构的传统跟踪方法进行比较,结果表明基于UKF的准开环跟踪方法能够有效地完成高动态环境下的载波跟踪。     

电离层色散对DS/FH-BPSK信号解调性能影响

相位连续的DS/FH(Direct Sequence/Frequency Hopping,直接序列/跳频)扩频信号的扩频带宽比直扩信号更宽,在电离层的非线性相位以及跳频频点变化这两者的共同作用下,该信号的BPSK(Binary Phase Shift Keying,二相相移键控)解调性能明显恶化。依据随机变量概率分布的数学规律,推导得到了在背景电离层色散条件和跳频频点均匀分布前提下,某种DS/FH卫星测控信号的引导信号和长周期信号BPSK误码率的变化规律,并在特定信号参数条件下进行了误码率仿真。     

Carrier loop architectures for tracking weak GPS signals

The performance of various carrier recovery loop architectures (phase lock loop (PLL), Doppler-aided PLL, frequency lock loop (FLL), and Doppler-aided FLL) in tracking weak GPS signals are analyzed and experimentally validated. The effects of phase or frequency detector design, oscillator quality, coherent averaging time, and external Doppler aiding information on delaying loss of lock are quantified. It is shown that for PLLs the metric of total phase jitter is a reliable metric for assessing low C/N performance of the tracking loop provided the loop bandwidth is not too small (~> 5 Hz). For loop bandwidths that are not too small, total phase jitter accurately predicts carrier-to-noise ratio (C/N) at which loss of lock occurs. This predicted C/N is very close to the C/N predicted by bit error rate (BER). However, unlike BER, total phase jitter can be computed in real-time and an estimator for it is developed and experimentally validated. Total phase jitter is not a replacement for BER, since at low bandwidths it is less accurate than BER in that the receiver loses lock at a higher C/N than predicted by the estimator. Similarly, for FLLs operating at small loop bandwidths, it is found that normalized total frequency jitter is not a reliable metric for assessing loss of lock in weak signal or low C/N conditions. At small loop bandwidths, while total frequency jitter may indicate that a loop is still tracking, the Doppler estimates provided by the FLL will be biased.     

Low C/N_0 Carrier Tracking Loop Based on Optimal Estimation Algorithm in GPS Software Receivers

Suppressing jitter noises in a phase locked loop(PLL) is of great importance in order to keep precise and continuous track of global positioning system(GPS) signals characterized by low carrier-to-noise ratio(C/N0).This article proposes and analyzes an improved Kalman-filter-based PLL to process weak carrier signals in GPS software receivers.After reviewing the optimal-bandwidth-based traditional second-order PLL,a Kalman-filter-based estimation algorithm is implemented for the new PLL by decorrelating the model error noises and the measurement noises.Finally,the efficiency of this new Kalman-filter-based PLL is verified by experimental data.Compared to the traditional second-order PLL,this new PLL is in position to make correct estimation of the carrier phase differences and Doppler shifts with less overshoots and noise disturbances and keeps an effective check on the disturbances out of jitter noises in PLL.The results show that during processing normal signals,this improved PLL reduces the standard deviation from 0.010 69 cycle to 0.007 63 cycle,and for weak signal processing,the phase jitter range and the Doppler shifts can be controlled within ±17° and ±5Hz as against ±25° and ±15 Hz by the traditional PLL.     

PAM approach to weak CPM and its application to flight termination receivers

A method for computing the PAM representation for weak continuous phase modulation (CPM) is presented and applied to the modulation defined in the enhanced flight termination system (EFTS) standard. The pulse-amplitude modulation (PAM) representation was used to formulate a reduced-complexity detector whose performance is within 0.7 dB of maximum likelihood detection and 5.6 dB better than limiter-discriminator detection in the additive white Gaussian noise (AWGN) environment. The complexity of the reduced-complexity detector is less than 25% that of the maximum likelihood detector but, unlike the limiter-discriminator detector, requires a carrier phase PLL. In the presence of phase noise, the reduced-complexity detector outperforms limiter-discriminator detection when the RMS frequency deviation due to phase noise is less than 10% of the bit rate.     

A suboptimal algorithm for modulation classification

In this paper we present a suboptimal algorithm for modulation classification to classify the general M-ary phase-shifted keying (MPSK) signal buried in additive white Gaussian noise (AWGN). We first derive the phase density functions of MPSK signals, then develop the required statistics for modulation classification and demonstrate a classifier for CW, binary phase-shifted keying (BPSK), quadrature phase-shifted keying (QPSK), and 8PSK. The structure of the proposed classifier is flexible and is easy to expand. The performance of classifier is evaluated in terms of the probability of successful classification. An example (BPSK/QPSK case) is provided to demonstrate the capabilities of the proposed classifier. The performance is evaluated through the theoretical approach and the Monte Carlo computer simulations and is compared with that previously published in 1992. It is shown that the performance of the proposed classifier is better. Further improvement in performance can be obtained by increasing the length of observation interval.     

基于数字包络检波的RNSS通道时延标定方法

提出一种采用数字处理的时延测试方法,用于对导航卫星导航信号发射通道分数码片时延的精确测量。该方法是通过高速A/D（模/数）转换器,对导航卫星下行的BPSK（二进制相移键控）信号和卫星导航秒脉冲进行双通道采样,读取采样数据并进行数据处理。根据秒脉冲信号触发门限上升沿确定时延测量起点,对BPSK采样数据进行平方律检波,获取码片换相点,计算换相点和秒脉冲之间的分数码片时延,并进行滤波器时延校准,从而得到导航卫星发射链路的分数码片时延,该方法不需要进行伪随机信号的捕获和跟踪,测量精度主要取决于采样器采样率。通过在测试中使用一根校准电缆对该方法进行验证,验证结果表明,采用本文提出测试方法的测量误差优于0.3ns。     

Carrier Tracking by Smoothing Filter Improves Symbol SNR

The potential benefit of using a smoothing filter to estimate a carrier phase over use of phase-locked loops (PLL) is determined. Numerical results are presented for the performance of three possible configurations of an all-digital coherent demodulation receiver. These are residual carrier PLL, sideband-aided residual carrier PLL, and finally sideband aided with Kalman smoother. The average symbol SNR after losses due to carrier phase estimation is computed for different total power SNRs, symbol rates, and symbol SNRs. It is found that smoothing is most beneficial for low symbol SNRs and low symbol rates. Smoothing gains up to 0.7 dB over sideband-aided residual carrier PLL, and the combined benefit of smoothing and sideband aiding relative to residual carrier loop is often in excess of 1 dB.     

Double Dither Loop for Pseudonoise Code Tracking

A new type of phase detector for pseudonoise code tracking is introduced and analyzed in comparison with the delay lock loop (DLL) and tau-dither loop (TDL) configurations. It is shown that the double dither loop (DDL) combines the best features of the DLL and the TDL in that the DDL is insensitive to gain and offset imbalances and does not suffer the 3-dB degradation in noise performance typically associated with the TDL. The double dither concept is applicable to other dual channel detectors such as in a Costas-type carrier tracking loop.     

高动态下惯性加速度辅助三阶锁相环性能分析

针对高阶跟踪环路稳定性比低阶环路差,大带宽带来测量误差大的问题。研究在高动态环境下,惯导加速度信息辅助卫星接收机三阶载波锁相环跟踪算法,以及不同环路参数下跟踪环路的性能。对载体高动态场景、加速度信息延迟进行建模,并对算法进行了数学仿真。仿真分析结果表明,在加速度信息辅助下,即使压缩载波跟踪环路等效噪声带宽到3Hz,在高达1200g/s的加速度动态下,环路跟踪同样稳定可靠。     

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。     

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。     

Transient Frequency-Error Statistics in Acquisition of Noiseless First-Order Phase Lock Loop

After a certain time interval from the appearance of a reference signal in a synchronizing system employing a first-order phase lock loop (PLL), the probability that the output frequency error will be higher than a maximum tolerated value is determined. The system is assumed to be noise free.     

Analysis of Squaring Circuit Mechanizations in Costas and Squaring Loops

Two different implementations of the carrier recovery loop for suppressed carrier binary phase-shift keyed (BPSK) signals are considered. In particular, the tracking performance of the squaring loop in which the squaring circuit is mechanized by a limiter/multiplier lier combination to produce the absolute value of the incoming signal, followed by appropriate bandpass filtering, is compared with that of the usual squaring loop whose squaring circuit is the timestwo wo multiplier which exhibits a square law characteristic.     

一种高动态低信噪比下载波快速捕获跟踪方法

针对高动态、低信噪比的接收信号,首先对整个多普勒频率范围进行分段,并在每一段内利用本地产生的带有多普勒频率变化率的复信号来抵消接收信号中多普勒频率变化率的影响,然后在每一段内利用FFT（FastFourierTransform,快速傅里叶变换）进行载波频率并行捕获,从而同时完成载波多普勒频率及其变化率的初步估计。利用载波多普勒频率及其变化率估计信息辅助锁频环快速入锁,进而利用锁频环辅助三阶锁相环完成载波信号的锁频锁相跟踪。使用这种方法,可以快速获取信号的多普勒频率及其变化率信息,并且在极短时间内完成载波的稳定跟踪,使接收设备具备快速捕获跟踪大动态弱信号的能力。