Combined Effects of Frequency Quantization and Additive Input Noise in a First-order Digital PLL

AbstractA recent work by Gardner [Gardner, F.M., Frequency granularity in digital phase-locked loops, IEEE Trans. Commun., 44 (1996), 749758] on the subject of digital phase-locked loops (DPLLs) investigated, via simulation, the characteristics of the phase-jitter caused by frequency quantization in the numerically-controlled oscillator. Further works by Feely, Teplinsky et al [Feely, O., Rogers, A., and Teplinsky, A., Phase-jitter dynamics of digital phaselocked loops, IEEE Trans. Circuits and Systems, Part I: Fundamental Theory and Applications, 46 (1999), 545–558], [Feely, O., and Teplinsky, A., Phase-jitter dynamics of digital phase-locked loops: Part II, IEEE Trans. Circuits and Systems, Part I: Fundamental Theory and Applications., 47 (2000), 458–473] used the theory of nonlinear dynamics to provide a complete analytical explanation of this phase-jitter.This paper examines in detail the case where the input signal is embedded in additive noise, a scenario earlier investigated by Gardner where no satisfactory method of characterising the phase-jitter was found. Here, further numerical results for the 1-D DPLL are presented and it is shown analytically how the DPLL noise-jitter dynamics may be approximated by a noisy circle rotation map for reasonable levels of additive noise. The noise in this case is unique and highly nonlinear in nature and thus not amenable to traditional analysis. By considering the the probability flow over time, a time-dependent difference-delay equation is derived for the probability density function (PDF) of the phase-jitter. It is shown that this PDF reaches a steady-state and that this state is described by a non-local equation. The solutions of this equation are investigated, both numerically and analytically, and used to explain the interaction between the additive and quantization noise that was previously not understood

Performance analysis of sequential carrier- and code-tracking receivers in the context of high-precision space-borne metrology systems

Future space observatories achieve detection of gravitational waves by interferometric measurements of a carrier phase, allowing to determine relative distance changes, in combination with an absolute distance measurement based on the transmission of pseudo-random noise chip sequences. In addition, usage of direct-sequence spread spectrum modulation enables data transmission. Hereafter, we report on the findings of a novel performance evaluation of planned receiver architectures, performing phase and distance readout sequentially, addressing the interplay between both measurements. An analytical model is presented identifying the power spectral density of the chip modulation at frequencies within the measurement bandwidth as the main driver for phase noise. This model, verified by numerical simulations, excludes binary phase-shift keying modulations for missions requiring pico-meter noise levels at the phase readout, while binary offset carrier modulation, where most of the power has been shifted outside the measurement bandwidth, exhibits superior phase measurement performance. Ranging analyses of the delay-locked loop reveal strong distortion of the pulse shape due to the preceding phase tracking introducing ranging bias variations. Numerical simulations show that these variations, however, which originate from data transitions, are compensated by the delay tracking loop, enabling sub-meter ranging accuracy, irrespective of the modulation type.Comment: 10 pages, 6 figure

A design strategy for phase synchronization in precoding-enabled DVB-S2X user terminals

This paper address the design of a phase tracking block for the DVB-S2X user terminals in a satellite precoding system. The spectral characteristics of the phase noise introduced by the oscillator, the channel, and the thermal noise at the receiver are taken into account. Using the expected phase noise mask, the optimal parameters for a second-order PLL intended to track channel variations from the pilots are calculated. To validate the results a Simulink model was implemented considering the characteristics of the hardware prototype. The performance of the design was evaluated in terms of the accuracy and stability for the frame structure of superframe Format 2, as described in Annex E of DVB-S2X.This work was supported by the Fond National de la Recherche Luxembourg, under the CORE project COHESAT: Cognitive Cohesive Networks of Distributed Units for Active and Passive Space Applications and the Bridges Program DISBuS: Dynamic Beam Forming and In-band Signalling for Next Generation Satellite Systems.Peer ReviewedPostprint (author's final draft

Investigation of techniques for high speed CMOS arbitrary waveform generation

Today a growing number of applications in design engineering, production and environmental testing, and system service require specific analog waveforms and digital patterns. Such requirements are neither satisfactorily nor easily met by the use of standard function or single purpose, custom generators. Traditional methods of waveform generation suffer from undesirable complexity or mediocre performance and are otherwise limited. For the majority of arbitrary waveform generation applications, including medical engineering, modal analysis and electronic engineering, direct digital synthesis techniques are satisfactory. Direct digital synthesis, based generally on periodic retrieval of predetermined amplitude values, may be used to 2 generate such waveforms. Within the limits imposed by the system\u27s maximum sample rate and the Nyquist criteria, any waveform may be produced using these techniques. The objective of this inquiry, within a particular set of constraints, is to extend the cost/performance envelope of direct digital synthesis techniques for the generation of arbitrary waveforms. Performance is enhanced, particularly in the areas of output bandwidth and signal purity

Voyager Spacecraft Phase B, Task D. Annex to Volume 4 - Spacecraft Electrical Subsystems Definition Final Report

Systems analysis and tradeoff data on electrical subsystems for recommended Voyager spacecraft configuratio

Distributed synchronization algorithms for wireless sensor networks

The ability to distribute time and frequency among a large population of interacting agents is of interest for diverse disciplines, inasmuch as it enables to carry out complex cooperative tasks. In a wireless sensor network (WSN), time/frequency synchronization allows the implementation of distributed signal processing and coding techniques, and the realization of coordinated access to the shared wireless medium. Large multi-hop WSN\u27s constitute a new regime for network synchronization, as they call for the development of scalable, fully distributed synchronization algorithms. While most of previous research focused on synchronization at the application layer, this thesis considers synchronization at the lowest layers of the communication protocol stack of a WSN, namely the physical and the medium access control (MAC) layer. At the physical layer, the focus is on the compensation of carrier frequency offsets (CFO), while time synchronization is studied for application at the MAC layer. In both cases, the problem of realizing network-wide synchronization is approached by employing distributed clock control algorithms based on the classical concept of coupled phase and frequency locked loops (PLL and FLL). The analysis takes into account communication, signaling and energy consumption constraints arising in the novel context of multi-hop WSN\u27s. In particular, the robustness of the algorithms is checked against packet collision events, infrequent sync updates, and errors introduced by different noise sources, such as transmission delays and clock frequency instabilities. By observing that WSN\u27s allow for greater flexibility in the design of the synchronization network architecture, this work examines also the relative merits of both peer-to-peer (mutually coupled - MC) and hierarchical (master-slave - MS) architectures. With both MC and MS architectures, synchronization accuracy degrades smoothly with the network size, provided that loop parameters are conveniently chosen. In particular, MS topologies guarantee faster synchronization, but they are hindered by higher noise accumulation, while MC topologies allow for an almost uniform error distribution at the price of much slower convergence. For all the considered cases, synchronization algorithms based on adaptive PLL and FLL designs are shown to provide robust and scalable network-wide time and frequency distribution in a WSN

Theoretical Analysis of the Processof Doppler and Doppler Rate Estimation in Standard and High Sensitivity GNSS Receivers

Due to the capability of the Global Positioning System (GPS) to provide accurate, stablelong-term navigation information, the use of a GPS receiver as a velocity and accelerationsensor has gained an increasing research interest. Navigation and control, airbornegravimetry and integration with inertial navigation systems (INS) are just some of thepotential applications. GPS velocity and acceleration measurements are typically determined using Doppler and Doppler rate observations provided by the receiver carrier tracking loops. Thus, the finalquality of the velocity/acceleration measurements depends on the variance of the Dopplerand Doppler rate observations and on the approach used for the velocity/accelerationcomputation. It is therefore desirable to be able to predict the quality of Doppler andDoppler rate observations, not only for quality control and for estimating the uncertainty ofthis information, but also for properly weighting the measurements in the LS and KFsolution. This thesis introduces a cohesive analysis describing the noise propagation process from theinput of the carrier tracking loops to the final Doppler and Doppler rate estimates. Two different approaches used by GNSS receivers are considered namely the sequential carriertracking, including the standard and memory discriminator based approaches, and blockprocessing techniques. For each approach, a theoretical framework for Doppler estimationrelating the variance and biases of the Doppler estimates to C/N0, the user dynamics and thealgorithm parameters is introduced. Also, based on the proposed theoretical framework a new approach to loop filter designproviding control over the noise variance of the Doppler measurements is introduced.The developed theoretical framework and the proposed approach to loop filter design havebeen verified by performing a number of static and dynamic pedestrian-based field testsand simulations with the major focus on the environments with strong signal attenuationand multipath.PhD i elektronikk og telekommunikasjonPhD in Electronics and Telecommunicatio

Timing Signals and Radio Frequency Distribution Using Ethernet Networks for High Energy Physics Applications

Timing networks are used around the world in various applications from telecommunications systems to industrial processes, and from radio astronomy to high energy physics. Most timing networks are implemented using proprietary technologies at high operation and maintenance costs. This thesis presents a novel timing network capable of distributed timing with subnanosecond accuracy. The network, developed at CERN and codenamed “White- Rabbit”, uses a non-dedicated Ethernet link to distribute timing and data packets without infringing the sub-nanosecond timing accuracy required for high energy physics applications. The first part of this thesis proposes a new digital circuit capable of measuring time differences between two digital clock signals with sub-picosecond time resolution. The proposed digital circuit measures and compensates for the phase variations between the transmitted and received network clocks required to achieve the sub-nanosecond timing accuracy. Circuit design, implementation and performance verification are reported. The second part of this thesis investigates and proposes a new method to distribute radio frequency (RF) signals over Ethernet networks. The main goal of existing distributed RF schemes, such as Radio-Over-Fibre or Digitised Radio-Over-Fibre, is to increase the bandwidth capacity taking advantage of the higher performance of digital optical links. These schemes tend to employ dedicated and costly technologies, deemed unnecessary for applications with lower bandwidth requirements. This work proposes the distribution of RF signals over the “White-Rabbit” network, to convey phase and frequency information from a reference base node to a large numbers of remote nodes, thus achieving high performance and cost reduction of the timing network. Hence, this thesis reports the design and implementation of a new distributed RF system architecture; analysed and tested using a purpose-built simulation environment, with results used to optimise a new bespoke FPGA implementation. The performance is evaluated through phase-noise spectra, the Allan-Variance, and signalto- noise ratio measurements of the distributed signals

The Telecommunications and Data Acquisition Report

This publication, one of a series formerly titled The Deep Space Network Progress Report, documents DSN progress in flight project support, tracking and data acquisition research and technology, network engineering, hardware and software implementation, and operations. In addition, developments in Earth-based radio technology as applied to geodynamics, astrophysics and the radio search for extraterrestrial intelligence are reported