Spectral correlation of a digital pulse stream modulated by a cyclostationary sequence in the presence of timing jitter

Cyclostationarity is an inherent characteristic of many communication signals, which can be exploited for performing various signal processing tasks. Imperfections in the signal generation that affect the cyclic statistics of a signal may lead to a degradation in the performance of signal processing algorithms which make use of this cyclostationary behaviour. One typical source of imperfection encountered in digital signalling techniques is random jitter in the pulse timing. In this work, we systematically derive analytical expressions for the cyclic statistics of digital baseband signalling schemes in the presence of timing jitter, under the assumption that the generating wide sense cyclostationary data sequence and the stationary jitter process are statistically independent.     

Presence of residual echo and impulsive noise

A general analysis is presented for the jitter performance of a common type of symbol timing recovery (STR) system employed in a digital subscriber loop (DSL) transceiver for high-speed digital data transmission over twisted copper pair cables in the presence of residual echo and impulsive noise (IN). Numerical results, obtained for an experimental study of a timing recovery system, show that the presence of these disturbing signals can substantially degrade the STR performance     

Filtered multitone modulation for very high-speed digitalsubscriber lines

A filter-bank modulation technique called filtered multitone (FMT) and its application to data transmission for very high-speed digital subscriber line technology are described. The proposed scheme leads to significantly lower spectral overlapping between adjacent subchannels than for known multicarrier techniques such as discrete multitone (DMT) or discrete wavelet multitone. FMT modulation mitigates interference due to echo and near-end crosstalk signals, and increases the system throughput and reach. Signal equalization in an FMT receiver is accomplished in the form of per-subchannel symbol-spaced or fractionally spaced linear or decision-feedback equalization. The problem of channel coding for this type of modulation is also addressed, and an approach that allows combined removal of intersymbol-interference via precoding and trellis coding is described. Furthermore, practical design aspects regarding filter-bank realization, initial transceiver training, adaptive equalization, and timing recovery are discussed. Finally, simulation results of the performance achieved by FMT modulation for very high-speed digital subscriber line systems, where upstream and downstream signals are separated by frequency-division duplexing, are presented and compared with DMT modulation     

Optimized interpolator filters for timing error correction in DMTsystems for xDSL applications

Discrete multitone (DMT) modulation is a multicarrier technique that allows the transmission of high speed data over band limited channels. This type of system is very sensitive to synchronization errors when used in digital subscriber loop applications (xDSL), due to the high number of carriers and high density constellations involved. This paper addresses the topic of all-digital timing error correction in a DMT system for xDSL applications, where the timing error correction procedure is based entirely on signal interpolation. An analytical study of the interpolator filter performance is carried out, arriving at an expression for the signal-to-distortion ratio (SDR) at the output of the receiver, as a merit figure. In this derivation, the fixed frequency domain equalizer (FEQ) plays an important role since it compensates for a great part of the distortion introduced by the interpolator. From this study, the design of the optimal interpolator filter in terms of SDR, based on a multirate approach with Kaiser window, is presented. Specific designs for ASIC and for DSP-based implementations are obtained. Performance results are excellent, yielding SDR values above 50 dB for all carriers while keeping the computational cost low     

Simulation of MC-CDMA in the Presence of Timing Errors

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Block Codes for Linear Timing Recovery in Data Transmission Systems

A method is proposed for launching and extracting the timing wave in a PAM digital transmission system, which combines the simplicity of linear self-timing, the economy in bandwidth of nonlinear self-timing, and the high performance of the added timing wave approach. The method requires that the digital signal is cyclostationary with a period which is an even multiple of the symbol periodT; the simplest solution for deriving such a signal from a stationary message is to apply it to a periodically time-varying system, as a memoryless block coder. With reference to such a scheme we derive the spectrum of the timing jitter. Very simple conditions are found on block encoding in order that the encoded message exhibits the desired characteristics. Finally, ternary codes are discussed and the performance of a specific code is evaluated and compared to that of conventional extraction schemes.     

The effects of timing jitter and tracking on the performance of impulse radio

Impulse radio (IR) is a promising ultra-wideband technique for tactical military communications. A key feature of time-hopping IR are the very narrow pulses used to convey information. Analysis of such time-hopping schemes under a variety of assumptions have been reported in the literature. However, none of these studies to date consider the effects of timing jitter and tracking on time-hopping in a ultra-wideband (UWB) setting. We consider the effects of timing jitter and tracking on the performance of binary and 4-ary UWB communications. We find that the performance of IR is very sensitive to timing jitter and tracking, at least in part due to the very narrow pulses. We also find that in the presence of timing jitter and tracking, orthogonal 4-ary pulse position modulation (PPM) out performs binary offset PPM at all jitter levels in thermal and pulse noise. Simulation results are presented that quantify the sensitivity of binary and 4-ary IR to timing jitter and tracking error.     

Symbol timing recovery in digital subscribers loops in the presenceof residual echo and crosstalk

A general analysis is presented for the jitter performance of a common symbol timing recovery (STR) system used in a digital subscriber loop (DSL) transceiver that uses adaptive echo cancellation for high-speed digital communications. Exact analytical expressions for the mean and variance of the timing wave and for the RMS phase jitter are derived as a function of the bandwidth of the postfilter for a given set of input parameters representing a particular digital subscriber loop and its noise environment, including such effects as residual echo and crosstalk. Numerical results show that the presence of these disturbing signals can substantially degrade the STR performance. The effect of the excess bandwidth factor of the prefilter on this degradation is investigated     

On the power spectral density of digital pulse streams generated byM-ary cyclostationary sequences in the presence of stationary timingjitter

The spectral occupancy and composition of a chosen digital signaling technique when the data pulse stream is nonideal, due, for instance, to implementation imperfections, are important considerations in the design of a practical communication system. One source of imperfection is timing jitter where the rising and falling transitions do not occur at the nominal data transition time instants; nevertheless, the time instants are offset by random amounts relative to the nominal one. The amount of timing shift per transmission interval is random and is typically characterized by a discrete stationary random process (independent of the data sequence) with known statistical properties. The purpose of this paper is to characterize the power spectral density (PSD) of baseband signaling schemes in the presence of arbitrary timing jitter. Although general PSD results are first obtained for arbitrary timing jitter statistics, specific results are then given for the cases of practical interest, namely, uniform and Gaussian-distributed jitter. Examples of an uncorrelated data pulse stream, an independent identically distributed data stream, and a Markov source are given. Interesting results emerge when the generating sequence {a_n} is uncorrelated. For generating sequences {a_n} that are nonzero-mean, timing jitter has the effect of widening the main lobe of the spectrum and increasing the sidelobes. When the generating sequence is zero-mean and uncorrelated, a rather surprising result is that the timing jitter does not affect the PSD. Simulation results are also presented to verify the analysis     

Adjacent-Channel and Quadrature-Channel Interference in Minimum Shift Keying

In this paper we present formulas for the computation of error probability in the presence of quadrature-channel or adjacentchannel interference in addition to intersymbol interference in a minimum shift keying system. The filters in the receiver and transmitter are arbitrary but with a finite number of poles. The effect of phase jitter in the main channel, phase and symbol timing misalignment in the interfering channels, and sampling time jitter is taken into account. The probability of error is averaged over the phase and symbol timing misalignment. Numerical results are presented for Butterworth filters in the receiver and transmitter with two, three, and four poles. Curves of error probability as a function of various variables (signal-to-noise ratio, bandwidth of receiver and transmitter filters, number of poles, channel frequency separation, phase jitter, sampling time, and symbol timing and phase misalignment) are presented. The method of this paper can readily be applied to other filters; hence, it can be used in the design and prediction of the performance of digital communication systems.     

The effect of timing jitter on MC-DS-CDMA

In this paper, we consider the effect of timing jitter on the performance of a multicarrier direct-sequence code-division multiple-access system for both uplink and downlink transmission, assuming orthogonal spreading sequences. Theoretical expressions are derived for the performance degradation caused by the timing jitter, in the presence of a multipath channel. Assuming an additive white Gaussian noise channel, perfect power control, and full load, it is shown that the performance degradation for the downlink transmission is independent of the number of subcarriers, of the spreading factor, and of the spectral contents of the jitter at the receiving mobile station, but only depends on the jitter variance. Under the same assumptions, we point out that, if the jitter spectra of all transmitting mobile stations are the same, the degradation on the uplink is the same as the degradation on the downlink.     

Analysis of true jitter arising from pulse-stuffing schemes

In synchronous digital hierarchy and plesiochronous digital hierarchy networks, it is frequently necessary to recover a data clock from a gapped clock derived from stuff information present at the desynchronizer. In this paper, a comprehensive analysis of the timing jitter resulting from phase-locked loop-type desynchronizers is presented. This analysis is different from the conventional analysis where the jitter is represented using a phase-error sequence. It is shown that such a simplified approach cannot accurately describe the jitter at the output of the desynchronizer. From the detailed analysis, it is also shown how the use of threshold modulation at the synchronizer reduces the low-frequency jitter at the desynchronizer. It has been demonstrated in the paper that when threshold modulation is used at the synchronizer, the dominating low-frequency jitter terms cannot be explained by the conventional jitter analysis methods. Therefore, in future networks, where tighter jitter performances are to be imposed on the synchronizers, jitter characterization using the proposed true jitter analysis technique would be very useful.     

时钟抖动对射频脉宽调制性能的影响分析

在全数字发信机系统中,射频脉宽调制(RF-PWM)将基带调制信号的幅度与相位信息编码为输出脉冲的宽度和位置。由于数字信号处理器件的非理想特性,其时钟信号的上升沿和下降沿存在抖动误差,影响RF-PWM的输出信号质量。基于3种RF-PWM实现方案,本文通过公式推导确定了时钟抖动引入的非线性失真项,并给出了时钟抖动影响下不同方案输出脉冲信号底噪的数学解析式。最后利用Matlab软件,对不同方案在时钟抖动条件下的基波、奇次谐波和底噪进行仿真验证,结果证明理论推导正确;同时对信号的矢量幅度误差(EVM)和邻信道功率比(ACPR)进行仿真,分析出时钟抖动对信号带内外性能的影响。结果表明,时钟抖动引入的非线性失真主要体现为底噪的抬高;不同RF-PWM实现方案时钟抖动的影响特性各有不同,其中五电平方案对时钟抖动影响具有抑制效果,且随时间分辨力的增大而增大。     

Simulation is essential for embedded control systems with task jitter

Sampling or task jitter affects the performance of digital control systems but realistic simulation of this effect has not been possible to date. Our previous work has developed a novel method to simulate sampling jitter in MATLAB/Simulink simulation software where the jitter is generated randomly. What has been missing is a way to capture sampling jitter from a target platform and then feed this timing information into the simulation. This paper presents a low-cost and novel solution to these problems. The method uses an Arduino board to capture task jitter from two different hardware platforms with multiple stressing conditions. Then the recorded performance data is used to drive realistic simulations of a control system. Measurement shows that the task jitter data does not follow any specific random distribution such as Gaussian or Uniform. Furthermore, very occasional timing patterns, which may not be picked up while testing a real system, can result in extreme controller responses. This novel method allows comparisons of different platforms and reduces the effort required to choose the most appropriate platform for full implementation.

     

Analysis of a serial symbol timing recovery technique employingExclusive-OR circuit

An analysis is presented of the performance of a serial symbol timing recovery (STR) circuit which employs an Exclusive-OR circuit for conventional coherent digital modulated communication systems. The output of the timing circuit is a nearly sinusoidal wave whose zero crossings indicate the appropriate sampling instants for extraction of the data. Assuming that the data pulses entering the timing path are even symmetric, exact analytical expressions for the mean and mean-squared values of the timing wave and for the RMS phase jitter are derived as a function of various system parameters such as channel band limiting, postfiltering, delay element, and power spectral density of noise. Numerical results, also checked by computer simulations, show that considerable improvement can be obtained in jitter performance, in addition to the advantages over other STR techniques of lower cost and simpler hardware implementation     

Effect and Compensation of Colored Timing Jitter in Pulsed UWB Systems

Ultra-wideband (UWB) systems impose a stringent requirement on the jitter performance of the system clock. So far, only the effect of white Gaussian timing jitter has been considered in the literature via numerical simulation. However, practical clocks commonly exhibit colored jitter. In this paper, we first investigate the bit error rate (BER) performance of a single-user binary pulse position modulation UWB system subjected to white and colored Gaussian jitter. It is shown that colored jitter degrades BER performance much more than white jitter, and the extent of degradation increases as the jitter bandwidth decreases. Motivated by this result, we then propose a new jitter compensation scheme to improve the BER performance under colored jitters with small jitter bandwidth, in which each information-bearing data symbol is coupled with a pilot symbol. The proposed scheme attempts to track first the jitter for the current pilot symbol by making use of the pulse-template correlation function. This information is then used together with the known clock jitter bandwidth and jitter root-mean-square (RMS) value to detect the current data symbol according to the maximum likelihood criterion. Simulation results show that the algorithm is effective in improving the BER performance for colored jitters with small jitter bandwidth. Lei Huang received the B.Sc. degree from Xi'an Jiaotong University, China, in 1993, the M. Sc. degree from South China University of Technology in 1996, and the Ph.D. degree from Victoria University of Technology (VUT), Australia, in 2003, all in Electrical Engineering. From 1996 to 1999, he was a Lecturer at South China University of Technology. From March 2003 to December 2005, he was with National University of Singapore as a Research Fellow. Since January 2006, he has been working in Panasonic Singapore Laboratories as an R & D Engineer. His research interests focus on physical layer aspects on wireless communication systems, especially CDMA, ultrawideband and millimeter wave communications.     

Performance of a Binary PPM Ultra-Wideband Communication System with Direct Sequence Spreading for Multiple Access

In this paper, we present an analysis of the BER performance of an ultra-wideband (UWB) system with pulse position modulation (PPM) for data modulation and direct sequence (DS) spreading for multiple access over indoor lognormal fading channels. A rake receiver is used to combine a subset of the resolvable multipath components using the maximal ratio combining technique. Inter-path and multiple-access interferences are modeled and incorporated into the bit-error-rate expressions. The analytical and simulation results allow one to quantify many critical aspects of a DS-PPM UWB system such as the gain of the optimally spaced signaling scheme over the orthogonal signaling scheme, the potential error floor given a specific channel multipath delay spread and the number of interfering users, tolerance of the system to timing jitter, and impact of user codes.     

高速光传输系统的带内非线性作用

分析了高速光传输系统中带内非线性作用的产生原因和影响．因素,通过数值仿真和分析,得到了结论：在抑制带内非线性作用方面,相位调制优于幅度调制;色散后补偿优于色散预补偿,对于功率较大的情况尤为明显;对于一定的发射功率,脉冲占空比有一个最优值。     

A simple model of EMI-induced timing jitter in digital circuits, its statistical distribution and its effect on circuit performance

A simple model has been developed to characterize electromagnetic interference induced timing variations (jitter) in digital circuits. The model is based on measurable switching parameters of logic gates, and requires no knowledge of the internal workings of a device. It correctly predicts not only the dependence of jitter on the amplitude, modulation depth and frequency of the interfering signal, but also its statistical distribution. The model has been used to calculate the immunity level and bit error rate of a synchronous digital circuit subjected to radio frequency interference, and to compare the electromagnetic compatibility performance of fast and slow logic devices in such a circuit.     

Timing Jitter Effects on Digital Subscriber Loop Echo Cancellers: Part II--Considerations for Squaring Loop Timing Recovery

The performance of an adaptive echo canceller at the looptimed subscriber end of a digital subscriber loop has been shown to be sensitive to jitter arising from the timing recovery subsystem. We evaluate this degradation for the common timing recovery subsystem consisting of a prefilter, a squarer, and a second-order phase-locked loop. The evaluation shows the influence of equalization, prefilter shape, and phaselocked loop parameters. A narrow-band accurately tuned prefilter, line equalizer, and a narrow-band phase-locked loop are found to be necessary for adequate performance in a 144 kbit/s bipolar-coded digital subscriber loop system employing echo cancellation.