Rohde & Schwarz; Signal Model Based Approach To Joint .
SIGNAL MODEL BASED APPROACH TO JOINT JITTERAND NOISE DECOMPOSITIONWhite paper Version 01.00 Adrian Ispas, Julian Leyh, Andreas Maier, Bernhard NitschFirst published at DesignCon 2020
ABSTRACTWe propose a joint jitter and noise analysis framework for serial PAM transmission basedon a parametric signal model. Our approach has several benefits over state-of-the-artmethods. First, we provide additional measurements. Second, we require shorter signal lengths for the same accuracy. Finally, our method does not rely on specific symbolsequences. In this paper, we show example measurement results as well as comparisonswith state-of-the-art methods.AUTHORS BIOGRAPHYAdrian Ispas received Dipl.-Ing. and Dr.-Ing. degrees in Electrical Engineering andInformation Technology from RWTH Aachen University, Aachen, Germany, in 2007 and2013, respectively. Since 2013, he has been with Rohde & Schwarz GmbH & Co. KG,Munich, Germany, where he is now a Senior Development Engineer in the Center ofCompetence for Signal Processing.Julian Leyh obtained his M.Sc. degree in the field of Electrical Engineering from TUMunich in 2017 specializing in communications engineering. He then began his professional career as a member of the Center of Competence for Signal Processing at Rohde & Schwarz. His current focus is on time domain high-speed digital signal analysis.Andreas Maier received an M.S. degree in Electrical Engineering and Ph.D. degreefrom the Karlsruhe Institute of Technology (KIT), Germany in 2005 and 2011, respectively. In 2011, he joined Rohde & Schwarz, Munich, Germany. His areas of expertise aredigital signal processing and signal integrity. He is a lecturer at the Baden-WuerttembergCooperative State University Stuttgart, Germany.Bernhard Nitsch is the director of the Center of Competence of Signal Processing at Rohde & Schwarz in Munich, Germany. He and his team focus on signal processing algorithms and systems in the area of signal analysis, spectral analysis, power measurement,security scanners and oscilloscopes. Rohde & Schwarz products contain software, FPGAor ASIC based signal processing components developed in the Center of Competence.He joined Rohde & Schwarz in 2000 and holds a PhD degree in Electrical Engineering andInformation Technology from Darmstadt University of Technology, Germany and an M.S.degree in Electrical Engineering from Aachen University of Technology, Germany. He isauthor of one book and seven technical papers and holds more than 25 patents.ACKNOWLEDGEMENTWe want to thank Thomas Kuhwald for initiating the development of the joint jitter andnoise framework, Guido Schulze for motivating us to submit the paper to DesignCon andfinally Andrew Schaefer, Guido Schulze and Josef Wolf for their valuable feedback onthe paper.2
CONTENTS1Introduction.42Signal model.53 Jitter and noise decomposition.63.1 Source and analysis domains.63.2 Decomposition tree.74 Joint jitter and noise analysis framework.84.1 Estimation of model parameters.94.2 Analysis al values and histograms.11Duty cycle distortion and level distortion.11Autocorrelation functions and power spectral densities.11Symbol error rate calculation.11Jitter and noise characterization at a target SER.126 Framework results.136.1 Example analysis.136.2 Signal length influence.197Comparison with competing algorithms.198Conclusion.229References.23Rohde & Schwarz White paper Signal model based a pproach to joint jitter and noise d ecomposition 3
1 INTRODUCTIONThe identification of jitter and noise sources is critical when debugging failure sources inthe transmission of high-speed serial signals. With ever increasing data rates accompanied by decreasing jitter budgets and noise margins, managing jitter and noise sources isof utmost relevance. Methods for decomposing jitter have matured considerably over thepast 20 years; however, they are mostly based on time interval error (TIE) measurementsalone [1, 2]. This TIE-centric view discards a significant portion of the information presentin the input signal and thus limits the decomposition accuracy.The field of jitter separation was conceived in 1999 by M. Li et al. with the introductionof the Dual-Dirac method [3]. The Dual-Dirac method was augmented and improved overthe next two decades. Originally, it was meant to isolate deterministic from random jitter components based on the probability density of the input signal’s TIEs. It uses thefact that deterministic and random jitter are statistically independent and that deterministic jitter is bounded in amplitude, while random jitter is generally unbounded. Threeyears later, M. Li et al. reported that their Dual-Dirac method systematically overestimatesthe deterministic component [4]. Despite this flaw, modelling jitter using the Dual-Diracmodel has maintained significance in commercial jitter measurement solutions due to itssimplicity [5].Throughout the years, additional techniques were added to the original Dual-Diracmethod to separate additional jitter sources such as intersymbol interference (ISI), periodic jitter (PJ) and other bounded uncorrelated (OBU) jitter. For example, PJ componentscan be extracted using the autocorrelation function [6] or the power spectral density[7, 8] of the TIEs, while the ISI part of deterministic jitter can be determined by averaging periodically repeating or otherwise equal signal segments [13]. Yet another methodfor estimating ISI makes use of the property that ISI can be approximately described asa superposition of the effect of individual symbol transitions on their respective TIE [12].Once the probability density function of one jitter component is known, any second component can be estimated from a mix of the two by means of deconvolution approaches,as long as the components are statistically independent of each other [9, 10, 11].Collectively, over 40 IEEE publications and more than 50 patents can be found on thetopic of jitter analysis alone. Despite this, applications in industrial jitter measurementscommonly use a combination of the previously described methods [14, 15, 16], all basedsolely on TIEs.In this paper, we first introduce a parametric signal model for serial pulse-amplitude modulated (PAM) transmission that includes jitter and noise contributions. The key to thismodel is a set of step responses, which characterizes the deterministic behavior of thetransmission system, similar to the impulse response in traditional communication systems. Based on the signal model, we propose a joint jitter and noise analysis frameworkthat takes into account all information present in the input signal. This framework relieson a joint estimation of model parameters, from which we readily obtain the commonlyknown jitter and noise components. Therefore, we provide a single mathematical baseyielding the well-known jitter/noise analysis results for PAM signals and thus a consistentimpairment analysis for high-speed serial transmission systems.4
known jitter/noise analysis results for PAM signals and thus a consistent impairmentanalysis for high-speedsystems.Additionally,we provideserialdeeptransmissionsystem insightthrough the introduction of new measurements, such as what-if signal reconstructions based on a subset of the underlyingAdditionally, we provide deep system insight through the introduction of newimpairments. These reconstructions enable the visualization of eye diagrams for a selecmeasurements, such as what-if signal reconstructions based on a subset of the underlyingtionof e visualizationofdecisionseye diagramsfor thea ermineselectivesymbolerrorrate(SER)jitter/noise components, thereby allowing informed decisions about the relevance calculationof(selective)peak-to-peakselected components. Similarly, we determine selective symbol error rate (SER) and biterrorandratenoise(BER)extrapolationsallowingfor a fast calculation of (selective) peak-to-peakjitteramplitudesat lowerror rates.jitter and noise amplitudes at low error rates.Signal Model-Based Approach to a Joint Jitter &The proposed framework is inherently able to perform accurate measurements even forrelativelyNoiseshort input signals.This is due to the significant increase in information extractedDecompositionfrom the signal. Furthermore, our approach has no requirements regarding specific inputThe proposed framework is inherently able to perform accurate measurements evenusing relatively short input signals. This is due to the significant increase in informationextracted from the signal. Furthermore, our approach has no requirements regarding specificinputsequences,symbol sequences,such as compliancepredefined patterns.complianceOn randomthe contrary,symbolsuch as predefinedOn patterns.the contrary,ortherandominputor scrambledinputencountereddata typicallyencounteredin real-worldscrambleddata typicallyin real-worldscenariosis ideallyscenariossuited to istheideallysuited to the framework.framework.Abstract2 SIGNAL MODEL2 Signal ModelI NTRODUCTIONTheproposedproposed joint jitter I.andframeworkis basedon aonsignalmodelfor serialTheandnoisenoiseanalysisanalysisframeworkis baseda signalmodelforPAMPAMdata datatransmission.modelassumesthe totalsignal,i.e., thesignalII.ThisS IGNALMODELserialtransmission.Thismodelassumesthe totalsignal,i.e. receivedthe receivedsignalcontaining allallcomponents,components, totobebecontaining y(t) [k] · h (tApproach T [k] [k], s) (t).Signal Model-Basedtoy a JointJitter &(1)(1)NoiseandHere,s denotesthe vector Decompositionof the transmitted PAM symbol sequence T s[k] [k],thesymbolindexMoreover,ℎ , Δ[k]s[k1] 1 k h .[k]}).(t,s) Jitterh Δ(t [k] s)Approach hsymbol(t differenceT [k] at to[k], {s[k],Signal Model-BasedaJoint& (2) denotes the step response for the symbolvector attime , thereferenceclocktimest T [k]at symbol index , and the initial signal value. The disturbance sources are split intok NoiseyDecompositionhorizontal(time) and vertical(signal level) parts: is the total horizontal sourceϵ [k]disturbance and isthe totalvertical source disturbance. Contrary to traditionalAbstractssrclkhk Here,A.B. (1)v denotes the vector of the transmitted PAM symbol sequence and sr the step ––thesymboldifferenceatsymbolindex.denotessr sclkhsrclkhssrclkresponse for the symbol vector at time , clkthe reference clock time at symbol signal value. The disturbance sources are split into horizontalindex , and – the initial (time) and vertical (signalis the totalhorizontal source disturbance andNPlevel)(h) 1 parts: h otraditionalcommunicationsysvcommunicationa h,lstepsin(2πfresponseh,linsteadanφimpulse h [k] h,P [k] h,OBU[k] h,R systems,[k] we useATh,l [k]of model h,R[k]h,l ) responseh,OBU onsetomodelthetotalsignal.the total signal. This is surel 0Thisis dueto the underfact thatan 1impulseresponseis neitherableto ensuresignal continuitysignalcontinuitynon-linear(in thesignal leveldomain)horizontaldisturbancesnorNP (v)I.INTRODUCTIONable tononlinearreproducetransitionasymmetries.The stepresponse includestransmitter,under(insymbolthe signallevel domain)horizontaldisturbancesnor ableto reproAbstractAbstract(t) and v,R(t) receiverAt φresult in v,OBU(t) v,Rchannel(t). v (t) v,P (t) v,OBUv,l sin(2πfv,l a data-dependentsignal smitter,II. S e.Moreover,thestepresponsedependsonl 0possibly receiver effects, all of which result in a data-dependent signal disturbance,thei.e.symbol vector in order toMoreover,account foreffectslike symboltransitiondependenciesin the s thesymbolvectorANDN OISE D ECOMPOSITIONIII. system.J ITTERII NTRODUCTIONtransmissionInI.following, we assume the step response to depend only on theI.theNTRODUCTIONfor effectsorder to accountlike symbol transition dependencies in the transmission syssymbolsymbolSource and AnalysislastDomainsy(t) and the slast[k]· hS(t transition: theTclk[k] response h [k], s)to dependy (t).II.MODELII.SsrIGNALIGNALMstepODELtem. In the following,we assumeonlyv on the last symbolDecomposition Treeand the lastk symbol transition: y(t) [k]hy {s[k], v (t).h(t T[k]s) (t T clk[k] s) h [k], s [k]}). h [k],srsr[k]n Ty(t) 1 clk ss [k] h··[k],hsrsr (t(tThclkclk [k] h [k], s) y v (t). k yR(h) (t) s [k] · n hsr (t Tclk [k], {s[k], s [k]}) · ( h,R [k])n .k n! tn 1k Information Classification: GeneralWe thus have up to N (N(3)(4)(1)(2) (1)(1) (2)(5)– 1) step responses for a signal of PAM order N. 1PAM NP (h)PAMPAMh T h [k],s) h T[k] h [k],{s[k], sr (tclk [k]sr sturbancesϵ[k]andϵ(t),respectively,fur- (2)hh(t T[k] [k],s) h(t T[k] [k],{s[k], [k]}).h [k] srh Th,l [k] φh,ls ) h,OBU [k] are h [k] h,P [k] sr h,OBUclk[k] h,RAh,lclksin(2πfh,l h,R[k] (2) (3) ther decomposed asỹR(h) (t) s [k] · l 0hsr (t Tclk [k], {s[k], s [k]}) · h,R [k].(6)NP t(v) 1k NP (h) 1NP(h) 1(t) (t) (t) (t) Av,l sin(2πf v,OBU(t) v,R h,R(t). vv,Pv,OBUv,Rv,l t φv,l )h,l h [k]A(3) (4)[k] h,P [k][k] h,OBU [k][k] h,R [k][k] Ah,l sin(2πfsin(2πfh,l TTh,l [k][k] φφ )) h,OBU [k][k] [k][k](3)hA.A.B.B.h,Ph,OBUh,Rl 0 l 0l 0NP (v)AND 1J ITTERNP(v) 1h,lh,l h,lh,lh,OBUh,RN OISE D ECOMPOSITIONIII.(t) (t) (t) (t) Asin(2πfv,l t φv,l ) v,OBU (t) v,R (t).(4) A.SourceandDomains vv (t) v,P(t) Analysis v,OBU v,RAv,lv,Pv,OBU (t)v,R (t) v,l sin(2πfv,l t φv,l ) v,OBU (t) v,R (t).(3) (4)l 0l 0B. Decomposition TreeITTERANDIII.JN OISEOISE DD ECOMPOSITIONECOMPOSITIONIII. J ITTER AND NSource Source andand AnalysisAnalysis DomainsDomains n Signal model based a pproach to joint jitter and noise d ecomposition1 &RohdeSchwarz White paper5y(t) [k]·hsr (t Tclk [k], {s[k], s [k]}) · ( h,R [k])n .(5)DecompositionTreesR(h)nDecomposition Treen! tn 1k
The horizontal and vertical periodic components ϵh,P [k] and ϵv,P (t ), respectively,are characterized by the amplitudes Ax,l , the frequencies fx,l and the phases ϕx,l forl 0, , NP(x) – 1 and x {h,v}, respectively, and Th,l [k] denotes the relevant point in timefor the horizontal periodic component l at symbol k. The terms ϵh,OBU [k] and ϵv,OBU (t ) designate other bounded uncorrelated (OBU) 1) components, and the random componentsϵh,R [k] and ϵv,R (t ) denote additive noise for the horizontal and vertical case, respectively.At this point, we do not impose any statistical properties on the random components.3 JITTER AND NOISE DECOMPOSITIONAs introduced in section 2, various effects cause disturbances in transmitted data. Thetransmitter and the channel have the most influence on the step responses that determine the data-dependent disturbance of the signal (intersymbol interference). Periodicand OBU disturbances make up the remaining deterministic and bounded components.Finally, there are random and unbounded disturbances such as thermal noise. Apart frombeing deterministic and bounded, very little information is available about OBU components at the receiver end. Therefore, we omit OBU components from now on. Theirinfluence will be visible in the extracted random components.3.1 Source and analysis domainsWith the exception of data-dependent components, all disturbances are either of horizontal or vertical origin. The horizontal components constituting ϵh [k] originate at thetransmitter, whereas the vertical components in ϵv (t ) may also be added in the channel orat the receiver end. The data-dependent components have their origin in the combinationof the data, i.e. the transmitted symbols, and the step responses that overlap to build thesignal. We thus define the source domain to be either “horizontal”, “vertical” or “data”.Analyzing the disturbances in the time domain is referred to as jitter analysis. Timingerrors with respect to a reference clock signal are determined and analyzed. This is usually done by means of the TIE. However, the disturbances can also be analyzed in thesignal level domain, which is referred to as noise analysis. In this case, signal level errorswith respect to reference levels are determined and analyzed at symbol sampling timesgiven by a reference clock signal. Fig. 1 depicts the definition of the TIE and the levelerror (LE). The choice between jitter analysis and noise analysis is a choice of the analysisdomain, which we accordingly define to be either “jitter” or “noise”.Fig. 1: TIE and LE definitionLESignal levelReference levelThreshold levelTIESampling timeClock timeTransition point1)6The word “other” in OBU refers to the nonperiodicity of the disturbance and the word “uncorrelated” to the nonexistence ofany correlation between the disturbance and the symbol sequence.
1 Tclk [k] h [k], {s[k], s [k]}).hsr (t Tclk [k] h [k], s) NPh(h)(2sr (t h [k] h,P 3.2[k] Decomposition h,OBU [k] tree h,R [k] Ah,l sin(2πfh,l Th,l [k] φh,l ) h,OBU [k] h,R [k]The decomposition tree of total jitterl 0 and total noise i
Rohde & Schwarz White paper Signal model based approach to joint jitter and noise decomposition 5 Additionally, we provide deep system insight through the introduction of new mea-surements, such as what-if signal reconstructions
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