Jitter Limitations on a Gigabit Copper Multi- Carrier System

Transcription

1 Jitter Limitations on a Gigabit Copper Multi- Carrier System Jan H. Rutger Schraer, Eric A.M. Klumperink, Jan L. Visschers, Bram Nauta University of Twente, IC-Design Group, P.O. Box 7, 75 AE, Enschee, The Netherlans. National Institute for Nuclear Physics an High-Energy Physics, P.O. Box 488, 9 DB, Amsteram, The Netherlans. j.h.r.schraer@utwente.nl Abstract The feasibility of a multi-carrier system for ata-transmission over copper wires at gigabit rates is analyze. More specific, we look at the effects of jitter an uty-cycle eviations on the SNR an error rate using Matlab simulations. Jitter causes crosstalk between the inphase an quarature channels of a given tone frequency. Given a certain rms jitter variance, low frequency tones can carry more bits than higher frequency tones for the same error rate. Duty-cycle eviations cause crosstalk both from other carrier frequencies an from quarature channels. These problems seem so big that a PAM system is likely to be the better choice for gigabit transmission. Keywors ata-communication, jitter, multi-carrier moulation In this paper, Matlab simulations will be presente that give insight into the system-level trae-offs an possibilities of such a system. More specific, the effect of jitter an uty-cycle eviations on such a system will be analyze. We will calculate SNRs an error rates for a number of ifferent values for the rms jitter, an for a number of ifferent uty-cycle eviations. II. ARGUMENTS FOR MULTI-CARRIER Transmission of signals over copper wires suffers from skin-effect an ielectric losses resulting in a frequency-epenent attenuation an ispersion (=frequency-epenent propagation elay). I. INTRODUCTION Very high spees have been achieve in the area of copper wire transmission. For example, using an equalize Pulse Amplitue Moulation (PAM) system, a bit rate of ~7Gbps has been reache over a istance of m at a Bit Error Rate (BER) of ~ - []. There is a continuing eman for higher bit rates. The banwith an signal-to-noise ratio of short cables can be high enough to allow this. This stuy explores the possibilities of aapting telephone moem an Digital Subscriber Line (DSL) techniques using Orthogonal Frequency Division Multiplexing (OFDM) to GHz banwiths, possibly enabling >Gbps transmission spees over copper wires. In general, these systems are implemente using DSP techniques, but this is unfeasible for a banwith in the gigahertz range. Therefore the architecture has to be funamentally ifferent. We will introuce an architecture that solves some of these problems. v(t) v(t) x -9 time Figure Baseline waner x Impulsresponse Secons time Figure Copper meium impulse response If the signaling spee of a PAM signal is increase x - 594

2 past the banwith of the channel, the (unequalize) receive signal will show baseline waner as shown in figure. In figure, the impulse response of a copper cable or PCB trace is shown. The very long tail causes intersymbol-interference (ISI). (More information on moeling these cables can be foun in [4].) Lowering the PAM bau rate will ecrease ISI, because the signal spectrum is move to the lower frequencies where skin effect an ielectric losses have less effect. (This explains the effort being put into PAM4 signaling [].) It is important to note that ISI is epenent of the bau rate an not the total bit rate. Multiplexing several bits into one symbol will ecrease ISI while the total bit rate can remain the same. Each sub-channel has a much lower bit rate, making it possible to have much larger symbol uration. This is exactly what happens in multicarrier moulation, so using such a system will ecrease the emans on channel equalization. Furthermore, using multi-carrier techniques enables spectrally efficient moulation like QAM. Also a multi-carrier system is useful when the channel contains spectral nulls as is sometimes the case with PCB traces an connectors. III. OFDM BASICS The transmitte ata is moulate on several orthogonal carriers. In orer to avoi interference these have to comply with the orthogonality constraint, which is efine as T c c t = δ, δij = i j ij op i j i = j where c i,j (t) are the carriers an T op is the length of the receiver integration perio ( orthogonality perio ). Caniates for tone frequencies f c are harmonic frequencies n/t op. Integration over exactly T op elivers perfectly orthogonal carriers. The total bit rate b tot of such a system will be b tot = T N t s i= log( N where N l,i is the number of / levels use on the i th tone, N t the number of tone frequencies in the system (where each tone is moulate with both an inphase- an quarature component) an T s the total symbol length (optionally incluing guar time T gt []). l, i ) () () IV. SYSTEM ARCHITECTURE The multi-carrier communication system architecture that we will stuy is shown in figure 3. On the left, the transmitter is shown an on the right the receiver. We use (passive or active) mixers for multiplication of the ata streams with the carrier signals. For the integration over the symbol perio, an integrate-an-ump block is use which can be implemente using a capacitor an switches. s an s can be ae to provie more levels an thus a higher spectral efficiency. One architectural avantage now becomes apparent: parallelization is use for the converters an integratean-ump blocks, which relaxes banwith requirements. s i ct i 9 s cr q q s ni x(t) ct ni 9 s cr nq nq cr i 9 cr q r(t) cr ni 9 cr nq Figure 3 System architecture q i q q q ni q nq In-phase an quarature carriers can be generate using a voltage-controlle ring-oscillator. The multiple phases coming from the ring oscillator can also be use to control the integrate-an-ump blocks. Of course a clock-an-ata-recovery (CDR) block will also have to be inclue in the receiver. This architecture puts a number of constraints onto the carrier waveforms that we can use. In an implementation with simple switching mixers, a sine wave on the local oscillator port will generate a square wave on the output. This will prouce harmonics that fall onto other tone frequencies, creating unusable areas in the spectrum. A solution to the problem coul be the use of harmonic rejection mixers [3]. Because of the above mentione problems, it is likely that the best chances for such a system are for a low number of carriers. The signals are efine as follows. The symbol streams s ni (t) an s nq (t), chosen from {-, }, are moulate onto the (in-phase an quarature) carrier signals ct ni (t) an ct nq (t) an ae up, resulting in the sum signal x(t) which is put onto the transmission line. At the receiver sie the receive signal r(t) is emoulate using a correlator receiver consisting of a multiplication with locally generate (in-phase an quarature) carrier signals cr ni (t) an cr nq (t) an an 595

3 integrate-an-ump. The recovere symbol streams are q ni (t) an q nq (t). The transmitte signal x(t) an the receive signal r(t) can be escribe as follows: Nt x( t) = ctni sni ctnq sni, = (3) n r = x( λ) h( t λ) λ, where h(t) is the impulse response of the channel. V. ANALYSIS For the system escribe above we will analyze the impact of jitter an uty-cycle eviations. The multicarrier receiver is a correlator receiver (multiplication followe by integrate-an-ump) as oppose to the sampling receiver use in most PAM systems. The analysis goal is to etermine the variance in the integrator output as a function of variance in τ (time shift between transmitter an receiver), as illustrate in figure 4. Time offsets over the symbol, cause by jitter, lea to imperfect separation of the in-phase an quarature component of the carrier. Duty cycle errors lea to other types of crosstalk. τ Figure 4 Influence of τ VI. SIMULATION RESULTS A. Impact of jitter We will estimate the influence of jitter on the error rate of the system. In orer to analyze this it is recognize that this error rate is a function of the SNR. We will calculate an effective SNR as a function of jitter. It is assume that the jitter coming from the PLL has a Gaussian time istribution with an rms variance of σ t. Its size is etermine by the PLL noise an loop banwith. For a state-of-the-art LC-base PLL this is currently in the orer of ps rms. For a ring oscillator it will be aroun 5ps rms. The effective SNR as a function of this jitter is expecte to be epenent on carrier frequency f c an number of levels N l use in moulation. We will o the following simulations: f c =.5GHz, N l =4, σ t =ps (4) f c =.5GHz, N l =4, σ t =ps f c =.5GHz, N l =6, σ t =ps A jitter of ps is taken because this will enable us to etect errors in a relatively short simulation (time step size=ps). Now let s look at the results of the statistical Matlab simulations (5 symbols) an focus on the error rate for the in-phase component. We use only a single carrier frequency for the sake of simplicity, an analyze crosstalk between in-phase an quarature component as a function of variance in τ cause by jitter. The jitter has been moele by aing a Gaussian ranom variable to the receiver time axis. Furthermore, the channel response is set to ieal (impulse response is a Dirac pulse). The SNR per symbol values have been calculate by sampling the ata, emoulating the ata an applying a normal istribution fitting routine. This routine estimates the amplitue variance σ A of the integrator output which is use to obtain the SNR per symbol SNR sm as SNR sm h = σ A (5) where h is the istance between two ajacent levels. Next, the probability of error P e for the in-phase component can be calculate as P e = Q( SNR sm ). (6) We will use histograms of the integrator output to graphically show the variance σ A /3 -/3 Figure 5 Output hist. (jitter σ t =ps, f c =.5GHz, N l =4) When we a a jitter of σ t =ps in the receiver generate carrier, an the frequency an number of 596

4 levels are set at f c =.5GHz an N l =4 levels (= bits) we can transmit ata relatively well. This is shown in figure 5. From the simulation, the calculate SNR sm =5B, which gives an excellent Pe« Figure 6 Output hist. (jitter σ t =ps, f c =.5GHz, N l =4) However when we try to increase the frequency to f c =.5GHz (number of levels remains N l =4), the jitter starts to have a severe impact, causing SNR sm =B, which gives a ba Pe= -3. (This is shown in figure 6.) /3 -/3 B. Impact of uty-cycle Another circuit non-ieality that is a threat to the carrier orthogonality is uty cycle istortion. The correlator output is epenent on the uty cycle of the signal, so eterministic eviations an/or variations in the uty cycle can isturb the orthogonality. We simulate these effects for a system with two tone frequencies (f =f ) using squarewave carriers, where each frequency is moulate with both in-phase an quarature components. (Therefore the total number of carriers is four.) The uty-cycle of the receiver generate in-phase carrier cr,i at f is varie, while the uty-cycle of all the transmitte carriers is exactly 5%. Below, a short summary of the simulation setup is given. Transmitter carriers: ct,i : f c =f, in-phase component ct,q : f c =f, quarature component ct,i : f c =f, in-phase component ct,q : f c =f, quarature component Receiver carrier: cr,i : f c =f, in-phase component, eviations in uty-cycle We will calculate the following correlations as a function of the uty-cycle of cr,i : corr = between cr,i an ct,i corr = between cr,i an ct,q corr = between cr,i an ct,i corr = between cr,i an ct,q These are all possible correlation for this two-tone system corr - -/3 -/3. Figure 7 Output hist. (jitter σ t =ps, f c =.5GHz, N l =6) corr A comparable jitter impact can be seen (in figure 7) when we o not increase f c (remains at f c =.5GHz) but rather increase the moulation epth to N l =6 levels. The signal to noise ratio per symbol SNR sm =B, which gives an equally ba Pe= -6. The observation to be mae is that, for a given jitter rms variance, low frequency tones can carry more bits than higher frequency tones for the same error rate Figure 8 corr an corr versus uty cycle Figure 8 shows the correlation of cr,i with the wante transmitte signal ct,i an with the quarature 597

5 component ct,q at that same frequency (respectively corr an corr ). Figure 9 shows the correlation of cr,i with the ouble frequency carriers ct,i an ct,q (respectively corr 3 an corr 4 ). The values have been normalize to one corr corr Figure error rate P e as a function of uty cycle Figure 9 corr 3 an corr 4 versus uty cycle All eviations from 5% uty-cycle introuce intercarrier interference (crosstalk) an lea to a limite SNR, as shown in figure. The peak at 5% correspons to an infinite SNR. [B] Figure - SNR as a function of uty cycle The error rate as a function of the uty cycle is shown in figure. The observation to be mae is that a multicarrier system is very sensitive to uty-cycle variations, with the error rate becoming unacceptably high for >5% variation. VII. CONCLUSIONS A transceiver architecture for gigabit multi-carrier transmission over short copper wires has been presente. It offers avantages concerning an requirements by using parallelization. A short feasibility analysis has been mae. Harmonics cause by switching mixers hiner the use of a large number of carriers. A state-of-the-art PLL rms jitter will impose a serious limit on the bit rate of a gigabit multi-carrier system. For a given rms jitter variance, low frequency tones can carry more bits than higher frequency tones for the same error rate. Furthermore, a uty cycle eviation of more than 5% causes the error rate of a two frequency multi-carrier system to rop below acceptable numbers. It is emonstrate that a lot of problems can be expecte from the above mentione sensitivity to jitter an uty cycle errors. It seems that a PAM system is the better choice for very high (giga-) bit rates on copper meia. REFERENCES [] R. Farja-Ra, C. K. Yang, M. Horowitz, an T. Lee, A.3µm CMOS 8-Gb/s 4-PAM serial link transceiver, IEEE J. Soli- State Circuits, vol. 35, pp , May. [] J. A. C. Bingham, Multicarrier moulation for ata transmission: an iea whose time has come, IEEE Commun. Mag., vol. 8, pp. 5 4, May 99. [3] J. A. Welon et al., A.75-GHz highly integrate narrow-ban CMOS transmitter with harmonic-rejection mixers, IEEE J. Soli-State Circuits, vol. 36, pp. 3 5, Dec.. [4] J. H. R. Schraer, E. A. M. Klumperink, J. L. Visschers an B. Nauta, Data communication in rea-out systems: how fast can we go over copper wires?, Nuclear Instruments an Methos in Physics Research Section A, vol. 53, issues -, pp. -7, Sep