Theoretical Determination of Sensitivity

8/13/2019 Theoretical Determination of Sensitivity

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JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 11,NO. 12, DECEMBER 1993 2145

Theoretical Determination of SensitivityPenalty for Burst Mode Fiber OpticReceiversC h a r l e s A. E l d e r i n g

Abstract-Digital burst mode fiber optic receivers are beingdeveloped that establish the threshold for determination of areceived 1 or 0 based on receptionof the first few received 1s.Such receivers can provide a large dynamic range while allowingthe use of a minimum burst preamble. However, a sensitivitypenalty with respect to continuous mode receivers which estab-lish an ideal threshold exists. In this article we show the originof this penalty and show by numerical evaluation that, forsystems in which the noise can be modeled as Gaussian, thepenalty is exactly 3.00 dB when a single bit is used for establish-ing the threshold. This penalty decreases as the number of bitsused to establish the threshold is increased, dropping to 0.51 dBwhen 8 bits are used as a preamble, and 0.28 dB when 16 bitsare used.

I. INTRODUCTIONUR ST m ode fiber optic receivers ar e presently beingB eveloped for a number of applications includingfiber optic networks based on Passive Optical Networks(PONs), and optical buses. Such networks typically use aTime Division Multiple Access (TDM A) protocol, in whichbursts of information are transmitted from the remotenodes to the central office (in the case of the PON) orfrom one node to another on the optical bus. The burstsarrive to the receiver originating from various locationson the network and exhibit large differences in optical

power. It is therefore necessary to have receivers whichcan adapt to the variations in power on a burst-to-burstbasis. A large dynamic range is desirable in or der to allownetwork flexibility; for PONs this permits variations inthe splitting ratio for two nodes connected to the centraloffice while for optical buses it allows flexibility in thenumber of optical taps placed on the bus.To realize burst mode reception, a preamble is nor-mally add ed to the beginning of each burst, consisting of aguard field, (to allow some desynchronization of the bustswithout collisions) an amplitude recovery field which al-lows the receiver to adapt to the received power in theburst, and a clock recovery field. It is desirable to reducethe length of this preamble to a minimum in order tomainta in a high inform ation transm ission efficiency. ThisManuscript received September 14, 1992.This work was performed while the author was with Alcatel SESA,Spain. Author is presently with Jerrold Communications, General In-strument Corp., Hatboro, PA 19040.IEEE Log Number 9210191.

is particularly impo rtant in telephony applications, whereshort bursts (e.g. 40 bits) containing a few voice samplesare transmitted from the subscriber to the central office.In such applications it is not possible to build long burstsdue to the delay which would be incurred waiting foradditional voice samples. This delay results in an increasein the total network delay, which when combined withecho produced at the 2-wire to 4-wire conversion can leadto perceivable echo for the user.l,* It is thus necessary todevelop receivers that can perform the task of amplituderecovery in a few bits.The requirements for components (transmitters andreceivers) for TDh4A PON networks have been previouslyoutlined [3] and devices are presently being developed fo rsubscriber loop applications. Previously reported devices[4], [ 5 ] for burst mode reception have shown a largedynamic range and performance up to 1 Gb/s. The fun-damental differences between traditional receivers andthese new burst m ode devices are that D C or pseudo-DCcoupling (in which a DC restoration circuit is used inconjunction with an AC coupled circuit) must be usedthroughout the receiver instead of AC coupling, due tothe low frequency spectral content of the burst modedata,3 and th at a rapid threshold ge neratio n circuit is usedto establish the threshold for logical Is and Os nsteadof a feedback AGC circuit with a time constant on theorder of several thousand bits, as is typically used in fiberoptic receivers.In this article we determine the penalty for burst modeoperation with respect to continuous mode operation forany receiver for which the Gaussian noise approximationholds. This penalty arises from the fact that the first bitexhibits statistical variations in amplitude, and thus estab-lishing the threshold based on this bit alone will result ina threshold voltage which shows identical statistical varia-tions. The variations in the threshold voltage will result ina degradation in the BER as compared to continuousmode systems which average (typically by low-pass filter-ing) a large number of 1s to establish the threshold oradjust the gain of one of the amplifier stages. We showthat the exact penalty incurred in using a single bit fordetermination of the threshold as opposed to systemswhich establish a perfect threshold is 3.00 dB. This penaltydecreases as the number of bits used to establish thethreshold increases, and when the average of 36 bits are

0733-8724/93 03.00 1993 IEEE


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2146 JOURNAL OF LIGHTWAVE TECHNOLOGY , VOL. 11,NO. 12, DECEMBER 1993

PREAMPLIFIER

used to establish the threshold the penalty is negligible,being less than 0.2 dB.11.MODEL ND ASSUMPTIONS

Fig. l(a) shows a traditional fiber optic receiver inwhich a preamplifier and automatic gain control circuit( A G O is used in conjunction with a p-i-n photodiod e. Thepreamplifier is AC coupled to a gain controlled amplifier(GCA), whose gain is controlled by a signal proportionalto the low-pass filtered outpu t. The resulting AG C circuitproduces an eye diagram of constant amplitude, and acomparator with a fixed threshold level V , ) can be used todetermine binary values from the eye diagram. Suitablelow pass filtering for the data signal is included in thepreamplifier to reduce noise.A an example of an idealized burst mode receiver isshown in Fig. l(b) and consists of a P-I-N and preampli-fier which is DC coupled to a integrating sample and holdcircuit which is used to determine the correct thresholdV,) based on the reception of a preamble which containsa field of n pulses representing 1s.As will be discussed,the exact type of preamplifier is not important for thisanalysis as long as the receiver perform ance is limited byadditive white Gaussian noise. For this analysis we assumethat the burst timing remains fixed, and that the timingshown in Fig. 2can be used for the gated buffer andintegrator re set con trol signals. Th e threshold voltage isdetermined by integrating the n pulses and scaling theresult:

. SCALERFR INTEGRATOR

where y,, is the input voltage from the preamplifier(DATA IN) and T is the symbol duration. The constant Kwill depend on the pulse shape. If we consider pulseswhich may vary in amplitude from burst to burst butwhich all have the same pulse shape, the constant K willbe given by

*

where g t ) is the normalized pulse shape. The output ofthe circuit will be a voltage which is an estimate of theoptimal threshold value, halfway between the level for a1 and a 0. This assumes that the power received for a0 s negligible with respect to that for a 1, although ifthat is not the case it would be possible to incorporate anoffset in (2) to account for the non-zero level in the 0.The pe ak detector circuit shown in Fig. l(c) can be usedas an approximation to the ideal integrating sample andhold of Fig. l(b) since by proper choice of the RC con-stant in the peak detector it is possible to make thecharging time correspond to the n bits of the preamble.During charging the circuit acts as an approximate inte-grator, integrating the n pulses of the preamble andestablishing the proper threshold through the use of asimple voltage divider at the output. This circuit has theadvantage that no control (sampling) signal is necessarysince once the capacitor is fully charged, subsequent Os

p+ t

= IN

INTEGRATINGS/H

PREAMPLIFIER

PIN

RESET -5 c i; IwPEAKDETECTOR....~~~~~ ........~~~ ........~ ~ ~ ~ ~ ~ ~ ~ ~ . . .(d

Fig. 1. (a) Feedback AGC circuit based on gain controlled amplifierGCA), (b) ideal feedforward burst mode receiver based on the use of anintegrating sample and hold for the determination of the proper thresh-old and (c) simplified peak detector used as an approximation to theideal burst mode feedforward circuit of (b).

will not discharge the capacitor due to the presence of thediode.The assum ptions which have been used fo r the determi-nation of the penalty for burst mode reception with re-spect to continuous mode reception in this analysis are:1) each burst contains a noise corrupted n bit pream-ble consisting of a string of 1s which ar e used toestablish the threshold V , which is used fo r determi-nation of 1s an d Os in the subsequent data stream.The n bits in the preamble are not considered to be


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ELDERING: THEORETICAL DETERMINATION OF SENSITIVITY PENALTY 2147

bum 2.b

DATA IN

Fig. 2. Timing diagram for the ideal burst mode receiver shown in Fig.l(b). The signal DATA IN is the output from the p-i-n preamplifier.

data and are not considered in the calculation of thebit error rate BER),2 ) averaging of the n bits in the preamble can be usedto reduce the error in V,,by using an ideal circuit tofilter the noise in the preamble, resulting in anenergy to noise power spectral density ratio ofn E b / N o ,where Eb No s the energy to noise powerspectral density ratio for any single bit in the pream-ble or data stream, and

3) receiver sensitivity is limited by additive whiteGaussian noise, in which the noise statistics for thedetermination of a 1or a 0 are equal. This willapply to all types of PIN receivers (transimpedance,high impedance, or low impedance) and some typesof APD receivers which are far from the sensitivitylimit and limited by amplifier rather than detectornoise.

It should be noted that a number of different configu-rations for the burst mode receiver can be used. Theauthors of [4] use a differential input/output trans-impedance amplifier with a peak detector forming thefeedback loop. It is also possible to use a rapid AGCcircuit in which the gain of one of the stages is adjustedbased on the measurement of the amplitude of the n bitsof the preamble. However, no circuit will be able toincrease the energy to noise power spectral density ratioof the received preamble to greater than nEb/Nn. Be-cause of this it is possible to calculate the minimumpenalty for burst mode operation with respect to continu-ous mode operation, independent of the receiver type andexact c ircuit configuration.In addition, we note that the analysis presented here isindepe ndent of the bit rate an d pulse shape, as long as thepulses are such that intersymbol interference (ISI) at thesampling point is negligible. This will remain valid at highbit rates, as long as the channel remains limited byGaussian noise. and not bv severe distortion of the eve

diagram resulting in closure at the sampling point. In thefollowing calculations, we assume that at the transmitterrectangular non-return-to-zero NRZ) pulses are trans-mitted and that at the receiver a x/s in x amplitudeequalizer and Nyquist brick-wall or raised cosine filteringis used. However, this assumption is made only for conve-nience and results in the minimum theoretical values of, /No (at the receiver) for a given bit error rate. Sinceour comparison is between burst and continuous modereception, the actual pulse shape and receive filter is notof consequence as long as the negligible IS1 condition ismaintained. For real fiber optic systems in which mini-mum filtering at the receiver is performed, the actualvalues of Eb/N , , for a given BER would be higher thanthe values shown here, but the penalty for burst modereception would be the same.

111.ANALYSISTh e probability of erro r for binary systems is the proba-bility of detection of a logical 1when a 0was transmit-ted, plus the probability of detection of a logical 0whena 1was transmitted. For a fixed threshold system thesequantities can be determined by the probability densityfunctions of the received signal r when a 0 or 1 aretransmitted, which are f r I 0) and f r 1) respectively.P, I I 0) and P,(O 1) are

3 )

P,(O 1) = / f r I 1) dr (4)For many systems, the Gaussian distribution is valid forthe descriptions of f r 0) and f r 11, which become

w

and

where U is the variance of the power in the receivedsignal (average noise power) and so and s are the trans-mitted power values for a 0 and 1 respectively. Weassume normalized voltage levels in the following calcula-tions. Graphical representation of f r I 0) and f r l ,assuming Gaussian distributions are shown in Fig. 3. Insuch cases, and when 0 and I are equiprobable, theprobability of erI-or P is

For fiber optic systems we can assume that an On-OffKeying (OOK) format is used, and that a good extinction


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2148 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 11,NO. 12, DECEMBER 19934 I

1 0 1 2r

Fig. 3. Probability density functions f r I O ) and f r l , and idealthreshold y which has a probability density function which can berepresented by a delta Dirac function located halfway between the meanreceived values for 0and 1.The density functions are Gaussian andcorrespond to an E,/ of 12.6 dB. BER is given as the sum of theintegrals of the tails of the distributions f r 0) and f r 1)from to V ,and from --r to V , , respectively.ratio > 10 dB) is maintained in the transmitter. Forequiprobable data, and with the threshold placed opti-mally (halfway between the voltage level for a 1 and thelevel for a 0) P, is

where U = No No being the noise power spectral den-sity, and E , is the energy per bit. The function Q isQ z )= i e r f c z / fi) nd the complementary error func-tion is defined as erfc(x) (2,Demonstration that PINFET transimpedance receiverswhich are fa r from the sensitivity limit can be modeled bya Gaussian process and described by 8) is shown in Fig. 4,where 8) is plotted along with experimentally determ inedvalues of PIN FE T sensitivity for a commercially availablePINFE T (Alcatel SE L Model 68-LD R, optimized for op-eration at 68 Mb/s). For convenience, the sensitivityvalues were normalized to the values of E /N withE,/No = 15.6 dB corresponding to a sensitivity of 44.5dBm at a BER ofFor burst mode operation the threshold voltage will becorrupted by noise, and the distribution of the values ofthe threshold voltages will be similar to that of the distri-bution of the values corresponding to logical 1s. This isrepresented in Fig. 5, where Gaussian distributions areassumed for 0, 1, and V,, assuming that only one bit isused to determine the threshold voltage. In the case thatmore than one bit is used to establish the threshold, thevariance U will decrease, and under ideal conditions willdecrease as cri/n where n , is the num ber of bits used toestablish the threshold. For the general case of n bits thedistribution of the threshold voltages will be given by

exp - ) dh

~:~~~0 60 4m 10-8

1 0 910.10

log -. 1 0 1 2 1 4 16 18EblNO

Fig. 4. BER versus E assuming a fixed threshold and Gaussiandistributions for f r I 0) and f r I l , and measured values from a PIN-FET, with the sensitivity (received power) corresponding to a BER ofnormalized to an Eb/Noof 15.6 dB.

rFig. 5. Probability density functions f r I 0 and f r l , and probabil-ity density function for the threshold V,, when calculated from the first1 received. The threshold voltage has the same probability densityfunction as f ( r I 1) with the mean located at the ideal value of V,. Thedensity functions are Gaussian and correspond to an E , / N , of 12.6 dB.

probability of er ror will be given by

In burst mode systems, the BER can be expected tovary from burst-to-burst, depending on the accuracy withwhich the threshold value has been determined. Theexpected value of the BER, denoted Pe BURST),s

This assumes that f v ) s ergodic, and thus the averageburst-mode BER can be calculated from a sufficientlylarge number of bursts and is independent of the burstlength.Numerical evaluation of (11) was perform ed assuming aGaussian distribution for f V , ) , and breaking the integralinto increasingly smaller regions near the peak, with thesmallest division being a0/2.The results of the calcula-tion are shown in Fig. 6, where it can be seen that thef v ) xp . (9) penalty incurred by determining the threshold based onreception of the first bit is 3.00 dB. This value was foundto be constant over the BE R range of to lo-. Fig.7 shows the penalty as a function of the number of bits

1 -+ lja 2 - 2U

When the threshold has a non-optimal value, the total


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ELDERING: THEORETICAL DETERMINATION OF SENSITIVITY PENALTY

~

2149

10 sU0.10 0 2 4 6 8 1 12 14 16 18 2

Eb/NoFig. 6 . BER versus E,,, for continuous mode operation, where thethreshold is assumed to be determined without error, and for burst modeoperation when the threshold is determined from the first 1 received.The penalty for burst mode operation in these conditions is 3.00 dB.

P 2 1 \

2 4 6 8 1 12 14 16n number of bits in preamble)

Fig. 7. Penalty for burst mode operation as a function of the number ofbits in the preamble used to establish the threshold.used to establish the threshold, which drops from 3.00 dBwhen a single bit is used to establish the threshold to 0.94dB when 4 bits are used, 0.51 when 8 bits are used and0.28 when 16 bits are used. With 36 bits in the preamblefor amplitude recovery the penalty is less than 0.2 dB.

IV. CONCLUSIONSIn conclusion, we note that burst mode receivers whichutilize a single bit for threshold determination offer thepossibility of a large dynamic range with a minimum burst

preamble, but will incur a 3.00 dB penalty with respect tocontinuous mode receivers which establish a near idealthreshold by averaging a large number of received 1s.Byincreasing the number of bits in the preamble used foramplitude recovery the penalty fo r burst mod e operationcan be reduced substantially. Further physical insight intothe 3.00 dB penalty incurred w hen using a single bit todetermine th e threshold can be gained by considering theeye diagram with superimposed threshold, in noisy condi-tions, for the case of continuous mode reception (idealthreshold level) and for burst mode reception. For contin-uous reception the ideal threshold can be viewed as anarrow line centered between the traces for a 1and a O which have an observable width due to the noise in thesignal. For burst mode reception, the threshold is nolonger a narrow line but becomes a wide trace, with thewidth depending on the number of bits used to establishthe threshold. With a single bit used to establish thethreshold the width of the threshold is identical to thewidth of the levels for a 1 or 0. The effective eyeopening, considered as the distance between the threshold

and the 1and 0 levels, will be reduced; the fact that a3.00 dB penalty corresponds to a reduction of the openingto one half of its value for continuous mode receptionwith an ideal threshold makes intuitive sense.We note that the authors of [5] eport a 3.00 dB burstmode penalty for their APD receiver, but show that thepenalty is due to threshold offset, not threshold variationsas discussed in this article. The threshold offset is inten-tional, and serves to prevent random noise present in thepreamplifier from being detected as data when the re is nooptical signal present. The results of this study suggestthat even if this threshold offset were reduced, an inher-ent burst m ode penalty would be present, thus the use ofan offset for noise suppression with no optical signalpresent has little impact on their final receiver sensitivity.The exact penalty for burst mode operation with nothreshold offset could be calculated using the methoddescribed in this article and a noise model6 appropriatefor th e high sensitivity APD receiver.

V. ACKNOWLEDGMENTThe author would like to thank the reviewers of this

article for their careful study and helpful comments.M. M. Mamblona and R. M. G6m ez are acknowledged forhelpful discussions.REFERENCES

CCIIT Recommendation G.131, Stability and Echo, Fascicle111.1, pp. 143-155, 1988.CCITI Recommendation G.114, Mean One-way PropagationTime, Fascicle 111.1, pp. 84-94, 1988.C. A. Eldering e t . al, Transmitter and receiver requirements forTDMA passive optical networks, Proc. Third ZEEE Conf. LocalOptical Networks September 24-25, 1991, Tokyo,Japan).Y. Ota and R. G. Swartz, Burst-mode compatible optical receiverwith a large dynamic range, J Lightwave Technol., vol. 8, no. 12pp. 1897-1903, December 1990.Y .Ota, R. G. Swartz, and V. D. Archer, DC-lGb /s Burst-ModeCompatible Receiver for Optical Bus Applications, J LightwaveTechnol., vol. 10, no. 2, pp. 244-249, February 1992.S. Personick, P. Balban, J. H. Bobsin, and P. R. Kumar, Adetailed comparison of four approaches to the calculat ion of thesensitivityof optical fiber system receivers,ZEEE Trans.Cornnun .vol. 25, pp. 541-548, May 1977.

Charles A Eldering received the B.S. degree inPhysics from Carnegie-Mellon University in1981, the M.S. degree in Solid State Science andEngineering from Syracuse University in 1985,and the Ph.D. degree in Electrical Engineeringfrom the University of California at Davis in1989. During 1981 to 1985 Dr. Eldering servedas an officer in the U.S. Air Force Rome Labo-ratory where he developed electron and opticalbeam test methods for internal node testing ofintegrated circuits. From 1985 to 1990 he per-formed research at the UnGersity of California in the area of optidallynonlinear polymer materials and developed novel etalon structures forthe characterization of new materials and for use as modulators inoptically interconnected computing systems. From 1990 to 1993 he waswith Alcatel SESA, Madrid, Spain, where he developed point-to-multi-point fiber optic systems for subscriber loop applications. At present heis with the Jerrold Communications Division of the General InstrumentCorporation, working on hybrid fiber/coax systems for telephony. Dr.Eldering is a member of the IEEE, OSA and SPIE.

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Theoretical Determination of Sensitivity