( I = 0 mm, 1 = 7.5 mm, and 1 = 12.5 mm). For a patch without slots, the current flows primarily in a straight line from one side to the other. From Figures 5(b) and 5k), it is clear that the presence of the slots forces the current to travel through a much longer path. This explains the decrease in the resonance frequency of the meander patch antenna. Also, it is evident from the figures that the patch length of the current flow increases with increasing slot length. This confirms the experimental observation of the reduction in the resonant frequency with an increase of the slot length. From the figures i t is also clear that an increase in the slot width does not significantly increase the path length to the flow of the current. This validates the earlier results that the change in the slot width does not bring any significant change in the resonance frequency.

4. CONCLUSION The design of a compact meander patch antenna has been presented. The length of the antenna is 70% less than that of a half-wave microstrip patch antenna. I t is anticipated that this design will find application in hand-held communication systems where light weight and compactness are the most desirable criteria.

REFERENCES 1. K. Hiraswa and M. Haneishi, Analysis. Design and Measurement of

Sniall and Low-Profile Antennas, Artech House, London, 1992, Chap. 5.

2. J . R . Mosig, Numerical Techniqice~ for Microwac,e und Millimeter- Wai,e Passive Structures, John Wiley & Sons, New York, 1989, Chap. 3.

Microwave and Optical Technology Letters. 13/I, 12-14 0 1996 John Wiley & Sons. Inc. CCC 0895-2477/96

SENSITIVITY EVALUATION OF EDFA PPM SYSTEMS UNDER CHROMATIC DISPERSION

A. Hussain, J. M. H. Elmirghani, and R. A. Cryan Department of Electrical Electronic Engineenng and Physics University of Northumbrla at Newcastle Newcastle Upon Tyne, NE1 8ST

KEY TERMS Optical communication, optical amplifiers, dispersion, PPM

ABSTRACT An optically preamplified pulse position modulation (PPM) system oper- ating at 622 Mbit / s and h = 1.53 p m is analyzed, and is shown to offer a sensiticQ benefit of 9.2 dB oc,er an equiralent OOK system. Fiber chromatic dispersion is taken into account and is used to estimate the receiced pulse shape. Pulse dispersion can potentially induce a significant performance penalty in PPM system because of the temporal nature of the PPM format. Thr results show that for a transmitted pulse of

duration 80 ps, the receiced pulses have full widths at half maximum (FWHM) of 160 and 320ps forfiber lengths equaling 120 and 240 km, respectiL,ely. The system sensitivity degradation due to dispersion is explicitly eilaluated. It is shown that a sensitivivpenal(y of up to 5 dB can be incurred over the transmission spans considered. 0 1996 John Mley & sons, Inc.

1. INTRODUCTION

Pulse position modulation (PPM) has been proposed as a format that can exploit the abundant monomode-fiber band- width to offer high sensitivity over the optical link. The typical sensitivity improvement (using p-i-n-FET and p-i-n-BJT receivers) over direct detection and coherent OOK systems is in the range of 5-12 dB [l-41. The implications of the extra sensitivity over a long-haul link or in a multiuser environment are apparent.

Recently there has been increased theoretical and practi- cal interest in using optical amplifiers, particularly erbium- doped fiber amplifiers (EDFA), as front ends to optical receivers in order to improve the sensitivity [5-71. The use of erbium-doped optical amplifiers has greatly increased the transmission distance in optical-fiber communication systems. In consequence, chromatic dispersion has become one of the main limiting factors to long-haul transmission at high data rates. It can produce distortion in the demodulated wave- form, resulting in intersymbol interference in the received signal and in a reduction of transmission system performance.

We propose a new hybrid EDFA PPM system and investi- gate its sensitivity over a dispersive optical-fiber channel. We demonstrate that such a system can offer up to 9.2-dB sensi- tivity improvement over a comparable optically preamplified OOK system. Pulse dispersion has more important conse- quences in PPM systems because of the temporal nature of the PPM format, where the pulse position is utilized to convey the data. Using computer simulation techniques, this article determines the effects of chromatic dispersion with fibre length and investigates the behavior of the received pulse shape with respect to the fiber length. The pulse shape at the receiver end of the fiber is obtained through mathe- matical modeling of the dispersive effect of the single-mode fiber. I t is shown that a sensitivity penalty of up to 5 dB can be incurred in a transmission span equaling 240 km. The use of equalization techniques to reduce this penalty is the sub- ject of further work.

2. FIBER MODELING

The optical signal observed at the output of the fiber, x,,,(t>, is calculated from x, , ( t ) , with the use of the equivalent low-pass representation of the transfer function of a single- mode fibre [8]:

where

1 A2 y --D(A)--B*L.

?I C (2)

B is the bit rate, D is the fiber chromatic dispersion, A is the operating wavelength, c is the speed of light, L is the fiber length, and f is the frequency offset from the optical carrier frequency (f, = c/A) under dc operation of the laser.

14 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol 13, No 1. September 1996

We assume the input pulse, xi&), launched from the laser into the fiber is an ideal rectangular pulse. The signal at the output of the fiber, xoul(f), is given by

zo,,(f) and A?&) are given by

( 3 )

and

where ~ o , , ( f ) and zii,(f) are the Fourier transforms of x,,,(t) and xi&), respectively. No fiber nonlinearities are included in the model, so that the single effect of dispersion can be investigated. The direct detection process of a photo- diode is represented by squaring the magnitude of xou,(t). As such, the baseband electrical input to the matched filter (optimum filter for PPM systems [ 2 ] ) is given by u,,,(t)

The baseband receiver shaping filter will be matched to the pulse shape at the output of the detector. The realization and implementation of such an optimum filter has previously been addressed [9]. The PPM system has been assumed to transmit constant pulses of duration 80 ps at all coding levels. This particular pulse duration has been selected to corre- spond to the maximum available bandwidth at the receiver. Figure 1 illustrates the effects of dispersion on the transmit- ted pulse for single-mode fiber at various transmission spans ranging from 60 to 240 km. The results clearly show that an increase in the fiber length results in pulse dispersion as depicted by the increase in the pulse FHWM. It is seen that fiber lengths of 120 and 240 km subjected to a rectangular transmitted pulse of unity amplitude and duration 80 ps give rise to received pulses of FWHM 160 ps and 320 ps. The aim of the next section is to evaluate the EDFA PPM system sensitivity under dispersion and with the received pulse shapes of Figure 1.

3. SYSTEM SENSITIVITY The EDFA PPM system is shown in Figure 2. A complete receiver system consists of two main subsystems: a detection subsystem and a synchronization subsystem. Only the detec- tion subsystem is shown, and as such ideal synchronization

1

Pulse duration (seconds)

Figure 1 spans

Chromatically dispersed pulses at various transmission

PPM I \

y Matched Threshold H Dec;$x- p i n a r y Detection

Filter Device Timing Code

Figure 2 EDFA PPM receiver structure

has been assumed. The PPM signal synchronization has pre- viously been considered in [4] . The detection subsystem con- sists of an EDFA front end of gain G and spontaneous emission parameter nsp followed by an optical bandpass filter (OBPF) of bandwidth B centered at the signal frequency u. The detector is a p-i-n photodiode of quantum efficiency 17. This is followed by an electrical preamplifier, a matched filter, a threshold detector, and finally the PPM to OOK decoder. The amplified spontaneous emission (ASE) noise PSD output from the optical amplifier can be written as

(7) SASE = m,n,,hu(G - 11,

and the optical noise power incident on the photodetector can be written as

PN = mlnsphu(G - 1)B, (8)

where m, is the number of orthogonally polarized modes, which is two, and h is the Planck constant. Following the approach in [ lo] , the noise power spectral density in the electrical domain can be written as

s - -(2PsignsP(G 2q2 - N - hu

1) + m,n:phu(G - 112B

+Psig + m,nSphu(G - 1)B) + Spa, (9)

where q is the electronic charge and 17 was taken to be unity. Spa is the electrical preamplifier noise PSD and Psig is the average signal power incident on the photodetector and is given by

bhu p . = - (10) T, '

where T, = mTf/n is the PPM slot duration and b is the number of photons in the pulse. The received dispersed pulse shapes in Figure 1 were approximated by a Gaussian pulse shape at the various transmission spans. This yields simple, easy-to-handle analytic expressions for the signal at the out- put of the detector and at the output of the matched filter. At the same time the mismatch between the pulses of Figure 1 and the Gaussian approximation was found to be minimal. As such the output current from the photodetector can be writ- ten as

- ( t 2 /4lY 2 )

i ( t ) = bq ( 1 1 ) 2J;;a '

where a is

0.2Tf M ( L / L , ) '

f f = ( 1 2 )

MICROWAVE AND OPTICAL TECHNOLOGY LE'TTERS / Vol. 13, No. 1, September 1996 15

where L is the transmission span in kilometers and Lo is a normalization constant that givcs the best fit at a given transmission distance. The ratio L / L , for a best fit was 9.47, 4.73, 3.15, and 2.36 at transmission spans of 60, 120, 180, and 240 km, respectively. M is the number of information bits transmitted per PPM frame.

In order to compare the PPM system with an equivalent OOK system, an equivalent binary error probability P, is specified. In the case of PPM, assuming that all the PPM symbols are equally likely, the probability of a PPM symbol error is given by

As wrong slot errors (WSE) occur in the slots that are directly before or after the slot containing the pulse, a conservative estimate of the WSE probability is given with the use of the noise when a pulse is present. The WSE probability can be written as

(21 1

where

(13) (22)

The derivative of the output current can be written as where Pr, PI, and Pf are the erasure error probability, the wrong slot error probability, and the false alarm error proba- bility, respectively [2]. The average binary error probability is related to the average symbol error probability by [ 113

The peak receiver current is

(24) and so the performance criterion becomes

and the current at the detection instant td is

In general P, is specified for optical-fiber communication systems as P, = lo-'.

The EDFA PPM system has a noise that depends on the signal, as is clear from (9). The system false alarm errors occur when the signal is absent; the value of S, under this condition is denoted by S,, where S, is given by

(25) id = bq 2avG .

The detection time t d is given by

29' S, = -[m,n:phc(G - 1)'B

hi Under perfect synchronization the receiver sensitivity was evaluated with the use of the following algorithm: +mfn,phc,(G - 1)B) + Spa, (16)

1. From knowledge of the received pulse shape and the receiver noise PSD, the system parameters i , , id, t d , i ' ( r d ) , N,, and Nslg are evaluated for a given pulse energy b and threshold detection time t , or current id.

2. A numeric optimization routine then searches in the b > 0 and 0 < i , < i , space for the smallest value of b that meets the performance criterion.

3. The receiver sensitivity in photons per information bit can be obtained by dividing b by M.

and the equivalent noise at the output of the matched filter N, is

(17)

(18)

where G & w ) is the matched filter transfer function. One can then evaluate the false alarm error probability by following [2] and [3] and using a conservative estimate of T, at T, = a. Erasure errors occur when the PPM signal is present. Under this condition the noise is as given by (9); this will be denoted by SSlg. The noise at the output of the matched filter in this case, NSlg . is given by

For sensitivity evaluation purposes the system was speci- fied to operate at an error rate of To enable compari- son with an EDFA OOK system, the practical parameters reported in [6] were adopted in this study. The relevant parameters are shown in Table 1.

The sensitivity of the EDFA PPM system is shown in Figure 3 as a function of the coding level M . As the coding level is increased, the single PPM pulse is used to convey more bits of information (M bits); thus the sensitivity of the system improves. As the PPM coding level is increased, the PPM frame is continuously subdivided into finer subdivisions (n = 2 M slots). Accordingly, the time slot duration decreases and the PPM probability of wrong slot errors increases. As a result the sensitivity degrades at large values of M. The

(19)

(20)

thus the erasure error probability can be evaluated [2, 31.

16 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol 13, No 1, September 1996

TABLE 1 The EDFA PPM Receiver Parameters

I /

Wavelength 1.53 p m Bit rate 622 Mbit/s EDFA gain 27 dB OBPF bandwidth B 76.14 GHz Spontaneous emission parameter nsp 1.3 Electrical preamplifier noise Spa 1.25 x lowz3 A2/Hz Quantum efficiency 7) 1

E e i

i 2 3 4 s e r 8 9

PPY ordw

Figure 3 Sensitivity as a function of the PPM coding order

system sensitivity also degrades with dispersion as the trans- mission distance increases, as depicted in Figure 3. The system bit-error-rate performance is evaluated in Figure 4 at M = 4 and L = 180 km and at M = 5 and L = 60 km, which are both optimum sensitivity values in the curves of Figure 3. The equivalent optically preamplified OOK system BER is also shown in Figure 4. The OOK system performance was evaluated with the use of the results in [5]. The performance improvement achieved by using PPM rather than OOK is best illustrated by comparing the results of Figure 3 with the widely available EDFA OOK results. The best predicted sensitivity as depicted in Figure 3 is 18.5 photons/bit ( L = 60 km, A4 = 5). The sensitivity predicted for EDFA OOK with the use of the same parameters and the closed solution in [5] is 110 photons/bit, to which the experimental 152 photons/bit result in [61 can be compared. The EDFA PPM system thus offers a 9.2-dB sensitivity improvement over the EDFA OOK system. The best predicted sensitivity for ideal optically preamplified OOK comes from a study by Henry [71, who predicted 38 photons/bit. The EDFA PPM hybrid offers a sensitivity that outperforms this fundamental limit for OOK.

The system sensitivity degradation with transmission dis- tance is shown in Figure 5. The sensitivity deteriorates by about 5 dB from -58.2 dBm to -53.2 dBm as the transmis- sion span is increased from 60 to 240 km. Work is currently

-52 1

-60 J 1 60 120 180 240

Tnnwnhslon d h b n a (km)

Figure 5 Sensitivity variation with transmission distance

being carried out on the design of equalization networks to minimize this sensitivity degradation.

4. CONCLUSIONS An analysis for an EDFA PPM system has been presented, illustrating that this system can offer a 9.2-dB sensitivity improvement over a comparable OOK system. The impact of chromatic dispersion on the PPM (temporal format) has been evaluated. In particular, it has been shown that a sensitivity penalty of up to 5 dB can be incurred over the transmission span considered. The sensitivity benefit achieved by with the use of PPM rather than OOK has significant impact on both the transmission and the multiuser environments.

REFERENCES 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

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R. A. Cryan, R. T. Unwin, A. J. Massarella, M. J. N. Sibley, and I. Garrett, “A Comparison of Coherent PPM with PCM,” Eur. Trans. Telecommun., Vol. 3, No. 4, 1992, pp. 331-340. J. M. H. Elmirghani, R. A. Cryan, and F. M. Clayton, “On the Spectral Estimation and Synchronisation of the Cyclostationary Optical Fibre PPM Process,” IEEE Trans. Commun., Vol. COM-

0. K. Tonguz and L. G. Kazovsb, “Theory of Direct-Detection Lightwave Receivers Using Optical Amplifiers,” J. Lighhvaue Technol., Vol. 9, No. 2, 1991, pp. 174-81. P. Smyth, R. Wyatt, A. Fidler, P. Eardley, A. Sayles, and S. Craig-Ryan, “152 Photons per bit Detection at 622 Mbit/s to 2.5 Gbit/s Using an Erbium Fibre Amplifier,” Electron. Lett.,

P. S. Henry, “Error Rate Performance of Optical Amplifiers,” OFC ’89 Tech. Dig., Houston, TX, Feb. 1989, Paper No. THK3. A. F. Elrefaie et al. “Chromatic Dispersion Limitation in Coher- ent Lightwave Transmission Systems,” J. Lightwave Technol., Vol.

A. Hussain, J. M. H. Elmirghani, and R. A. Cryan, “Realisation and Implementation of an Optimal Postdetection Filter for a 10 Gbit/s Transmission System Using Single-Mode Fibre,” Proc. IEEE ICC’96, Dallas, June 1996. A. J. Phillips, R. A. Cryan, and J. M. Senior, “Optical Fibre PPM with Optical Preamplification,” 5th IEE Bangor Symposium on Communications, 1993, pp. 284-287. J. J. Proakis, Digital Communications, McGraw-Hill, New York, 1983, p. 152.

137, NO. 2, 1990, pp. 89-96.

43, NO. 3, 1995, pp. 1001-1012.

Vol. 26, NO. 19, 1990, pp. 1604-1605.

LT-6, NO. 5, 1988, pp. 704-709.

Received 3-28-96

Microwave and Optical Technology Letters, 13/1, 14-17 0 1996 John Wiley & Sons, Inc. CCC 0895-2477/96

MICROWAVE AND OPTICAL TECHNOLOGY LETERS / Vol. 13, No. 1, September 1996 17