Performance evaluation of EDFA preamplified receivers taking into account intersymbol interference

JOURNAL. OF LIGHTWAVE TECHNOLOGY, VOL. 13, NO. 2, FEBRUARY 1995 225

Performance Evaluation of EDFA Preamplified Receivers Taking into Account Intersymbol Interference

Luis F. B. Ribeiro, JosC R. F. Da Rocha, Member, IEEE, and Jog0 L. Pinto

Abstract-Exact mathematical derivation of the moment generating function for an optically preamplilied receiver output current is carried out. Amplified spontaneous emission noise as well as Poisson shot-noise and thermal noise originated at the receiver front-end are considered. Optical bandpass filter is also taken into account. This new global description of the stochastic processes involved in optical signal detection enabld analytical assessment of the overall receiver performance without restric- tions on the optical input pulse and the electronic filter response. Various bit error rate evaluation methods such as Chernoff bound, modified Chernoff bound, Gaussian approximation and saddlepoint approximation are developed based on the moment generating function and their precision compared.

Index Terns- Optical amplifiers, receivers.

I. INTRODUCTION SSESSMENT of error probabilities has been a main A issue concerning communication systems [ 13. Different

methods have been developed to analytically evaluate the statistics and performance of optically preamplified receivers [21-[101.

Personick [6] derived a moment generating function (MGF) for the photo-electron number in a preamplified receiver. This was used to evaluate the corresponding Chernoff Bound on the bit-error-rate (BER). Marcuse [7] derived a characteristic function to obtain an approximate expression for the BER when an integrate-and-dump filter is used in the receiver. However, these results are not applicable to many practical cases such as optical receivers where the generated electrical current is processed by a raised-cosine equaliser.

A rigorous general analytical expression for the worst case noise variance at the receiver output is given by Yamamoto [8]. Nevertheless, this model is applicable only to zero-forcing equalisers and an approximation was used by considering Gaussian statistics.

Fyath and O’Reilly [9] obtained a MGF considering the effective detected signal statistics and an arbitrary filter. Still, when this MGF is used to obtain the signal variance, it is

Manuscript received October 13, 1994. This work has been supported by a JNICT (Junta Nacional de Investigagao Cientifica e Tecnol6gica) grant and RACE project TRAVEL (R2011).

J. L. Ribeiro and J. Rocha are with the Optical Communications Group, Dept. of Electronics & Telecommunications, University of Aveiro, 3800 Aveiro, Portugal.

U Pinto is with the Physics Department, University of Aveiro, 3800 Aveiro, Portugal.

IEEE Log Number 9407818.

necessary to modify some parameters to achieve agreement with the generally accepted Yamamoto’ s formulation. Lane et al. [lo] presented a modification to the formulation in [9] but the derived variances do not coincide with Yamamoto’s.

In this contribution we derive a new MGF for the output signal of an optically amplified receiver, considering arbitrary received optical pulses and receiver equaliser impulse response. The MGF is then used to derive the signal variance, which coincides exactly with Yamamoto’s expression, men- tioned above. Furthermore, when this MGF is applied to the special cases considered in [6] and [7], the resulting expression is in agreement with the corresponding equations.

The receiver and the EDFA models are presented in Sections I1 and 111, respectively. The new MGF is derived in Section IV and compared with published formulation. In Section V we apply the new analytical expression to BER evaluation of an EDFA system using alternative methods: Chernoff bound (CB), modified Chernoff bound (MCB), Gaussian approximation (GA) and saddlepoint approximation (SPA). In this section, expressions for the optimum decision threshold are also presented. Finally, the conclusions are presented in Sec- tion VI.

11. RECEIVER MODEL The optical as well as the electronic path will be considered

for the assessment of overall receiver performance. To this pur- pose, realistic statistical description of the random processes occurring in the several receiver stages must be taken into account. The receiver model can be seen in Fig. 1, where ei,(t) is the optical preamplifier input electrical field and eisE(t) is the amplified spontaneous emission (ASE) noise electrical field at the preamplifier output, which is assumed white Gaussian. Bo represents the optical filter bandwidth.

The sources of randomness are the ASE noise, the shot noise originated by the detection Poisson process in the PIN photodiode and the thermal noise, nth(t), due to the receiver electronic circuitry.

Due to the optical filter, the noise field at the photodiode input eAsE(t ) is narrowband Gaussian and can rigorously be described in the time interval AT by means of the Karhunen- LoCve (K-L) expansion [15]

0733-8724/95$04.00 0 1995 IEEE

~ 226 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 13, NO. 2, FEBRUARY 1995

PIN Photodiode Re{n} and y = Im{n}, (6) is rewritten as ...............................................

m

n(t) = Czeae(t) + jyeQe(t), t E AT. (9)

We consider a stationary bandpass noise process eASE(t) with bandwidth Bo. In this case the solutions of (8) are the prolate spheroidal wave functions [ 181. Every eigenvalue Xe corresponds to two equal degenerated eigenvalues pe. The non-degenerated series of eigenvalues p can be taken from the double-sided power spectral density (PSD) of the ASE noise SASE(W) by [161

e=i

N(t)

Eledronic Preampliier and Equalii

i IThermal ........... NoyB”” ................................................ i

Fig. 1. Preamplified receiver model.

The complete set of orthonormal functions{cpk(t)} obeys

‘ P k ( t ) . cpj*(t)dt = S k j . (2)

The coefficients { c k } are complex Gaussian random variables given by [16]

ck = L, eASE(t) . cpz(t)dt* (3)

The coefficients { c k } are uncorrelated if the set of orthonormal functions obeys the following integral equation

Re(t, t’) ‘ ‘Pk(t’)dt’ = p k ’ P k ( t ) (4)

where Re$, t’) is the autocorrelation function of e A s E ( t ) and{pk} is the set of eigenvalues associated with the functions {‘Pk (t> 1-

Now, we define the relation between the complex envelope n(t) and the ASE noise electrical field eASE(t)

LT

eAsE(t) = &Re{n(t) . ejazvst 1

Furthermore, we consider an uniform PSD given by

( 0, otherwise

where No is the ASE noise single-sided PSD. From (10) and (1 1) we conclude that only M = BOAr eigenvalues p’ are different from zero and equal to N0/2. It can be shown that the variances of IC and y are related to the eigenvalues corresponding to the bandpass process eAsE(t ) [16] by

The complex envelope m(t) of the signal electrical field at the optical filter output is given by

e;,(t) = h Re{m(t) . e jaTvs t } (13)

where G is the EDFA optical power gain. We have neglected the phase delay in the EDFA and the laser phase noise. Using the Karhunen-Loeve basis { @ e ( t ) } for the complex envelope, results in

M M

m(t) me@e(t) = C(ae + j b e ) @ e ( t ) (14) where vs is the optical carrier frequency. Expanding n(t) into a Karhunen-Mve series, we obtain

e=i e = i

where components {me} are given by m

with components {ne} being given by and a = Re{m}, b = Im{m}.

(7) 111. EDFA NOISE MODEL

The {ne} are independent if the basis {ae(t)} satisfies the following equation

One Of the fundamental parameters for performance evaluation is the ASE noise PSD. We consider an EDFA with active length L. The preamplifier gain G and ASE noise PSD NO, with forward pumping, are given by [ 111 R,(t,t’) . @e(t’)dt’ = X e @ e ( t > (8)

where %(t,t’) is the autocorrelation function of n(t>. Defin- G = exp{ 2 . [%I 77s - 77P . (qo - qL) - L ~ ( z)} (16) ing the real and imaginary parts of n respectively as IC =

RIBEIRO et al.: PERFORMANCE EVALUATION OF EDFA PREAMPLIHED RECEIVERS TAKING INTO ACCOUNT INTERSYMBOL INTERFERENCE 221

where 71 is the emission to absorption cross section ratio and Q is the fibre attenuation. Subscripts s and p refer to signal and pump wavelength, respectively. The auxiliary parameters I+, qo and qL are defined by

I+ = II' e x p ( E 4 X ( " S / " P ) dx

40 = 440) (18)

qL = q(L)

where

In (19) Pp(z) represents the pump power along the doped fiber and the pump power threshold Pi" is given by

where h is Planck constant, A is the area of the active fiber core, r the fluorescence lifetime, up the pump frequency and aa(vp) is the absorption cross-section at vp. The parameters PO, U and gs in (17) and (18) take the values

9 s = 71s * Qs- (23)

In order to obtain q L , the following transcendental equation must be numerically solved

(24) 40 4L

qr, - qo = -ap . L + -.

IV. MOMENT GENERATING FUNCTION DERIVATION

A. Single Bit MGF Formulation

Given a time interval Ar, centered around instant ti, the PIN photodiode current is the result of a Poisson process. The rate of hole-electron pairs integrated over the interval [ti - T , ti + %] is given by [6] AT

t%+Y N; = N ( t ; ) = R . 1 lm(r) + .(.)Iz . d r (25)

where R = 71 f hu, and 17 is the quantum efficiency of the PIN photodiode. Substituting (9) and (14) into (25) and using the orthogonality of { @ e ( t ) ) results in

t,-9

M

~2 = R . [(me + ne>[' e= 1 M

= R . C ( a e + .e)' + (be + (26) e=i

Since a and b are constants for a given input field and x and y are Gaussian random variables (RV), Ni is a sum of 2M squared Gaussian RVs, each with variance N0/2. Given the statistical independence of 2 and y, the sum has a x' distribution with 2M degrees of freedom. Its MGF has the form [12]

exp [ EmL] (27)

l-ZR+.s MN,(s ) = 2M

(1 - 2R% . s ) -i-

where W(t;) is the optical input energy arriving at the PIN in time interval Ar around ti:

M

= lme1' = G . hp(tz)Ar. (28) e= 1

hp( t ) represents the optical power pulse at the EDFA input. Consider the contribution of the photoelectrons generated at

time t, to the output electrical current at instant t , y 2 ( t ) . For a given N,, and taking into account that the current is described by a filtered Poisson process, the MGF of RV Y, = y,(t) is given by [13]

M y ( s 1 N , ) = exp[N,(e" * hv( t - t ' ) - l)] (29)

where h,(t) is the receiver impulse response and q is the electron charge. From (29), the non-conditioned MGF is given by

MY% ( 3 ) = E N , [ M y ( 3 I N%)1 = EN, [exp{N,(es hr ( t - t t ) - 1 ))I - - MN* ( e S * hv(t--tc) - 1). (30)

Using (27) and (30) and taking into account the contributions of photoelectrons generated in all time intervals [t, - q, t, + %] with t, = i . Ar and z = -00,. . . , +m, results in the following MGF (Appendix I)

L

exp{sTm Bo . In [l - RNo(esqhT(t-T) - 1 )I d r } ' (31)

The consistency of this new expression with previous estab- lished results can be tested by applying it to the following cases: 1) Receiver with an integrate-and-dump impulse response and 2) Receiver with an arbitrary impulse response.

MY(S) =

1) Applying the integrate-and-dump response

1, O S t l T 0, otherwise hT(t) =

to expression

MyrD(3) =

(31), one obtains

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 13. NO. 2, FEBRUARY 1995 228

where L = BOT. This equation coincides exactly with (9) of [6] if we take into account the difference of notation and the fact that in [6] the random variable considered is the number of photo-electrons, while in our case the variable studied is the photo-current. Further- more, (33) agrees with the characteristic function (10) of [7] for a symbol “0” and the characteristic function used in (20) of [7] for a symbol “1”. For this comparison note that in [7] the decision variable is proportional to the rate of the Poisson process describing the detected current, integrated over the bit period.

2) Considering an arbitrary filter, from the properties of the MGF, we derive the average and variance of the output

(34)

(35)

Inserting (31) in (34) and (33, and after some algebraic manipulation, we obtain

+W

P = RG, 1- hp( t ) . hT(ts - t ) d t

+ BoRNoq I+” hT(ts - t ) d t -W

and

B. Accounting for Intersymbol-Intelference To take into account the intersymbol interference (ISI),

consider a sequence of information bits { U k } to be transmitted using the following sequence of optical power pulses

+m

pin(t) = ak . hp(t - kT). (42) k = - m

Considering now that a decision is made on bit a 0 by ob- serving the output signal ~ ( t ) at the appropriate time, pulses corresponding to a k , k # 0 will also influence the decision due to ISI. To analyse this influence, we define the sequence conditioned MGF of the output M y ( s 1 { U k } ) . Replacing hp(t) in (31) with pin(t) of (42) yields

M Y ( s I 1

k = - w

where

(46)

Averaging (43) over all possible sequences { U k } , for a given ao, results in the symbol conditioned MGF

M Y j (3) = E { a , l a ~ = j } [ ~ Y ( ~ I { U k ) > l

where

j = 0 , l . (40) I1 = 2R2GNoq2 * PON- T (47)

2 ffspsp = B o R 2 N i q 2 . !? T‘

The components a:, aZp, c,2-sp, o~p-sp represent signal quantum noise, spontaneous emission quantum noise, signal-spontaneous emission beat noise and spontaneous-spontaneous emission beat noise, respectively. The various parameters in (36)-(41) are defined in appendix 11. Equations (36) and (37) coincide exactly with (8) and (12) of Yamamoto [8]. The second term in (36) has been neglected by Yamamoto but we include it here for completeness.

Assuming independence of all Uk’S and performing the statistical averaging of (47) yields

I 111

RIBEIRO et al.: PERFORMANCE EVALUATION OF EDFA PREAMPLIFIED RECEIVERS TAKING INTO ACCOUNT INTERSYMBOL INTERFERENCE 229

With the same procedure one obtains for the "1" conditioned MGF

In (47)-(49) a sequence {ah} with 2n interferers has been considered. Considering now the additive thermal noise, with variance & and taking into account the statistical independence between this noise and the current y(t), the MGF for the decision variable 2 = ~ ( t ) is given by

where

Equations (48), (49) and (50) provide a full statistical description of the signal at the decision device input. They acco- modate quantum noise, signal-spontaneous and spontaneous- spontaneous beat noise, thermal noise and ISI. Additionally, they are applicable to any type of post-detection filter.

V. BER ESTIMATES USING FOUR ALTERNATIVE METHODS

A. Theory In this section, we will present an application of the new

MGF formulation to four different BER evaluation methods: Chernoff Bound (CB), Modified Chernoff Bound (MCB), Gaussian Approximation (GA) and Saddle-Point Approxima- tion (SPA).

Given a decision threshold D, the CB for the BER has the following expression [ 131

1 2

C B = - ( e s o D ~ M z o ( - s o ) + e S I D . M z , ( - s l ) ) ; s1 > 0,so < 0. (52)

Where Mz0(s ) and Mz,(s) are given by (50). The variables s1 and SO should be optimised for the most tight bound. In practice, however, one may perform a one-dimensional optimisation on the variable s = SI = --SO. The slight loss of tightness is compensated by simplicity [ 131.

The MCB for the BER is given by [ 131

s1 > 0,so < 0. (53)

Though bearing some similarities with (52), this bound has proven tighter in many cases of pratical interest [13]. A different approach to BER evaluation is provided by the SPA ~ 4 1

s1 > 0,so < 0. (54)

Compared with the MCB, the thermal noise variance is here substituted by the second derivative of functions Q(s) defined as

Finally, the well known Gaussian Approximation assumes the decision RV has Gaussian distribution, so that the error probability can be easily obtained from the signal to noise ratio and the threshold level D

G A = - Q 2 '[ (DiF)+Q(y)] - (57)

where

1 F - c - m

Following the procedure of [20], the optimum threshold for the CB is given by the solution of the following equation

Making s = s1 = -SO, substituting (52) into (61) and performing the derivation, results in the following optimum value for the decision threshold

Since this threshold is very close to the optimum [20], it is used also for the MCB and SPA. For the Gaussian approximation, we take for the optimum threshold the value that makes P(l I 0) = P(0 I 1) [19]

Substituting the optimum thresholds into (52)-(54) and (57) results in

MCB=-. Mth(S) JMYl ( - s ) . My0(s) , s > 0 (65) s a t h a

230 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 13, NO. 2, FEBRUARY 1995

TABLE I PARAMETERS USED FOR STUDY OF EDFA RECEIVER PERFORMANCE

PARAMETER Low-Gain Amplif. High-Gain Amplif. A, Optical Signal Wavelength 1550 nm 1550 nm A, Pump Wavelength T Flourescence lifetime L EDFA length p Fiber core radius a, Fiber attenuation @A, a, fiber attenuation @A, vs cross-section ratio @ A , qp cross-section ratio @ A, P,- Pump power Ua (A,)

982 nm 10.6 ms 5 m 0.6 pm 1.3 dBlm 0.98 dB/m 1 .o 0 7 dBm 3.08eCZ6 m2

982 nm 10.6 ms 25 m 0.6 pm 1.3 dBlm 0.98 dBlm 1 .o 0 17 dBm 3.08e-26 m2

B. Numerical Results

The EDFA parameters used in this section are listed in Table 1. The input optical pulse is a 3% FU and the receiver output pulse is a 100% raised-cosine function. The optical filter bandwidth is Bo = 1.15 nm.

The thermal noise [17] is dependent on the electronic FET preamplifier which is assumed with transconductance gain gm = 40 mS, noise factor r = 1.78. The bias resistance and quantum efficiency of the PIN are taken as 50 0 and q = 1, respectively. The input capacitance of PIN plus FET is C;, = 1 pF. The bit-rate considered is 10 Gbit/s.

The results obtained using the four BER bounds/ approximations are shown in Fig. 2 as a function of the optical input power. For a low-gain EDFA (Fig. 2.a), apart from the CB, all the other methods provide relatively dose estimates.

The high-gain amplifier results of Fig. 2.b show significant differences depending on the method used. The SPA is now significantly far away from the MCB. The MCB and CB are allmost coincident. This result is expected since the signal dependent noise is now dominant.

Fig. 2b also shows that for the high-gain case the GA can lead to very pessimistic results since it is situated above the CB curve. As shown in [ 131 for the particular case of an avalanche photodiode receiver, the signal dependent noise dominance leads to a marked loosening of the GA.

VI. CONCLUSION

A new formula for the MGF of an optically preamplified receiver output current is derived. This formula takes into account the amplified spontaneous emission noise of the optical amplifier, detection quantum noise, additive thermal noise, equalisation filter response and intersymbol interference, thus providing the basis for realistic performance analysis.

The agreement of the new formula with widely accepted Yamamoto mean and variance expressions and the exact verification of previous results, obtained for photon-counting and integrate-and-dump receivers gives a high degree of confidence in the new result.

The new MGF enables BER evaluation through alternative bounds and approximations. Results show that for low amplifier gain, MCB, SPA and GA are in good agreement and the CB presents a looser bound. However, for higher values of the optical amplifier gain, the MCB becomes rather close to

-1

-3

-5 6

!i -7 -9

-1 1

-13

-42 -41 -40 -39 -30 -37 -36 -35 -1

-3

-5 6 8 -7

-9

-1 1

-13 (b)

Fig. 2. BER for an optically preamplified receiver as a function of optical power using four different methods with a) low-gain EDFA (G = 8.8 dB) and b) high-gain EDFA (G = 30.6 dB). CB-Chernoff bound, MCB-modified Chemoff bound, GA-Gaussian approximation, and SPA-saddlepoint approximation.

the CB and the Gaussian approximation is an underestimation of receiver performance.

Since the difference between the MCB and the SPA curves is small in terms of optical power (-0.5 dB for BER = lOe-’), and the MCB gives a guarantee of receiver performance, this bound should be used in practical system evaluation.

APPENDIX A

The MGF of the contribution of photoelectrons generated within time interval AT centred at t; to the output current at time t , g ( t ) , is given by (27), (28) and (30)

MY, (3) = MN, (esqhy(t-t*) - 1)

where we have substituted M = BOAT, the number of non- zero eigenvalues considered in (14).

The contributions of all time intervals AT centred at ti are taken into account by assuming statistical independence between them. This assumption is valid for AT > 2 /&, since we are considering Gaussian noise envelope n(t) with bandwidth Bo/2. Then the correlations between samples is neglegible for intervals greater than 2/B0 and the final MGF

I 1 1 1

RIBEIRO er al.: PERFORMANCE EVALUATION OF EDFA PREAMPLIFIED RECEIVERS TAKING INTO ACCOUNT INTERSYMBOL INTERFERENCE 231

will be the product of the partial MGFs

+a,

My(3)= n MK(3) i=-a

q e s q h r ( t - +m m r -

I I If the bit period T is such that T >> AT, the above summation

can be approximated by the following integral

(A-3)

APPENDIX B

We use the following normalisations for the input and output pulses

+CO

1 J p ( t ) d t = 1, h,,t(O) = 1 (B-1) T -,

where

In (B-2) PON is the total energy of one pulse divided by T. The following normalized integrals are also used

+oo 11 = T + [, p ( ~ ) . [h,(t - 7)I’d-r.

12 = T . S_, [h,(t - T)]’dT.

ILF = [, h,(t - T)dT.

03-31

03-4) +a

Furthermore, we define +cm

03-5)

The receiver impulse response is given by

where F denotes Fourier transform and Hout(w), Hp(w) are, respectively the Fourier transforms of hout(t) and p ( t ) .

ACKNOWLEDGMENT Useful1 suggestions of Isabel S . Pereira on statistics and

MArio Ferreira on quantum physics are gratefully acknowl- edged. The authors wish also to thank Prof. John O’Reilly and Carmo Medeiros of the University of Wales for helpful discussions.

REFERENCES

[I] B. R. Saltzberg, “Error probabilities for a binary signal perturbed by intersymbol interference and Gaussian noise,” IEEE Trans. Commun., vol. COM-12, pp. 117-120, 1964.

[2] J. Zhou and S. D. Walker, “Application of the Edgeworth series expansion method to optically-preamplified receiver bit-error-ratio calcula- tion,” Optical Amplifers and their Applications Topical MeetingSanta Fe, New Mexico, 1992 Technical Digest Series, vol. 17, pp. 123-126, 1992.

[3] Y. E. Dallal and S. Shamai, “Analytical techniques assessing the performance of optical amplifiers,” Optical Amplifers and their Applications Topical Meet,Santa Fe, New Mexico, 1992 Technical Digest Series, vol.

[4] 0. K. Tonguz, “Impact of spontaneous emission noise on the sensi- tivity of direct-detection lightwave receivers using optical amplifiers,” Electron. Lett,, vol. EL26, pp. 1343-1344, 1990.

[5] G. Saplakoglu and M. Celik, “Output photon number distribution of erbium-doped fiber amplifiers,” Optical Amplijsers and their Applica- tions Topical Meet, Santa Fe, New Mexico, 1992 Technical Digest Series,

[6] S. Personick, “Applications for quantum amplifiers in simple digital optical communication systems,” Bell Syst. Tech. J. , vol. BSTJ-52, pp.

[7] D. Marcuse, “Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers.” IEEE J. Lightwave Technol., vol. LT-8, pp. 1816-1823, 1990.

[8] Y. Yamamoto, “Noise and error rate performance of semiconductor laser amplifiers in PCM-JM optical transmission systems,” IEEE J. Quantum Electron., vol. QE-16, pp. 1073-1081, 1980.

[9] R. Fyath and J. J. O’Reilly, “Comprehensive moment generating function characterisation of optically preamplified receivers,” IEE Proc. J. Optoelectronics, vol. 137, pp. 391-396, 1990.

[lo] P. M. Lane, C. R. Medeiros and J. J. O’Reilly, “Moment based optimization of optically preamplified systems in the presence of jitter,” Optical Amplifers and their Applications Topical Meet,Santa Fe, New Mexico, 1992 Technical Digest Series, vol. 17, pp. 119-122, 1992.

[ 111 E. Desurvire, M. Zimgibl, H. Presby, and D. DiGiovanni, “Characteri- sation and modelling of amplified spontaneous emission in unsaturated erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett., vol.

[12] V. K. Rohatgi, An Introduction to Probability Theory and Mathematical Statistics. New York Wiley, 1976, pp. 310-317.

[ 131 J. OReilly and J. R. F. da Rocha, “Improved error probability evaluation methods for direct detection optical communication systems,” IEEE Trans. Inform. Theory, vol. IT-33, pp. 839-848, 1987.

[ 141 C. Helstrom, “Approximate evaluation of detection probabilities in radar and optical communications,” IEEE Trans. Aerosp. Electron. Syst., vol.

[ 151 A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd Ed. New York McGraw-Hill, pp. 412420, 1991.

[ 161 B. Saleh, Photoelectron Statistics. Berlin: Springer-Verlag, 1978, pp.

[17] R. Smith and S. Personick, “Receiver design for optical communication systems,” in Topics in Applied Physics, vol. 39, Semiconductor Devices for Optical Communications, H. Kressel, Ed. New York Springer- Verlag, 1980, pp. 89-160.

[18] D. Slepian and H. Pollak, “Prolate spheroidal wave functions, Fourier analysis and uncertainty-I,” Bell Syst. Tech. J., vol. BSTJ-40, pp. 43-63, 1961.

[19] S. Personick, “Receiver design for digital fiber optic communication systems I,” Bell Sysr. Tech. J., vol. BSTJ-52, pp. 843-874, 1973.

[20] J. R. F. da Rocha and J. J. O’Reilly, “Linear direct-detection fiber-optic receiver optimization in the presence of intersymbol interference,” IEEE Trans. Commun., vol. COM-34, pp. 365-374, 1986.

17, pp. 127-130, 1992.

vol. 17, pp. 115-118, 1992.

117-133, 1973.

FTL-3, pp. 127-129, 1991.

AES-14, pp. 630-640, 1978.

29-53.

Luis F. B. Ribeiro was born in Santo Tho, Por- tugal, on November 17, 1967. He graduated in Electronics and Telecommunications at the Univer- sity of Aveiro in 1990. Since then he has been a Ph.D. student in Optical Communications at the same university.

His main research interests include EDFA optical preamplifiers, direct detection sytems modelling and non-linear transmission.

232 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 13, NO. 2, FEBRUARY 1995

Jose R. F. Da Rocha (S’83-M’83) received the degree of “Licenciatura” in Electrical Engineering from the University of Lourenqo Marques (now Eduardo Mondlane), Mozambique, in 1973, and the M.Sc. degree in Telecommunication Systems and the Ph.D. in Electrical Engineering from the University of Essex, England, in 1980 and 1983, respectively.

From 1973 to 1977 he worked as an assistant lecturer at the University of Lourenqo Marques and from 1977 to 1979 as a Lecturer at the University

of Aveiro, Portugal. From 1979 to 1983 he carried out post-graduate research work at the University of Essex, England, in the area of optical communications receiver optimization. In 1983 he returned back to the University of Aveiro where he is at present an Associate Professor and coordinates the research activities of the Optical Communications Group. He coordinates the University of Aveiro participation in one national and three European R&D projects. He has published some 90 papers mainly in international journals and conferences and his present research interests include communication systems based on low noise quantum states of light, modulation formats and receiver design for very high capacity optical communication systems based on linear and non-linear (soliton) transmission, and optical networks for mobile radio applications.

Mr. da Rocha is the member (Telecommunications area) of a National Advisory Committee for European Union investment programs. Since 1992 he has been acting as a technical auditor and evaluator of projects included in the European Union RACE (Research for Advanced Communications in Europe) program.

Jog0 L. Pinto (PM) was born in Viseu, Portugal. He received his electrical Engineering degree from the University of Porto, Portugal, in 1975, and his Ph.D. from the Department of Applied Physics of Aveiro University as an assistant lecturer.

In 1977 he became an assistant lecturer and in 1991 an associate professor. He is presently leading a research group on optics and laser technology. For his Ph.D thesis he worked on remote sensing in refractive turbulence. His present research interests include coherent optical systems applied to optical communications.

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Performance evaluation of EDFA preamplified receivers taking into account intersymbol interference