An evaluation of the performance of a coherent optical receiver for binary PSK (phase-shift keying) is carried out. Both AM and FM noise due to transmitter and local oscillator semiconductor lasers have been taken into account. The nonlinear dependence between the phase noise variance and the laser linewidth is considered. A heterodyne receiver is studied in terms of its output SNR (signal-to-noise ratio), taking into account AM noise and both thermal and shot noises. The required SNR to achieve a BER (bit error rate) of 10-9 is studied, considering the FM noise in both semiconductor lasers. The importance of taking into account the effects of AM and FM noise in the investigation of the receiver sensitivity in a binary PSK coherent optical system is demonstrated. An accurate evaluation of the penalty in the sensitivity due to the laser quantum noise is obtained. It is shown that the AM noise due to the laser working as local oscillator degrades the expected SNRPeer ReviewedPostprint (published version

Junyent Giralt, Gabriel

Ruiz Boqué, Sílvia

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LASER NOISE IMPACT IN THE DESIGN OF AN HETERODYNE OPTICAL PSK RECEIVER S.Ruiz-Bow&, J.Vall-llosera, J.A.Navarro and G.Junyent Signal Theory and Communications Department E. T. S. Ingenieros de Telecomunicaci6n Barcelona. Spurn SUMMARY In this paper an evaluation of the perfor- mance of a coherent optical receiver for binary PSK has been carried out. Both the AM and FM noise due to transmitter and LO semiconductor lasers have been taken into account. Also the nonlinear dependence bet- ween the phase noise variance and the laser linewidth is considered. 1. INTRODUCTION Coherent lightwave transmission systems show great advantages compared to intensity modulation and direct detection systems. This is due, in the first place, to an im- provement in the receiver sensitivity because of the modulation techniques used. Moreover, the use of local oscillator (LO) high power levels reduces the thermal noise and the photodetector dark current noise contributions. In this case the signal to noise ratio improves to the theoretical shot noise limit (assuming an ideal LO) allowing the design of larger links 111. Nevertheless, SC lasers generate quantum noise giving place to AM and FM fluctua- tions. It is necessary to evaluate the degradation introduced by a non ideal LO and transmitter as is done in this work. The paper is structured as follows: I n  Part 1 there is a short explanation of the different physical phenomena that gene- rate the laser quantum noise. A charac- terization of the electrical field emitted is obtained through the study of the power spectral densities of the AM and FM noise. In Part 2 an heterodyne receiver is studied in terms of its output SNR taking into account AM noise and both thermal and shot noises. An optimum value for the LO power injected on the fiber coupler is found. In Part 3 the required SNR to achieve a BER of is studied considering the FM noise in both SC lasers. The use of general expressions allows the comparation with the results obtained when considering, as a simplified model, a linear relation between phase noise variance and linewidth. As far as we know this study has been carried out only for ASK transmitted signals. Finally. in Part 4, there is a summary of the main conclusions obtained in this work. 2. CHARACTERIZATION OF THE AM AND FM NOISE The electric field in a laser cavity can be studied as a plane wave propagating in a dielectric medium between two planar mir- rors separated a distance L Taking into account the active medium and the fluc- tuations in the refraction index due to the spontaneous emission, it  is possible to de- termine the rate equations for the inten- sity or photon number, I(t), the phase, @(t), and the carrier density, N(t) In order to evaluate the fluctuations of the former parameters it is necessary to solve the rate equations for small signal analysis and add the Langevin fluctuation terms [31 By so doing and calculating the autocorrelation and the Fourier transform of AI(t) and A@(t) (fluctuations around the stationary values Io and @ , I ,  the power spectral densities of the AM and FM noises (SAI(f) and SA@(f) respectively) are ob- tained [41 as a function of the operating conditions and physical parameters of the laser This characterization allows the electric field to be expressed as where - Eo is the stationary amplitude and e(t) a random variable wlth zero mean value which represents the fluctuations around Eo asso- ciated to AI(t) Taking into account that [E +e(t) I is proportional to [Io+AI (t) l‘”, we can express the power spectral density of the electric field amplitude fluctua; tions as Se(f)= RIN(f)Et/4, being SAI(f)/Io = RIN(f (relative intensity noise) . - A@ (t) is a random variable of zero mean value which stand-: for the fluctuations in the instantaneous signal frequency 3 RECEIVER SENSITIVITY: AM NOISE INFLUENCE In optical svstems with heterodyne detec- tion, fiber a LO A f  = f l  the electric field coming from the is combined with the one coming from whose center frequency is shifted from the received signal carrier. If 573 both the received and LO signals were etable in amplitude and frequency, only the shot noise associated to the photo- detection process would be present. In that case, the SNR would attain a theoretical maximum known as the quantum limit. Never- theless, the performance is degraded when we take into account the AM and FM noises. The electric field coming from the fiber and from the LO for a PSK signal can be expressed in the following way: xS(t) = Es cos(wst + #s + A#s(t)) E, and Eo are the field amplitudes in the stationary state and +s is the modulation. e(t) and A+,(t) are terms associated to the AM and Fm LO noises, respectively, and &,(t) is the FM noise due to xs. In the analysis we assume that the amplitude fluc- tuations of xs are negligible. The signal incident on the photodetector is x(t) - p"' xs(t) + K1/' (l-p)"'xo(t) (3) In this expression we have considered the power transmission factor of the combiner. p ,  as well as the losses in the LO emitted signal, K. The electrical current generated by the photodiode is proportional to x (t) and can be expressed as: where we have eliminated the terms outside the photodiode bandpass and the ones at zero frequency than can be filtered. In order to evaluate the thermal noise due to the receiver we have used the same model as in [51 and so. the voltage at the equalizer output is: vo(t) = d"i(t)*hi(t) + vth(t) (7) where h.(t) stands for the impulsional res- ponse of the convolution of the amplifier plus photodiode frontend, the bandpass fil- ter and equalizer responses. If we assume that the receiver preserve the input pulse shape : Z 0 outside the bandpass -BIF/2 I f - fI 5 BIF/2 (9 )  lHi(f) I * where BIF is the IF bandwidth. In the following we will calculate each noise contribution. With a development si- milar to the one described in [ 5 1 ,  and using the 6&me parameters, we have for the shot and thermal noises, respectively: - 2G ZZST (11) The expression for the AM noise power is: where SAM(f) is the power spectral density of the current fluctuations associated to the LO AM noise. This density is calculated as the Fourier transform of: where Re(') is the autocorrelation of the amplitude fluctuations. The relationship between Se(f) and the power spectral density of the photon number fluctuation has been given in the previous part, so PAM = Finally we have: ps SNR- E (15) R' (1-p) P, FI where P, = KPo Starting from (15) we can obtain the mini- mum detectable power for a given value of the SNR. It is then obvious the existance of an optimum value for the LO injected Power.PLopt, which can be expressed as: (16) 4 BER ChLCULATION: FM NOISE INFLUENCE We are now going to determine the degra- dation introduced by the FM noise in the system bit error rate (BER). The output receiver voltage (7) can be rewritten as: v(t) = A cos(wIt + #s + +(t)) + n(t) (17) where n(t) stands for all the considered noise terms and A = ZG'/2R Jp(l-p)K EoEs. We assume that n(t) is a gaussian noise of zero mean value and variance given by the sum of the different noise contributions, this is: shot, thermal and AM noises. 574 In a PSK transmission system a phase locked loop (PLL) is required. The phase shift at its output will be: A+(t) = +(t)-@(t<) ; T = PLL delay (18) The IF signal is demodulated, translated to baseband and sampled giving: x = A/2 cos(A+) + nif (19) where nif = n(t) cos(wIt) ; 0:. = ai/4 if The received signal has phase noise and an additive amplitude noise, so x can be ex- pressed as the sum of two random variables, w and n, being w = A/2 cos(A+). Assuming that the phase noise can be characterized by a gaussian random variable we can derive the PDF (probability density function) of w. We can then express the BER of a binary PSK system with heterodyne detection as [61  : - -  -OD - O D  where h(x) = - 4 SNRcos(fluA+ x) and SNR = A2/(2u2) which agrees with expression (15). aA+ Fig.1 shows the SNR as a function of taking the BER as parameter. We can ob- serve that for small phase variance (high power emitted by the laser) the BER depends critically on the SNR. However, a high pha- se variance can be the limiting factor to achieve a given BER, producing a dramatic drop of sensitivity. For obtaining the receiver sensitivity as a function of Po it is necessary to determine the expression for aA+ ( T )  . Assuming that the phase noise is a random variable with zero mean value, the variance is: After some calculation we obtain (Fig.11) :re/2r Ra2 cos36-e cos (n0r-36) u;+=2rrAvr + 210yecos6 (22) where AV is the laser linewidth, R the spontaneous emission rate, ye is the damping coefficient, a the quotient between real and imaginary variation of the refraction index due to spontaneous emission, no is the relaxation oscillation frequency and cos6 = no/wR [31. cases has been represented for a fixed bit rate (vt = 560 Mbit/s) and different LO emitted powers Finally in Fi9.V the sensi- tivity considering the general expression for uA4(7) is given for different bit rate. 5 CONCLUSION It has been shown the importance of taking into account the effects of the AM and FM noise in order to study the receiver sensi- tivity in a binary PSK coherent optical system. An accurate evaluation of the penalty in the sensitivity due to the laser quantum noise is obtained. We show that the AM noise due to the laser working as local oscillator degrades the expected SNR. The sensitivity of the recei- ver can be optimized by choosing an appro- priate LO injection level on the combiner. The BER calculation carried out taking into account FM noise and the expression for the SNR obtained in Part 2, allows the determi- nation of the minimum signal power neces- sary at the receiver input to obtain a de- sired error probability. The sensitivity values shown in the figures for low LO emitted power are too low to be of inte- rest This is due to the fact that the lasers used for the computer simulation have a high spectral linewidth and it increases when P is decreased. REFERENCES E.E.Bash,T.G.Brown. "Introduction to coherent optical fiber transmission", IEEE Comm. Magazine. Vo1.23, pp.23-30. 1985. C.H.Henry."Theory of the phase noise and power spectrum of a single mode injection laser", IEEE JQE, Vol.19, pp.1391-1397, 1983. P.Spano. S.Piazzolla, M.Tamburrini. "Phase noise in SC lasers: A theoretical approach", IEEE JQE, Y .Yamamoto. "Recevier Performance Evaluation of Various Digital Optical Modulation-Demodulation Systems in the 0.5-10 wrn Wavelength Region." IEEE JQE. Vol.QE-16, pp.1251-1259, November 1980. J.Franz. "Evaluation of the probability density Function and Bit Error Rate in Coherent Optical Transmission System including Lase Phase Noise and Additive Gaussian Noise", Journal of Optical V01.15. pp.1195-1199, 1983. C o m m . ,  V01.6, No.2, ~p.51-57, 1985. Most of the authors take into account only the first term in the expression above given and neglect the term of damping oscillations. This simplifies the analysis but implies a considerable error, specially at low LO powers and high bit rate. This degradation is showed in Fig.111 where the quotient between the exact formula and the linear aproximation has been represented. Also in Fig.IV the sensitivity for both 575 0 3  0 L5 0 1  0 1 5  0 1  0 05 a 8 0  15 2 0  2 5  30 3 5  S N R ' d B )  Figure I Phase noise dev.as function of SNR for different BER (r = O.l/vt) Figure I I Phase noise variance as function of the bit rate for different LO emitted powers. I '  1 (,+3m -10 -28 -3 0 -40 F ' r g u r e  I V  Sensitivity for both, general and linear aproximation, as a function of the LO injected power.(bit rate = 560 Mbit/s) and considering AM and FM noises. - 2 5  -35 -45  -55  -30 -25 -20 - 1 5  -10  -5 0 5 ie pLctam) Frgure V Sensitivity in the general case as function of PL and for different bit rate. (AM and FM noise degrada- tion are included) Relation between the general and linear expressions for the phase nose variance as function of the bit rate for different LO emitted powers. 5 76 

Laser noise impact in the design of an heterodyne optical PSK receiver

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