%? 100.0 m. 1 so.o=/ v -120.22

START 0.045000WO CHI SrOP 0.- GHx

Figure 3 Relative phase shift between the inverter and the nonin- verter structures

The use of a dual-gate transistor as part of the auxiliary amplifier of the second loop, allowing electric control of the intermodulation and avoiding the need of a cut-and- try adjustment in attenuation. Dual-gate FETs have the advantage of gain varying, without phase changes The inclusion of a lumped phase inverter (bifilar, ferrite based) and a corresponding dummy one, noninverter, just to ensure the symmetry of the insertion losses and the correct phase relation between the two loop branches. Figure 3 shows the actual phase response of these devices in the range of 0.045-2.6 GHz The use of two capacitors (C, and C,, in Figure 2) in series with the transmission lines, in the second loop, can provide a better electric compensation of the auxil- iary amplifier of this loop, resulting in an impressive performance improvement, especially at low frequen-

DB[S2l] AMP

30.00

0.0000

-30.00 0.1000 0.8OOO PREP-CHZ I .so0

Figure 4 The relative intermodulation improvement. The upper curve is the measured output of the system without feed forward; the difference between that curve and the lower ones is the intermodula- tion reduction. (a) C , nonexistent, C, = 1 nF; (b) C, = 1 nF, C, = 47 p F (c) C, = 220 pF, C , = 47 pF

cies, when compared with previous results [l]. If the capacitors are replaced by varactors, electrical control of the intermodulation reduction shape can be achieved.

Figure 4 shows the responses of an implemented proto- type under several conditions of the compensating capacitors. As shown, it is possible to achieve an intermodulation-level reduction greater than 25 dB over more than 3 octaves. This improvement allows driving the amplifier 8 dB higher, for the same desired linearity (reducing the required backoff).

CONCLUSIONS

Some changes on the usual implementation of feed-forward power amplifiers have been presented, aiming at broadband operation. The simulated and measured performances have shown approximately 25-dB improvement in intermodulation canceling over more than 800-MHz bandwidth. This broad- band response could be improved even further if the circuit were implemented in a monolithic form and if more ad- vanced phase-inversion structures were used.

REFERENCES 1. M. L. Coimbra and R. F. Souza, “Some Improvements on Feed-

forward Amplifiers,” 1994 RF Design / West Conference Proceed- ings, San Jose, CA, Feb. 1994, pp. 233-240.

2. C. C. Hsieh and S . P. Chan, “A Feedforward S-Band MIC Ampli- fier System,’’ IEEE J. Solid-state Circuits, Vol. SSC-11, No. 2, 1976, pp. 271-278.

3. R. G. Meyer et al., “A Wide-Band Feedforward Amplifier,” IEEE J. Solid-state Circuits, Vol. SSC-11, No. 12, 1974, pp. 422-428.

Received 2-21-94

Microwave and Optical Technology Letters, 12/4, 213-215 0 1996 John Wiley & Sons, Inc. CCC 0895-2477/96

IMPACT OF LASER PHASE NOISE=

OPTICAL SYSTEMS USING MULTIPLE OPTICAL AMPLIFIERS

BINARY- AND M-ARY-PSK COHERENT

Fatima N. Farokhrooz Photonics Laboratory Department of Electrical Engineering Indian Institute of Technology Madras 36, India

H. A. Tafti School of Electronics and Communications Engineering Anna University Madras 25, India

J. P. Raina Photonics Laboratory Department of Electrical Engineering Indian Institute of Technology Madras 36, India

KEY TERMS Laser phase noise, amplified spontaneous emission, optical ampl@etx, coherent optical communication, PSK schemes

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 12, No. 4, July 1996 215

ABSTRACT This study evaluates the pe$ormance of binary- and M-ary-PSK coherent optical systems using cascaded optical amplifiers in the presence of noise originating from the detector, receiver, optical amplijiers, and the laser phase fluctuations. Our results on the analysis of these systems indicate that at an amplifier input power of -20 dBm and a system length of 10,000 km, the power penalties incurred due to the laser phase noise at a bit error rate of 10- linewidths of 770.31, 101.86, and 6.37 kHz for binary-PSK four-PSK, and eight-PSK systems, respectively. 0 1996 John Wiley & Sons, Inc.

correspond to 0.57, 0.99, and 3.38 dB at

" = L S Y N C H R O - .-L . NlZER X + j Y

INTRODUCTION The advent of optical amplifiers has made it possible to realize multigigabit-rate transmission systems over several thousands of kilometers. Moreover, it has been shown that the potential of optical amplifiers can be utilized more effi- ciently when coherent detection schemes are used in con- junction with multiple optical amplifiers, as the dominant broadband spontaneous emission noise generated by optical amplifiers can be effectively filtered out outside the i.f. band

PHASE !OUTPUT -DETEC- i

Fiber Optical O(S (Span loss) 1 amolifier 1

[l]. Research and development on the use of coherent optical systems with multiple in-line amplifiers is therefore progress- ing rapidly [2] . The performances of multiple-amplifier-based asynchronous coherent optical systems such as ASK, FSK, and DPSK detection schemes have been analyzed previously [3]. However, synchronous coherent optical systems such as the binary-PSK scheme that results in improved sensitivity has not been studied in terms of important optical amplifier parameters. In this article we analyze the system perfor- mance of binary and M-ary synchronous PSK coherent opti- cal systems with optical amplifiers by taking into account the effects of shot noise, receiver noise, and amplifier-dependent noise. Further, we include the degradation due to the trans- mitter and local-oscillator laser phase noise, which are known to seriously degrade the receiver sensitivity.

SYSTEM DESCRIPTION AND THEORETICAL ANALYSIS Figure 1 shows a typical block schematic of binary and M-ary synchronous PSK coherent detection systems employing mul- tiple optical amplifiers. In the absence of optical amplifiers,

Transmitter) / G (Gain) N5 G=1 P, pout / ~ , i ~ o p u t power)

3

s a ( ( S p a n Lon + Additional loss)

Receiver ved signal power)

I '0 I

L---,---,--,,,,---------~

( b) Figure 1 Block schematic of coherent optical systems using optical amplifiers and (a) binary-PSK (b) M-ary-PSK demodulation

216 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 12, No. 4, July 1996

the system performance is impaired mainly by the shot noise due to the local oscillator (LO).

However, additional noise that is generated by the optical amplifiers should be accounted for when the system perfor- mance is investigated in the presence of multiple in-line amplifiers.

The expression for the bit error rate (BER) of binary-PSK heterodyne systems with an optical amplifier chain is given by

where SNR is the signal-to-noise ratio at the i.f. stage, and is given by

S SNR = . ( 2 )

(NL,,-shot + NL,,-sp + q p - s p + Ncircuit)

S is the signal power given by

where

FYP = Tpa,nspK’(C - 1). 4(e)

The system parameters are defined in Table 1. Further, owing to the advantage of bandwidth reduction in

M-ary-PSK schemes [4], we have analyzed their performance by including effects due to the presence of multiple ampli- fiers. The bit error rate of an M-ary-PSK ( M > 2) modula-

TABLE 1 System Parameter Definitions and Values

tion scheme is given by [5]

where k = log, A4 and the SNR is represented by Eq. (2).

BIT-ERROR RATE ANALYSIS BY ACCOUNTING FOR THE LASER PHASE NOISE In PSK synchronous detection systems, the i.f. signal is syn- chronized with a reference signal, which is generated by a phase control circuit [6]. In the presence of phase noise associated with the wide linewidth of semiconductor lasers [7], it becomes difficult for the phase control circuit to gener- ate a reference signal synchronized precisely with the i.f. signal, thereby resulting in a residual phase error A +(f, 7)

between the i.f. and reference signals, which is assumed to be Gaussian distributed with zero mean and variance a& = 2rr A v T. A v is the total 3-dB linewidth of the transmitter and local-oscillator laser spectrum, and T represents the inherent delay of the phase control circuit. The bit error rate in this case becomes a function of shot noise, receiver noise, noise due to the optical amplifiers, and laser phase noise. Hence the signal power term in Eq. (3) can be represented as

S = 2R2PsPL cos2(A+), (6 )

and the expression for the bit error rate of a binary-PSK scheme is modified as

where p(A+) is the probability distribution of A+. For M-ary-PSK modulation, the bit-error-rate characteris-

tics that depend on the amplifier-related parameters, and the

Transmitter source power Fiber loss Total fiber loss between two successive amplifiers Spacing between two successive amplifiers Gain of each amplifier Bit rate Electrical bandwidth

Optical bandwidth

Local oscillator power Noise figure of each amplifier Wavelength of signal Equivalent input circuit noise current Amplifier input power Loss between the last amplifier and optical receiver without (Y,

Received signal power

Pout = 0 dBm aF = 0.2 dB/km

L = 100 !un (from assumption as . G = 11 G = 20dB B = 1 Gb/s Be = B / 2 homodyne receiver

L, = 50 nm in wavelength domain B, is optical bandwidth in frequency domain PL = 10dBm N F = 5 d B A = 1.536 Krn i, = lOpA/&

= exp(-a,.L)

= B heterodyne receiver

PO

PS (Y

Spontaneous emission factor Number of amplifier stages Detector responsivity R = e g / h v

Electronic charge e Photon energy h u Frequency of signal V

Detector quantum efficiency g = 1

MICROWAVE AND OPTICAL TECHNOLOGY LElTERS / Vol. 12, No. 4, July 1996 217

laser phase noise can be studied by modifying Eq. (5 ) as

Equations (7) and (8) are used to study the performance of binary- and M-ary-PSK schemes as functions of the optical amplifier parameters and of the variance of laser phase noise. We have assumed in the analysis that the 3-dB laser linewidth is unaffected by the phase noise of optical amplifiers [S].

RESULTS AND DISCUSSION A. Results in the Absence of Laser Phase Noise. The accumu- lation of amplified spontaneous emission imposes a restric- tion on the maximum number of amplifier stages and hence on the total system length. The power penalty incurred due to the increase in system length is calculated by computing the additional signal power required to maintain the same bit error rate as in systems without amplifiers. The power penalty at BER = lo-' is plotted against the system length in Fig- ure 2(a) for binary- and M-ary-PSK ( M = 4,8,16) schemes by assuming that the amplifier input power is fixed at -20

4r

9 LU a2 "I BER =

dBm. It is seen that for a system length of 10,000 km, the penalty is close to 0.3 dB for binary- and four-PSK schemes, and is increased to 0.7 dB for an eight-PSK signaling scheme. Although the system is degraded for large M in M-ary PSK systems, the bandwidth can in turn be utilized more effi- ciently, particularly in the case of four-PSK, as the bandwidth is improved for the same amount of power penalty as in a binary-PSK signaling schemes. The magnitude of the input power to the amplifier also influences the system behavior, and is used to estimate the amount of improvement in the system dynamic range [3]. Figure 2(b) shows the power penalty plotted against the amplifier input power for various PSK systems. It is seen that for a system length of 10,000 km, the power penalty at BER = lo-' exceeds 1 dB when the ampli- fier input powers are reduced below - 24.5, - 20, and - 16 dBm for binary, 4-, 8-, and 16-PSK systems, respectively. We have compared the performance of PSK systems with the DPSK scheme (which was the best among the asynchronous ASK, FSK, and DPSK systems [3]) at various bit rates in Table 2 in terms of achievable system lengths and amplifier input powers for a 1-dB penalty at BER = lop9.

B. Results when Laser Phase Noise is Present. The influence of laser phase noise of the transmitter source and local oscilla- tor is decisive for the ultimate system performance [9], partic- ularly when semiconductor lasers are used. The plots for the bit error rate against the received power for the ideal case (zero laser linewidth) using binary-PSK schemes are shown in Figure 3(a) for various values of amplifier input powers, and the bit-error-rate characteristics accounting for the amplifier and laser phase noise at uA4 = 0.22 are shown in Figure 3(b). Comparison of Figures 3(a) and 3(b) shows that a bit error rate as low as is achievable in the absence of amplifiers and laser phase noise, whereas a bit-error-rate floor is ob- served at lo-'' when phase noise is included in the absence of amplifiers. The bit-error-rate performance is seen to dete- riorate further because of the combined action of amplifier and laser phase noise. For example, in the absence of phase noise, an error-rate floor is observed at lo-'' for an amplifier input power of -31 dBm, whereas in the presence of laser phase noise (uA4 = 0.22), the same value of amplifier input power results in an error-rate floor at lo-*. Results of power penalty as a function of system length and amplifier input

8-PSK !,I, a Binary 4-PSK PSK

0 0 2000 4000 6000 8000 10000 12000

SYSTEM LENGTH (km) (a)

TABLE 2 Comparison of PSK and DPSK Systems in Terms of Bit Rate, (a) System Length, and (b) Amplifier Input Power at I-dB Penalty and BER =

>. I-

Y 82 "t 0 -35

binary PSK I I / , - P S K 8-PSK

-16PSK

AMPLIFIER INPUT POWER (darn) (b)

Figure 2 Power penalty versus (a) system length (b) amplifier input power for binary- and M-ary-PSK systems in the absence of laser phase noise

System System System Modulation length (km) length (km) length (km)

at 1 Gb/s at 5 Gb/s at 10 Gb/s (a) Formats ~ ~

DPSK 25,500 5,100 2,550 Binary PSK 28,370 5,670 2,835 4 PSK 28,370 5,670 2,835

M > 2 {8PSK 12,800 2,560 1,280 16 PSk 4,600 920 460

Modulation Po (dBm) Po (dBm) Po (dBm) Formats at 1 Gb/s at 5 Gb/s at 10 Gb/s (b)

DPSK - 24.10 - 17.12 - 14.12 Binary PSK - 24.58 - 17.60 - 14.60

- 24.58 - 17.60 - 14.60 M > 2 8PSK -21.17 - 14.10 -11.10 1 :6';1K - 16.68 - 9.68 - 6.68

218 MICROWAVE AND OPTICAL TECHNOLOGY LETERS / Vol. 12, No. 4, July 1996

RECEIVED POWER (dBm) (a)

lo-’

E a a

-70 -65 -60 -55 -50 -45 -40

lo-’

10”

0 lo4 f!Z 10-7

Z 10-9

10-’O 10-l1

5 lo-‘

a

w

-70 -65 -60 -55 -50 -45 -4 RECEIVED POWER (dRrn)

(b)

Figure 3 BER performance of a binary-PSK system (a) without phase noise, and (b) with phase noise at uA+ = 0.22. Dashes, refer- ence curve when amplifiers are absent

power are shown in Figures 4(a) and 4(b), respectively, for different uA4. A negligible penalty is incurred at uA4 = 0.18, whereas the dynamic range (with reference to absence of phase noise) is reduced by 5 dB at 1-dB power penalty and f f A 4 = 0.24. In Figures 5 and 6, we have compared the power-penalty curves for the four- and eight-PSK modulation schemes by including the amplifier and laser phase noise. Although binary- and four-PSK systems behaved similarly in the absence of phase noise, four-PSK schemes are seen to be

a nz W 3 0.5 8

0 0 2000 4000 6000 8000 10000 12000

SYSTEM LENGTH (km) (a)

“:t 0 - 40

-9

I I -35 -30 -25 -20 -15 -10 -5 0

AMPLIFIED INPUT POWER (dBm) (b)

Figure 4 Variation of power penalty with (a) system length, (b) amplifier input power for the binary PSK scheme

more sensitive to phase noise than their binary counterpart. Further in binary- and four-PSK systems, the penalty rises gradually with system length, whereas for the same amount of laser phase noise, the choice of amplifier input power be- comes critical because of the severe nonlinearity seen in the power penalty plots [Figures 4(b) and 5(b)]. Eight-PSK sys- tems have been shown to be seriously degraded for uA4 as low as 0.02, with a penalty close to 1 dB at Po = -15 dBm. The power penalties incurred due to phase noise at various

TABLE 3 Limitations of Phase Noise on Input Power to Amplifier to Maintainlng a BER = 10 - Using PSK Systems

Power penalty (dB) at BER = Modulation 3-dB Linewidth (Av) Schemes of Source and LO Lasers Po = - 15 dBm Po = - 20 dBm Po = -25dBm

0 0.10 0.32 1.02 Binary PSK 770.31 kHz 0.17 0.57 2.13

9 16.73 kHz 0.35 1.20 3.36 0 0.10 0.32 1.02

Four PSK 101.86 kHz 0.29 0.99 4.49

Eight PSK 6.37 kHz 0.81 3.38 W

192.58 kHz 0.60 2.26 m

0 0.50 0.91 3.22

39.79 kHz 1.79 m W

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 12, No. 4, July 1996 219

- m 2!

!i a a

r

z w 2

SYSTEM LENGTH (km) (a)

I I I I

r I !i I a 6 - l z w \

\ a

w

2 2 -phase noise \

0 I I L

-40 -35 -30 -25 -20 -15 -10 -5 0 AMPLIFIER INPUT POWER (dBm)

(bi

Figure 5 Power penalty of four-PSK systems as a function of phase noise and (a) system length, (b) amplifier input power

values of amplifier input power and laser linewidths (the 3-dB linewidths are computed from a& = 25- A v T by assum- ing T = at a bit rate of 1 Gb/s [6]) with binary- and M-ary-PSK systems are compared in Table 3.

CONCLUSIONS

Quantitative analyses of optical-amplifier-based synchronous PSK systems have been presented by including the effect of phase noise in transmitter source and local-oscillator lasers. Limitations of multiple amplifiers as well as laser phase noise on the maximum achievable transmission span and the ampli- fier input power were estimated and compared for the vari- ous schemes in terms of bit error rate and power penalty. The relative performance of synchronous FSK and ASK modula- tion schemes are currently being investigated.

REFERENCES 1. M. C. Brain, M. J. Creaner, R. C. Steele, N. G. Walker, G. R.

Walker, J. Mellis, S. Al-Chalabi, J. Davidson, M. Rutherford, and I. C. Sturgess, “Progress towards the Field Deployment of Coher- ent Optical Fiber Systems,” J. Lightwaue Technol., Vol. 8, March

2. E. Desuvire, Erbium-Doped Fiber Amplifiers, Wiley, New York, 1990, pp. 423-437.

1994.

a z W LL

LT

0 a Y

t

I

$6 = 0.05 J /

SYSTEM LENGTH (km) (ai

10 I BER = 10“

I I I \ \

6 -

4 - \

2 -absence o f laser‘, phase noise

0 I 1

-35 -30 -25 -20 -15 -10 -5 0 AMPLIFIER INPUT POWER (dBrn)

(b)

Figure 6 Power penalty of eight-PSK systems as a function of phase noise and (a) system length, (b) amplifier input power

3. S. Ryu, S. Yamamoto, H. Taga, N. Edagawa, Y. Yoshida, and H. Wakabayashi “Long-Haul Coherent Optical Fiber Communi- cation Systems Using Optical Amplifiers,” J. Lightwave Technol., Vol. LT-9, Feb. 1991, pp. 251-259.

4. F. Derr, “Optical QPSK Homodyne Transmission of 280 Mb/s,” Electron. Lett., Vol. 26, June 1990, pp. 401-403.

5 . J. C. Proakis, Digital Communications, McGraw-Hill, New York, 1989, Chapter 4.

6. G. Nicholson, “Optical Source Linewidth Criteria for Heterodyne Communication Systems with PSK Modulation,” Opt. Quantum Electron., Vol. 17, June 1985, pp. 399-410.

7. D. J. M. Sabido, M. Tabara, T. K. Fong, R. F. Kalman, and L. G. Kazovsky, “Experimental Linewidth-Insensitive Coherent Analog Optical Link,” J. Lightwuue Technol., Nov. 1994, pp. 1976-1985.

8. G. J. Cowle, P. R. Morkel, R. I. Laming, and D. N. Payne, “Spectral Broadening due to Fibre Amplifier Phase Noise,” Elec- tron. Lett., Vol. 26, March 1990, pp. 424-425.

9. R. Gangopadhyay and S. P. Majumder, “Impact of Laser Linewidth on Performance of Heterodyne Single Filter FSK System with Optical Preamplifier,” Electron. Lett., Vol. 27, Oct. 1991, pp. 1927-1929.

Received 2-20-96

Microwave and Optical Technology Letters, 12/4, 215-220 0 1996 John Wiley & Sons, Inc. CCC 0895-2477/96

220 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 12, No. 4, July 1996