10.5. SENSITIVITY DEGRADATION 497 Table 10.2 Sensitivity of asynchronous receivers Modulation Format Bit-Error Rate N p N p ASK heterodyne 1 2 exp( ηn p /4) 80 40 FSK heterodyne 1 2 exp( ηn p /2) 40 40 DPSK heterodyne 1 2 exp( ηn p) 20 20 Direct detection 1 2 exp( ηn p ) 20 10 10.4.6 Asynchronous DPSK Receivers As mentioned in Section 10.2.2, asynchronous demodulation cannot be used for PSK signals. A variant of PSK, known as DPSK, can be demodulated by using an asynchronous DPSK receiver [see Fig. 10.6(b)]. The filtered current is divided into two parts, and one part is delayed by exactly one bit period. The product of two currents contains information about the phase difference between the two neighboring bits and is used by the decision current to determine the bit pattern. The BER calculation is more complicated for the DPSK case because the signal is formed by the product of two currents. The final result is, however, quite simple and is given by [11] BER = 1 2 exp( ηn p). (10.4.26) It can be obtained from the FSK result, Eq. (10.4.24), by using a simple argument which shows that the demodulated DPSK signal corresponds to the FSK case if we replace I 1 by 2I 1 and σ 2 by 2σ 2 [13]. Figure 10.7 shows the BER by a dashed line (the curve marked DPSK). For η = 1, a BER of 10 9 is obtained for N p = 20. Thus, a DPSK receiver is more sensitive by 3 db compared with both ASK and FSK receivers. Table 10.2 lists the BER and the receiver sensitivity for the three modulation schemes used with asynchronous demodulation. The quantum limit of a direct-detection receiver is also listed for comparison. The sensitivity of an asynchronous DPSK receiver is only 3 db away from this quantum limit. 10.5 Sensitivity Degradation The sensitivity analysis of the preceding section assumes ideal operating conditions for a coherent lightwave system with perfect components. Many physical mechanisms degrade the receiver sensitivity in practical coherent systems; among them are phase noise, intensity noise, polarization mismatch, and fiber dispersion. In this section we discuss the sensitivity-degradation mechanisms and the techniques used to improve the performance with a proper receiver design.
498 CHAPTER 10. COHERENT LIGHTWAVE SYSTEMS 10.5.1 Phase Noise An important source of sensitivity degradation in coherent lightwave systems is the phase noise associated with the transmitter laser and the local oscillator. The reason can be understood from Eqs. (10.1.5) and (10.1.7), which show the current generated at the photodetector for homodyne and heterodyne receivers, respectively. In both cases, phase fluctuations lead to current fluctuations and degrade the SNR. Both the signal phase φ s and the local-oscillator phase φ LO should remain relatively stable to avoid the sensitivity degradation. A measure of the duration over which the laser phase remains relatively stable is provided by the coherence time. As the coherence time is inversely related to the laser linewidth ν, it is common to use the linewidth-tobit rate ratio, ν/b, to characterize the effects of phase noise on the performance of coherent lightwave systems. Since both φ s and φ LO fluctuate independently, ν is actually the sum of the linewidths ν T and ν LO associated with the transmitter and the local oscillator, respectively. The quantity ν = ν T + ν LO is often called the IF linewidth. Considerable attention has been paid to calculate the BER in the presence of phase noise and to estimate the dependence of the power penalty on the ratio ν/b [41] [55]. The tolerable value of ν/b for which the power penalty remains below 1 db depends on the modulation format as well as on the demodulation technique. In general, the linewidth requirements are most stringent for homodyne receivers. Although the tolerable linewidth depends to some extent on the design of phase-locked loop, typically ν/b should be < 5 10 4 to realize a power penalty of less than 1 db [43]. The requirement becomes ν/b < 1 10 4 if the penalty is to be kept below 0.5 db [44]. The linewidth requirements are relaxed considerably for heterodyne receivers, especially in the case of asynchronous demodulation with the ASK or FSK modulation format. For synchronous heterodyne receivers ν/b < 5 10 3 is required [46]. In contrast, ν/b can exceed 0.1 for asynchronous ASK and FSK receivers [49] [52]. The reason is related to the fact that such receivers use an envelope detector (see Fig. 10.5) that throws away the phase information. The effect of phase fluctuations is mainly to broaden the signal bandwidth. The signal can be recovered by increasing the bandwidth of the bandpass filter (BPF). In principle, any linewidth can be tolerated if the BPF bandwidth is suitably increased. However, a penalty must be paid since receiver noise increases with an increase in the BPF bandwidth. Figure 10.8 shows how the receiver sensitivity (expressed in average number of photons/bit, N p ) degrades with ν/b for the ASK and FSK formats. The BER calculation is rather cumbersome and requires numerical simulations [51]. Approximate methods have been developed to provide the analytic results accurate to within 1 db [52]. The DPSK format requires narrower linewidths compared with the ASK and FSK formats when asynchronous demodulation based on the delay scheme [see Fig. 10.6(b)] is used. The reason is that information is contained in the phase difference between the two neighboring bits, and the phase should remain stable at least over the duration of two bits. Theoretical estimates show that generally ν/b should be less than 1% to operate with a < 1 db power penalty [43]. For a 1-Gb/s bit rate, the required linewidth is 1 MHz but becomes < 1 MHz at lower bit rates. The design of coherent lightwave systems requires semiconductor lasers that oper-
10.5. SENSITIVITY DEGRADATION 499 Figure 10.8: Receiver sensitivity N p versus ν/b for asynchronous ASK and FSK heterodyne receivers. The dashed line shows the sensitivity degradation for a synchronous PSK heterodyne receiver. (After Ref. [49]; c 1988 IEEE; reprinted with permission.) ate in a single longitudinal mode with a narrow linewidth and whose wavelength can be tuned (at least over a few nanometers) to match the carrier frequency ω 0 and the local-oscillator frequency ω LO either exactly (homodyne detection) or to the required intermediate frequency. Multisection DFB lasers have been developed to meet these requirements (see Section 3.4.3). Narrow linewidth can also be obtained using a MQW design for the active region of a single-section DFB laser. Values as small as 0.1 MHz have been realized using strained MQW lasers [56]. An alternative approach solves the phase-noise problem by designing special receivers known as phase-diversity receivers [57] [61]. Such receivers use two or more photodetectors whose outputs are combined to produce a signal that is independent of the phase difference φ IF = φ s φ LO. The technique works quite well for ASK, FSK, and DPSK formats. Figure 10.9 shows schematically a multiport phase-diversity receiver. An optical component known as an optical hybrid combines the signal and local-oscillator inputs and provides its output through several ports with appropriate phase shifts introduced into different branches. The output from each port is processed electronically and combined to provide a current that is independent of φ IF. In the case of a two-port homodyne receiver, the two output branches have a relative phase shift of 90, so that the currents in the two branches vary as I p cosφ IF and I p sinφ IF. When the two currents are squared and added, the signal becomes independent of φ IF. In the case of three-port receivers, the three branches have relative phase shifts of 0, 120, and 240. Again, when the currents are added and squared, the signal becomes independent of φ IF. The preceding concept can be extended to design receivers with four or more branches. However, the receiver design becomes increasingly complex as more branches
500 CHAPTER 10. COHERENT LIGHTWAVE SYSTEMS Figure 10.9: Schematic of a multiport phase-diversity receiver. are added. Moreover, high-power local oscillators are needed to supply enough power to each branch. For these reasons, most phase-diversity receivers use two or three ports. Several system experiments have shown that the linewidth can approach the bit rate without introducing a significant power penalty even for homodyne receivers [58] [61]. Numerical simulations of phase-diversity receivers show that the noise is far from being Gaussian [62]. In general, the BER is affected not only by the laser linewidth but also by other factors, such as the the BPF bandwidth. 10.5.2 Intensity Noise The effect of intensity noise on the performance of direct-detection receivers was discussed in Section 4.6.2 and found to be negligible in most cases of practical interest. This is not the case for coherent receivers [63] [67]. To understand why intensity noise plays such an important role in coherent receivers, we follow the analysis of Section 4.6.2 and write the current variance as σ 2 = σ 2 s + σ 2 T + σ 2 I, (10.5.1) where σ I = RP LO r I and r I is related to the relative intensity noise (RIN) of the local oscillator as defined in Eq. (4.6.7). If the RIN spectrum is flat up to the receiver bandwidth f, r 2 I can be approximated by 2(RIN) f. The SNR is obtained by using Eq. (10.5.1) in Eq. (10.1.11) and is given by 2R 2 P s P LO SNR = 2q(RP LO + I d ) f + σt 2 + 2R2 PLO 2. (10.5.2) (RIN) f The local-oscillator power P LO should be large enough to satisfy Eq. (10.1.12) if the receiver were to operate in the shot-noise limit. However, an increase in P LO increases the contribution of intensity noise quadratically as seen from Eq. (10.5.2). If the intensity-noise contribution becomes comparable to shot noise, the SNR would decrease unless the signal power P s is increased to offset the increase in receiver noise. This increase in P s is just the power penalty δ I resulting from the local-oscillator intensity noise. If we neglect I d and σt 2 in Eq. (10.5.2) for a receiver designed to operate in the shot-noise limit, the power penalty (in db) is given by the simple expression δ I = 10log 10 [1 +(η/hν)p LO (RIN)]. (10.5.3)
10.5. SENSITIVITY DEGRADATION 501 Figure 10.10: Power penalty versus RIN for several values of the local-oscillator power. Figure 10.10 shows δ I as a function of RIN for several values of P LO using η = 0.8 and hν = 0.8 ev for 1.55-µm coherent receivers. The power penalty exceeds 2 db when P LO = 1 mw even for a local oscillator with a RIN of 160 db/hz, a value difficult to realize for DFB semiconductor lasers. For a local oscillator with a RIN of 150 db/hz, P LO should be less than 0.1 mw to keep the power penalty below 2 db. The power penalty can be made negligible at a RIN of 150 db/hz if only 10 µw of local-oscillator power is used. However, Eq. (10.1.13) is unlikely to be satisfied for such small values of P LO, and receiver performance would be limited by thermal noise. Sensitivity degradation from local-oscillator intensity noise was observed in 1987 in a two-port ASK homodyne receiver [63]. The power penalty is reduced for threeport receivers but intensity noise remains a limiting factor for P LO > 0.1 mw [61]. It should be stressed that the derivation of Eq. (10.5.3) is based on the assumption that the receiver noise is Gaussian. A numerical approach is necessary for a more accurate analysis of the intensity noise [65] [67]. A solution to the intensity-noise problem is offered by the balanced coherent receiver [68] made with two photodetectors [69] [71]. Figure 10.11 shows the receiver design schematically. A 3-dB fiber coupler mixes the optical signal with the local oscillator and splits the combined optical signal into two equal parts with a 90 relative phase shift. The operation of a balanced receiver can be understood by considering the photocurrents I + and I generated in each branch. Using the transfer matrix of a 3-dB coupler, the currents I + and I are given by where φ IF = φ s φ LO + π/2. I + = 1 2 R(P s + P LO )+R P s P LO cos(ω IF t + φ IF ), (10.5.4) I = 1 2 R(P s + P LO ) R P s P LO cos(ω IF t + φ IF ), (10.5.5)
502 CHAPTER 10. COHERENT LIGHTWAVE SYSTEMS Figure 10.11: Schematic of a two-port balanced coherent receiver. The subtraction of the two currents provides the heterodyne signal. The dc term is eliminated completely during the subtraction process when the two branches are balanced in such a way that each branch receives equal signal and local-oscillator powers. More importantly, the intensity noise associated with the dc term is also eliminated during the subtraction process. The reason is related to the fact that the same local oscillator provides power to each branch. As a result, intensity fluctuations in the two branches are perfectly correlated and cancel out during subtraction of the photocurrents I + and I. It should be noted that intensity fluctuations associated with the ac term are not canceled even in a balanced receiver. However, their impact is less severe on the system performance because of the square-root dependence of the ac term on the local-oscillator power. Balanced receivers are commonly used while designing a coherent lightwave system because of the two advantages offered by them. First, the intensity-noise problem is nearly eliminated. Second, all of the signal and local-oscillator power is used effectively. A single-port receiver such as that shown in Fig. 10.1 rejects half of the signal power P s (and half of P LO ) during the mixing process. This power loss is equivalent to a 3-dB power penalty. Balanced receivers use all of the signal power and avoid this power penalty. At the same time, all of the local-oscillator power is used by the balanced receiver, making it easier to operate in the shot-noise limit. 10.5.3 Polarization Mismatch The polarization state of the received optical signal plays no role in direct-detection receivers simply because the photocurrent generated in such receivers depends only on the number of incident photons. This is not the case for coherent receivers, whose operation requires matching the state of polarization of the local oscillator to that of the signal received. The polarization-matching requirement can be understood from the analysis of Section 10.1, where the use of scalar fields E s and E LO implicitly assumed the same polarization state for the two optical fields. If ê s and ê LO represent the unit vectors along the direction of polarization of E s and E LO, respectively, the interference term in Eq. (10.1.3) contains an additional factor cos θ, where θ is the angle between ê s and ê LO. Since the interference term is used by the decision circuit to reconstruct the transmitted bit stream, any change in θ from its ideal value of θ = 0 reduces the signal
10.5. SENSITIVITY DEGRADATION 503 Figure 10.12: Schematic of a polarization-diversity coherent receiver. and affects the receiver performance. In particular, if the polarization states of E s and E LO are orthogonal to each other (θ = 90 ), the signal disappears (complete fading). Any change in θ affects the BER through changes in the receiver current and SNR. The polarization state ê LO of the local oscillator is determined by the laser and remains fixed. This is also the case for the transmitted signal before it is launched into the fiber. However, at the fiber output, the polarization state ê s of the signal received differs from that of the signal transmitted because of fiber birefringence, as discussed in Section 2.2.3 in the context of single-mode fibers. Such a change would not be a problem if ê s remained constant with time because one could match it with ê LO by simple optical techniques. The source of the problem lies in the polarization-mode dispersion (PMD) or the fact that ê s changes randomly in most fibers because of birefringence fluctuations related to environmental changes (nonuniform stress, temperature variations, etc.). Such changes occur on a time scale ranging from seconds to microseconds. They lead to random changes in the BER and render coherent receivers unusable unless some scheme is devised to make the BER independent of polarization fluctuations. Although polarization fluctuations do not occur in polarization-maintaining fibers, such fibers are not used in practice because they are difficult to work with and have higher losses than those of conventional fibers. Thus, a different solution to the polarizationmismatch problem is required. Several schemes have been developed for solving the polarization-mismatch problem [72] [77]. In one scheme [72], the polarization state of the optical signal received is tracked electronically and a feedback-control technique is used to match ê LO with ê s. In another, polarization scrambling or spreading is used to force ê s to change randomly during a bit period [73] [76]. Rapid changes of ê s are less of a problem than slow changes because, on average, the same power is received during each bit. A third scheme makes use of optical phase conjugation to solve the polarization problem [77]. The phase-conjugated signal can be generated inside a dispersion-shifted fiber through four-wave mixing (see Section 7.7). The pump laser used for four-wave mixing can also play the role of the local oscillator. The resulting photocurrent has a frequency component at twice the pump-signal detuning that can be used for recovering the bit stream.
504 CHAPTER 10. COHERENT LIGHTWAVE SYSTEMS Figure 10.13: Four-port coherent DPSK receiver employing both phase and polarization diversity. (After Ref. [80]; c 1987 IEE; reprinted with permission.) The most commonly used approach solves the polarization problem by using a two-port receiver, similar to that shown in Fig. 10.11, with the difference that the two branches process orthogonal polarization components. Such receivers are called polarization-diversity receivers [78] [82] as their operation is independent of the polarization state of the signal received. The polarization-control problem has been studied extensively because of its importance for coherent lightwave systems [83] [90]. Figure 10.12 shows the block diagram of a polarization-diversity receiver. A polarization beam splitter is used to separate the orthogonally polarized components which are processed by separate branches of the two-port receiver. When the photocurrents generated in the two branches are squared and added, the electrical signal becomes polarization independent. The power penalty incurred in following this technique depends on the modulation and demodulation techniques used by the receiver. In the case of synchronous demodulation, the power penalty can be as large as 3 db [85]. However, the penalty is only 0.4 0.6 db for optimized asynchronous receivers [78]. The technique of polarization diversity can be combined with phase diversity to realize a receiver that is independent of both phase and polarization fluctuations of the signal received [91]. Figure 10.13 shows such a four-port receiver having four branches, each with its own photodetector. The performance of such receivers would be limited by the intensity noise of the local oscillator, as discussed in Section 10.5.2. The next step consists of designing a balanced phase- and polarization-diversity receiver by using eight branches with their own photodetectors. Such a receiver has been demonstrated using a compact bulk optical hybrid [92]. In practical coherent systems, a balanced, polarization-diversity receiver is used in combination with narrow-linewidth lasers to simplify the receiver design, yet avoid the limitations imposed by intensity noise and polarization fluctuations. 10.5.4 Fiber Dispersion Section 5.4 discussed how fiber dispersion limits the bit-rate distance product (BL) of direct-detection (IM/DD) systems. Fiber dispersion also affects the performance of
10.5. SENSITIVITY DEGRADATION 505 Figure 10.14: Dispersion-induced power penalty as a function of the dimensionless parameter β 2 B 2 L for several modulation formats. The dashed line shows power penalty for a directdetection system. (After Ref. [95]; c 1988 IEEE; reprinted with permission.) coherent systems although its impact is less severe than for IM/DD systems [93] [97]. The reason is easily understood by noting that coherent systems, by necessity, use a semiconductor laser operating in a single longitudinal mode with a narrow linewidth. Frequency chirping is avoided by using external modulators. Moreover, it is possible to compensate for fiber dispersion (see Section 7.2) through electronic equalization techniques in the IF domain [98]. The effect of fiber dispersion on the transmitted signal can be calculated by using the analysis of Section 2.4. In particular, Eq. (2.4.15) can be used to calculate the optical field at the fiber output for any modulation technique. The power penalty has been calculated for various modulation formats [95] through numerical simulations of the eye degradation occurring when a pseudo-random bit sequence is propagated through a single-mode fiber and demodulated by using a synchronous or asynchronous receiver. Figure 10.14 shows the power penalty as a function of the dimensionless parameter combination β 2 B 2 L for several kinds of modulation formats. The dashed line shows, for comparison, the case of an IM/DD system. In all cases, the low-pass filter (before the decision circuit) is taken to be a second-order Butterworth filter [99], with the 3-dB bandwidth equal to 65% of the bit rate. As seen in Fig. 10.14, fiber dispersion affects the performance of a coherent lightwave system qualitatively in the same way for all modulation formats, although quantitative differences do occur. The power penalty increases most rapidly for CPFSK and MSK formats, for which tone spacing is smaller than the bit rate. In all cases system performance depends on the product B 2 L rather than BL. One can estimate
506 CHAPTER 10. COHERENT LIGHTWAVE SYSTEMS the limiting value of B 2 L by noting that the power penalty can be reduced to below 1 db in most cases if the system is designed such that β 2 B 2 L < 0.1. For standard fibers with β 2 = 20 ps 2 /km near 1.55 µm, B 2 L is limited to 5000 (Gb/s) 2 -km, and L should be <50 km at B = 10 Gb/s. Clearly, dispersion becomes a major limiting factor for systems designed with standard fibers when transmission distance is increased using optical amplifiers. Dispersion management would solve this problem. Electronic equalization can be used for compensating dispersion in coherent systems [100]. The basic idea is to pass the intermediate-frequency signal through a filter whose transfer function is the inverse of the transfer function associated with the fiber (see Section 7.2). It is also possible to compensate fiber dispersion through optical techniques such as dispersion management [101]. PMD then becomes a limiting factor for long-haul coherent systems [102] [104]. 10.5.5 Other Limiting Factors Several other factors can degrade the performance of coherent lightwave systems and should be considered during system design. Reflection feedback is one such limiting factor. The effect of reflection feedback on IM/DD systems has been discussed in Section 5.4.5. Essentially the same discussion applies to coherent lightwave systems. Any feedback into the laser transmitter or the local oscillator must be avoided as it can lead to linewidth broadening or multimode operation of the semiconductor laser, both of which cannot be tolerated for coherent systems. The use of optical isolators within the transmitter may be necessary for controlling the effects of optical feedback. Multiple reflections between two reflecting surfaces along the fiber cable can convert phase noise into intensity noise and affect system performance as discussed in Section 5.4.5. For coherent systems such conversion can occur even inside the receiver, where short fiber segments are used to connect the local oscillator to other receiver components, such as an optical hybrid (see Fig. 10.10). Calculations for phasediversity receivers show that the reflectivity of splices and connectors should be below 35 db under typical operating conditions [105]. Such reflection effects become less important for balanced receivers, where the impact of intensity noise on receiver performance is considerably reduced. Conversion of phase noise into intensity noise can occur even without parasitic reflections. However, the power penalty can be reduced to below 0.5 db by ensuring that the ratio ν/b is below 20% in phase diversity ASK receivers [106]. Nonlinear effects in optical fibers discussed in Section 2.6 also limit the coherent system, depending on the optical power launched into the fiber [107]. Stimulated Raman scattering is not likely to be a limiting factor for single-channel coherent systems but becomes important for multichannel coherent systems (see Section 7.3.3). On the other hand, stimulated Brillouin scattering (SBS) has a low threshold and can affect even single-channel coherent systems. The SBS threshold depends on both the modulation format and the bit rate, and its effects on coherent systems have been studied extensively [108] [110]. Nonlinear refraction converts intensity fluctuations into phase fluctuation through self- (SPM) and cross-phase modulation (XPM) [107]. The effects of SPM become important for long-haul systems using cascaded optical amplifiers [111]. Even XPM effects become significant in coherent FSK systems [112].
10.6. SYSTEM PERFORMANCE 507 Four-wave mixing also becomes a limiting factor for WDM coherent systems [113] and need to be controlled employing high-dispersion locally but keeping the average dispersion low through dispersion management. 10.6 System Performance A large number of transmission experiments were performed during the 1980s to demonstrate the potential of coherent lightwave systems. Their main objective was to show that coherent receivers are more sensitive than IM/DD receivers. This section focuses on the system performance issues while reviewing the state of the art of coherent lightwave systems. 10.6.1 Asynchronous Heterodyne Systems Asynchronous heterodyne systems have attracted the most attention in practice simply because the linewidth requirements for the transmitter laser and the local oscillator are so relaxed that standard DFB lasers can be used. Experiments have been performed with the ASK, FSK, and DPSK modulation formats [114] [116]. An ASK experiment in 1990 showed a baseline sensitivity (without the fiber) of 175 photons/bit at 4 Gb/s [116]. This value is only 10.4 db away from the quantum limit of 40 photons/bit obtained in Section 10.4.4. The sensitivity degraded by only 1 db when the signal was transmitted through 160 km of standard fiber with D 17 ps/(nm-km). The system performance was similar when the FSK format was used in place of ASK. The frequency separation (tone spacing) was equal to the bit rate in this experiment. The same experiment was repeated with the DPSK format using a LiNbO 3 phase modulator [116]. The baseline receiver sensitivity at 4 Gb/s was 209 photons/bit and degraded by 1.8 db when the signal was transmitted over 160 km of standard fiber. Even better performance is possible for DPSK systems operating at lower bit rates. A record sensitivity of only 45 photons/bit was realized in 1986 at 400 Mb/s [114]. This value is only 3.5 db away from the quantum limit of 20 photons/bit. For comparison, the receiver sensitivity of IM/DD receivers is such that N p typically exceeds 1000 photons/bit even when APDs are used. DPSK receivers have continued to attract attention because of their high sensitivity and relative ease of implementation [117] [125]. The DPSK signal at the transmitter can be generated through direct modulation of a DFB laser [117]. Demodulation of the DPSK signal can be done optically using a Mach-Zehnder interferometer with a one-bit delay in one arm, followed by two photodetectors at each output port of the interferometer. Such receivers are called direct-detection DPSK receivers because they do not use a local oscillator and exhibit performance comparable to their heterodyne counterparts [118]. In a 3-Gb/s experiment making use of this scheme, only 62 photons/bit were needed by an optically demodulated DPSK receiver designed with an optical preamplifier [119]. In another variant, the transmitter sends a PSK signal but the receiver is designed to detect the phase difference such that a local oscillator is not needed [120]. Considerable work has been done to quantify the performance of various