Sensitivity Degradation Mechanisms in Practical Coherent and Delay Demodulation Optical Receivers
The discussion of shot noise and bit-error rate of coherent and delay demodulation in the previous tutorial assumed ideal operating conditions in which system performance is only limited by shot noise. Several other noise sources degrade the receiver sensitivity in practical coherent systems. In this tutorial, we consider a few important sensitivity degradation mechanisms and also discuss the techniques used to improve the performance with a proper receiver design.
1. Intensity Noise of Lasers
The effect of intensity noise of lasers on the performance of direct-detection receivers has been discussed in the optical receiver sensitivity degradation tutorial and was found to be negligible in most cases of practical interest. This is not the case for coherent receivers. To understand why intensity noise plays such an important role in heterodyne receivers, we follow the analysis in the optical receiver sensitivity degradation tutorial and write the current variance as
where σI = RPLOrI and rI is related to the relative intensity noise (RIN) of the local oscillator. If the RIN spectrum is flat up to the receiver bandwidth Δf, rI2 can be approximated by 2(RIN)Δf. The SNR is obtained by using the current variance expression above in the following equation:
and is given by
The local-oscillator power PLO should be large enough to make σT2 negligible in this equation so that the heterodyne receiver operates in the shot-noise limit. However, an increase in PLO increases the contribution of intensity noise quadratically. If the intensity-noise contribution becomes comparable to shot noise, the SNR would decrease unless the signal power 
is increased to offset the increase in receiver noise. This increase in is the power penalty δI resulting from the local-oscillator intensity noise. If we neglect Id and σT2 in the SNR equation above for a receiver designed to operate in the shot-noise limit, the power penalty (in dB) is given by the simple expression
The figure below shows δI as a function of RIN for several values of PLO using η = 0.8 and hν = 0.8 eV. The power penalty exceeds 2 dB when PLO = 1 mW even for a local oscillator with a RIN of -160 dB/Hz, a value difficult to realize for DFB semiconductor lasers. Indeed, sensitivity degradation from local-oscillator intensity noise was observed in 1987 for a homodyne receiver. The optical delay demodulation scheme also suffers from the intensity-noise problem.
Balanced detection provides a solution to the intensity-noise problem. The reason can be understood from the figure below showing a balanced heterodyne receiver.
The dc term is eliminated completely 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 is noteworthy that intensity noise of a local oscillator affects even a balanced heterodyne receiver because the current difference, I+ - I-, still depends on the local-oscillator power. However, because this dependence is of the form of 
, the intensity-noise problem is much less severe for a balanced heterodyne receiver.
Optical delay-demodulation schemes shown in the figure below also makes use of balanced detection. In this case, a local oscillator is not used, and it is the intensity noise of the transmitter laser that must be considered. The dc part of the photocurrents I+ and I- is again cancelled during the subtraction of the two currents, which helps to reduce the impact of intensity noise. However, now the current difference ΔI depends linearly on the signal power Ps. This situation is similar to the direct-detection case discussed in the optical receiver sensitivity degradation tutorial, and the impact of intensity noise is again not that severe.
2. Phase Noise of Lasers
An important source of sensitivity degradation for lightwave systems making use of any PSK format is the phase noise associated with the transmitter laser (and the local-oscillator in the case of coherent detection). The reason is obvious if we note that current generated at the receiver depends on the carrier phase, and any phase fluctuations introduce current fluctuations that degrade the SNR at the receiver. In the case of coherent detection, both the signal phase φs and the local-oscillator phase φLO 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 related inversely to the laser linewidth Δν. To minimize the impact of phase noise, the coherence time should be much longer than the symbol duration Ts. In practice, it is common to use a dimensionless parameter ΔνTs for characterizing the effects of phase noise on the performance of coherent lightwave systems. Since the symbol rate Bs = 1/Ts, this parameter is just the ratio Δν/Bs. In the case of heterodyne detection involving a local oscillator, Δν represents the sum of the two linewidths, ΔνT and ΔνLO, associated with the transmitter and the local oscillator, respectively.
Considerable attention has been paid to calculate the BER in the presence of phase noise and to estimate the dependence of power penalty on the ratio Δν/Bs. As an exact solution is not possible, either a Monte-Carlo-type numerical approach is employed or a perturbation technique is used to obtain approximate analytic results. Recently, the use of an approximation, called the phase-noise exponent computation (PNEC), has resulted in simple analytic BER expressions for both the PSK and DPSK formats. This approach also allows one to take into account the actual shape of RZ pulses commonly employed in modern lightwave systems.
The main conclusion in all cases is that the BER increases rapidly with the parameter ΔνTs. The increase in BER becomes so rapid for ΔνTs > 0.01 that a BER floor appears above a BER at a certain value of this parameter. If this BER floor occurs at a level > 10-9, the system BER will exceed this value irrespective of the amount of signal power reaching the receiver (an infinite power penalty). The following figure shows how the BER floor changes with ΔνTs for BPSK, QPSK, 8PSK, and DBPSK formats. In all cases, the BER floor is above the 10-9 level when ΔνTs exceeds a value of about 0.02.
An important metric from a practical standpoint is the tolerable value of ΔνTs for which power penalty remains below a certain value (say, 1 dB) at a BER of 10-9. As expected, this value depends on the modulation format as well as on the demodulation technique employed. The linewidth requirements are most stringent for homodyne receivers. Although the tolerable value depends to some extent on the design of the phase-locked loop, typically ΔνTs should be < 5 x 10-4 for homodyne receivers to ensure a power penalty of less than 1 dB.
The linewidth requirements are relaxed considerably for heterodyne receivers. For synchronous heterodyne receivers needed for the BPSK format, ΔνTs < 0.01 is required. As seen from figure (a) above, this requirement becomes more severe for the QPSK format. In contrast, ΔνTs can exceed 0.1 for asynchronous ASK and FSK receivers. The reason is related to the fact that such receivers use an envelop detector that throws away 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 because receiver noise increases with an increase in the BPF bandwidth.
The DBPSK format requires narrower linewidths compared with the asynchronous ASK and FSK formats when a delay-demodulation scheme 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. Figure (b) and other estimates show that ΔνTs should be less than 1% to operate with a < 1 dB power penalty. At a 10-Gb/s bit rate, the required linewidth is <10 MHz, but is increases by a factor of 4 at 40 Gb/s. Since DFB lasers with a linewidth of 10 MHz or less are available commercially, the use of the DBPSK format is quite practical at bit rates of 10 Gb/s or more. The requirement is mcuh tighter for the DQPSK format for which the symbol rate Bs plays the role of the bit rate. An approximate analytic expression for the BER predicts that a laser linewidth of <3 MHz may be required at 10 GBd. Of course, this value increases by a factor of 4 if the DQPSK format is used at a symbol rate of 40GBd.
The preceding estimates of the required laser linewidth are based on the assumption that a BER of 10-9 or less is required for the system to operate reliably. Modern lightwave systems employing forward-error correction can operate at a BER of as high as 10-3. In that case, the limiting value of the parameter ΔνTs for < 1 dB power penalty may increase by a factor of 2 or more. However, if the allowed power penalty is reduce dto a level below 0.2 dB, ΔνTs again goes back to the limiting values discussed earlier.
An alternative approach solves the phase-noise problem for coherent receivers by adopting a scheme known as phase-diversity receivers. Such receivers use multiple photodetectors whose outputs are combined to produce a signal that is independent of the phase difference φIF = φs - φLO. The following figure 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 φIF. In the case of a two-port homodyne receiver, the two output branches have a relative phase shift of 90°, so that their currents vary as IpcosφIF and IpsinφIF. When the two currents are squared and added, the signal becomes independent of φIF. In the case of three-port receiver, 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 φIF.
3. Signal Polarization Fluctuations
Polarization 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 (SOP) of the local oscillator to that of the signal received. The polarization-matching requirement can be understood from the analysis of coherent detection tutorial, where the use of scalar fields Es and ELO implicitly assumed the same SOP for the two optical fields. If 
and 
represent the unit vectors along he direction of polarization of Es and ELO, respectively, the interference term in the following equation contains an additional factor cosθ, where θ is the angle betweenand .
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 and affects the receiver performance. In particular, if the SOPs of Es and ELO are orthogonal to each other, the electrical signal disappears altogether (complete fading). Any change in θ affects the BER through changes in the receiver current and SNR.
The polarization state 
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 receiver end, the SOP of the optical signal differs from that of the signal transmitted because of fiber birefringence. Such a change would not be a problem if 
remained constant with time because one could match it with by simple optical techniques. However, as discussed in the dispersion in single-mode fibers tutorial, changes randomly inside most fiber links because of birefringence fluctuations related to environmental changes. Such changes occur on a time scale ranging from seconds to microseconds. They lead to random changes in the BER and render coherent receivers unstable, unless some scheme is devised to make the BER independent of polarization fluctuations.
Several schemes have been developed for solving the polarization-mismatch problem. In one scheme, the polarization state of the received optical signal is tracked electronically and a feedback-control technique is used to match with . In another, polarization scrambling or spreading is used to force to change randomly during a symbol period. Rapid changes of 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. The phase-conjugated signal can be generated inside a dispersion-shifted fiber through four-wave mixing. 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.
The most commonly used approach solves the polarization problem by using a two-port receiver with the difference that the two branches process orthogonal polarization components. Such receivers are called polarization-diversity receivers, as their operating is independent of the SOP of the optical signal reaching the receiver. The following figure 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. However, the penalty is only 0.4-0.6 dB for optimized asynchronous receivers.
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. The following figure 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. The next step consists of designing a balanced, phase- and polarization-diversity, coherent receiver by using eight branches with their own photodetectors. Such a receiver was first demonstrated in 1991 using a compact bulk optical hybrid. Soon after, the attention turned toward developing integrated balanced receivers. By 1995, a polarization-diversity receiver was fabricated using InP-based optoelectronic integrated circuits. More recently, the attention has focused on coherent receivers that employ digital signal processing. With this approach, even homodyne detection can be realized without relying on a phase-locked loop.
4. Noise added by Optical Amplifiers
As discussed in the electrical signal-to-noise ratio tutorial, optical amplifiers degrade considerably the electrical SNR in the case of direct detection because of the noise added to the optical signal in the form of amplified spontaneous emission (ASE). As expected, amplifier noise also degrades the performance of coherent receivers. The extent of degradation depends on the number of amplifiers employed and becomes quite severe for long-haul systems that may employ tens of amplifiers along the fiber link. Even for relatively short fiber links without in-line amplifiers, an optical preamplifier is often used for the signal or the local oscillator. In the case of optical delay demodulation, the use of an optical preamplifier before the receiver is almost a necessity because the receiver performance would otherwise be limited by the thermal noise of photodetectors.
The noise analysis of the electrical signal-to-noise ratio tutorial can be extended to heterodyne and delay-demodulation receivers. Two new noise currents that contribute to the total receiver noise are σ2sig-sp and σ2sp-sp representing, respectively, the impact of beating between the signal and ASE and between ASE and ASE. Although a general analysis is quite complicated, if we assume that a narrowband optical filter is employed after the preamplifier to reduce ASE noise and retain only σ2sig-sp that is the dominant noise term in practice, it turns out that the SNR of the signal is reduced from ηNp to ηNp/nsp, where nsp is the spontaneous emission factor introduced in the erbium-doped fiber amplifier (EDFA) tutorial and defined as
We can write nsp in terms of the noise figure Fn of optical amplifiers using the relation Fn ≈ 2nsp given in this following equation:
If multiple amplifiers are employed, the SNR is degraded further because the effective noise figure of a chain of amplifiers increases with the number of amplifiers.
Another polarization issue must be considered because of the unpolarized nature of the amplifier noise. As discussed in the electrical signal-to-noise ratio tutorial, in addition to the ASE noise component copolarized with the signal, the orthogonally polarized part of the ASE also enters the receiver and adds additional noise. One can avoid this part by placing a polarizer before the photodetector so that the noise and the signal are in the same polarization state. This situation is referred to as polarization filtering. When polarization filtering is done at the receiver and a single optical preamplifier is used to amplify either the optical signal or the local oscillator, the BER for different modulation formats can be obtained from expressions given in the shot noise and bit-error rate for coherent and delay demodulation tutorial by replacing Np with Np/nsp in them. The receiver sensitivity at a given BER is degraded by a factor nsp because the incident optical power must be increased by the same factor.
In the absence of polarization filtering, orthogonally polarized noise should be included and it leads to an increase in the BER. In the case of a DBPSK signal demodulated using an optical delay interferometer, the BER is found to be
indicating that the BER is increased by a factor of 1+ηNp/4. The resulting increase in required SNR is not negligible because a BER of 10-9 is realized at a SNR of ηNp = 22 rather than 20. However, this increase corresponds to a power penalty of less than 0.5 dB. When a DQPSK signal is received without polarization filtering, the BER is found to be given by
where I1(x) is the modified Bessel function of order one. Compared with the case of polarization filtering, another term is added to the BER because of additional current fluctuations produced by ASE polarized orthogonal to the signal. However, this increase is almost negligible and leads to a power penalty of < 0.1 dB.
5. Fiber Dispersion
As discussed in the dispersion-induced pulse broadening tutorial and sources of power penalty tutorial, dispersive effects occurring inside optical fibers affect all lightwave systems. Such impairments result not only from group-velocity dispersion (GVD) governed by the parameter D but also from polarization-mode dispersion (PMD) governed by the parameter Dp. As expected, both of them affect the performance of coherent and self-coherent systems, although their impact depends on the modulation format employed and is often less severe compared with that for intensity modulation/direct detection (IM/DD) systems. 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 also avoided by using external modulators.
The effect of fiber dispersion on the transmitted signal can be calculated by following the analysis of the dispersion-induced pulse broadening tutorial. In particular, the following equation can be used to calculate the optical field at the fiber output for any modulation technique as long as the nonlinear effects are negligible:
In a 1988 study, the GVD-induced power penalty was calculated for various modulation formats through numerical simulations of the "eye-opening" degradation occurring when a pseudo-random bit sequence was propagated through a single-mode fiber. A new method of calculating the BER in the presence of dispersive effects was proposed in 2000 and used to show that the eye degradation approach fails to predict the power penalty accurately. This method can include preamplifier noise as well and has been used to calculate power penalties induced by GVD and PMD for a variety of modulation formats, including DBPSK and DQPSK formats implemented with the delay-demodulation technique.
Figure (a) below shows the GVD-induced power penalty as a function of DB2L, where B is the bit rate and L is the fiber-link length, for several modulation formats. Figure (b) below shows the PMD-induced power penalty as a function of the dimensionless parameter Δτ/Tb, where Tb = 1/B is the bit duration and Δτ is the average value of the differential group delay, after setting D = 0. The case of on-off keying (OOK) is shown for comparison. Also, both the RZ and NRZ cases are shown for each modulation format to emphasize how dispersive effects depend on them. Although the results depend to some extent on the specific shape of RZ pulses and the specific transfer functions employed for the optical and electrical filters in numerical simulations, they can be used for drawing qualitative conclusions.
As seen in figure (a), the power penalties at a given value of DB2L are smaller for the DBPSK format compared with the OOK format in both the RZ and NRZ cases but the qualitative behavior is quite similar. In particular, the penalty can be reduced to below 1 dB in both cases by making DB2L < 5 x 104 (Gb/s)2ps/nm. In contrast, power penalties are reduced dramatically for the DQPSK format, and much larger values of DB2L can be tolerated. The reason is easily understood by noting that at a given bit rate B the symbol rate Bs is reduced by a factor of 2. This allows the use of wider optical pulses and results in a smaller power penalty. The PMD-induced power penalty in figure (b) shows similar qualitative behavior for the same physical reason. These results indicate clearly that, as far as dispersion effects are concerned, their impact can be reduced considerably by adopting a format that allows the transmission of multiple bits during the time slot allocated to a single symbol. This is the reason why the use of DQPSK format is becoming prevalent in modern, high-performance systems.
If dispersive effects begin to limit a coherent system, one can employ a variety of dispersion-management techniques discussed in the dispersion problem and its solution tutorial series. In the case of long-haul systems, periodic compensation of fiber dispersion with dispersion-compensating fibers is employed routinely. It is also possible to compensate for fiber dispersion through an electronic equalization technique implemented within the receiver. This approach is attracting considerable attention since 2005 with the implementation of a digital signal processing in digital coherent receivers.