Keang-Po Ho

• Ph.D.
• Institute of Electrical and Electronics Engineers

Mode-dependent loss and gain (MDL and MDG) of multimode components are fundamental impairments that reduce the capacity of mode-division-multiplexed (MDM) systems. MDL of components is commonly quantified either in terms of the root-mean-square (rms) or peak-to-peak (P-P) gain and loss variations. It is incorrect to specify only the P-P MDL of comp...

Multi-input multi-output (MIMO) digital signal processing (DSP) for mode-division multiplexing (MDM) may have high complexity, owing to a plurality of modes and a potentially long group delay (GD) spread in multimode fiber (MMF). This paper addresses the management of GD in MMF and its implications for the complexity and performance of MIMO DSP. Fi...

Reduction of the group delay (GD) spread is crucial for minimizing signal processing complexity in mode-division multiplexing. Strong mode coupling and GD compensation (concatenating different fibers with opposing GD ordering) are two approaches for reducing the end-to-end GD spread. In this paper, we study the GD behavior in systems where mode cou...

We review channel models for mode-division multiplexing (MDM) systems, the statistics derived from them, and their implications for system performance and complexity. We present the fundamentals of architectures and algorithms for multi-input multi-output (MIMO) equalization. With careful physical link design and judicious choice of signal processi...

The increase in growing traffic explosion in wireless communication system has recently drawn great attention to the large amount of underutilized spectrum is millimetre wave (mmWave) communication system as a potential candidate. Beamforming (BF) is an efficient technique to increase the capacity of the wireless communication systems. We proposed...

As the bit rates of routed data streams exceed the throughput of single wavelength-division multiplexing channels, spectral and spatial traffic aggregation become essential for optical network scaling. These aggregation techniques reduce network routing complexity by increasing spectral efficiency to decrease the number of fibers, and by increasing...

Wavelength-selective switches for mode-division-multiplexing systems are designed by scaling switches from single-mode systems. All modes at a given wavelength are switched as a unit, which is necessary in systems with substantial mode coupling, and minimizes the number of ports required to accommodate a given traffic volume. When a pure mode is pr...

Beamforming is indispensable in the operation of 60-GHz millimeter-wave directional multi-gigabit Wi-Fi. Simple power method and its extensions enable the transmitting and receiving antenna arrays to form a beam for single spatial stream. To further improve the spectral efficiency in future 60-GHz directional Wi-Fi, alternating least square (ALS) a...

We present the fundamentals of multiple-input, multiple-output (MIMO) signal processing for mode-division multiplexing (MDM) in multimode fiber (MMF). As an introduction, we review current long-haul optical transmission systems and how continued traffic growth motivates study of new methods to increase transmission capacity per fiber. We describe t...

In this paper, we review linear propagation effects in a multimode fiber (MMF) and their impact on performance and complexity in long-haul mode-division multiplexing (MDM) systems. We highlight the many similarities to wireless multi-input multioutput (MIMO) systems. Mode-dependent loss and gain (MDL), analogous to multipath fading, can reduce aver...

Wavelength-selective switches for mode-division-multiplexing systems are designed by scaling switches from single-mode systems. All modes at a given wavelength are switched as a unit, which is necessary in systems with substantial mode coupling, and minimizes the number of ports required to accommodate a given traffic volume. When a pure mode is pr...

Mode coupling is a key to overcoming challenges in mode-division-multiplexed transmission systems in multimode fiber. This chapter provides an in-depth description of mode coupling, including its physical origins, its effect on modal dispersion (MD) and mode-dependent loss or gain (MDL), and the resulting impact on system performance and implementa...

When an electronic equalizer is used to compensate the modal dispersion in a mode-division multiplexed system, receiver phase noise induces interference to the multi-input- multi-output (MIMO) receiver. Based on the statistics of the modal dispersion in the strong coupling regime, the interference variance is evaluated analytically based on an exac...

This article consists of a collection of slides from the author's conference presentation. Some of the specific areas/topics discussed include: Mode coupling (Sources, effects and models); Modal dispersion (Principal modes, Statistics of group delays, MDM system complexity); Modal gains and losses (Statistics of gains/losses and noise, MDM system p...

The performance and complexity of mode-division-multiplexing systems depend on the statistics of modal gains/losses and group delays. Under strong mode coupling, these statistics may be derived from the eigenvalue distributions of random matrices. Strong coupling optimizes performance and minimizes complexity.

In the strong mode coupling regime, the delay spread of multimode fiber is statistically the same as the difference between the maximum and minimum eigenvalues of a Gaussian unitary ensemble. We study the delay-spread distribution using three methods: 1) numerical evaluation of the Fredholm determinant; 2) numerical integration based on the Andréie...

Mode coupling is a key to overcoming major challenges in coherent mode-division-multiplexed systems. Strong mode coupling reduces the modal group delay spread, minimizing the complexity of multi-input multi-output signal processing. Likewise, strong mode coupling mitigates the mode-dependent gain of optical amplifiers, maximizing average channel ca...

Mode coupling is a key to overcoming major challenges in mode-division-multiplexed (MDM) long-haul systems using coherent detection. Strong mode coupling reduces the modal group delay spread, minimizing the complexity of digital multi-input multi-output (MIMO) signal processing. Likewise, strong mode coupling mitigates the mode-dependent gain of op...

Using the unlicensed 60-GHz millimeter-wave band, an antenna array driven by CMOS circuitry enables low-cost multi-gigabit broadband wireless transmission. The CMOS transceiver can consistently achieve data rates up to 3.8 Gb/s for video area network operation. Using beam-search techniques, the antenna arrays steer the beam to avoid line-of-sight b...

In the strong mode coupling regime, the model for mode-dependent gains and losses (collectively referred as MDL) of a multimode fiber is extended to the region with large MDL. The MDL is found to have the same statistical properties as the eigenvalues of the summation of two matrices. The first matrix is a random Gaussian matrix with standard devia...

In mode-division-multiplexed systems using coherent detection, strong mode coupling is beneficial. Mode coupling reduces modal dispersion, minimizing signal processing complexity. In combination with modal dispersion, mode coupling creates frequency diversity, mitigating the mode-dependent gain of optical amplifiers.

In the regime of strong mode coupling, the modal gains and losses and the modal group delays of a multimode fiber are known to have well-defined statistical properties. In mode-division multiplexing, mode-dependent gains and losses are known to cause fluctuations in the channel capacity, so that the capacity at finite outage probability can be subs...

In multimode fiber transmission systems, mode-dependent loss and gain (collectively referred to as MDL) pose fundamental performance limitations. In the regime of strong mode coupling, the statistics of MDL (expressed in decibels or log power gain units) can be described by the eigenvalue distribution of zero-trace Gaussian unitary ensemble in the...

In multimode fiber transmission systems, mode-dependent loss and gain (collectively referred to as MDL) pose fundamental performance limitations. In the regime of strong mode coupling, the statistics of MDL (expressed in decibels or log power gain units) can be described by the eigenvalue distribution of zero-trace Gaussian unitary ensemble in the...

The modal group delays (GDs) are a key property governing the dispersion of signals propagating in a multimode fiber (MMF). A MMF is in the strong-coupling regime when the total length of the MMF is much greater than the correlation length over which local principal modes can be considered constant. In this regime, the GDs can be described as the e...

For a quadriphase-shift keying (QPSK) or differential QPSK (DQPSK) signal in a wavelengthdivision- multiplexed (WDM) system, cross-phase modulation (XPM) induces nonlinear phase noise from adjacent WDM channels. The impact of XPM-induced nonlinear phase noise is investigated when the adjacent WDM channels are either constant-intensity phase-modulat...

In electronic digital signal processing based optical communication systems, digital equalization for chromatic dispersion interacts with local oscillator phase noise to produce equalization-enhanced phase noise (EEPN). In addition to both phase and intensity noises, EEPN also induces timing jitter to the equalized signal. For a 100 Gbit / s quadra...

The central limit for the products of identically-distributed positive free random variables are studied by evaluating all the moments of the limit distribution. If the logarithm of the free random variables are zero mean with unity variance, the central limit is found to confine between exp(+/- c_0) with c_0 ~ 2.08. This central limit distribution...

The linear minimum-mean-square error (LMMSE) estimator is herein derived to estimate phase-noise of Levy statistics (including Wiener phase-noise) and of arbitrarily large magnitude. This estimator may be pre-set to any latency and any number of tabs. This estimator depends only on the signal-to-(additive)-noise ratio and the phase-noise variance,...

The exact error probability of quadriphase shift keying (QPSK) signals with homodyne crosstalk is derived analytically. With respect to the signal, homodyne crosstalk may be from the same, the worst, or random polarization. Valid for many interferers, Gaussian model overestimates the SNR penalty for homodyne crosstalk from a single interferer. For...

The linear minimum-mean-square error (LMMSE) estimator is herein derived to estimate phase-noise of Levy statistics (including Wiener phase-noise) and of arbitrarily large magnitude. This estimator may be pre-set to any latency and any number of tabs. This estimator depends only on the signal-to-(additive)-noise ratio and the phase-noise variance,...

The probability density function and impact of equalizationenhanced phase noise (EEPN) is analytically investigated and simulated for 100 Gb/s coherent systems using electronic dispersion compensation. EEPN impairment induces both phase noise and amplitude noise with the former twice as much as the latter. The effects of transmitter phase noise on...

The probability density function and impact of equalization-enhanced phase noise (EEPN) is analytically investigated and simulated for 100 Gb/s coherent systems using electronic dispersion compensation. EEPN impairment induces both phase noise and amplitude noise with the former twice as much as the latter. The effects of transmitter phase noise on...

Electronic-equalizer based on DSP techniques enhances phase noise impairment. This equalization-enhanced phase noise (EEPN) interference imposes a tighter constraint on the laser linewidths in systems with high symbol-rate and large electronically-compensated chromatic dispersion.

Optical duobinary signal has narrow spectrum, tolerance to chromatic dispersion, and resistance to filter distortion. With many early patents from different organizations, optical duobinary modulation was actually invented earlier and described in a thesis by L. C. Blank. The later development of optical duobinary modulation is reviewed, including...

For 100-Gb/s quadriphase-shift keying (QPSK) signal with on-off keying (OOK) signal in neighboring wavelength-division-multiplexed (WDM) channel, the smoothing filter in the feedforward phase estimation scheme must be optimized to minimize the phase error. With optimal Wiener filter, typical 0-dBm launched power 10-Gb/s OOK signals give a SNR penal...

The statistical properties of nonlinear phase noise, often called the Gordon- Mollenauer effect, is studied analytically when the number of fiber spans is very large. The joint characteristic functions of the nonlinear phase noise with electric field, received intensity, and the phase of amplifier noise are all derived analytically. Based on the jo...

An oversampled subband equaliser is designed for chromatic dispersion of singlemode optical fibre. The signal of each subband is equalised individually and delayed to align with other subbands. From simulation, the overall number of equaliser taps is approximately reduced by the upsampling ratio.

When a signal is highly saturated and clipped by an analog-to-digital converter, the maximum-likelihood power estimator for the clipped signal is derived analytically for Gaussian-distributed input signal. The estimator error is also found numerically by simulation. The power estimator may find its applications in automatic gain control.

We study the impact of equalization-enhanced phase noise (EEPN) for 100 Gb/s coherent systems using electronic dispersion compensation through simulations. Power penalties are compared with theoretical predictions and the effects of transmitter phase noise are investigated.

To estimate Wiener phase noise of arbitrarily large magnitude (relative to the symbol duration), this work pioneers a linear minimum-mean-square error (LMMSE) discrete-time estimator. This proposed estimator may be pre-set to any arbitrary number of taps and any arbitrary latency. The coefficients of this linear estimator depend only on the values...

For an optical short pulse with white background noise, an optical filter preceding the photodetector can reduce the noise. The optimal optical filter is derived to balance the amount of the output noise with the energy of the output signal. As a numerical example, for a Gaussian optical pulse with a Gaussian receiver filter, the optimal optical fi...

Chromatic dispersion induces to a phase-modulated optical signal a constant phase rotation that was never included in most previous studies. When the constant phase shift is removed by a phase-locked loop, the dispersion tolerance of a coherent-detection system is increased. The dispersion tolerance of phase-shift keying (PSK) signal is compared wi...

In coherent optical systems employing electronic digital signal processing, the fiber chromatic dispersion can be gracefully compensated in electronic domain without resorting to optical techniques. Unlike optical dispersion compensator, the electronic equalizer enhances the impairments from the laser phase noise. This equalization-enhanced phase n...

Fiber-optic communication systems using phase shift keying (PSK) modulation may suffer from nonlinear phase noise. In this paper, an asymptotic approximation of the probability density function (p.d.f.) of the normalized nonlinear phase noise is derived by taking the inverse Laplace transform of its moment generating function and using the method o...

In this letter, we analyze the transmitter design for coherent optical orthogonal frequency-division multiplexing (CO-OFDM) employing predistortion. Digital clipping and digital predistortion processes are introduced to the radio frequency OFDM transmitter to compensate the nonlinearity effect introduced by the optical in-phase/quadrature modulator...

A parallel-type, dispersion compensating C+L band erbium-doped fiber amplifier/Raman fiber amplifier (EDFA/RFA) is constructed by sharing a common 1480-nm pump source. The gain spectra of C+L band are flattened by optimally dividing the pump power ratio to 1:29 for EDFA and RFA, respectively. In a signal input power of -20 dBm, the average gain is...

A detailed analysis is presented on the optimal design for coherent optical OFDM transmitter employing predistortion. The optimal design shows 4-bit DAC resolution is sufficient and the excess loss for optical IQ modulator is 5.0 dB.

The exact log-likelihood ratio for a direct-detection DPSK signal is derived analytically. A 7%-overhead low-density parity check (LDPC) code provides 9.7 dB net coding gain.

The performance of differential phase-shift keying signals with a balanced receiver is exactly analyzed by using a closed-form expression without approximation. The numerical results are well matched with previous results based on the saddle-point approximation. The error probability is calculated exactly using the well-known Marcum Q function.

The phase and amplitude responses of a narrowband optical filter are measured simultaneously using a microwave network analyzer. The measurement is based on an interferometric arrangement to an split optical carrier into two paths and then combine them. In one of the two paths, a Mach-Zehnder modulator generates two tones without carrier, and the n...

Chromatic dispersion and PMD can be compensated using linear feedforward equalizer with or without DFE. Correlated to the received intensity, nonlinear phase noise can be compensated by combining the received phase with the received intensity.

The variance of nonlinear phase noise is analyzed by including the effect of intrachannel cross-phase modulation-induced nonlinear phase noise. Consistent with Ho and Wang [IEEE Photon. Technol. Lett.17, 1426 (2005)] for a lightwave transmission system but contrary to the conclusions of both Kumar [Opt. Lett.30, 3278 (2005)] and Green [Opt. Lett.28...

A miniature-size erbium doped fibre amplifier (MS-EDFA) is constructed with a saturation power of 17.0 dBm and low noise figure of 5.2 dB using an uncooled pump laser. The MS-EDFA has achieved low polarization dependent gain, large signal gain and small signal gain of 0.05 dB, 15 dB (at Pin = +2 dBm) and 42 dB (at Pin = −30 dBm), respectively, with...

In highly dispersive return-to-zero differential phase-shift keying (RZ-DPSK) transmission systems, the overlap of optical pulses gives a nonperiodic optical intensity that induces nonperiodic phase modulation to adjacent channels through cross-phase modulation (XPM). The variance of the differential phase induced by XPM and pulse overlap is derive...

Time-resolved optical filtering (TROF) measures the spectrogram or sonogram by a fast photodiode followed a tunable narrowband optical filter. For periodic signal and to match the spectrogram, numerical TROF algorithm is used to find the original complex electric field or equivalently both the amplitude and phase. For phase-modulated optical signal...

The complex-value electric field of a periodic phase-modulated optical signal is retrieved from the spectrogram/sonogram that is measured by a fast photodiode followed a tunable narrow-band optical filter. With an initial guess from the craters and ridges of the spectrogram, the numerical algorithm converges very fast to a mean-square error less th...

To simplify the analysis, the performance of differential phase-shift-keying signals with nonlinear phase noise is usually calculated for receiver with an optical matched filter. With a special single-span experimental setup to isolate the contribution from nonlinear phase noise, the measured signal-to-noise ratio (SNR) penalty is within ±0.15 dB o...

The electric field of a periodic optical signal is retrieved from sonogram by numerical time-resolved optical filtering algorithm. With initial guess from the craters and ridges of the sonogram, the algorithm converges within 20 iterations.

Information-theoretic limits to spectral efficiency in dense wavelength-division-multiplexed systems are reviewed. Various modulation techniques (unconstrained, constant-intensity), detection techniques (coherent, direct) and propagation regimes (linear, nonlinear) are considered.

When a soliton signal is detected by the maximum-likelihood principle, other than walk-out of the bit interval, timing jitter does not degrade the performance of the receiver. When the maximum-likelihood detector (MLD) is simulated by using the importance sampling method, even with a timing-jitter standard deviation the same as the full width at ha...

When a differential-phase-shift-keying (DPSK) signal is directly detected using an asymmetric interferometer and balanced receiver, the exact error probability of the signal with homodyne crosstalk is derived analytically. Homodyne crosstalk from many interferers is Gaussian distributed, but the Gaussian model overestimates the signal-to-noise rati...

Self-phase-modulation-induced nonlinear phase noise is reduced with the increase of fiber dispersion but intrachannel four-wave mixing (IFWM) is increased with dispersion. Both degrading differential phase-shift keying signals, the standard deviation of nonlinear phase-noise-induced differential phase is about three times that from IFWM even in hig...

A semianalytical method evaluates the error probability of differential phase-shift keying signals with intrachannel four-wave mixing in a highly dispersive fiber link with strong pulse overlap. Depending on initial pulsewidth, the mean nonlinear phase shift of the system can be from 1 to 2 rad for signal-to-noise ratio penalty less than 1 dB. An a...

Based on a rigorous model without approximation, the channel capacity is evaluated numerically for intensity-modulated direct-detection systems dominated by optical amplifier noises. With a discrete probability at zero intensity, the optimal input distribution is both discrete and continuously distributed. For small signal-to-noise ratio less than...

Regardless of the number of constellation points, all quadrature-amplitude modulation (QAM) signals can be generated using a single dual-drive Mach–Zehnder modulator. When the general method is applied to quadrature-phase-shift-keying (QPSK) signals, three different QPSK transmitters are shown with drive signals having four, three, or two levels. T...

In all optical communication systems, a light source must be used to originate an optical signal. Because of its small size, low power consumption, reliability, and compatible with electronic circuits, semicon-ductor diode lasers are the most widely used light source for communication applications. Virtually all optical communication systems use se...

The nonlinear phase noise, often called the Gordon–Mollenauer effect, is correlated with the intensity of the optical signal. With a single linear compensator, the optimal location is not preceding the receiver but located at about 2/3 of the fiber link. When N compensators are approximately optimally placed, the standard deviation of nonlinear pha...

Self-phase modulation induced nonlinear phase noise is reduced with the increase of fiber dispersion but intrachannel four-wave-mixing (IFWM) is increased with dispersion. Both degrading DPSK signals, the standard deviation of nonlinear phase noise induced differential phase is about three times that from IFWM even in highly dispersive transmission...

Various binary and non-binary modulation techniques, in conjunction with appropriate detection techniques, are compared in terms of their spectral efficiencies and signal-to-noise ratio requirements, assuming amplified spontaneous emission is the dominant noise source. These include (a) pulse-amplitude modulation with direct detection, (b) differen...

Fiber-optic communication systems have revolutionized our telecommunication infrastructures -- currently, almost all telephone land-line, cellular, and internet communications must travel via some form of optical fibers. In these transmission systems, neither the phase nor frequency of the optical signal carries information -- only the intensity of...

When the dependence between linear and nonlinear phase noise is taken into account, the exact error probability of DPSK signals with nonlinear phase noise is derived analytically for a fiber system with finite number of fiber spans. For the same mean nonlinear phase shift, the SNR penalty is reduced with the number of fiber spans. The discrepancy b...

Regardless of complexity, all types of quadrature-amplitude modulated (QAM) signal can be generated using a single dual-derive Mach-Zehnder modulator. Three different quadrature phase-shift keying (QPSK) transmitters are proposed as examples.

When a differential phase-shift keying signal is contaminated by nonlinear phase noise, various models to evaluate the error probability are compared. The simplest method is based on the Q factor. The exact method takes into account the dependence between amplifier noise and nonlinear phase noise. All approximated models underestimate both the erro...

Nonlinear phase noise induced by the interaction of fiber Kerr effect and amplifier noises is a quadratic function of the electric field. When the dependence between the additive Gaussian noise and the quadratic phase noise is taking into account, the joint statistics of quadratic phase noise and additive Gaussian noise is derived analytically. Whe...

Nonlinear phase noise, often called the Gordon-Mollenauer effect, can be compensated electronically by subtracting from the received phase a correction proportional to the received intensity. The optimal scaling factor is derived analytically and found to be approximately equal to half of the ratio of mean nonlinear phase noise and the mean receive...

The error probability is derived analytically for differential phase-shift keying (DPSK) signals contaminated by both self- and cross-phase modulation (SPM and XPM)-induced nonlinear phase noise. XPM-induced nonlinear phase noise is modeled as Gaussian distributed phase noise. When fiber dispersion is compensated perfectly in each fiber span, XPM-i...

Information-theoretic limits to spectral efficiency in dense wavelength-division-multiplexed (DWDM) transmission systems are reviewed, considering various modulation techniques (unconstrained, constant-intensity, binary), detection techniques (coherent, direct), and propagation regimes (linear, nonlinear). Spontaneous emission from inline optical a...

The optical power spectrum of a signal externally modulated using a Mach-Zehnder modulator is calculated analytically. Optical power spectra are calculated for binary signals for which the drive signal has either raised-cosine or Bessel-filtered pulse shape as well as for duobinary signals created by Bessel filtering. While the optical power spectr...

The characteristic function of soliton phase jitter is found analytically when the soliton is perturbed by amplifier noise. In addition to that from amplitude jitter, the nonlinear phase noise due to frequency and timing jitter is also analyzed. With nonlinear phase noise, the overall phase jitter is non-Gaussian distributed. For a fixed mean nonli...

Based on the well-known Marcum's Q function, closed-form formulae are derived to evaluate the error probability of direct-detected differential phase-shift keying (DPSK) and differential quadrature phase-shift keying (DQPSK) signals with interferometer phase error. For a signal-to-noise ratio penalty less than 1 dB, the phase error must be less tha...

Differential quadrature phase-shift keying (DQPSK) signal has received renewed attention recently for spectral-efficiency transmission systems. Nonlinear phase noise is the major degradation for phase-modulated signals. Correlated with received intensity, nonlinear phase noise can be compensated by the received intensity. The exact error probabilit...

The paper investigates the probability density function of an electric signal containing nonlinear phase noise. The marginal pdf of the received phase is also given analytically.

Based on first-order perturbation theory of the soliton, the Gordon–Haus timing jitter induced by amplifier noise is found to be non-Gaussian distributed. Both frequency and timing jitter have larger tail probabilities than Gaussian distribution given by the linearized perturbation theory. The timing jitter has a larger discrepancy from Gaussian di...

The error probability is calculated for phase-modulated systems with nonlinear phase noise. Using the assumption that the phase of amplifier noise and nonlinear phase noise are independent of each other, the error probability and penalty are calculated for both phase-shift keying (PSK) and differential phase-shift keying (DPSK) systems. The mean no...

When nonlinear phase noise is compensated by the received intensity, simple formulas are derived for the error probability of differential phase-shift keying signals. Simulation is conducted to verify the error probability. The tolerance of nonlinear phase noise is doubled by the compensator, allowing doubling of the transmission distance if nonlin...

The probability density of nonlinear phase noise, often called the Gordon–Mollenauer effect, is derived analytically. The nonlinear phase noise can be accurately modeled as the summation of a Gaussian random variable and a noncentral chi-square random variable with two degrees of freedom. Using the received intensity to correct for the phase noise,...

The asymptotic probability density of nonlinear phase noise, often called the Gordon–Mollenauer effect, is derived analytically when the number of fiber spans is large. Nonlinear phase noise is the summation of infinitely many independently distributed noncentral χ 2 random variables with two degrees of freedom. The mean and the standard deviation...

Polarization control is used in a tri-directional wavelength-reused system to reduce the power penalty caused by coherent mixing of the signal with Rayleigh backscattering noise. For a 25 + 25 km, 10 Gb/s tri-directional transmission system, the power penalty is 4.0 dB under the worst polarization control and could be reduced to 0.4 dB under optima...

The nonlinear phase noise, often called the Gordon–Mollenauer effect, is correlated with the received intensity. The optimal compensator is the minimum mean-square error (MMSE) compensator to estimate the nonlinear phase noise using the received intensity. The MMSE compensator is derived analytically and approximated by subtracting a correction ter...

In a bidirectional wavelength-reused system, polarization control is used to reduce power penalty induced by coherent mixing of the signal with Rayleigh backscattering. The reduction of the effect of Rayleigh backscattering is theoretical study and experimental demonstration. For a 50 km, 10 Gb/s bidirectional transmission system, an error floor of...