arXiv subjects
Publications and source records attributed to Keang-Po Ho.
The central limit for the product of free random variables are studied by evaluating all the moments of the limit distribution. The logarithm of the central limit is found to be the same as the sum of two independent free random variables: one semicircularly distributed and another uniformly distributed. The logarithm of central limit has a moment-generating function of $\exp(ξ^2 s/2) {_{1}F_{1}}\left(1-s; 2; -ξ^2 s \right)$.
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 present at the input, modal transmission and coupling coefficients are mode-dependent and may be computed using a simple mode-clipping model. When multiple modes are present, interference between modes alters the transmission and coupling coefficients, shifting the passband center frequency and changing its bandwidth. Mode-coupling matrices are used to compute mixed modes having the narrowest or widest bandwidths, or having the largest center-frequency offsets. In a specific design for graded-index fiber, five mode groups and 50-GHz channel spacing, the one-sided bandwidth may change up to $\pm$3.6 GHz. In a system with many cascaded switches and strong mode coupling, the end-to-end response per switch may be characterized by a mode-averaged transmission coefficient.
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) algorithm can form multiple beams between the transmitter and receiver for multi-input-multi-output (MIMO) operations. For both shared and split MIMO architecture, the ALS beamforming algorithm can be operated in both frequency-flat and frequency-selective channels. In the split architecture, MIMO beamforming approximately maximizes the capacity of the beam-formed MIMO channel.
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 eigenvalues of zero-trace Gaussian unitary ensemble, and the probability density function (p.d.f.) of the GDs is the eigenvalue distribution of the ensemble. For fibers with two to seven modes, the marginal p.d.f. of the GDs is derived analytically. For fibers with a large number of modes, this p.d.f. is shown to approach a semicircle distribution. In the strong-coupling regime, the delay spread is proportional to the square root of the number of independent sections, or the square root of the overall fiber length. This revision also made clarification to the original paper, the group delay statistics is also extended to high number of modes.
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 deviation proportional to the accumulated MDL. The other matrix is a deterministic matrix with uniform eigenvalues proportional to the square of the accumulated MDL. The results are analytically correct for fibers with two or large number of modes, and also numerically verified for other cases.
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 substantially lower than the average capacity. Mode-dependent gains and losses, when frequency-dependent, have a coherence bandwidth that is inversely proportional to the modal group delay spread. When mode-division-multiplexed signals occupy a bandwidth far larger than the coherence bandwidth, the mode-dependent gains and losses are averaged over frequency, causing the outage capacity to approach the average capacity. The difference between the average and outage capacities is found to be inversely proportional to the square-root of a diversity order that is given approximately by the ratio of the signal bandwidth to the coherence bandwidth.
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 small-MDL region that is expected to be of interest for practical long-haul transmission. Information-theoretic channel capacities of mode-division-multiplexed systems in the presence of MDL are studied, including average and outage capacities, with and without channel state information.
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 penalty of 0.66 and 0.30 dB for standard single-mode and nonzero dispersion-shifted fibers, respectively.
The phase and amplitude responses of a narrow-band optical filter are measured simultaneously using a microwave network analyzer. The measurement is based on an interferometric arrangement to split light into two paths and then combine them. In one of the two paths, a Mach-Zehnder modulator generates two tones without carrier and the narrow-band optical filter just passes through one of the tones. The temperature and environmental variations are removed by separated phase and amplitude averaging. The amplitude and phase responses of the optical filter are measured to the resolution and accuracy of the network analyzer.
The variance of nonlinear phase noise is analyzed by including the effect of intrachannel cross-phase modulation (IXPM)-induced nonlinear phase noise. Consistent with Ho and Wang [1] but in contrary to the conclusion of both Kumar [2] and Green et al. [3], the variance of nonlinear phase noise does not decrease much with the increase of chromatic dispersion. The results are consistent with a careful reexamination of both Kumar [2] and Green et al. [3].
A semi-analytical method evaluates the error probability of DPSK signals with intrachannel four-wave-mixing (IFWM) in a highly dispersive fiber link with strong pulse overlap. Depending on initial pulse width, the mean nonlinear phase shift of the system can be from 1 to 2 rad for signal-to-noise ratio (SNR) penalty less than 1 dB. An approximated empirical formula, valid for penalty less than 2 dB, uses the variance of the differential phase of the ghost pulses to estimate the penalty.
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 systems.
Using the maximum-likelihood detector (MLD) of a soliton with timing jitter and noise, other than walk-out of the bit interval, timing jitter does not degrade the performance of MLD. When the MLD is simulated with important sampling method, even with a timing jitter standard deviation the same as the full-width-half-maximum (FWHM) of the soliton, the signal-to-noise (SNR) penalty is just about 0.2 dB. The MLD performs better than conventional scheme to lengthen the decision window with additive noise proportional to the window wide.
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. When the error probability for differential phase-shift keying (DPSK) signals is evaluated, depending on the number of fiber spans, the signal-to-noise ratio (SNR) penalty is increased by up to 0.23 dB due to the dependence between the Gaussian noise and the quadratic phase noise.
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 joint characteristic function of nonlinear phase noise with the phase of amplifier noise, the error probability of signal having nonlinear phase noise is calculated using the Fourier series expansion of the probability density function. The error probability is increased due to the dependence between nonlinear phase noise and the phase of amplifier noise. When the received intensity is used to compensate the nonlinear phase noise, the optimal linear and nonlinear minimum mean-square error compensators are derived analytically using the joint characteristic function of nonlinear phase noise and received intensity. Using the joint probability density of received amplitude and phase, the optimal maximum a posteriori probability detector is derived analytically. The nonlinear compensator always performs better than linear compensator.
The characteristic function of soliton phase jitter is found analytically when the soliton is perturbed by amplifier noise. In additional to that from amplitude jitter, the nonlinear phase noise due to frequency and timing jitter is also analyzed. Because the nonlinear phase noise is not Gaussian distributed, the overall phase jitter is also non-Gaussian. For a fixed mean nonlinear phase shift, the contribution of nonlinear phase noise from frequency and timing jitter decreases with distance and signal-to-noise ratio.
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 received intensity. Using optimal compensation, the standard deviation of residual phase noise is halved, doubling the transmission distance in systems limited by nonlinear phase noise.
Based on the first-order perturbation theory of soliton, the Gordon-Haus timing jitter induced by amplifier noise is found to be non-Gaussian distributed. Compared with Gaussian distribution given by the linearized perturbation theory, both frequency and timing jitter have larger tail probability. The timing jitter has a larger discrepancy to Gaussian distribution than that of frequency jitter.