690 research outputs found
Information Transmission using the Nonlinear Fourier Transform, Part I: Mathematical Tools
The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and
exactly solvable models, is a method for solving integrable partial
differential equations governing wave propagation in certain nonlinear media.
The NFT decorrelates signal degrees-of-freedom in such models, in much the same
way that the Fourier transform does for linear systems. In this three-part
series of papers, this observation is exploited for data transmission over
integrable channels such as optical fibers, where pulse propagation is governed
by the nonlinear Schr\"odinger equation. In this transmission scheme, which can
be viewed as a nonlinear analogue of orthogonal frequency-division multiplexing
commonly used in linear channels, information is encoded in the nonlinear
frequencies and their spectral amplitudes. Unlike most other fiber-optic
transmission schemes, this technique deals with both dispersion and
nonlinearity directly and unconditionally without the need for dispersion or
nonlinearity compensation methods. This first paper explains the mathematical
tools that underlie the method.Comment: This version contains minor updates of IEEE Transactions on
Information Theory, vol. 60, no. 7, pp. 4312--4328, July 201
Information Transmission using the Nonlinear Fourier Transform, Part III: Spectrum Modulation
Motivated by the looming "capacity crunch" in fiber-optic networks,
information transmission over such systems is revisited. Among numerous
distortions, inter-channel interference in multiuser wavelength-division
multiplexing (WDM) is identified as the seemingly intractable factor limiting
the achievable rate at high launch power. However, this distortion and similar
ones arising from nonlinearity are primarily due to the use of methods suited
for linear systems, namely WDM and linear pulse-train transmission, for the
nonlinear optical channel. Exploiting the integrability of the nonlinear
Schr\"odinger (NLS) equation, a nonlinear frequency-division multiplexing
(NFDM) scheme is presented, which directly modulates non-interacting signal
degrees-of-freedom under NLS propagation. The main distinction between this and
previous methods is that NFDM is able to cope with the nonlinearity, and thus,
as the the signal power or transmission distance is increased, the new method
does not suffer from the deterministic cross-talk between signal components
which has degraded the performance of previous approaches. In this paper,
emphasis is placed on modulation of the discrete component of the nonlinear
Fourier transform of the signal and some simple examples of achievable spectral
efficiencies are provided.Comment: Updated version of IEEE Transactions on Information Theory, vol. 60,
no. 7, pp. 4346--4369, July, 201
Information Transmission using the Nonlinear Fourier Transform, Part II: Numerical Methods
In this paper, numerical methods are suggested to compute the discrete and
the continuous spectrum of a signal with respect to the Zakharov-Shabat system,
a Lax operator underlying numerous integrable communication channels including
the nonlinear Schr\"odinger channel, modeling pulse propagation in optical
fibers. These methods are subsequently tested and their ability to estimate the
spectrum are compared against each other. These methods are used to compute the
spectrum of various signals commonly used in the optical fiber communications.
It is found that the layer-peeling and the spectral methods are suitable
schemes to estimate the nonlinear spectra with good accuracy. To illustrate the
structure of the spectrum, the locus of the eigenvalues is determined under
amplitude and phase modulation in a number of examples. It is observed that in
some cases, as signal parameters vary, eigenvalues collide and change their
course of motion. The real axis is typically the place from which new
eigenvalues originate or are absorbed into after traveling a trajectory in the
complex plane.Comment: Minor updates to IEEE Transactions on Information Theory, vol. 60,
no. 7, pp. 4329--4345, July 201
Upper Bound on the Capacity of a Cascade of Nonlinear and Noisy Channels
An upper bound on the capacity of a cascade of nonlinear and noisy channels
is presented. The cascade mimics the split-step Fourier method for computing
waveform propagation governed by the stochastic generalized nonlinear
Schroedinger equation. It is shown that the spectral efficiency of the cascade
is at most log(1+SNR), where SNR is the receiver signal-to-noise ratio. The
results may be applied to optical fiber channels. However, the definition of
bandwidth is subtle and leaves open interpretations of the bound. Some of these
interpretations are discussed.Comment: The main change is to define the noise as bandlimited already in (8)
rather than before (15). This serves to clarify subsequent step
Nonlinear Frequency-Division Multiplexing in the Focusing Regime
Achievable rates of the nonlinear frequency-division multiplexing (NFDM) and
wavelength-division multiplexing (WDM) subject to the same power and bandwidth
constraints are computed as a function of transmit power in the standard
single-mode fiber. NFDM achieves higher rates than WDM.Comment: Invited paper to be presented at The Optical Fiber Communications
Conference and Exposition (OFC), March 201
Diet Selection by Goats at Kalemando, North Darfur, Sudan
Pressure on rangelands of Sudan has increased in the last few decades due to increase in human population and in animal numbers. The rangelands were also impacted by climate change, desertification, agricultural expansion, mining, and overgrazing. Decreased amounts of rainfall have impoverished the natural rangelands. Goats are capable of grazing on semi-desert regions characterized by low rainfall and scarce grazing plants. It is therefore necessary to know and enhance plant species preferred by goats to properly manage the rangelands. The present study was conducted at Kalemando, North Darfur State during the rainy season of year 2017 when most plants were flowering. The aim was to investigate plant preference by goats under free grazing conditions. A range site of one km2 was selected for the study. The Parker loop method was used to determine botanical composition of herbaceous plants while the point centre quarter method was used to determine density and relative density of trees and shrubs. The bite count technique was used to determine goat diet botanical composition. The herbaceous layer manifested 34 species of which 50.76% were forbs, while grasses constituted 49.24%. The dominant herbaceous plants were Dactyloctenium aegyptium (16.08%), Aristida spp (13.04%), Zaleya Pentandra (9.27%), Trigonella hamosa (8.70%), Echinocloa colona (6.38%) and Aerva javonica (5.36%). Tree and shrub of highest relative density were Acacia tortils (67.86%), Boscia sengalensis (14.29%), and Grewia tenax (3.57%). The diet selected by goats comprised trees/shrubs (42.17%), forbs (36.15%) and grasses (21.68%). Plants most preferred were Commelina kotschyi, Justicia kotschyi, Tribulus terrestris, Trigonella hamosa, Echinocloa colona, Permina resinosa, Grewia tenax. and Acacia mellifera. It is concluded that rehabilitation of rangelands can best be effected by resort to plant species preferred by goats
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