Browsing by Author "Shaw, John Kenneth"

Now showing 1 - 16 of 16
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    Analysis and Characterization of Fiber Nonlinearities with Deterministic and Stochastic Signal Sources
    Lee, Jong-Hyung (Virginia Tech, 2000-02-10)
    In this dissertation, various analytical models to characterize fiber nonlinearities have been applied, and the ranges of validity of the models are determined by comparing with numerical results. First, the perturbation approach is used to solve the nonlinear Schrödinger equation, and its range of validity is determined by comparing to the split-step Fourier method. In addition, it is shown mathematically that the perturbation approach is equivalent to the Volterra series approach. Secondly, root-mean-square (RMS) widths both in the time domain and in the frequency domain are modeled. It is shown that there exists an optimal input pulse width to minimize output pulse width based on the derived RMS models, and the functional form of the minimum output pulse width is derived. The response of a fiber to a sinusoidally modulated input which models an alternating bit sequence is studied to see its utility in measuring system performance in the presence of the fiber nonlinearities. In a single channel system, the sinusoidal response shows a strong correlation with eye-opening penalty in the normal dispersion region over a wide range of parameters, but over a more limited range in the anomalous dispersion region. The cross-phase modulation (CPM) penalty in a multi-channel system is also studied using the sinusoidally modulated input signal. The derived expression shows good agreement with numerical results in conventional fiber systems over a wide range of channel spacing, ∆f, and in dispersion-shifted fiber systems when ∆f > 100GHz. It is also shown that the effect of fiber nonlinearities may be characterized with stochastic input signals using noise-loading analysis. In a dense wavelength division multiplexed (DWDM) system where channels are spaced very closely, the broadened spectrum due to various nonlinear effects like SPM (self-phase modulation), CPM, and FWM (four-wave mixing) is in practice indistinguishable. In such a system, the noise-loading analysis could be useful in assessing the effects of broadened spectrum due to fiber nonlinearities on system performance. Finally, it is shown numerically how fiber nonlinearities can be utilized to improve system performance of a spectrum-sliced WDM system. The major limiting factors of utilizing fiber nonlinearities are also discussed.
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    Analysis and simulation of the Kerr effect in long haul in-line fiber amplifier transmission systems
    Ma, Xiaobing (Virginia Tech, 1994-12-05)
    The next generation of transoceanic submarine cable systems will use in-line fiber amplifiers to replace electrical regenerators. This new approach requires a better understanding of the fiber waveguide, especially the nonlinear characteristics. It has been demonstrated, both by numerical simulation and experiments, that the Kerr effect has the most significant degradation effects on these systems with a single or a few channels. In this dissertation, the numerical simulation is the principal approach but this is supplemented with some analytical studies. There are two phenomena that are directly associated with the Kerr effect: spectrum broadening and four wave mixing (FWM). The broadened signal spectrum enhances the dispersion effect and consequently increases the inter symbol interference. This distortion is significant when the dispersion is relatively large. U sing erbium doped fiber amplifiers, amplified spontaneous emission (ASE) noise is added to the signal The FWM effect between the noise and signal causes a loss in the signal power. In the close vicinity of the zero dispersion wavelength, the FWM effect is maximized due to the loose phase match condition. In order to reduce these degradation effects, dispersion compensation has recently been proposed. Using this approach, it is possible to optimize the system configuration to achieve the best performance. In this dissertation, the dispersion compensation distance, dispersion coefficient, channel bandwidth, bit rate and the degree of imperfect compensation are all subject to the optimization. The evaluation is obtained by the numerical simulation using the mean squared error (MSE), which can be derived as the difference between the wavefronts received by a back-to-back receiver and a receiver at the end of the channel. Although the MSE can't be related to the bit error directly, this research provides the insight into how dispersion and noise behave in the presence of the Kerr effect and points the direction for future experimental research.?
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    Application of the Herschel-Quincke Tube Concept to Higher-Order Acoustic Modes in Two-Dimensional Ducts
    Brady, Lori Ann (Virginia Tech, 2002-03-01)
    The application of the Hershcel-Quincke (HQ) tube as a noise reduction device for one-dimensional plane-wave sound fields has been studied in great detail in previous years. In this thesis, an analytical technique is developed to investigate the potential of the HQ tube concept to control higher-order duct modes. This analytical method involves modeling the tube-duct interfaces as finite piston sources, which couple the acoustic field inside the main duct with the acoustic field within the HQ tube(s). The acoustic field within the HQ tube is modeled as plane-waves and the acoustic field within the main duct is modeled by expanding the sound field in terms of the higher-order modes. This model is then used to investigate the noise reduction mechanisms behind the attenuation of higher-order modes. These mechanisms involve both the reflection of the incident wave as well as the reconstruction and recombination of the modal content of the incident disturbance into other modes. The effects of the modal content of the disturbance along with the HQ tube geometric parameters, such as tube axial position, length, distance between interfaces, and cross-sectional area, are studied with respect to the frequencies of attenuation and the reduction obtained. These results show the potential of the Herschel-Quincke tube concept to reduce higher-order modes in ducts.
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    Combined Space-Time Diversity and Interference Cancellation for MIMO Wireless Systems
    Tsai, Jiann-An (Virginia Tech, 2002-05-02)
    There is increasing interest in the exploitation of multiple-input and multiple-output (MIMO) channels to enhance the capacity of wireless systems. In this study, we develop and evaluate a channel model, evaluate the corresponding channel capacity, and design and analyze a simple orthogonal transmit waveform for MIMO channels in mobile radio environments. We also evaluate the system performance of various interference cancellation techniques when employing multiple-receive antenna in interference-limited systems. The first part of this dissertation presents two major contributions to MIMO systems. The analytical expression for space-time MIMO channel correlation is derived for a Rayleigh fading channel. The information-theoretic channel capacity based on this correlation is also evaluated for a wide variety of mobile radio channels. The second part of this dissertation presents two major contributions to the area of orthogonal waveform design. We analyze the bit-error-rate (BER) performance of a proposed space-time orthogonal waveform for MIMO mobile radio communications. The application of the proposed space-time orthogonal waveform to a conventional cellular system is also evaluated and briefly discussed. Finally, this dissertation investigates a number of interference cancellation techniques for multiple-receive antenna systems. Both adaptive beamforming and multiuser detection are evaluated for various signal waveforms over a variety of mobile radio channels.
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    Improvement of Fiber Optic System Performance by Synchronous Phase Modulation and Filtering at the Transmitter
    Wongpaibool, Virach (Virginia Tech, 2003-01-31)
    In this dissertation the performance of a novel variant of a return-to-zero (RZ) modulation format, based on square-wave phase modulation and filtering of a continuous-wave (CW) signal, is investigated and compared with various modulation formats considered in the literature. We call this modulation format continuous-wave square-wave (CWSW). With CWSW an RZ pulse train is generated by phase modulating the CW signal by a periodic square-wave phase function having an amplitude of and frequency of half the bit rate, and then filtering the signal. The filter performs phase-to-amplitude conversion, resulting in an alternate-sign RZ pulse train, which is shown to be resistant to fiber dispersion. The alternate-sign RZ pulse train is then amplitude modulated with the data before the transmission. Alternate signs between adjacent pulses makes this signal format robust to impairments caused by the optical fiber, similar to a conventional alternate-sign RZ signal format. However, the unique property of the CWSW signal format is that individual pulses can induce peak intensity enhancement (PIE), a phenomenon by which the peak of a pulse increases during the initial propagation in the presence of dispersion. The PIE in effect delays the decrease in the pulse peak, which represents the signal level for bit 1. Thus, the eye opening at the receiver is improved. An analytically tractable model is developed to explain the occurrence of the PIE, which cannot be achieved with a conventional pulse shape. The sources of performance degradations for different modulation formats in single-channel 40 Gb/s systems are also discussed in this dissertation. Various transmission system configurations of practical interest are considered and the performance of CWSW is compared with alternative modulation formats. It is found that the CWSW signal format performs significantly better than the other considered modulation formats in systems not employing dispersion compensation and is comparable to the others in dispersion-managed systems. Furthermore, the transmitter configuration of the CWSW signal format is simpler than the other approaches.
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    Influence of the Number of Degrees of Freedom on the Capacity of Incoherent Optical Fiber Communication Systems
    Teotia, Seemant (Virginia Tech, 2006-05-01)
    The purpose of this dissertation is to find the channel capacity in optical fiber communication systems when incoherent detection is used with single (polarization filtering) and two-polarizations (no polarization filtering). Optical fiber systems employ photodetectors that convert optical intensity to electrical current. Bandpass vector fields may be represented by four orthogonal baseband components corresponding to two quadrature phases and two orthogonal polarizations. Intensity is proportional to the sum of the squares of these four components. In the case of a coherent receiver, a strong optical local oscillator (in phase and with same polarization as the signal) is added to the signal prior to the photodetector. This results in the removal of the quadrature phase and polarization components, and reduces to the one degree of freedom (DOF) case of signal plus local oscillator shot noise for which the Shannon channel capacity formula applies. Electrical noise following the photodetector may also be neglected if there is an optical amplifier before the photodetector in the receiver. The amplifier introduces amplified spontaneous emission noise containing both quadrature phase components and both polarizations (4 DOFs), but the 2 DOF case would result if a polarization filter were used. Although the 1 and 2 DOF cases are of less practical interest than the 4 DOF case, they provide useful benchmarks for comparing performance limits. We evaluate both spectral efficiency limits (bps/Hz) in the limit of high and low SNR for the 1,2 and 4 DOF cases and also find the power efficiency (minimum number of photons per bit) for each of these cases. It is shown that for high SNR the spectral efficiency is the same independent of the number of DOFs and that the half-Gaussian distribution is the optimum distribution. We are able to thus obtain a compact equation for spectral efficiency which behaves in a similar way to the Shannon capacity formula but with the SNR scaled by a constant. We also show that for low SNR the half-Gaussian distribution is not the optimum distribution as the slope of the mutual information changes with the square of SNR which would lead to the number of photons per bit becoming infinite in the limit of SNR going to zero. We use a modified half-Gaussian distribution which has a discrete component (an impulse function at the origin) and provide a simple proof that this distribution results in a mutual information that goes to zero linearly with SNR resulting in a minimum number of photons per bit. Furthermore, by increasing the magnitude of the discrete component at the origin, it is shown that the minimum number of photons per bit for the incoherent channel approaches that of the coherent channel.
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    Inverse scattering on the line for a Dirac system
    Hinton, D. B.; Jordan, A. K.; Klaus, Martin; Shaw, John Kenneth (AIP Publishing, 1991-11)
    The whole-line version of the Gelfand-Levitan-Marchenko (GLM) equation for a Dirac system is studied. A new derivation of the GLM equation is given, under weaker hypotheses than Frolov's earlier treatment [Sov. Math. Dok1. 13, 1468 (1972)], and the complete inversion is carried out in some explicit cases in which a spectral gap is present. Previous calculations of this type are restricted either to a scalar potential or degenerate gap. Applications are discussed in connection with optical couplers and soliton equations.
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    IPSec Overhead in Wireline and Wireless Networks for Web and Email Applications
    Hadjichristofi, George Costa (Virginia Tech, 2001-11-29)
    This research focuses on developing a set of secure communication network testbeds and using them to measure the overhead of IP Security (IPSec) for email and web applications. The network testbeds are implemented using both wireline and wireless technologies. The testing involves a combination of authentication algorithms such as Hashed Message Authentication Code-Message Digest 5 (HMAC-MD5) and Hashed Message Authentication Code-Secure Hash Algorithm 1 (HMAC-SHA1), implemented through different authentication protocols such as ESP and AH, and used in conjunction with the Triple Digital Encryption Standard (3DES). The research examines the overhead using no encryption and no authentication, authentication and no encryption, and authentication and encryption. A variety of different sizes of compressed and uncompressed files, are considered when measuring the overhead. The testbed realizes security using IPSec to secure the connection between different nodes. The email protocol that is used is the Simple Mail Transfer Protocol (SMTP) and the web protocol considered is the Hyper Text Transfer Protocol (HTTP). The key metrics considered are the network load in bytes, the number of packets, and the transfer time. This research emphasizes the importance of using HTTP to access files than using SMTP. Use of HTTP requires fewer packets, lower network loads, and lower transfer times than SMTP. It is demonstrated that this difference, which occurs regardless of security, is magnified by the use of authentication and encryption. The results also indicate the value of using compressed files for file transfers. Compressed and uncompressed files require the same transfer time, network load and number of packets since FreeS/WAN IPSec does not carry any form of compression on the data before passing it to the data link layer. Both authentication algorithms, HMAC-MD5 and HMAC- SHA1, result in about the same network load and number of packets. However, HMAC-SHA1 results in a higher transfer time than HMAC-MD5 because of SHA1's higher computational requirements. ESP authentication and ESP encryption reduce the network load for small files only, compared to ESP encryption and AH authentication. ESP authentication could not be compared with AH authentication, since the FreeS/WAN IPSec implementation used in the study does not support ESP authentication without using encryption. In a wireless environment, using IPSec does not increase the network load and the number of transactions, when compared to a wireline environment. Also, the effect of security on transfer time is higher compared to a wireline environment, even though that increase is overshadowed by the high transfer time percentage increase due to the wireless medium.
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    Iterative Detection and Decoding for Wireless Communications
    Valenti, Matthew C. (Virginia Tech, 1999-07-08)
    Turbo codes are a class of forward error correction (FEC) codes that offer energy efficiencies close to the limits predicted by information theory. The features of turbo codes include parallel code concatenation, recursive convolutional encoding, nonuniform interleaving, and an associated iterative decoding algorithm. Although the iterative decoding algorithm has been primarily used for the decoding of turbo codes, it represents a solution to a more general class of estimation problems that can be described as follows: a data set directly or indirectly drives the state transitions of two or more Markov processes; the output of one or more of the Markov processes is observed through noise; based on the observations, the original data set is estimated. This dissertation specifically describes the process of encoding and decoding turbo codes. In addition, a more general discussion of iterative decoding is presented. Then, several new applications of iterative decoding are proposed and investigated through computer simulation. The new applications solve two categories of problems: the detection of turbo codes over time-varying channels, and the distributed detection of coded multiple-access signals. Because turbo codes operate at low signal-to-noise ratios, the process of phase estimation and tracking becomes difficult to perform. Additionally, the turbo decoding algorithm requires precise estimates of the channel gain and noise variance. The first significant contribution of this dissertation is a study of several methods of channel estimation suitable specifically for turbo coded systems. The second significant contribution of this dissertation is a proposed method for jointly detecting coded multiple-access signals using observations from several locations, such as spatially separated base stations. The proposed system architecture draws from the concepts of macrodiversity combining, multiuser detection, and iterative decoding. Simulation results show that when the system is applied to the time division multiple-access cellular uplink, a significant improvement in system capacity results.
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    Limitations and Improvement of Subcarrier Multiplexed Systems over Optical Fiber
    Tebben, Daniel James (Virginia Tech, 2006-04-17)
    Optical coherent techniques are used to eliminate the power fading found in optical subcarrier multiplexed systems. In a double-side band optical subcarrier system the signal experiences a periodic power fading that is dependent on the fiber dispersion and subcarrier frequency. This power fading is manifested during the direct detection of the subcarrier system using a square-law photodetector. Using a modified optical local oscillator to coherently detect the subcarrier channel this power fading can be eliminated. An optical local oscillator is centered at the optical carrier in order to perform homodyne detection. However, the local oscillator is modulated by a term equal the subcarrier frequency of interest. This is then a dual-frequency optical local oscillator. By controlling the phases of the local oscillator and the local subcarrier oscillator independently in the homodyne detection scheme, both the phase error and power fading of the detected subcarrier channel can be eliminated. This technique also allows the subcarrier to be selected optically, before the optical-to-electrical conversion. Analytical and simulation results are given to show the benefits of optical coherent detection in double-sideband subcarrier systems. By eliminating the periodic power loss found in the double-sideband subcarrier system the signal becomes dispersion limited and not power limited. A comparison of double-sideband and single-sideband subcarrier systems is presented. Multiple subcarriers and subcarrier spacing are also investigated for both double sideband and single sideband subcarrier systems. Optical phase and modulator noise are also considered in the analysis and simulation of coherent detection using a dual frequency optical local oscillator. Since the implementation used to eliminate the power fading is a phase correction based process, the phase noise of both the source and local oscillator lasers must be considered and the technique compared to typical direct and coherent detection techniques. Also, the effects of modulator nonlinearity are simulated for multichannel subcarrier multiplexed systems and comparisons made between the performance of using the dual-frequency local oscillator and typical detection techniques. It is shown that the advantages of the dual-frequency LO are retained in the presence of both phase noise and modulator nonlinearity.
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    Modeling, Analysis, and Design of Subcarrier Multiplexing on Multimode Fiber
    Kanprachar, Surachet (Virginia Tech, 2003-03-14)
    This dissertation focuses on the use of subcarrier multiplexing (SCM) in multimode fibers, utilizing carrier frequencies above what is generally utilized for multimode fiber transmission, to achieve high bit rates. In the high frequency region (i.e., frequencies larger than the intermodal bandwidth), the magnitude response of multimode fiber does not decrease monotonically as a function of the frequency but is shown to become relatively flat (but with several deep nulls) with an amplitude below that at DC. The statistical properties of this frequency response at high frequencies are analyzed. The probability density function of the magnitude response at high frequencies is found to be a Rayleigh density function. The average amplitude in this high frequency region does not depend on the frequency but depends on the number of modes supported by the fiber. To transmit a high bit rate signal over the multimode fiber, subcarrier multiplexing is adopted. The performance of the SCM multimode fiber system is presented. The performance of the SCM system is significantly degraded if there are some subcarriers located at the deep nulls of the fiber. Equalization and spread spectrum techniques are investigated but are shown to be not effective in combating the effects of these nulls. To cancel the effects of these deep nulls, training process and diversity coding are considered. The basic theory of diversity coding is given. It is found that the performances of the system with training process and the system with diversity coding are almost identical. However, diversity coding is more appropriate since it requires less system complexity. Finally, the practical limits and capacity of the SCM multimode fiber system are investigated. It is shown that a signal with a bit rate of 1.45 Gbps can be transmitted over a distance up to 5 km.
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    A nonlinear Volterra equation of nonconvolution type
    Smith, Manfred Charles (Virginia Tech, 1977-12-05)
    The purpose of this paper is to study the asymptotic behavior of bounded solutions x(t) of the integrodifferential equation.
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    Optimal Dispersion Precompensation By Pulse Chirping
    Jacobs, Ira; Shaw, John Kenneth (Optical Society of America, 2002-03-01)
    For the procedure of dispersion precompensation in fibers by prechirping, we found that there is a maximum distance over which a pulse initially compressed by prechirping can return to its original width. The distance constraint comes in the form of a mathematical relationship involving the distance, dispersion, initial pulse width, and peak power, implying that the restriction governs all the fiber parameters. Simple closed-form approximations for the constraint and for the corresponding required prechirp, are derived on the basis of a variational approach. The validity of the analytical formulas is confirmed by split-step Fourier numerical simulation.
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    Purely imaginary eigenvalues of Zakharov-Shabat systems
    Klaus, Martin; Shaw, John Kenneth (American Physical Society, 2002-03)
    Zakharov-Shabat systems with single-hump and real, but not necessarily symmetric, potentials are shown to have purely imaginary eigenvalues only. Coupled with examples of double-hump potentials with nonimaginary eigenvalues, this establishes that confinement of Zakharov-Shabat eigenvalues to the imaginary axis is a characteristic of potentials whose energy is concentrated in a single region of the time axis.
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    Variational Calculation of Optimum Dispersion Compensation for Nonlinear Dispersive Fibers
    Wongsangpaiboon, Natee (Virginia Tech, 2000-05-17)
    In fiber optic communication systems, the main linear phenomenon that causes optical pulse broadening is called dispersion, which limits the transmission data rate and distance. The principle nonlinear effect, called self-phase modulation, can also limit the system performance by causing spectral broadening. Hence, to achieve the optimal system performance, high data rate and low bandwidth occupancy, those effects must be overcome or compensated. In a nonlinear dispersive fiber, properties of a transmitting pulse: width, chirp, and spectra, are changed along the way and are complicated to predict. Although there is a well-known differential equation, called the Nonlinear Schrodinger Equation, which describes the complex envelope of the optical pulse subject to the nonlinear and dispersion effects, the equation cannot generally be solved in closed form. Although, the split-step Fourier method can be used to numerically determine pulse properties from this nonlinear equation, numerical results are time consuming to obtain and provide limited insight into functional relationships and how to design input pulses. One technique, called the Variational Method, is an approximate but accurate way to solve the nonlinear Schrodinger equation in closed form. This method is exploited throughout this thesis to study the pulse properties in a nonlinear dispersive fiber, and to explore ways to compensate dispersion for both single link and concatenated link systems. In a single link system, dispersion compensation can be achieved by appropriately pre-chirping the input pulse. In this thesis, the variational method is then used to calculate the optimal values of pre-chirping, in which: (i) the initial pulse and spectral width are restored at the output, (ii) output pulse width is minimized, (iii) the output pulse is transform limited, and (iv) the output time-bandwidth product is minimized. For a concatenated link system, the variational calculation is used to (i) show the symmetry of pulse width around the chirp-free point in the plot of pulse width versus distance, (ii) find the optimal dispersion constant of the dispersion compensation fiber in the nonlinear dispersive regime, and (iii) suggest the dispersion maps for two and four link systems in which initial conditions (or parameters) are restored at the output end. The accuracy of the variational approximation is confirmed by split-step Fourier simulation throughout this thesis. In addition, the comparisons show that the accuracy of the variational method improves as the nonlinear effects become small.
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    Weighted sensitivity optical fiber sensors: theory and applications
    Fogg, Brian Russell (Virginia Tech, 1992-09-05)
    The polarimetric behavior of conventional dual mode, elliptical-core, optical fiber sensors is investigated. To compliment the experimental results, a novel linearly polarized modal analysis of elliptical-core geometries is performed. The method numerically finds solutions of a waveguide equation described by Mathieu differential equations. To move beyond conventional dual mode fiber sensing applications, selected placement of the dual mode fiber endpoints upon a flexible structure is investigated. Modal filtering behavior will result if the endpoints are chosen to span two antinodes of the underlying structure. To truly achieve signal processing capabilities, spatially weighting the sensitivity of the sensor becomes necessary. Experimental results are described and future applications are proposed.