Applications of wavelet transforms to optical fiber communications networks

Number of theoretical models have been developed to characterize system components behavior using classical numerical techniques. In this framework, wavelet theory provides a novel solid platform to address the various aspects of the modeling with a broader applications scope and more versatile analysis. Using continuous and discrete wavelet transforms to model the fundamental problem of pulse propagation in nonlinear dispersive media has proven to be an efficient alternative to the classical numerical methods. The proposed Split Step Discrete Wavelet algorithm has lower complexity than the Split Step Fourier algorithm. For highly regular wavelet functions, it achieves an accuracy of 2.98 x 10-5 which is comparable to the Fourier algorithm. This technique brings all the wavelet inherent capabilities of efficient signal decomposition with fewer coefficients, compression, denoising and estimation. A wavelet-based modeling can address transient behavior as well as any time-dependent spectral analysis which are commonly encountered at various levels of optical communications networks. In addition, wavelet filters, which are the basis of the discrete implementation of the wavelet transform algorithm, can be used to perform an in-line analysis and noise suppression. This is shown to improve the performance of coherent lightwave receivers performance by greatly reducing the bit error rate in the system. Wavelet and wavelet packets based techniques reduced the bit error rate in a FSK coherent detection scheme from 10-1 to 10 -6 when the initial SNR is only 7 dB. With a deeper understanding of signal behavior in the wavelet domain, the proposed technique can be utilized in various other aspects: any undesirable dispersion, chirping and higher order nonlinear effects can be analyzed and potentially attenuated if not excised using an in-line wavelet filters. This can be achieved by developing algorithm similar to the denoising ones that attenuate the signal components in the wavelet domain that are directly responsible for performance degradation. Finally, wavelets are used to analyze the self-similar nature of data traffic. The H parameter or self-similarity parameter is embedded in the detail coefficients of the wavelet transform of the self-similar process and can be estimated using straightforward variance computation. A detailed study of chaos onset in data networks is also presented. This is a crucial problem in analyzing, dimensioning and predicting the performance of emerging networks. The multitude of services in future IP networks will induce a variety of traffics of different statistical natures that are expected to be carried over one unified optical network. If chaos is onset, arbitrarily similar traffic conditions may lead to exponentially different network behaviors in terms of queing delays and network utilization. Applying nonlinear dynamic theory to data and telephony networks showed that chaos will not be onset since the necessary condition of broad spectra is not satisfied for self-similar and Poisson models.