Phase estimation receiver for full-field detection: a novel receiver structure for electronic dispersion compensation of metropolitan area networks

The development of ultra high speed (~20 Gsamples/s) analogue to digital converters (ADCs), and the delayed deployment of 40 Gbit/s transmission due to the economic downturn, has stimulated the investigation of digital signal processing (DSP) techniques for compensation of optical transmission impairments. In the future, DSP will offer an entire suite of tools to compensate for optical impairments and facilitate the use of advanced modulation formats. Chromatic dispersion is a very significant impairment for high speed optical transmission. This thesis investigates a novel electronic method of dispersion compensation which allows for cost-effective accurate detection of the amplitude and phase of the optical field into the radio frequency domain. The first electronic dispersion compensation (EDC) schemes accessed only the amplitude information using square law detection and achieved an increase in transmission distances. This thesis presents a method by using a frequency sensitive filter to estimate the phase of the received optical field and, in conjunction with the amplitude information, the entire field can be digitised using ADCs. This allows DSP technologies to take the next step in optical communications without requiring complex coherent detection. This is of particular of interest in metropolitan area networks. The full-field receiver investigated requires only an additional asymmetrical Mach-Zehnder interferometer and balanced photodiode to achieve a 50% increase in EDC reach compared to amplitude only detection.

On classical and other methods of discriminant analysis and estimation of log-odds

For two multinormal populations with equal covariance matrices the likelihood ratio discriminant function, an alternative allocation rule to the sample linear discriminant function when n1 ≠ n2 ,is studied analytically. With the assumption of a known covariance matrix its distribution is derived and the expectation of its actual and apparent error rates evaluated and compared with those of the sample linear discriminant function. This comparison indicates that the likelihood ratio allocation rule is robust to unequal sample sizes. The quadratic discriminant function is studied, its distribution reviewed and evaluation of its probabilities of misclassification discussed. For known covariance matrices the distribution of the sample quadratic discriminant function is derived. When the known covariance matrices are proportional exact expressions for the expectation of its actual and apparent error rates are obtained and evaluated. The effectiveness of the sample linear discriminant function for this case is also considered. Estimation of true log-odds for two multinormal populations with equal or unequal covariance matrices is studied. The estimative, Bayesian predictive and a kernel method are compared by evaluating their biases and mean square errors. Some algebraic expressions for these quantities are derived. With equal covariance matrices the predictive method is preferable. Where it derives this superiority is investigated by considering its performance for various levels of fixed true log-odds. It is also shown that the predictive method is sensitive to n1 ≠ n2. For unequal but proportional covariance matrices the unbiased estimative method is preferred. Product Normal kernel density estimates are used to give a kernel estimator of true log-odds. The effect of correlation in the variables with product kernels is considered. With equal covariance matrices the kernel and parametric estimators are compared by simulation. For moderately correlated variables and large dimension sizes the product kernel method is a good estimator of true log-odds.