In this thesis, α-stable distributions are used to model non-Gaussian phenomena. To justify the applicability of additive stable noise models to a large class of communication systems, an analytical proof is presented which shows that symmetric α-stable (SαS) random variables (RVs) approximate accurately noise resulting from the superposition of small effects. This is demonstrated by considering the nature of noise sources, their temporal and spatial distributions, and propagation conditions. Under very general assumptions, stable distributions are applied to model impulsive noise, multiple access interference in radio networks, and backscattered echo in radar systems. A novel approach to stable noise modeling is introduced based on the LePage series representation. This establishes grounds to investigate practical constraints in the system model adopted. The results presented are useful for the prediction of noise statistics in a wide range of environments with deterministic and stochastic power propagation laws.

Under the assumptions of α-stable and independent noise observations, the performance of classical receivers, which are optimal in Gaussian noise, is investigated. Optimum detectors are then examined. The unsatisfactory performance of conventional receivers and the difficulty in deriving optimal receivers lead to the design of suboptimum receivers. Special attention is paid to various detector structures with limiting nonlinearities, such as those based on locally optimum Bayes detection (LOBD) theory. Also, for non-coherent reception, receivers which are optimal in Cauchy noise are examined. For coherent discrete-time reception, new receivers are introduced based on the empirical characteristic function. In both cases, the trade-off between computational complexity and performance improvements favors simpler detectors with limiters. For most schemes considered, asymptotic or upper bound expressions for the probability of error (Pe) are derived. Numerical calculations and Monte Carlo simulations are provided to confirm the accuracy of the analysis presented. The results obtained are useful in the performance evaluation of digital communication links subject to a mixture of Gaussian and αstable noise.

Finally, detection in correlated noise is addressed. A noise estimation-cancellation technique is employed. Volterra type predictors designed under the minimum mean-squared error (MMSE) criterion are investigated, as well as linear predictors designed under minimum dispersion (MD) criterion. It is found that in the systems analyzed, the MD criterion is not as successful as the MMSE criterion.