Nonlinear Signal Processing and its Applications to Telecommunications

This dissertation is primarily concerned with the estimation of nonlinear communication systems that are modeled by Volterra series. The major methods used for estimating the unknown channel parameters can be classified into two main categories: training-based and blind. First, orthobasis representation and training-based identification through the respective Fourier series are investigated for most modulated signals of interest. Next, higher order cumulants are used for the blind identification of nonlinear channels. The proposed algorithms for blind nonlinear channel estimation take advantage of the inherent sparseness of the higher order cumulants of common communication signals. Then, sparse Volterra channels are employed to mitigate the enormous computational complexity of the full Volterra channels. Sparse Volterra channels are approached by two newly developed sparse adaptive (greedy and l1-regularized) algorithms. Last, the problem of blind sparse channel estimation is formulated by modifying the Expectation-Maximization framework to accommodate channel sparsity.