Convergence analyses and new algorithms in blind equalization/identification

The elimination of a training period makes blind equalization very attractive for applications. In this dissertation, the global convergence of blind equalizers is further investigated. Several new algorithms for blind equalization/identification are proposed.; The main problems are local convergence and slow convergence. For T-spaced equalizers (TSEs), it is shown that the recently proposed Shtrom-Fan cost function has local minima. For fractionally spaced equalizers (FSEs), the temporal or spatial diversity satisfying the “length-and-zero” condition makes all global minima reachable. Here, a new correct proof of the global convergence of constrained FSEs is provided. For the constrained equalizers, it is shown that channel diversity makes it very difficult, if not totally impossible, to avoid the all zero output.; In order to overcome the slow convergence problem, a Taylor series in complex form is developed. Based on the Taylor series, a Newton-like algorithm for complex variables is proposed. The new algorithm makes use of the second order derivative information. Thus, fast convergence can be achieved. Here, Stochastic Newton-like algorithms (SNLA) for two blind equalization cost functions are developed. Simulations show that the new algorithm performs better than the self-orthogonalizing algorithm (SOA). The fast convergence of the SNLA and SOA is at the expense of a higher computational load. In this dissertation, two fast algorithms for blind equalization are proposed. The computational complex is decreased by one order of the equalizer length by using fast algorithms, which is made possible by the innovative construction of a reference signal.; The attractive second-order statistics blind identification methods, which need far less symbols for channel, identification than the higher order statistics (HOS) method, are investigated in the frequency domain. Instead of using cyclic spectrum, a multichannel spectrum matrix is used. It is shown that one can identify a channel by properly factorizing the power spectrum. The relationship between the power spectrum matrix and the cyclic spectrum is discussed. The existing spectral factorization algorithms are investigated for extension to the case where the spectrum matrix is not of full rank. Finally, a numerical fitting algorithm is presented.