Algorithms for blind FIR channel estimation and signal restoration

Blind system identification (BSI) consists of identifying an unknown system that is driven by an (or multiple) unobservable input(s) and estimating the input(s) based on the output. The systems commonly considered can be (i) single-input and single-output (SISO), (ii) single-input and multi-output (SIMO), and (iii) multi-input and muIti-output (MIMO).; BSI has been an area of active research in the past decade or so, due to the growing interest in its applications. Significant progress has been made and enormous algorithms have been developed as a result of the research. However, the existing solutions to many of the BSI problems are far from satisfactory.; This thesis represents a continuation of the past effort in this important area of research. First, by effectively utilising the structure of the received data, a time domain method for the SIMO model with a deterministic input signal is developed to recover the original signal from its reverberant components. Second-order statistics (SOS) is used to suppress circumstances with strong noises and reverberations. Different noise conditions, e.g., two receivers with the same noises and with different but highly related noises, are discussed. By exploiting a constrained optimisation technique, an optimal solution of the FIR coefficients is obtained. Compared to the popular noise cancelling algorithm (ANC), the new algorithms recover the original signal with high accuracy and are not restricted to any particular type of noises even when the SNR is very small (e.g., SNR = −11dB). In addition, the adaptive algorithms offer quick convergence properties.; The situation with one receiver is thus considered and the problem of one-FIR-channel estimation for a SISO system driven by an unobservable i.i.d. non-Gaussian signal is addressed. Higher-order statistics (HOS) is employed as a developing tool since it can handle non-linear and non-minimum phase (NMP) system, and suppress Gaussian noises automatically. New algorithms of the present investigation have been designed to (i) suppress complicated noises, which may be MA Gaussian, ARMA Gaussian, i.i.d. non-Gaussian or a combination of these, and (ii) remove the additional post-processing step. Additionally, two general methods for FIR system identification by using cumulants with arbitrary selective orders are also proposed. For the parameter estimation of a third-order NMP system under the ARMA Gaussian noise and with a SNR of OdB, a noticeable improvement of 88% is achieved as compared to the best result obtained using the conventional algorithms.; Finally, a MIMO system is investigated. Two types of input signals, i.i.d non-Gaussian sequences and stationary signals, are considered. First, the closed-form and the least-squares solution of the multi-channel problem are obtained by using the Kronecker product. Second, the channel parameters are estimated by employing a reference signal vector. A recurrent formula is then used to separate various speech signals. Comparing our new algorithm with the extended fourth-order blind identification (EFOBI) algorithm, it is found that the former outperforms the latter in preserving both the signal waveforms and the amplitudes even in a very noisy environment. In addition the algorithm works well for the systems described by a memoryless model or FIR model. (Abstract shortened by UMI.)...