The use of sub-space transforms in signal and array processing

In multipath channels signal processing algorithms based on second order statistics will not properly work and new alternatives have to be developed. This is essentially due to the fact that in such scenarios the autocorrelation matrix is usually correlated due to the time shifting property of the input signals which causes the eigenvalue spread of the correlation matrix to be much larger than unity and this subsequently reduces the speed of convergence of the conventional adaptive algorithms (such as LMS). A direct approach is to use orthogonal transforms to pre-whiten the data to reduce the correlation between the input components before the adaptive filtering. In this paper new self-orthogonalising optimum and sub-optimum adaptive schemes are investigated based on the Karhunen-Loeve transform (KLT) which is implemented using singular value decomposition (SVD). These studies were extended to investigate the minimum norm solution which gives the steady state MSE performance directly. The performances of the proposed schemes are investigated for the equalisation of the real time UMTS channels subjected to wide-band Gaussian noise multipath fading and nonlinearities.