Adaptive algorithm using faddeev matric inversionmethod

Abstract

The Faddeev method has been used to find the characteristic polynomial of a given matrix and its inverse. In this dissertation, we have modified it for appliacation to the construction of orthogonal vectors and to the adaptive array processing. The latter is the main objective of this dissertation. Orthogonal vectors can be generated conventionally by the well known GramSchmidt method which ultimately makes a projection matrix. We suggest a new method that can obtain the same projection matrix. Theorems concerning orthogonalities are presented which may lead to the construction of the orthogonal vectors and provide a theoretical basis for the following adaptive algorithm. The adaptive array utilizing angle information on the desired signal suffers from degradation of the performance due to an error in the information, which causes the array to regard the desired signal as an interference to be rejected. We propose a new algorithm which can reduce the sensitivity to pointing errors, by employing the Faddeev method. In the proposed algorithm, the number of the pattern nulls to be formed on the directional signal can be constrinted as what one wants, and so these nulls may be made on the interference sources but not the desired signal. We have investigated some features of the proposed algorithm analytically and by computer simulation for single- and two-interference cases. These include the weight vector representation in a beam-space, the adapted pattern, and the output signal-to-interference-plus-noise ratio(SINR). Especially it is very easy to calculate the proposed weights for the rejection of a single interference, even if the covariance matrix is ill-conditioned. In the absence of a pointing error, the performance is virtually the same as the optimum. Although there is a pointing error, the drop in the SINR is smaller as the interferences are stronger. If all the interferences are much stronger than the desired signal, its output becomes equal to that of th...