The main objectives of this dissertation are to develop efficient LMS algorithms for channel equalization and to apply it to a NTSC channel equalization.
Generally, the convergence speed of weight vectors depends on the spread of the eigen values of input autocorrelation matrix(R). If the spread is large, the convergence speed is slow. From this kind of view point, the inverse matrix of R can be used for decreasing the spread of eigen value to make the convergence speed fast. But it is too complicated to get an inverse matrix of R and to update the weight vector due to a large of computation.
Thus we propose an efficient algorithm for computing an inverse matrix of R using DCT(Discrete Cosine Transform) in case of the short period pseudo random signal being used as the reference signal. In order to obtain optimum weight vector fast, this inverse procedure is applied to Newton/LMS algorithm. And through the quantization of inverse of R the complexity of the algorithm can be greatly reduced. The computational results show that the algorithm is efficient when the reference signal is periodic.
And the Newton/LMS algorithm with DCT is extended into the case of non periodic reference signal. The non periodic reference signal can be considered as a periodic signal with infinite period. But with the infinity, it's difficult to obtain $R^{-1}$. Thus we investigated the method of considering non periodic signal as periodic one while the error of inverse matrix is minimized and concluded that the minimum period to minimize the error is twice of the length of non periodic reference signal. From this concept, the modified Newton/LMS algorithm is proposed.
As an application area, there is a ghost cancellation problem in NTSC system in which the ghost cancellation reference signal is not periodic. So we apply the modified Newton/LMS algorithms to channel equalization in NTSC system. The computational results show that the proposed algorithm is efficient compared to previous algorithms to cancel ghost.
