Adaptive algorithms and multiprocessor implementation of Pisarenko's method for one-dimensional and two-dimensional applications

This dissertation presents adaptive algorithms and multiprocessor architectures for VLSI implementation of Pisarenko's method. First, it presents a gradient type LS algorithm for the adaptive implementation of Pisarenko's method using a Lagrange's multiplier. This algorithm has faster convergence with improved frequency tracking when compared to LMS type algorithms and smaller overshoot for tracking frequency in the transient region when compared to Reddy's LS algorithm. The algorithm is verified to have no bias by investigating convergence in the vicinity of a stationary point.;Second, it presents a procedure for implementing a LMS algorithm without normalizing the weight vector. This algorithm has almost the same convergence characteristics in frequency estimation as Thompson's LMS algorithm but requires less multiplications per iteration.;Third, it presents a modification to Pisarenko's method which achieves faster convergence with less computational complexity. The modified Pisarenko's method is extended to 2-D using three spectrum estimations corresponding to the horizontal, vertical and diagonal directions. The modified 2-D Pisarenko's method is still stable and unbiased even when the filter order selected is too large. A procedure is also developed to isolate the spurious spectrum components from the desired spectrum components when the filter order selected is too large.;Finally, this dissertation presents multiprocessor architectures for the gradient type LS algorithm and the modified 2-D Pisarenko's method with the LS performance index.