Eigenstructure decomposition of correlation matrices is an important pre-processing stage in many modern signal processing applications. In an unknown and possibly changing environment, adaptive algorithms that are efficient and numerically stable as well as readily implementable in hardware for eigen decomposition are highly desirable. Most modern real-time signal processing applications involve processing large amounts of input data and require high throughput rates in order to fulfill the needs of tracking and updating. The authors consider the use of a novel systolic array architecture for the high throughput online implementation of the adaptive simultaneous iteration method (SIM) algorithm for the estimation of the p largest eigenvalues and associated eigenvectors of quasi-stationary or slowly varying correlation matrices.>

In practical applications of importance sampling (IS) simulation, two basic problems are encountered, that of determining the estimation variance and that of evaluating the proper IS parameters needed in the simulations. The authors derive new upper and lower bounds on the estimation variance which are applicable to IS techniques. The upper bound is simple to evaluate and may be minimized by the proper selection of the IS parameter. Thus, lower and upper bounds on the improvement ratio of various IS techniques relative to the direct Monte Carlo simulation are also available. These bounds are shown to be useful and computationally simple to obtain. Based on the proposed technique, one can readily find practical suboptimum IS parameters. Numerical results indicate that these bounding techniques are useful for IS simulations of linear and nonlinear communication systems with intersymbol interference in which bit error rate and IS estimation variances cannot be obtained readily using prior techniques.>