FPGA Based Parallel Architecture for the Computation of Third-Order Cross Moments

Higher-order Statistics (HOS), also known as cumulants, cross moments and their frequency domain counterparts, known as poly spectra have emerged as a powerful signal processing tool for the synthesis and analysis of signals and systems. Algorithms used for the computation of cross moments are computationally intensive and require high computational speed for real-time applications. For efficiency and high speed, it is often advantageous to realize computation intensive algorithms in hardware. A promising solution that combines high flexibility together with the speed of a traditional hardware is Field Programmable Gate Array (FPGA). In this paper, we present FPGA-based parallel architecture for the computation of third-order cross moments. The proposed design is coded in Very High Speed Integrated Circuit (VHSIC) Hardware Description Language (VHDL) and functionally verified by implementing it on Xilinx Spartan-3 XC3S2000FG900-4 FPGA. Implementation results are presented and it shows that the proposed design can operate at a maximum frequency of 86.618 MHz.

Identification of Wideband Sources Using Higher Order Statistics in Noisy Environment

This paper deals with the localization of the wideband sources. We develop a new approach for estimating the wide band sources parameters. This method is based on the high order statistics of the recorded data in order to eliminate the Gaussian components from the signals received on the various hydrophones.In fact the noise of sea bottom is regarded as being Gaussian. Thanks to the coherent signal subspace algorithm based on the cumulant matrix of the received data instead of the cross-spectral matrix the wideband correlated sources are perfectly located in the very noisy environment. We demonstrate the performance of the proposed algorithm on the real data recorded during an underwater acoustics experiments.

Random Projections for Dimensionality Reduction in ICA

In this paper we present a technique to speed up ICA based on the idea of reducing the dimensionality of the data set preserving the quality of the results. In particular we refer to FastICA algorithm which uses the Kurtosis as statistical property to be maximized. By performing a particular Johnson-Lindenstrauss like projection of the data set, we find the minimum dimensionality reduction rate ¤ü, defined as the ratio between the size k of the reduced space and the original one d, which guarantees a narrow confidence interval of such estimator with high confidence level. The derived dimensionality reduction rate depends on a system control parameter β easily computed a priori on the basis of the observations only. Extensive simulations have been done on different sets of real world signals. They show that actually the dimensionality reduction is very high, it preserves the quality of the decomposition and impressively speeds up FastICA. On the other hand, a set of signals, on which the estimated reduction rate is greater than 1, exhibits bad decomposition results if reduced, thus validating the reliability of the parameter β. We are confident that our method will lead to a better approach to real time applications.