41,383 research outputs found
Reduced complexity adaptive filtering algorithms with applications to communications systems
This thesis develops new adaptive filtering algorithms suitable for communications applications with the aim of reducing the computational complexity of the implementation. Low computational complexity of the adaptive filtering algorithm can, for example, reduce the required power consumption of the implementation. A low power consumption is important in wireless applications, particularly at the mobile terminal side, where the physical size of the mobile terminal and long battery life are crucial. We focus on the implementation of two types of adaptive filters: linearly-constrained minimum-variance (LCMV) adaptive filters and conventional training-based adaptive filters.
For LCMV adaptive filters, normalized data-reusing algorithms are proposed which can trade off convergence speed and computational complexity by varying the number of data-reuses in the coefficient update. Furthermore, we propose a transformation of the input signal to the LCMV adaptive filter, which properly reduces the dimension of the coefficient update. It is shown that transforming the input signal using successive Householder transformations renders a particularly efficient implementation. The approach allows any unconstrained adaptation algorithm to be applied to linearly constrained problems.
In addition, a family of algorithms is proposed using the framework of set-membership filtering (SMF). These algorithms combine a bounded error specification on the adaptive filter with the concept of data-reusing. The resulting algorithms have low average computational complexity because coefficient update is not performed at each iteration. In addition, the adaptation algorithm can be adjusted to achieve a desired computational complexity by allowing a variable number of data-reuses for the filter update.
Finally, we propose a framework combining sparse update in time with sparse update of filter coefficients. This type of partial-update (PU) adaptive filters are suitable for applications where the required order of the adaptive filter is conflicting with tight constraints for the processing power.reviewe
Stochastic methods for solving high-dimensional partial differential equations
We propose algorithms for solving high-dimensional Partial Differential
Equations (PDEs) that combine a probabilistic interpretation of PDEs, through
Feynman-Kac representation, with sparse interpolation. Monte-Carlo methods and
time-integration schemes are used to estimate pointwise evaluations of the
solution of a PDE. We use a sequential control variates algorithm, where
control variates are constructed based on successive approximations of the
solution of the PDE. Two different algorithms are proposed, combining in
different ways the sequential control variates algorithm and adaptive sparse
interpolation. Numerical examples will illustrate the behavior of these
algorithms
- …