Efficient Rank-Adaptive Least-Square Estimation and Multiple-Parameter Linear Regression Using Novel Dyadically Recursive Hermitian Matrix Inversion
Least-square estimation (LSE) and multiple-parameter linear regression (MLR) are the important estimation techniques for engineering and science, especially in the mobile communications and signal processing applications. The majority of computational complexity incurred in LSE and MLR arises from a...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | International Journal of Antennas and Propagation |
| Online Access: | http://dx.doi.org/10.1155/2012/891932 |
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| Summary: | Least-square estimation (LSE) and multiple-parameter linear regression (MLR) are the important
estimation techniques for engineering and science, especially in the mobile communications and signal
processing applications. The majority of computational complexity incurred in LSE and MLR arises
from a Hermitian matrix inversion. In practice, the Yule-Walker equations are not valid, and hence the
Levinson-Durbin algorithm cannot be employed for general LSE and MLR problems. Therefore, the
most efficient Hermitian matrix inversion method is based on the Cholesky factorization. In this paper,
we derive a new dyadic recursion algorithm for sequential rank-adaptive Hermitian matrix inversions.
In addition, we provide the theoretical computational complexity analyses to compare our new dyadic
recursion scheme and the conventional Cholesky factorization. We can design a variable model-order
LSE (MLR) using this proposed dyadic recursion approach thereupon. Through our complexity analyses
and the Monte Carlo simulations, we show that our new dyadic recursion algorithm is more efficient than
the conventional Cholesky factorization for the sequential rank-adaptive LSE (MLR) and the associated
variable model-order LSE (MLR) can seek the trade-off between the targeted estimation performance
and the required computational complexity. Our proposed new scheme can benefit future portable and
mobile signal processing or communications devices. |
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| ISSN: | 1687-5869 1687-5877 |