Abstract
In this paper, the quasi-convexity of a sum of quadratic fractions in the form ∑i=1n 1+cix2/(1+d ix)2 is demonstrated where ci and di are strictly positive scalars, when defined on the positive real axis ℝ+. It will be shown that this quasi-convexity guarantees it has a unique local (and hence global) minimum. Indeed, this problem arises when considering the optimization of the weighting coefficient in regularized semi-blind channel identification problem, and more generally, is of interest in other contexts where we combine two different estimation criteria. Note that V. Buchoux have noticed by simulations that the considered function has no local minima except its unique global minimum but this is the first time this result, as well as the quasi-convexity of the function is proved theoretically.
Original language | English (US) |
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Article number | 5895068 |
Pages (from-to) | 4732-4739 |
Number of pages | 8 |
Journal | IEEE Transactions on Information Theory |
Volume | 57 |
Issue number | 7 |
DOIs | |
State | Published - Jul 2011 |
Externally published | Yes |
Keywords
- Asymptotic analysis
- channel estimation
- exponential polynomial
- minimum MSE
- quasi-convexity
- regularization
- semi-blind estimation
ASJC Scopus subject areas
- Information Systems
- Computer Science Applications
- Library and Information Sciences