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In this paper, the quasi-convexity of a sum of quadratic fractions in theform $\sum_{i=1}^n \frac{1+c_i x^2}{\left(1+d_ix\right)^2}$ is demonstratedwhere $c_i$ and $d_i$ are strictly positive scalars, when defined on thepositive real axis $\mathbb{R}^{+}$. It will be shown that this quasi-convexityguarantees it has a unique local (and hence global) minimum.  Indeed, this problem arises when considering the optimization of theweighting coefficient in regularized semi-blind channel identification problem,and more generally, is of interest in other contexts where we combine twodifferent estimation criteria.  Note that V. Buchoux {\it et.al} have noticed by simulations that theconsidered function has no local minima except its unique global minimum butthis is the first time this result, as well as the quasi-convexity of thefunction is proved theoretically.

Quasi-convexity of the asymptotic channel MSE in regularized semi blind estimation