  In this paper, the quasi-convexity of a sum of quadratic fractions in the
form $\sum_{i=1}^n \frac{1+c_i x^2}{\left(1+d_ix\right)^2}$ is demonstrated
where $c_i$ and $d_i$ are strictly positive scalars, when defined on the
positive real axis $\mathbb{R}^{+}$. 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 {\it et.al} 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.
