Corrections to “Secrecy Outage Analysis for Distributed Antenna Systems in Heterogeneous Cellular Networks”

In
[1]
, the calculation of
(8)
was erroneous. To be specific, as shown in
(8)
of
[1]
, the average transmit power of a specially-designed signal
${x_{m} = - {{\sqrt {P_{S}} {h_{Sm}}h_{Am}^{*}{x_{S}}}}/{{{{\left |{ {{h_{Am}}} }\right |}^{2}}}}}$
was obtained as
\begin{equation*}{P_{m} = \frac {{\sigma _{Sm}^{2}}}{{\sigma _{Am}^{2}}}}P_{S},\end{equation*}
where
$\sigma _{Sm}^{2} = E(|{h_{Sm}}{|^{2}})$
and
$\sigma _{Am}^{2} = E(|{h_{Am}}{|^{2}})$
. This calculation was obtained by mistaking an expectation of
$1/|h_{Am}|^{2}$
for
$E(1/|h_{Am}|^{2})=1/E(|h_{Am}|^{2})= 1/\sigma _{Am}^{2}$
, which is erroneous to be corrected. Actually, considering that
$|h_{Am}|^{2}$
is an exponentially distributed random variable with a mean of
$\sigma ^{2}_{Am}$
, the expectation of
$1/|h_{Am}|^{2}$
tends toward infinity, rather than
$1/\sigma _{Am}^{2}$
.