  Zero-forcing (ZF) decoder is a commonly used approximation solution of the
integer least squares problem which arises in communications and many other
applications. Numerically simulations have shown that the LLL reduction can
usually improve the success probability $P_{ZF}$ of the ZF decoder. In this
paper, we first rigorously show that both SQRD and V-BLAST, two commonly used
lattice reductions, have no effect on $P_{ZF}$. Then, we show that LLL
reduction can improve $P_{ZF}$ when $n=2$, we also analyze how the parameter
$\delta$ in the LLL reduction affects the enhancement of $P_{ZF}$. Finally, an
example is given which shows that the LLL reduction decrease $P_{ZF}$ when
$n\geq3$.
