  We have derived an analytical expression for variance of homogeneous-position
decoherent quantum walk (HPDQW) with general form of noise on its position, and
have shown that, while the quadratic ($t^2$) term of variance never changes by
position decoherency, the linear term ($t$) does and always increases the
variance. We study the walker with ability to tunnel out to $d$ nearest
neighbors as an example and compare our result with former studies. We also
show that, although our expression have been derived for asymptotic case, the
rapid decay of time-dependent terms cause the expressions to be correct with a
good accuracy even after dozens of steps.
