  We use high-resolution N-body simulations to develop a new, flexible,
empirical approach for measuring the growth rate from redshift-space
distortions (RSD) in the 2-point galaxy correlation function. We quantify the
systematic error in measuring the growth rate in a $1 \, h^{-3}$ Gpc$^3$ volume
over a range of redshifts, from the dark matter particle distribution and a
range of halo-mass catalogues with a number density comparable to the latest
large-volume galaxy surveys such as the WiggleZ Dark Energy Survey and the
Baryon Oscillation Spectroscopic Survey (BOSS). Our simulations allow us to
span halo masses with bias factors ranging from unity (probed by emission-line
galaxies) to more massive haloes hosting Luminous Red Galaxies. We show that
the measured growth rate is sensitive to the model adopted for the small-scale
real-space correlation function, and in particular that the "standard"
assumption of a power-law correlation function can result in a significant
systematic error in the growth rate determination. We introduce a new,
empirical fitting function that produces results with a lower (5-10%) amplitude
of systematic error. We also introduce a new technique which permits the galaxy
pairwise velocity distribution, the quantity which drives the non-linear growth
of structure, to be measured as a non-parametric stepwise function. Our
(model-independent) results agree well with an exponential pairwise velocity
distribution, expected from theoretical considerations, and are consistent with
direct measurements of halo velocity differences from the parent catalogues. In
a companion paper we present the application of our new methodology to the
WiggleZ Survey dataset.
