  The neutron star merger, GW170817, was followed by an optical-infrared
transient (a kilonova) which indicated that a substantial ejection of mass at
trans-relativistic velocities occurred during the merger. Modeling of the
kilonova is able to constrain the kinetic energy of the ejecta and its
characteristic velocity, but not the high-velocity distribution of the ejecta.
Yet, this distribution contains crucial information on the merger dynamics. In
this work, we assume a power-law distribution of the form
$E(>\beta\Gamma)\propto(\beta\Gamma)^{-\alpha}$ for the energy of the kilonova
ejecta and calculate the non-thermal signatures produced by the interaction of
the ejecta with the ambient gas. We find that ejecta with minimum velocity
$\beta_0\simeq 0.3$ and energy $E\sim 10^{51}$ erg, as inferred from kilonova
modeling, has a detectable radio, and possibly X-ray, afterglow for a broad
range of parameter space. This afterglow component is expected to dominate the
observed emission on a timescale of a few years post merger and peak around a
decade later. Its light curve can be used to determine properties of the
kilonova ejecta and in particular the ejecta velocity distribution $\alpha$,
the minimum velocity $\beta_0$ and its total kinetic energy $E$. We also
predict that an afterglow rebrightening, that is associated with the kilonova
component, will be accompanied by a shift of the centroid of the radio source
towards the initial position of the explosion.
