  We investigate compressive turbulence at sub-ion scales with measurements
from the Magnetospheric MultiScale Mission. The tetrahedral configuration and
high time resolution density data obtained by calibrating spacecraft potential
allow an investigation of the turbulent density fluctuations in the solar wind
and their three-dimensional structure in the sub-ion range. The wave-vector
associated with the highest energy density at each spacecraft frequency is
obtained by application of the Multi-point signal resonator technique to the
four-point density data. The fluctuations show a strong wave-vector anisotropy
$k_{\perp}\gg k_{\parallel}$ where the parallel and perpendicular symbols are
with respect to the mean magnetic field direction. The plasma frame frequencies
show two populations, one below the proton cyclotron frequency
$\omega<\Omega_{ci}$ consistent with kinetic Alfv\'en wave (KAW) turbulence.
The second component has higher frequencies $\omega > \Omega_{ci}$ consistent
with ion Bernstein wave (IBW) turbulence. Alternatively, these fluctuations may
constitute KAWs that have undergone multiple wave-wave interactions causing a
broadening in the plasma frame frequencies. The scale-dependent kurtosis in
this wave-vector region shows a reduction in intermittency at the small scales
which can also be explained by the presence of wave activity. Our results
suggest that small-scale turbulence exhibits linear-wave properties of kinetic
Alfv\'en and possibly ion-Bernstein/magnetosonic waves. Based on our results,
we speculate that these waves may play a role in describing the observed
reduction in intermittency at sub ion scales.
