  Antiferromagnets (AFMs) have great benefits for spintronic applications such
as high frequencies (up to THz), high speeds (up to tens of km/s) of magnetic
excitations, and field-free operation. Advanced devices will require high-speed
propagating spin waves (SWs) as signal carriers, i.e., SWs with high k-vectors,
the excitation of which remains challenging. We show that a domain wall (DW) in
anisotropic AFM driven by the spin current can be a source of such propagating
SWs with high frequencies and group velocities. In the proposed generator, the
spin current, with polarization directed along the easy anisotropy axis,
excites the precession of the N\'eel vector within the DW. The threshold
current is defined by the value of the anisotropy in the hard plane, and the
frequency of the DW precession is tuneable by the strength of the spin current.
We show that the above precession of spins inside the DW leads to robust
emission of high-frequency propagating SWs into the AFM strip with very short
wavelengths comparable to the exchange length, which is hard to achieve by any
other method.
