  In this paper, we discuss the gravitational waves in the context of gauge
theory gravity with a negative cosmological constant. The gauge theory gravity
is a gravity theory under gauge formulation in the language of geometric
algebra. In contrast to general relativity, the background spacetime in gauge
theory gravity is flat, the gauge freedom comes from the fact that equations in
terms of physical quantities should be kept in a covariant form under spacetime
displacement and rotation. Similar to the electromagnetism, the gauge
formulation enables us to interpret the gravitational force as a gauge force on
the background flat spacetime. The dynamical fields that describe the
gravitational interactions are those position and rotation gauge fields
introduced as the requirement of the gauge covariance. The gravitational field
equations can be derived from the least action principle with the action as a
gauge invariant quantity built from the covariant field strength. We discuss
the gravitational wave solutions of the field equations with a negative
cosmological constant, and show that these solutions are of Petrov type-N. We
also discuss the velocity memory effect by calculating the velocity change of
an initially free falling massive particle due to the presence of the
gravitational waves.
