The theory of mode-coupling instability in 2D plasma crystal is combined with a self-consistent model of plasma wakes. The wake model is based on the solution of a kinetic equation for ions, providing realistic representation of their kinetics for the sheath environment. Furthermore, the self-consistent approach allows us to express the interparticle interaction via experimentally measurable parameters. It is suggested that distinct features of dispersion relations predicted by different wake models can be identified experimentally. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3692738]