  We study the effect of the Coulomb interaction on the local density of states
(LDOS) and its Fourier component in disordered cuprates. It is shown that the
Coulomb interaction suppresses strongly the maximum value of the LDOS induced
by the dopant impurity at each energy and expands significantly the Friedel
oscillation in real space. The existence of the Coulomb interaction with a
moderate strength yields an energy-dependent checkerboard LDOS modulation
around the impurity, which is very different from that produced by pure
quasiparticle interference. The orientation and transformation of the
checkerboard pattern with energy and the relations among the modulation
vectors, dopings and the bias voltages agree qualitatively with the recent STM
experiments.
