  In this paper, we propose some new semidefinite relaxations for a class of
nonconvex complex quadratic programming problems, which widely appear in the
areas of signal processing and power system. By deriving new valid constraints
to the matrix variables in the lifted space, we derive some enhanced
semidefinite relaxations of the complex quadratic programming problems. Then,
we compare the proposed semidefinite relaxations with existing ones and show
that the newly proposed semidefinite relaxations could be strictly tighter than
the previous ones. Moreover, the proposed semidefinite relaxations can be
applied to more general cases of complex quadratic programming problems,
whereas the previous ones are only designed for special cases. Numerical
results indicate that the proposed semidefinite relaxations not only provide
tighter relaxation bounds but also improve some existing approximation
algorithms by finding better sub-optimal solutions.
