  Motivated by applications in wireless communications, this paper develops
semidefinite programming (SDP) relaxation techniques for some mixed binary
quadratically constrained quadratic programs (MBQCQP) and analyzes their
approximation performance. We consider both a minimization and a maximization
model of this problem. For the minimization model, the objective is to find a
minimum norm vector in $N$-dimensional real or complex Euclidean space, such
that $M$ concave quadratic constraints and a cardinality constraint are
satisfied with both binary and continuous variables. {\color{blue}By employing
a special randomized rounding procedure, we show that the ratio between the
norm of the optimal solution of the minimization model and its SDP relaxation
is upper bounded by $\cO(Q^2(M-Q+1)+M^2)$ in the real case and by
$\cO(M(M-Q+1))$ in the complex case.} For the maximization model, the goal is
to find a maximum norm vector subject to a set of quadratic constraints and a
cardinality constraint with both binary and continuous variables. We show that
in this case the approximation ratio is bounded from below by
$\cO(\epsilon/\ln(M))$ for both the real and the complex cases. Moreover, this
ratio is tight up to a constant factor.
