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.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 $O(Q^2(M-Q+1)+M^2)$ in the real case and by $O(M(M-Q+1))$ 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 $O(\epsilon∧ln(M))$ for both the real and the complex cases.Moreover,this ratio is tight up to a constant factor.