  In this paper, we consider a class of nonconvex complex quadratic programming
(CQP) problems, which find a broad spectrum of signal processing applications.
By using the polar coordinate representations of the complex variables, we
first derive a new enhanced semidefinite relaxation (SDR) for problem (CQP).
Based on the newly derived SDR, we further propose an efficient
branch-and-bound algorithm for solving problem (CQP). Key features of our
proposed algorithm are: (1) it is guaranteed to find the global solution of the
problem (within any given error tolerance); (2) it is computationally efficient
because it carefully utilizes the special structure of the problem. We apply
our proposed algorithm to solve the multi-input multi-output (MIMO) detection
problem, the unimodular radar code design problem, and the virtual beamforming
design problem. Simulation results show that our proposed enhanced SDR, when
applied to the above problems, is generally much tighter than the conventional
SDR and our proposed global algorithm can efficiently solve these problems. In
particular, our proposed algorithm significantly outperforms the
state-of-the-art sphere decode algorithm for solving the MIMO detection problem
in the hard cases (where the number of inputs and outputs is equal or the SNR
is low) and a state-of-the-art general-purpose global optimization solver
called Baron for solving the virtual beamforming design problem.
