In this chapter we will introduce a widely known optimization problem called

semidefinite program (previously abbreviated by SDP), which has been applied

in many signal processing problems in MIMO wireless communications. However,

the optimization problem of interest may often be NP-hard, and hence we may

have to resort to various problem reformulations and convex approximations to

either the objective function or the constraint functions or both of the original

problem, that either were presented in the previous chapters (e.g., the SCA (cf.

Section 4.7)) or are introduced in this chapter (e.g., the widely used semidefinite

relaxation). Consequently, we may come up with a solvable SDP together with a

suboptimal solution to the original problem instead. Nevertheless, the obtained

solution may be analytically proven to be an optimal solution or a stationary

point of the original problem for some practical scenarios. Though the SDP is the

focus of this chapter, the BSUM introduced in Section 4.7 (that may not involve

SDP at all) may be potentially a more powerful alternative than the SDP for

finding a stationary-point solution of the same problem. Hence some applications

using both the SDP and the BSUM will also be presented in this chapter for the

comparison of the two methods in terms of complexity and solution accuracy.