  This paper proposes two low-complexity iterative algorithms to compute the
capacity of a single-user multiple-input multiple-output channel with
per-antenna power constraint. The first method results from manipulating the
optimality conditions of the considered problem and applying fixed-point
iteration. In the second approach, we transform the considered problem into a
minimax optimization program using the well-known MAC- BC duality, and then
solve it by a novel alternating optimization method. In both proposed iterative
methods, each iteration involves an optimization problem which can be
efficiently solved by the water-filling algorithm. The proposed iterative
methods are provably convergent. Complexity analysis and extensive numerical
experiments are carried out to demonstrate the superior performance of the
proposed algorithms over an existing approach known as the mode-dropping
algorithm.
