  MIMO capacity with a joint total and per-antenna average power constraint is
considered in this work. The problem arises when, besides having a limited
available power at the transmitter, also the individual antennas cannot radiate
power beyond the limits of their corresponding RF chains. Closed-form results
are illustrated in specific cases and, in particular, in the unit-rank channel
matrix case. Lower-complexity optimization problems are derived for the other
cases. Numerical complexity is derived in terms of the number of equivalent
real variables for the optimization problem and a general formula is provided
depending on the channel matrix rank. Numerical results are included to
validate and illustrate the application of the proposed optimization algorithms
and also to evaluate the time complexity of its implementation.
