  Assuming that the number of possible decisions for a transmitter (e.g., the
number of possible beamforming vectors) has to be finite and is given, this
paper investigates for the first time the problem of determining the best
decision set when energy-efficiency maximization is pursued. We propose a
framework to find a good (finite) decision set which induces a minimal
performance loss w.r.t. to the continuous case. We exploit this framework for a
scenario of energy-efficient MIMO communications in which transmit power and
beamforming vectors have to be adapted jointly to the channel given under
finite-rate feedback. To determine a good decision set we propose an algorithm
which combines the approach of Invasive Weed Optimization (IWO) and an
Evolutionary Algorithm (EA). We provide a numerical analysis which illustrates
the benefits of our point of view. In particular, given a performance loss
level, the feedback rate can by reduced by 2 when the transmit decision set has
been designed properly by using our algorithm. The impact on energy-efficiency
is also seen to be significant.
