Optimal pilot design and power control in correlated MISO links

We study the maximization of an achievable ergodic rate expression of a multiple-input single-output (MISO) channel where both ends are cognizant of the same erroneous estimate of the current fading state, yet they have complete knowledge of channel statistics. A training procedure estimates each channel state by means of dedicated pilot symbols whose sum energy is fixed, while for data transmission a fixed average energy per channel access (i.e., average power) is available. The optimization consists, on one hand, in finding the optimal beamforming strategy and temporal power control policy, and on the other hand, in optimally constructing the pilot sequence according to the channel´s correlation structure.