Power allocation for multi-point joint transmission with different node activeness

We study the power allocation problem for the downlink of a cooperative system with different node activeness, i.e., each receiving node requests for data transmission according to a certain probability. Data symbols of the active nodes are jointly transmitted from cooperative transmission points using zero-forcing precoding. The problem is cast in form of maximizing the ergodic achievable rate subject to per-transmit-point average total power constraints. The derived power allocation indicates that depending on the channel conditions and receiving nodes´ activation probability, the optimal solution takes the form of either greedy power allocation or power sharing allocation.