One is given n ≥ 1 terminals each coming with a demand d _i  > 0 and m ≥ n communication channels each coming with a cost parameter p _j  > 0. The channels shall be assigned to the terminals in a way that each channel is mapped to at most one terminal and each terminal receives at least one channel. Additionally, each channel j needs to be assigned a communication rate r _j  > 0 such that the sum of the rates of the channels mapped to terminal i satisfies at least the demand d _i . Using the Shannon rate-power function, the energy requirement for channel j is assumed to be . The objective is to minimize the sum of the energy requirements over all channels.

We prove that the problem is NP-hard and cannot be approximated with approximation factor α, unless P = NP, where α> 1 is any polynomial time computable function. We then consider a complementary problem setting in which one is given a threshold on the energy requirement and the objective is to maximize λ such that each terminal receives a rate of at least λd _i . We show that this maximin version of the problem admits a PTAS if all demands are identical and a -approximation for general demands.