Gaussian Mixture Noise Channels With Minimum and Peak Amplitude Constraints

Motivated by the idea of “transmitting energy and information simultaneously,” we investigate, in this paper, the impact of constraints on the amount of energy that individual symbols carry, i.e., minimum amplitude constraints. We consider a Gaussian mixture noise channel with both minimum and peak amplitude constraints. First, we prove that the capacity-achieving input has a discrete distribution with a finite number of probability mass points. Then, we further investigate the number and positions of the probability mass points for the capacity-achieving input. Specifically, when the interference is constant and known at both the transmitter and the receiver, it can be totally eliminated so that the channel operates like an AWGN channel. In this case, we give a theorem to determine whether the optimal input is binary. For more general cases, such as non-binary inputs and non-constant interference, we investigate optimal inputs and capacities via numerical computations.