On the Sum-Rate Capacity of Poisson MISO Multiple Access Channels

Abstract

In this paper, we analyze the sum-rate capacity of two-user Poisson multiple access channels (MAC), when the receiver is equipped with single antenna. We first characterize the sum-rate capacity of the non-symmetric Poisson MAC when each transmitter has a single antenna. While the sum-rate capacity of the symmetric Poisson MAC with single antenna at each transmitter has been characterized in the literature, the special property exploited in the existing method for the symmetric case does not hold for the non-symmetric channel anymore. We obtain the optimal input that achieves the sum-rate capacity by solving a non-convex optimization problem. We show that, for certain channel parameters, it is optimal for a single user to transmit to achieve the sum-rate capacity. This is in sharp contrast to the Gaussian MAC, in which both users must transmit, either simultaneously or at different times, in order to achieve the sum-rate capacity. We then characterize the sum-rate capacity of the Poisson multiple-input single-output (MISO) MAC with multiple antennas at each transmitter and single antenna at the receiver. By converting a non-convex optimization problem with a large number of variables into a non-convex optimization problem with two variables, we show that the sum-rate capacity of the Poisson MISO MAC with multiple transmit antennas is equivalent to a properly constructed Poisson MAC with a single antenna at each transmitter.