In this paper, we analyze the sum-rate capacity of two-user Poisson multiple input multiple output multiple-access channels (MACs), when both the transmitters and the receiver are equipped with multiple antennas. Although the sum-rate capacity of Poisson MISO MAC when the receiver is equipped with a single antenna has been characterized by us, the inclusion of multiple antennas at the receiver makes the problem more challenging and requires the development of new analytical tools. We first characterize the sum-rate capacity of the Poisson MAC when each transmitter has a single antenna and the receiver has multiple antennas. 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, and for certain channel parameters, it is optimal for both users to transmit. We then characterize the sum-rate capacity of the channel where both the transmitters and the receiver are equipped with multiple antennas. We show that the sum-rate capacity of the Poisson MAC with multiple transmit antennas is equivalent to a properly constructed Poisson MAC with a single antenna at each transmitter, and has thus been characterized by the former case. We show this by developing a novel channel transformation argument.
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