Competitive Use of Multiple Antennas

A game theoretic framework is presented to analyze the problem of finding the optimal number of data streams to transmit in a multi-user MIMO scenario, where both the transmitters and receivers are equipped with multiple antennas. Without channel state information (CSI) at any transmitter, and using outage capacity as the utility function with zero-forcing receiver, each user is shown to transmit a single data stream at Nash equilibrium in the presence of sufficient number of users. Transmitting a single data stream is also shown to be optimal in terms of maximizing the sum of the outage capacities in the presence of sufficient number of users. With CSI available at each transmitter, and using the number of successful bits per Joule of energy as the utility function, at Nash equilibrium, each user is shown to transmit a single data stream on the best eigen-mode that requires the least transmit power to achieve a fixed signal-to-interference ratio. Using the concept of locally gross direction preserving maps, existence of Nash equilibrium is shown when the number of successful bits per Joule of energy is used as the utility function.