How Many Antennas Should Be Activated in Keyhole Channels Under a Holistic Power Model

In this letter, we investigate the problem of how many transmit or receive antennas should be activated in keyhole channels with the consideration of a holistic power model. In conventional works where the circuit power is ignored, the system performance in terms of both ergodic capacity and outage probability improves with the increase of active antennas. However, when a holistic power model which includes the circuit power of RF chains as well as the transmission power is considered, there will exist a fundamental trade-off between the number of active antennas and the residual transmission power. Based on this trade-off, we derive a closed-form formula for the optimal number of active transmit or receive antennas in keyhole channels. In particular, by adopting the Meijer's G-function, we present concise expressions for the optimal numbers of active antennas that maximize the ergodic capacity and minimize the outage probability. Simulations will be shown in agreement with the theoretical results in a large extent.