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Outage probability in multiple antenna systems

: Jorswieck, E.A.; Boche, H.


European transactions on telecommunications 18 (2007), No.3, pp.217-233
ISSN: 1124-318X
ISSN: 1120-3862
ISSN: 1541-8251
Journal Article
Fraunhofer HHI ()
antenna arrays; channel capacity; correlation methods; matrix algebra; mimo communication; optimisation; transmitting antennas

Multiple transmit antennas improve the ergodic and outage capacity of wireless systems. Spatial properties of the channel including the transmit antenna array affect the Optimum transmission strategy as well as the achievable capacity and average throughput. First, we study the outage probability of a multiple input single output (MISO) system with perfect channel state information (CSI) at the receiver under different types of CSI at transmitter and with transmit antenna correlation. We prove the conjecture given in Telatar's seminal paper and complete the analysis of the optimum transmit strategy without CSI at the transmitter and uncorrelated antennas. Furthermore, we show how the impact of correlation on the outage probability depends on the transmission rate and SNR. We show that the behaviour of the outage probability differs from the behaviour of the ergodic capacity. In terms of ergodic capacity there are clear instructions what is the optimum transmission strategy and what is the impact of correlation. In contrast, the outage probability behaves chameleonic. If the transmitter is aware of the channel correlation matrices, the optimum transmit strategy is to transmit along the eigenvectors of the known correlation matrix. The remaining power allocation problem is difficult since it is a non-convex optimisation problem. However, necessary conditions characterise the optimal allocation. Finally, we analyse the outage probability for the general multiple input Multiple Output (MIMO) system with spatially correlated transmit and receive antennas in asymptotic high and low SNR regime. The theoretical results are illustrated by numerical simulations.