Correlated MIMO Rayleigh Channels: Eigenmodes and Capacity Analyses

Equipping a wireless system’s transmitter and receiver with multiple antennas represents one of the most promising solutions to improve the bandwidth efficiency and system reliability without need to use extra bandwidth or transmitting more power into the channel. Such a system is called Multiple Input Multiple Output (MIMO) and offers high capacity. This gain in capacity is affected by the channel correlation and the number of receive and transmit antennas. In this paper, the MIMO Rayleigh channel matrix will be analyzed. The behaviour of channel matrix eigenmodes and the power levels allocated to them by the water-filling algorithm with SNR and with the channel correlation will be explored. Capacity of the channel eigenmodes and total capacity of the channel will also be studied. It was found that the transmitter allocates all transmitted power to the strongest eigenmode at low SNR, and divides this power equally among the eigenmodes at high SNRs. The strongest eigenmode of a channel matrix increases with correlation, while the other eigenmodes of the channel decrease. When the channel correlation approaches 1, the strongest eigenmode approaches the Mr * Mt, while the other eigenmodes approach zero. At low SNRs, the transmitter allocates the power to the strongest eigenmode only, so that the capacity of the channel increases with the channel correlation. The channel matrix is considered perfectly known at both sides of the wireless link.