Low-SNR Capacity of Multiple-Antenna Systems With Statistical Channel-State Information

This paper investigates the capacity of double-scattering and Rician fading multiple-input-multiple-output (MIMO) channels in the low signal-to-noise ratio (SNR) regime. We first derive analytical expressions for the two key low-SNR parameters-the minimum required
Eb
/
N
₀
for reliable communications and the wideband slope-assuming statistical channel state information (CSI) at the transmitter. Based on these results, we study the effects of transmit, scatter, and receive correlation, as well as the Rician
K
-factor. For double-scattering MIMO channels, we find that the minimum required
Eb
/
N
₀
improves with increasing transmit-side correlation and is independent of the scatter and receive correlation, whereas the wideband slope degrades with increasing the scatter and receive correlation and is independent of the transmit-side correlation. For Rician MIMO channels, we show that increasing the Rician
K
-factor leads to an improvement in the minimum required
Eb
/
N
₀
while degrading the wideband slope. We also analyze the low-SNR capacity for different levels of transmit CSI for special cases of both channels. Our results demonstrate that the additional beamforming gain due to more accurate CSI leads to a reduced minimum required
Eb
/
N
₀
but does not yield improvements in the wideband slope.