Comparison of space-time water-filling and spatial water-filling for MIMO fading channels

We compare the capacities achieved by space-time water-filling and spatial water-filling for MIMO fading channels. Both the effects of fast fading and shadowing are considered. It is found that for Rayleigh fast fading MIMO channels, the spectral efficiency per antenna achieved by one-dimensional spatial water-filling is close to two-dimensional space-time water-filling. However, with log-normal shadowing, space-time water-filling achieves significantly higher capacity per antenna than spatial water-filling at low to moderate SNR regimes. Furthermore, space-time water-filling has lower computational complexity than spatial water-filling. It is also shown that space-time water-filling requires a priori knowledge of the channel gain distribution, and for Rayleigh channels with log-normal shadowing, the spectral efficiency advantage over spatial water-filling comes with an increased channel outage probability.