On Comparability of Multiple Antenna Channels

Partial ordering relations, first developed by Shannon and Csiszar for discrete memoryless channels, can be used for comparing certain information-theoretic properties of channels. In this paper we extend their ideas to multiple antenna channels and introduce three partial ordering relations that enable us to compare multiple antenna channels in different senses, namely, strong sense, weak sense, and capability sense, that give insight into the analytical behavior of mutual information and coding performance of these channels. We provide sufficient conditions for transitivity of all three relations for three classes of channels: additive white Gaussian noise channels, flat-fading channels with full channels state information (CSI) at the receiver, and flat-fading channels with no CSI. These conditions are easily expressed in terms of the channel parameters such as the line-of-sight and scattering components of the channel. Moreover, these conditions show how the line-of-sight and scattering components of a channel affect the mutual information and coding performance of the channel. For example, in the presence of CSI at the receiver, the mutual information is monotonically increasing with respect to the variations of the line-of-sight component in certain geometrical directions. Index Terms Capacity, multiple antenna, mutual information, partial ordering, Rayleigh, Rician. ∗This work was supported in part by Texas Instruments Leadership University Program.