A Partial Ordering Relation on Flat-Fading Channels

In this correspondence, we establish a partial ordering framework to compare flatfading channels in a capability sense, which is based on the relative dominance of their mutual information functions over a convex set of input distributions. For this purpose, we address the effect of the line-of-sight and scattering components on the mutual information of flat-fading channels. For example, we show that in the presence of channel state information (CSI) at the receiver, the mutual information of flat-fading channels is monotonically increasing with respect to the absolute value of the line-of-sight component of the channel. In other words, for a fixed scattering component, channels with larger line-of-sight component are more capable than channels with smaller line-of-sight component. In contrast, in the absence of CSI, the mutual information is monotonically increasing with respect to the line-of-sight component, provided that it is smaller than or equal to the standard deviation of the scattering component. Furthermore, we briefly address applications of this work to the capacity assessment of simple and compound channels. Index Terms Capability, capacity assessment, compound channels, flat-fading, mutual information, partial ordering, Rayleigh, Rician. ∗This work was supported in part by Texas Instruments Leadership University Program.