On the Boundedness of the Support of Optimal Input Measures for Rayleigh Fading Channels

Sommerfeld, Jochen; Bjelakovic, Igor; Boche, Holger

On the Boundedness of the Support of Optimal Input Measures for Rayleigh Fading Channels

Authors

Sommerfeld, Jochen

Bjelakovic, Igor

Boche, Holger

Description

We consider transmission over a wireless multiple antenna communication system operating in a Rayleigh flat fading environment with no channel state information at the receiver and the transmitter with coherence time T=1. We show that, subject to the average power constraint, the support of the capacity achieving input distribution is bounded. Moreover, we show by a simple example concerning the identity theorem (or uniqueness theorem) from the complex analysis in several variables that some of the existing results in the field are not rigorous.
5 pages, submitted to ISIT 2008