On the Duality of Wireless Systems with Multiple Cooperating Transmitters and Wireless Systems with Correlated Antennas

We analyze the error performance of distributed space-time codes in a wireless system with multiple cooperating transmitters and a single receiver. Due to the distributed nature of the system, the transmitted signals are subject to different average path losses. As our analysis shows, this effect leads to reduced diversity gains. We explain this result on the basis of an interesting duality between systems with distributed transmitters and systems with densely-packed transmitters: For the case of Rayleigh fading, we prove that any system with distributed transmitters can be transformed into an equivalent co-located multiple-antenna system with correlated antennas. Specifically, the case of equal average path losses corresponds to an uncorrelated system. In order to quantify the performance loss resulting from distributed transmitters, we propose a simple performance measure between zero and one, which is equivalent to a certain correlation measure recently proposed for co-located multiple-antenna systems.