Equivalence of Spatially Correlated and Distributed MIMO Systems

Wireless communication systems with multiple antennas, so-called multiple-input multiple-output (MIMO) systems, offer huge advantages over conventional single-antenna systems – both with regard to capacity and error performance. Typically, quite restrictive assumptions are made in the literature concerning the antenna spacings at transmitter and receiver: On the one hand, one normally assumes that the individual antenna elements are co-located, i.e., they are part of some antenna array. On the other hand, it is often assumed that antenna spacings are sufficiently large so as to justify the assumption of uncorrelated antennas. From numerous publications it is known that spatially correlated links lead to a loss in capacity and error performance. We show that this is also the case when the transmit and/or the receive antennas are spatially distributed on a larger scale. (Possible applications include simulcast networks, reach-back links for wireless sensors, as well as relay-assisted wireless networks.) Specifically, we show that any spatially correlated system that obeys the so-called Kronecker-correlation model can be transformed into an equivalent (with regard to the capacity distribution) spatially distributed system, and vice versa. Correspondingly, both types of MIMO system can be treated in a single unified framework. We also prove (asymptotic) equivalence with regard to the pairwise error probability of space-time codes. Moreover, we consider a simple performance measure originally proposed for spatially correlated systems and find the equivalent measure for distributed systems. Finally, we discuss appropriate transmit power allocation schemes that are based on second-order channel statistics.