The Role of SNR in Achieving MIMO Rates in Cooperative Systems
Ng, C.T.K.
Laneman, J.N.
Goldsmith, A.J.
Dept. of Electrical Engineering, Stanford University, Stanford, CA 94305, Email: ngctk@wsl.stanford.edu;
This paper appears in: Information Theory Workshop, 2006. ITW '06 Punta del Este. IEEE
Publication Date: 13-17 March 2006
On page(s): 288-292
Location: Punta del Este, Uruguay,
ISBN: 1-4244-0035-X
Digital Object Identifier: 10.1109/ITW.2006.1633831
Current Version Published: 2006-06-05
Abstract
We compare the rate of a multiple-antenna relay channel to the capacity of multiple-antenna systems to characterize the cooperative capacity in different SNR regions. While it is known that in the asymptotic regime, at a high SNR or with a large number of cooperating nodes, cooperative systems lack full multiplexing gain, in this paper we consider cooperative capacity gain at moderate SNR with a fixed number of cooperating antennas. We show that up to a lower bound to an SNR threshold, a cooperative system performs at least as well as a MIMO system with isotropic inputs; whereas beyond an upper bound to the SNR threshold, the cooperative system is limited by its coordination costs, and the capacity is strictly less than that of a MIMO orthogonal channel. The SNR threshold depends on the network geometry (the power gain g between the source and relay) and the number of cooperating antennas M; when the relay is close to the source (g [unk] 1), the SNR threshold lower and upper bounds are approximately equal. As the cooperating nodes are closer, i.e., as g increases, the MIMO-gain region extends to a higher SNR. Whereas for a populous cluster, i.e., when M is large, the coordination-limited region sets in at a lower SNR.
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