Multi-antenna systems have been shown to offer a linear scaling of capacity under rich scattering conditions. The question of capacity scaling under correlated channel conditions is still not well understood. Earlier results in [3] and [4] which showed linear scaling of capacity under a Kronecker product correlation model and a D-connected model respectively, correspond to a quadratic scaling of channel power with the number of antennas. In this paper we show that channel power per antenna is the fundamental quantity that governs capacity scaling in correlated channels. We show that uniform power capacity scales as O( f (N)), where f(N) is a sub-linear function of N, if and only if channel power scales as O(N f (N)). Using a virtual representation of multi-antenna channels, we relate this capacity scaling result to the scaling of the number of paths captured by the antenna arrays. It is necessary and sufficient that the number of resolvable paths in the physical environment (also the number of independent degrees of freedom in the channel matrix) scale as O(N f (N)) to support an O (f (N)) scaling of capacity. Thus, our results establish new capacity scaling regimes for physical correlated MIMO channels.
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