# Capacity Scaling of (Long) Non-Regenerative MIMO Multi-Hop Channels

### Authors

Jörg Wagner and Armin Wittneben

### Reference

IEEE International Symposium on Information Theory, Toronto, ON, Canada, July 2008.

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### Abstract

We consider coherent wireless MIMO multihop communication where n_S non-cooperating source antennas communicate to $n_D$ fully cooperating destination antennas via $L$ clusters of $n_R$ non-cooperating relay antennas each. Assuming i.i.d. zero-mean (slow) fading coefficients of finite variance, the sum-capacity of this channel is proven to scale linearly in $min{n_S, n_D}$, when the receive SNR is kept constant and $n_R \in\Omega (min{n_S, n_D})$ in the limit$L \rightarrow-> \infty$. This capacity scaling is achieved by a quantization based forwarding strategy. Moreover, we show that Slepian & Wolf compression allows to reduce the growth rate of the transmit power per cluster that is necessary to sustain a constant receive SNR at the destination antennas from exponential to linear in $L$.

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