On Capacity Scaling of (Long) MIMO Amplify-and-Forward Multi-Hop Networks


Jörg Wagner and Armin Wittneben


IEEE Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA, Oct. 2008.

DOI: 10.1109/ACSSC.2008.5074422

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Consider a multiple-input-multiple-output multi-hop network consisting of n_S non-cooperating source antennas, n_D fully cooperating destination antennas, and L clusters of n_R non-cooperating relay antennas each. The source signals reach the destination antennas via L+1 hops by traversing all relay clusters. Relay antennas scale their receive signal by a common constant before retransmission (amplify-and-forward). We perform an asymptotic capacity analysis assuming the elements of the (per hop) channel matrices to satisfy the conditions for the Marcenko-Pastur law. Our result: In the limit L->\infty sum-capacity scales linearly with min{n_S,n_D}, if and only if L scales no faster than linearly with the ratio n_R/min{n_S,n_D}.

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