Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Distortion of the Eigenvalue Spectrum in MIMO Amplify-and-Forward
  Multi-Hop Channels   Consider a wireless MIMO multi-hop channel with n_s non-cooperating source
antennas and n_d fully cooperating destination antennas, as well as L clusters
containing k non-cooperating relay antennas each. The source signal traverses
all L clusters of relay antennas, before it reaches the destination. When relay
antennas within the same cluster scale their received signals by the same
constant before the retransmission, the equivalent channel matrix H relating
the input signals at the source antennas to the output signals at the
destination antennas is proportional to the product of channel matrices H_l,
l=1,...,L+1, corresponding to the individual hops. We perform an asymptotic
capacity analysis for this channel as follows: In a first instance we take the
limits n_s->infty, n_d->infty and k->infty, but keep both n_s/n_d and k/n_d
fixed. Then, we take the limits L->infty and k/n_d->infty. Requiring that the
H_l's satisfy the conditions needed for the Marcenko-Pastur law, we prove that
the capacity scales linearly in min{n_s,n_d}, as long as the ratio k/n_d scales
at least linearly in L. Moreover, we show that up to a noise penalty and a
pre-log factor the capacity of a point-to-point MIMO channel is approached,
when this scaling is slightly faster than linear. Conversely, almost all
spatial degrees of freedom vanish for less than linear scaling.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn