Communication on the Grassmann manifold: a geometric approach tothe noncoherent multiple-antenna channel
Lizhong Zheng; Tse, D.N.C.
Information Theory, IEEE Transactions on
Volume 48, Issue 2, Feb 2002 Page(s):359 - 383
Digital Object Identifier 10.1109/18.978730
Summary:We study the capacity of multiple-antenna fading channels. We
focus on the scenario where the fading coefficients vary quickly; thus
an accurate estimation of the coefficients is generally not available to
either the transmitter or the receiver. We use a noncoherent block
fading model proposed by Marzetta and Hochwald (see ibid. vol.45,
p.139-57, 1999). The model does not assume any channel side information
at the receiver or at the transmitter, but assumes that the coefficients
remain constant for a coherence interval of length T symbol periods. We
compute the asymptotic capacity of this channel at high signal-to-noise
ratio (SNR) in terms of the coherence time T, the number of transmit
antennas M, and the number of receive antennas N. While the capacity
gain of the coherent multiple antenna channel is min{M, N} bits per
second per Hertz for every 3-dB increase in SNR, the corresponding gain
for the noncoherent channel turns out to be M* (1 - M*/T) bits per
second per Hertz, where M*=min{M, N, [T/2]}. The capacity expression has
a geometric interpretation as sphere packing in the Grassmann manifold
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