## Noncoherent Multiple Antenna Communications

A key result in multiple antenna communications (Foschini 98) states
that in a fully scattered fading environment, the high SNR capacity of
a point-to-point link with M transmit and N receive antennas is
approximately min{M,N} log SNR bits/s/Hz. This result suggests that
the multiple antennas provide min{M,N} degrees of freedom, and is a
major stimulus for the recent excitement in the space-time
communication field . A key assumption behind this result is that the
channel is known perfectly at the receiver. This may not be realistic
in a fast fading environment or when there are many antennas. In
recent work we considered a non-coherent block fading model, first
introduced by Hochwald and Marzetta, where the
channel remains constant within blocks of T symbols but is not assumed
known at the receiver. It turns out that high SNR capacity is
approximately M*(1-M*/T) log SNR bits/s/Hz, where M* =
min{M,N,T/2}. This result suggests that while significant capacity
gain can be obtained from using multiple antennas even when the
channel is not known, a price must be paid for the channel
uncertainty. The solution is based on a geometric view of the problem
as that of communicating on the Grassmann manifold.
L. Zheng and D. Tse, ``Communicating
on the Grassmann Manifold: A Geometric Approach to the Non-coherent
Multiple Antenna Channel'', IEEE Transactions on Information
Theory, vol. 48(2), February 2002, pp. 359-383.

For a quick overview of the basic ideas, see the following
presentation:

"Packing Spheres
in the Grassmann Manifold", Talk at EPFL, July, 2000.

This work is supported by the National Science Foundation under
grant #NCR-9734090.