  Individual links in a wireless network may experience unequal fading
coherence times due to differences in mobility or scattering environment, a
practical scenario where the fundamental limits of communication have been
mostly unknown. This paper studies broadcast and multiple access channels where
multiple receivers experience unequal fading block lengths, and channel state
information (CSI) is not available at the transmitter(s), or for free at any
receiver. In other words, the cost of acquiring CSI at the receiver is fully
accounted for in the degrees of freedom. In the broadcast channel, the method
of product superposition is employed to find the achievable degrees of freedom.
We start with unequal coherence intervals with integer ratios. As long as the
coherence time is at least twice the number of transmit and receive antennas,
these degrees of freedom meet the upper bound in four cases: when the
transmitter has fewer antennas than the receivers, when all receivers have the
same number of antennas, when the coherence time of one receiver is much
shorter than all others, or when all receivers have identical block fading
intervals. The degrees of freedom region of the broadcast under identical
coherence times was also previously unknown and is settled by the results of
this paper. The disparity of coherence times leads to gains that are distinct
from those arising from other techniques such as spatial multiplexing or
multi-user diversity; this class of gains is denoted coherence diversity. The
inner bounds are further extended to the case of multiple receivers
experiencing fading block lengths of arbitrary ratio or alignment. Also, in the
multiple access channel with unequal coherence times, achievable and outer
bounds on the degrees of freedom are obtained.
