Coherence Disparity in Broadcast and Multiple Access Channels

Individual links in a wireless network may experience unequal fading coherence times due to differences in mobility or scattering environment. This paper studies broadcast and multiple access channels whose nodes experience unequal fading block lengths. Channel state information (CSI) is not available at the transmitters, and the cost of acquiring CSI at the receivers 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. When the number of symbols in any fading block is at least twice the number of antennas at any active node and the fading block lengths have integer ratios, achievable 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 length. 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 multiuser diversity. This new class of gains is denoted coherence diversity. The inner bounds in the broadcast channel are further extended to fading block lengths of arbitrary ratio or alignment. In addition, in the multiple access channel with unequal coherence times, achievable and outer bounds on the degrees of freedom are obtained.