Coherence Disparity in Broadcast and Multiple Access Channels

TL;DR

This paper investigates the fundamental limits of broadcast and multiple access channels with unequal fading coherence times, revealing new degrees of freedom bounds and introducing the concept of coherence diversity without requiring channel state information at the transmitter.

Contribution

It derives the degrees of freedom region for broadcast channels with unequal coherence times and establishes bounds for multiple access channels, advancing understanding of coherence disparity effects.

Findings

Achievable degrees of freedom meet upper bounds under certain conditions.

Identifies coherence diversity as a new gain mechanism.

Provides bounds for arbitrary ratios of fading block lengths.

Abstract

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.