  This paper provides a survey of the state-of-the-art information theoretic
analysis for overlay multi-user (more than two pairs) cognitive networks and
reports new capacity results. In an overlay scenario, cognitive / secondary
users share the same frequency band with licensed / primary users to
efficiently exploit the spectrum. They do so without degrading the performance
of the incumbent users, and may possibly even aid in transmitting their
messages as cognitive users are assumed to possess the message(s) of primary
user(s) and possibly other cognitive user(s). The survey begins with a short
overview of the two-user overlay cognitive interference channel. The evolution
from two-user to three-user overlay cognitive interference channels is
described next, followed by generalizations to multi-user (arbitrary number of
users) cognitive networks. The rest of the paper considers K-user cognitive
interference channels with different message knowledge structures at the
transmitters. Novel capacity inner and outer bounds are proposed. Channel
conditions under which the bounds meet, thus characterizing the information
theoretic capacity of the channel, for both Linear Deterministic and Gaussian
channel models, are derived. The results show that for certain channel
conditions distributed cognition, or having a cumulative message knowledge
structure at the nodes, may not be worth the overhead as (approximately) the
same capacity can be achieved by having only one global cognitive user whose
role is to manage all the interference in the network. The paper concludes with
future research directions.
