  This paper studies the two-user Gaussian interference channel with
half-duplex causal cognition. This channel model consists of two
source-destination pairs sharing a common wireless channel. One of the sources,
referred to as the cognitive, overhears the other source, referred to as the
primary, through a noisy link and can therefore assist in sending the primary's
data. Due to practical constraints, the cognitive source is assumed to work in
half-duplex mode, that is, it cannot simultaneously transmit and receive. This
model is more relevant for practical cognitive radio systems than the classical
information theoretic cognitive channel model, where the cognitive source is
assumed to have a non-causal knowledge of the primary's message. Different
network topologies are considered, corresponding to different interference
scenarios: (i) the interference-symmetric scenario, where both destinations are
in the coverage area of the two sources and hence experience interference, and
(ii) the interference-asymmetric scenario, where one destination does not
suffer from interference. For each topology the sum-rate performance is studied
by first deriving the generalized Degrees of Freedom (gDoF), or "sum-capacity
pre-log" in the high-SNR regime, and then showing relatively simple coding
schemes that achieve a sum-rate upper bound to within a constant number of bits
for any SNR. Finally, the gDoF of the channel is compared to that of the
non-cooperative interference channel and to that of the non-causal cognitive
channel to identify the parameter regimes where half-duplex causal cognition is
useless in practice or attains its ideal ultimate limit, respectively.
