A Gaussian interference channel (IC) with a relay is considered. The relay is
assumed to operate over an orthogonal band with respect to the underlying IC,
and the overall system is referred to as IC with an out-of-band relay (IC-OBR).
The system can be seen as operating over two parallel interference-limited
channels: The first is a standard Gaussian IC and the second is a Gaussian
relay channel characterized by two sources and destinations communicating
through the relay without direct links. We refer to the second parallel channel
as OBR Channel (OBRC). The main aim of this work is to identify conditions
under which optimal operation, in terms of the capacity region of the IC-OBR,
entails either signal relaying and/or interference forwarding by the relay,
with either a separable or non-separable use of the two parallel channels, IC
and OBRC. Here "separable" refers to transmission of independent information
over the two constituent channels. For a basic model in which the OBRC consists
of four orthogonal channels from sources to relay and from relay to
destinations (IC-OBR Type-I), a condition is identified under which signal
relaying and separable operation is optimal. When this condition is not
satisfied, various scenarios are identified in which interference forwarding
and non-separable operation are necessary to achieve optimal performance. In
these scenarios, the system exploits the "excess capacity" on the OBRC via
interference forwarding to drive the IC-OBR system in specific interference
regimes (strong or mixed). The analysis is then turned to a more complex
IC-OBR, in which the OBRC consists of only two orthogonal channels, one from
sources to relay and one from relay to destinations (IC-OBR Type-II). For this
channel, some capacity resuls are derived that parallel the conclusions for
IC-OBR Type-I.Comment: 52 pages, 12 figures, revised version for IT Transaction
