  Meeting the challenges of 5G demands better exploitation of the available
spectrum by allowing multiple parties to share resources. For instance, a
secondary unlicensed system can share resources with the cellular uplink of a
primary licensed system for an improved spectral efficiency. This induces
interference which has to be taken into account when designing such a system. A
simple yet robust strategy is treating interference as noise (TIN), which is
widely adapted in practice. It is thus important to study the capabilities and
limitations of TIN in such scenarios. In this paper, we study this scenario
modelled as Multiple Access Channel (MAC) interfered by a Point-to-Point (P2P)
channel. Here, we focus on rate maximization and power minimization problems
separately. We use improper Gaussian signaling (instead of proper) at the
transmitters to increase the design flexibility, which offers the freedom of
optimizing the transmit signal pseudo-variance in addition to its variance.
Furthermore, we allow correlation among the transmitted signals over orthogonal
resource basis (i.e., time or frequency) for the purpose of optimal signaling
design over the extended channel. We formulate the rate maximization problem as
a semidefinite program, and use semidefinite relaxation (SDR) to obtain a
near-optimal solution. Numerical optimizations show that, by improper Gaussian
signaling the achievable rates can be improved upto three times depending on
the strength of the interfering links. Furthermore, we observe significant
benefits in power consumption by improper Gaussian signaling with symbol
extensions compared to the traditional proper Gaussian signaling.
Interestingly, by minimizing sum power given the solution of the rate
maximization problem improves the energy efficiency significantly.
