Improper signaling and symbol extensions: How far can we go with Gaussian P2P codebooks in the interfering MAC with TIN?

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.