Heterogeneous Multi-Tier Networks: Improper Signaling for Joint Rate-Energy Optimization

Wireless nodes in future communication systems need to overcome three barriers when compared to their transitional counterparts, namely, to support significantly higher data rates, have long-lasting energy supplies, and remain fully operational in interference-limited heterogeneous networks. This could be partially achieved by providing three promising features, which are radio frequency (RF) energy harvesting, improper Gaussian signaling, and operating in full-duplex communication mode, i.e., transmit and receive at the same time within the same frequency band. In this paper, we consider these aspects jointly in a multi-antenna heterogeneous two-tier network. In this network, the users in the femtocell share the scarce resources with the cellular users in the macro-cell and have to cope with the interference from the macro-cell base station as well as the transmitter noise and residual self-interference due to imperfect full-duplex operation. Interestingly enough, while these impairments are detrimental from the achievable rate perspective, they are beneficial from the energy harvesting aspect, as they carry RF energy. In this paper, we consider this natural tradeoff jointly and propose appropriate optimization problems for beamforming and optimal resource allocation. Moreover, various receiver structures are employed for both information detection and energy harvesting (EH) capabilities. This paper aims at characterizing the tradeoff between the achievable rates and harvested energies. Rate and energy maximization problems are thoroughly investigated. Interestingly, with sufficiently high EH demands, we observe the convergence of the rate region obtained by non-linear precoding to the rate region achieved by widely linear precoding at the base station.