Improper Gaussian Signaling for Integrated Data and Energy Networking

Abstract

The paper considers the problem of beamforming design for a multi-cell network of downlink users, who either harvest energy or decode information or do both by receiving signals from the multi-antenna base station (BS) within a time slot and over the same frequency band. Our previous contributions have showed that the time-fraction based energy and information transmission, under which first the energy is transferred within the initial fraction of time and then the information is transferred within the remaining fraction, is the most efficient design alternative both in terms of its practical implementation and network performance. However, at the time of writing, both energy and information beamforming has only been implemented for proper Gaussian signaling (PGS), which has limited the network's throughput. Although the network throughput could be improved in some specific scenarios by using non-orthogonal multi-access (NOMA), this may compromise the user secrecy. In order to circumvent the above implementations, we conceive improper Gaussian signaling (IGS) for information beamforming, which enables the network to substantially improve its throughput in any scenario without jeopardizing the user secrecy despite its lowcomplexity signal processing at the user end. A simpler subclass of IGS is also considered, which also outperforms NOMA PGS and works under any arbitrary scenario.

Joint Design of Reconfigurable Intelligent Surfaces and Transmit Beamforming Under Proper and Improper Gaussian Signaling

“…1 is simulated for initialization and proposed Alg. all the algorithms converges rapidly within a few iterations (15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30). As expected, the PGS based algorithms converge rapidly than the IGS based algorithms because the latter need to handle more optimization variables.…”

Improper Gaussian Signaling for Computationally Tractable Energy and Information Beamforming

“…, γ (κ+1) ) for (9): (11), (12). (13) Note that γ (κ+1) and γ (κ) are the optimal value and a feasible value for (13) respectively, hence we have γ (κ+1) > γ (κ) as far as γ (κ+1) = γ (κ) .…”

“…By using the inequality (1), we obtain r PS (p Ne ,q Ne , p M , q M , β ) ≥ the transmit power budget of P = 31 dBm and e min = −20 dBm. Thus, the computation for RZF-BF and GZF-BF involves K + M = 16 real and M = 11 complex decision variables vs. the number N t (K + 2M ) = 270 of complex decision variables for the computation of beamformers in [11].…”

“…However, proper Gaussian signaling (PGS) is only optimal in interference-free systems [10]. As a further development, we have shown in [11] that improper Gaussian signaling (IGS) (see e.g. [12], [13] and references therein) is capable of substantially improving the information throughput of energy-harvesting aided networks.…”

“…(11) is an inner convex approximation of the nonconvex constraint (9c) in the sense that each feasible point for the former is also feasible for the latter and provides a lower bound for the optimal value of the former.…”