A Journey From Improper Gaussian Signaling to Asymmetric Signaling

Abstract

The deviation of continuous and discrete complex random variables from the traditional proper and symmetric assumption to a generalized improper and asymmetric characterization (accounting correlation between a random entity and its complex conjugate), respectively, introduces new design freedom and various potential merits. As such, the theory of impropriety has vast applications in medicine, geology, acoustics, optics, image and pattern recognition, computer vision, and other numerous research fields with our main focus on the communication systems. The journey begins from the design of improper Gaussian signaling in the interference-limited communications and leads to a more elaborate and practically feasible asymmetric discrete modulation design. Such asymmetric shaping bridges the gap between theoretically and practically achievable limits with sophisticated transceiver and detection schemes in both coded/uncoded wireless/optical communication systems. Interestingly, introducing asymmetry and adjusting the transmission parameters according to some design criterion render optimal performance without affecting the bandwidth or power requirements of the systems. This dual-flavored article initially presents the tutorial base content covering the interplay of reality/complexity, propriety/impropriety and circularity/non-circularity and then surveys majority of the contributions in this enormous journey.

When Probabilistic Shaping Realizes Improper Signaling for Hardware Distortion Mitigation

“…Despite the overwhelming benefits of IGS, it is practically infeasible owing to the high detection complexity and unbounded peak-to-average power ratio [2], [34]. This motivated the researchers to design some equivalent finite and discrete asymmetric signaling (AS) schemes for practical implementation.…”

“…In this paper, we propose PS as a method to realize improper signaling, which is beneficial in mitigating the impact of HWD on the BER performance. Motivated by IGS's theoretical results in various scenarios [2] and the issues associated with GS, such as high shaping gap and coarse granularity, we adopt PS to realize the IGS scheme and combat HWD to assure reliable communications. In the following, we summarize the main contributions as:…”

“…It requires some meticulously designed improper signaling like IGS for effective mitigation. However, IGS is difficult to implement because of the unbounded peak-toaverage power ratio and high detection complexity [2], [34]. Therefore, researchers resort to the finite discrete AS schemes obtained by GS.…”

“…Exponentially rising demands of high data rates and reliable communications given the limited power and bandwidth resources impose enormous challenges on the next generation of wireless communication systems [1], [2]. Various research contributions propose new configurations and novel techniques to address these challenges [3], [4].…”

Improper Gaussian Signaling for Computationally Tractable Energy and Information Beamforming

“…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. However, a beamforming design challenge of IGS is its computational tractability, since it poses largedimensional nonconvex problems, which involve N t (K + 2M ) complex decision variables for scenarios of an N t antenna base station (BS) serving K EH users (EUs) and M informationreceiving users (IUs).…”