A Journey from Improper Gaussian Signaling to Asymmetric Signaling

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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/noncircularity

and then surveys majority of the contributions in this

enormous journey.