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Hardware distortions (HWD) render drastic effects on the performance ofcommunication systems. They are recently proven to bear asymmetric signatures;and hence can be efficiently mitigated using improper Gaussian signaling (IGS),thanks to its additional design degrees of freedom. Discrete asymmetricsignaling (AS) can practically realize the IGS by shaping the signals' geometryor probability. In this paper, we adopt the probabilistic shaping (PS) insteadof uniform symbols to mitigate the impact of HWD and derive the optimal maximuma posterior detector. Then, we design the symbols' probabilities to minimizethe error rate performance while accommodating the improper nature of HWD.Although the design problem is a non-convex optimization problem, we simplifiedit using successive convex programming and propose an iterative algorithm. Wefurther present a hybrid shaping (HS) design to gain the combined benefits ofboth PS and geometric shaping (GS). Finally, extensive numerical results andMonte-Carlo simulations highlight the superiority of the proposed PS overconventional uniform constellation and GS. Both PS and HS achieve substantialimprovements over the traditional uniform constellation and GS with up to oneorder magnitude in error probability and throughput.

When Probabilistic Shaping Realizes Improper Signaling for Hardware Distortion Mitigation