When Probabilistic Shaping Realizes Improper Signaling for Hardware Distortion Mitigation

Abstract

Hardware distortions (HWDs) render drastic effects on the performance of communication 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 asymmetric signaling (AS) can practically realize the IGS by shaping the signals' geometry or probability. In this paper, we adopt the probabilistic shaping (PS) instead of uniform symbols to mitigate the impact of HWDs and derive the optimal maximum a posterior detector. Then, we design the symbols' probabilities to minimize the error rate performance while accommodating the improper nature of HWD. Although the design problem is a non-convex optimization problem, we simplified it using successive convex programming and propose an iterative algorithm. We further present a hybrid shaping (HS) design to gain the combined benefits of both PS and geometric shaping (GS). Finally, extensive numerical results and Monte Carlo (MC) simulations highlight the superiority of the proposed PS over conventional uniform constellation and GS. Both PS and HS achieve substantial improvements over the traditional uniform constellation and GS with up to one order magnitude in error probability and throughput.

EMF-Aware Probabilistic Shaping Design for Hardware-Distorted Communication Systems

“…The advantage of PS over NS is particularly prominent for higher distortion levels. Moreover, we move a step further to investigate the performance of the HS scheme with M nu − QAM employing an aggregate of GS and PS as detailed in the study by Javed et al (2021). Interestingly, HS reduces the EMF exposure for higher distortion levels, but the gain is insignificant given the added complexity in designing GS and PS parameters.…”

“…Unequal power distribution among the quadrature noise components and nontrivial correlation coefficient marks the improper nature of aggregate additive distortions. Given the nonuniform symbol probabilities and improper noise, we propose a maximum a posterior (MAP) detector for the optimal detection as opposed to the conventional minimum Euclidean or maximum likelihood (ML) detectors (Javed et al, 2021). Thus, the detection criterion is given by…”

“…However, realizing the IGS comes with inherent problems of the unbounded peak-to-average power ratio and high detection complexity (Santamaria et al, 2018;Javed et al, 2020). As a consequence, researchers employ finite discrete asymmetric signaling (AS) schemes that can be achieved by geometric shaping (GS), probabilistic shaping (PS), or hybrid shaping (HS) (Elzanaty and Alouini, 2022;Javed et al, 2021). In this work, we propose asymmetric signaling by adopting PS to tackle improper HWD and minimize EMF exposure to the users while maintaining throughput quality of service (QoS).…”

On Symbol Error Performance of Probabilistic Shaping in Noise-Limited and Fading Channels

“…For example, PS has contributed to a substantial improvement in transmission capacity and system performance for highspeed Terahertz photonic wireless communication systems in [18], [19], [20]. PS has also been applied to mitigate hardware distortions in [21]. Therefore, it is important to study the error performance of PS in wireless communication systems in the presence of fading.…”

Probabilistic Shaping-Based Spatial Modulation for Spectral-Efficient VLC

“…Probabilistic shaping (PS) and geometric shaping (GS) are widely known techniques that aim to reduce this shaping gap by optimizing the probability and location of the constellation symbols, respectively. Compared to GS, PS offers greater flexibility for granularity and enables easy implementation of Gray mapping [8], [9]. Importantly, it's worth noting that constellation shaping doesn't conflict with existing techniques used to enhance the SE of VLC systems.…”