signal constellation design

To address the challenge of modeling time-varying channels between high-speed low-Earth-orbit (LEO) mega-constellations (e.g., Starlink) and static ground users, this paper proposes a generic stochastic time-varying channel model. Methodologically, it innovatively employs a marked non-homogeneous binomial point process to jointly characterize satellite spatial distribution, motion direction, and dynamic geometric relationships; further, it introduces— for the first time—the channel scattering function to uniformly represent the power distribution in the delay-Doppler domain. Closed-form expressions are derived for the probability distributions and statistical properties of path loss, propagation delay, Doppler shift, and power gain. Validated via Starlink orbital simulations, the model achieves excellent agreement with simulation results for key channel statistics (error < 5%), demonstrating strong generality, scalability, and engineering predictability.

This work addresses the performance limitation of constellation modulation imposed by fixed symbol probability distributions and geometric structures. We propose a novel end-to-end joint optimization framework for probabilistic and geometric shaping. Specifically, an auxiliary shaping encoder is introduced to model non-uniform symbol priors, while constellation shaping is embedded into the full iterative detection-and-decoding loop. For the first time, deep unfolding is employed to enable differentiable joint learning across the entire physical-layer pipeline. Under block-fading channels, the proposed scheme significantly outperforms conventional APSK and QAM: it achieves 0.3 dB and 0.15 dB BER gains over APSK under two receiver configurations, with the iterative variant further improving performance by 0.1 dB relative to standard APSK. The key contribution lies in the first application of deep unfolding to joint constellation shaping within a full-chain iterative receiver architecture, enabling synergistic optimization across both probabilistic and geometric dimensions.

This work proposes a novel multidimensional signal constellation, termed SCOPT, to enhance the energy efficiency of high-speed communication systems without increasing transmit power or employing additional coding. By extending the normalized signal duration to enlarge the minimum Euclidean distance between signals, SCOPT achieves reliable communication below the conventional Shannon limit within a geometric framework—a first in the field—while preserving a simple structure compatible with standard modulation schemes such as QAM and APSK. Both theoretical analysis and simulations demonstrate that SCOPT substantially improves energy efficiency and significantly reduces the required signal duration, offering both theoretical novelty and practical relevance.

To address the low spectral efficiency, high bit error rate (BER), and excessive detection complexity of MIMO systems under highly dynamic low Earth orbit (LEO) satellite channels, this paper presents the first systematic performance trade-off analysis of spatial modulation (SM) and space shift keying (SSK) in LEO scenarios. Leveraging analytical modeling and Monte Carlo simulations, we establish an end-to-end link-level evaluation framework supporting both ideal and imperfect channel state information (CSI). Results demonstrate that SM/SSK achieves up to 35% higher spectral efficiency than conventional MIMO in LEO channels, significantly reduces BER, and cuts detection complexity by approximately 50%. The study identifies operational boundaries and critical design guidelines for deploying SM/SSK in 6G integrated space-air-ground networks, thereby providing both theoretical foundations and practical insights for LEO-assisted MIMO communications.

This work addresses the challenge of accurately modeling the performance of multilayer low Earth orbit (LEO) satellite Internet-of-Things (IoT) constellations over practical Rician fading channels. To this end, the authors propose a stochastic geometry–based analytical framework that characterizes the spatial distribution of satellites using a Cox point process and introduces a novel channel approximation method tailored for Rician fading. For the first time, closed-form expressions are derived for key performance metrics—including connection probability, coverage probability, and achievable transmission rate—enabling precise performance evaluation of such systems under Rician fading conditions. Theoretical results are validated through simulations, revealing fundamental relationships between constellation design parameters and channel characteristics, thereby offering both theoretical insights and practical guidance for the deployment of future multilayer LEO IoT networks.

This study addresses the severe degradation in downlink SINR coverage probability and spectral efficiency caused by densification in the Walker low Earth orbit (LEO) satellite constellation under full frequency reuse. By leveraging geospatial constraints of the Earth and a stochastic channel model, the work uncovers a fundamental tension between linearly growing interference and the boundedness of the desired signal. The authors introduce the “deterministic visible ring-block lemma” to derive, for the first time, an explicit finite-N performance upper bound applicable to arbitrarily large constellations and phase configurations, and establish corresponding scaling laws under frequency reuse. The analysis rigorously shows that under full frequency reuse, both coverage probability and ergodic spectral efficiency decay as O(1/N). In contrast, under independent sparse reuse with qN = O(1), the performance upper bound scales as O(1/(qN)).

This work addresses the challenge of designing constellations for integrated sensing and communication (ISAC) systems that simultaneously optimize both sensing and communication performance. To this end, the authors propose a two-dimensional geometric constellation design framework based on Gamma-distributed amplitudes and uniformly distributed phases. The constellation is optimized jointly with respect to detection probability and mutual information using a particle swarm optimization algorithm, marking the first application of the Gamma distribution in ISAC constellation design. Theoretical analyses derive joint bounds on symbol error rate and the Cramér–Rao bound. The proposed method operates without requiring training data, outperforms existing neural network–based approaches in both sensing detection performance and communication mutual information, and achieves these gains with significantly fewer parameters while maintaining compatibility with existing communication architectures.

This work addresses the fundamental trade-off between communication and sensing performance in integrated sensing and communication (ISAC) systems by proposing a semi-analytical amplitude phase-shift keying (APSK) signal design framework. Leveraging i.i.d. uniformly distributed discrete inputs, the approach links the communication capacity gap to the minimum Euclidean distance and quantifies sensing performance via symbol energy variance. A multi-ring parametric constellation family enables flexible control over the communication–sensing trade-off. Theoretical analysis yields explicit scaling laws for key design parameters, demonstrating that the proposed scheme maintains a constant capacity gap across all signal-to-noise ratios and, for the first time under discrete input constraints, asymptotically approaches the Pareto boundary achievable with continuous inputs. Simulations confirm that the designed APSK constellations achieve near-optimal joint performance, closely approaching theoretical limits.

This study addresses the suboptimal downlink throughput of low Earth orbit (LEO) satellite constellations caused by traditionally pre-specified ground station locations, which hinder globally optimal performance. To overcome this limitation, the authors propose SCORE (Sequential Coordinate Optimization with Refinement), a novel framework that enables flexible co-deployment of newly sited and existing ground stations within continuous geographic space. SCORE integrates sequential coordinate selection with iterative refinement to efficiently solve the high-dimensional non-convex optimization problem. Experimental results demonstrate that SCORE reduces the number of function evaluations required for convergence to one-fifth of that needed by differential evolution while achieving up to a 13% increase in downlink throughput. Compared to fixed-site baselines, SCORE improves total downlink capacity by up to 15% and retains over 92% of its performance gain even under infrastructure deployment constraints.