Constellation Design Research Articles

Codebook Design for PD-SCMA NOMA Systems

The hybrid power domain sparse code non-orthogonal multiple access (PD-SCMA) scheme multiplexes multiple users on a single resource element (RE) both in power and code domains, thus achieving a superior spectral efficiency. The multiplexing performance of such a scheme can be enhanced not only through deployment of sophisticated resource allocation schemes and low complexity robust multi-user detectors but also prudent multi-user multi-dimensional codebook design. By considering the key codebook design performance indicators (KPIs) in different channel use scenarios, this work assesses various known multi-dimensional constellation (MDC) design criterion on the performance of low-rate turbo-coded PD-SCMA NOMA system. In order to strike a balance with regard to good multi-dimensional modulation (MDM) and low complex detection, a low complex codebook design based on linear error correcting block codes is proposed. Unique user-specific rotation design based on quaternion rotation matrices is proposed with the aim of maintaining users symbol uniqueness for overloaded systems. Simulation results confirm that MDCs that satisfy design KPIs outperform others. Besides, the proposed user-specific rotation design remarkably enhances the BER performance of the block code based codebook design.

Characteristic area-based method for continuous coverage analysis of satellites constellation

Coverage capacity analysis of satellites constellation is the basis of satellite system design and performance evaluation, which is essential in the application of satellite technology. A characteristic area based method for continuous coverage analysis is proposed in this paper. The trajectory characteristics of the Walker constellation are first analyzed. The Earth's surface is partitioned into a group of characteristic areas, and the characteristic distance theory is defined and proposed accordingly. On this basis, the formulations of the characteristic point of each characteristic area and the corresponding characteristic distance with all different situations can be analytically obtained. Additionally, sufficient and necessary conditions for continuous coverage are given accordingly. The complex continuous coverage problem can be converted to the analysis of the relations between the critical geocentric angle of the satellite coverage range and the characteristic distance. Computational results indicate the effectiveness of the proposed method and reveal the feasibility in instructing the constellation design.

Unified Constellation Design Using Projection Over QAM: Concept and Examples

Unified Constellation Design Using Projection Over QAM: Concept and Examples

The Design and Maintenance of Low-Orbit Navigation Constellation for Traffic Control in a Smart City

The traffic control issue in the smart city scenario gives rise to the higher requirements of Global Navigation Satellite System (GNSS) services, especially in terms of navigation accuracy, together with coverage continuity, and multiplicity. The dense urban environment leads to higher elevation angles for navigation in such areas, which requires a lower altitude of the constellation, as well as a larger number of satellites. In the existing literature, the design and maintenance of the Low Earth Orbit (LEO) navigation constellation that fulfills the requirements of the smart city are not provided. Hence, based on the requirements and constraints of the smart city scenario, this article studies the relation between orbital height, user elevation angle, and coverage. It designs the configuration of an LEO navigation constellation that not only achieves global sensing coverage, but also provides a continuous lane-level navigation service with multiple coverages for the key area. In addition, considering the atmospheric drag in low orbits and the constraint of satellite power and attitude control, a method is proposed by rotating solar panels to change the effective frontal area of the satellite to achieve relative configuration maintenance of the LEO constellation. The results show that the LEO navigation constellation has a 0 s revisit time in five chosen smart cities, and each city has more than four-times coverage every second; the Geographic Dilution of Precision (GDOP) values of five cities are smaller than 0.47. The average navigation accuracy of five cities is 2.01. With the conduction of the one-year station-keeping simulation, the phase deviation of two satellites is less than 0.6° and it gradually converges to 0.1°, where the semi-major axis deviation is less than 80 m. With our proposed method, the active station-keeping control is not needed in one year, and the fuel consumption can be reduced. Finally, the continuity of the navigation service can be assured.

Constellation Design for Multiuser Non-Coherent Massive SIMO Based on DMPSK Modulation

Non-coherent (NC) schemes combined with massive antenna arrays are proposed to replace traditional coherent schemes in scenarios which require an excessive number of reference signals, since NC approaches avoid channel estimation and equalization. Differential <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary phase shift keying is one of the most appealing NC schemes due to its implementation simplicity in realistic scenarios. However, the analytical constellation design for multiuser scenarios is intractable, as discussed in this paper. We propose to solve this problem by using optimization techniques relying on evolutionary computation. We design two approaches, namely Gaussian-approximated optimization and Monte-Carlo based optimization. They can provide both individual constellations for each user equipment and a bit mapping policy to minimize the bit error rate. We perform a complexity analysis and propose strategies for its reduction. We propose a set of constellations for different number of users and constellation sizes, and evaluate the link-level performance of some illustrative examples to verify that our solutions outperforms the existing ones. Finally, we show via simulations that NC outperforms the coherent schemes in high mobility and/or low signal-to-noise ratio scenarios.

Flexible Quadrature Spatial Pulse Amplitude Modulation for VLC Systems

Quadrature-spatial modulation (QSM) offers high spectral efficiency (SE) without interchannel interference for both radio frequency and visible light communication (VLC) systems. In this article, a new QSM scheme called flexible quadrature spatial pulse amplitude modulation (FQSPAM) is proposed for VLC systems. In space modulation techniques (SMTs), the data bit stream is divided into two groups as the index bits and the signal bits. These grouped bits are mapped independently to modulation symbols and indices of light-emitting diodes (LEDs). However, this mapping strategy puts a constraint on the number of LEDs and the size of the signal constellation. FQSPAM jointly designs the signal and spatial components of the constellation to overcome these limitations. This approach removes the constraint on the number of LEDs and the size of the signal constellation. The constellation design problem is formulated as a convex optimization problem to identify power-efficient constellations with different <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> values. A dimming-controlled optimization algorithm has also been proposed to take into account both illumination and communication at the same time. Analytical and numerical results show the improved bit error rate performance of the proposed FQSPAM compared to spatial pulse amplitude modulation and channel adaptive bit mapping.

Optimization design of two-layer Walker constellation for LEO navigation augmentation using a dynamic multi-objective differential evolutionary algorithm based on elite guidance.

The online version contains supplementary material available at 10.1007/s10291-022-01366-5.

Constant Power Constellation Grouping for Reducing Nonlinearity Effects in Fiber Optics

Fiber nonlinearity is the main obstacle for increasing the capacity of existing fiber systems. This nonlinearity depends on the accumulated power launched into the wavelength division multiplexing (WDM) channels. In this article, we model the accumulated launched power and show the impact of the constellation design on the fiber nonlinearity. We analytically show that one can achieve the same noise power at longer distances by controlling the fluctuations in the launched power. We then propose the idea of constant power constellation grouping (CPCG) to control the power fluctuations and achieve significantly better system reach compared to conventional quadrature amplitude modulation (QAM) constellations. In comparison with constant power phase-shift keying (PSK) constellations, we achieve much higher data rates for the same signal to noise ratio (SNR). Our simulation study confirms our theoretical findings and demonstrates the benefits of the proposed CPCG method.

Joint Constellation Design for Noncoherent MIMO Multiple-Access Channels

We consider the joint constellation design problem for the noncoherent multiple-input multiple-output multiple-access channel (MAC). By analyzing the noncoherent maximum-likelihood detection error, we propose novel design criteria so as to minimize the error probability. As a baseline approach, we adapt several existing design criteria for the point-to-point channel to the MAC. Furthermore, we propose new design criteria. Our first proposed design metric is the dominating term in nonasymptotic lower and upper bounds on the pairwise error probability exponent. We give a geometric interpretation of the bound using Riemannian distance in the manifold of Hermitian positive definite matrices. From an analysis of this metric at high signal-to-noise ratio, we obtain further simplified metrics. For any given set of constellation sizes, the proposed metrics can be optimized over the set of constellation symbols. Motivated by the simplified metric, we propose a simple constellation construction consisting in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">partitioning</i> a single-user constellation. We also provide a generalization of our previously proposed construction based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">precoding</i> individual constellations of lower dimensions. For a fixed joint constellation, the design metrics can be further optimized over the per-user transmit power, especially when the users transmit at different rates. Considering unitary space-time modulation, we investigate the option of building each individual constellation as a set of truncated unitary matrices scaled by the respective transmit power. Numerical results show that our proposed metrics are meaningful, and can be used as objectives to generate constellations through numerical optimization that perform better, for the same transmission rate and power constraint, than a common pilot-based scheme and the constellations optimized with existing metrics.

Non-Self-Intersecting Trajectories and Their Applications to Satellite Constellation Design and Orbital Capacity

This work focuses on the generation of non-self-intersecting relative trajectories, and their applications to satellite constellation design, slotting architectures, and space traffic management. To that end, this paper introduces three theorems to determine when two spacecraft share the same relative trajectory, to identify the only conditions that allow the existence of non-self-intersecting relative trajectories, and to compute the minimum distances inside these relative trajectories. These results are then applied first to obtain an estimation of the limits of the orbital capacity at a given altitude and, second, in the design of satellite constellations and slotting architectures that present no conjunctions between any element compliant with these space structures.

General analysis method for global revisit characteristics of satellite constellation with repeating ground tracks

Coverage analysis is an essential process when designing a satellite constellation, and the variations of global revisit characteristics are usually elusive in discontinuous coverage problems. In dealing with this, a general method for analyzing the global revisit characteristics of constellations with repeating ground track orbits is proposed in this paper. Firstly, a two-dimensional map based analytical model for the point coverage of constellations is introduced. Then, the variations of revisit characteristics along both the parallel and meridian are analyzed based on the presented analytical model. Finally, numerical examples are carried out. On the one hand, the proposed analytical model for point coverage is demonstrated to be of high precision. On the other hand, all possible positions where the discontinuous changes of revisit characteristics occur can be analytically obtained, which can reveal the discontinuous variations of revisit characteristics along both the parallel and meridian, and can also ensure that all possible global or regional revisit characteristics are counted for a given constellation. The proposed method can contribute to constellation design and coverage performance analysis.

Low Earth orbit constellation design using a multi-objective genetic algorithm for GNSS reflectometry missions

Spaceborne global navigation satellite system reflectometry (GNSS-R) is an innovative bistatic radar remote sensing technique utilizing low Earth orbit (LEO) based GNSS-R instruments to acquire GNSS L-band opportunistic signals for measuring geophysical parameters. A GNSS-R LEO constellation with an optimization design for its specialized missions is very significant and necessary. However, the constellation design involves multi-parameter and multi-objective optimization, and the classical analytic solution is not capable of such a complicated issue. This study proposes a multi-objective LEO constellation design method with a genetic algorithm (GA) and presents a framework for designing two GNSS-R LEO constellations, termed “lower-latitude constellation” for typhoons and hurricanes observation in the tropics and “global constellation” for global geophysical parameter measurements. Then, the observation capability of both designed constellations is evaluated in terms of the number of reflection points, spatial coverage density, and revisit time to verify the GA efficiency in LEO constellation design. Results show that the two designed LEO constellations with high fitness function values possess optimal orbit parameter set configuration and outperform the existing CyGNSS constellations in observation performance. Compared with CyGNSS, the number of reflection points observed by the lower-latitude constellation and the global constellation increases by 38% and 45%, as well as the spatial coverage density increases by 28% and 36%. The revisit time for the lower-latitude constellation is reduced by 0.29 h, whereas the revisit time for the global constellation increases by one hour.

Constellation Design for Energy-Based Noncoherent Massive SIMO Systems Over Correlated Channels

This letter concerns the constellation design problem in energy-based noncoherent massive single-input multiple-output (SIMO) systems over correlated channels. Thanks to the large number of receiving antennas, we approximate the detection error minimization problem by the maximization of the minimum Kullback-Leibler (KL) divergence of the received signal vectors corresponding to different transmitted symbols. However, the max-min KL divergence problem is still difficult to solve. This is because the KL divergence expression involves summations of nonlinear functions of the transmitted signal powers induced by the channel correlation. We then resort to the Szegö’s theorem on large Hermitian Toeplitz matrices to simplify the formulated problem, which subsequently can be optimally solved by a one-dimensional bisection search. Simulation results demonstrate that the constellation designed by our approach outperforms its counterpart without considering the channel correlation, and the performance gain enlarges as the degree of correlation increases.

High-Cardinality Geometrical Constellation Shaping for the Nonlinear Fibre Channel

This paper presents design methods for highly efficient optimisation of geometrically shaped constellations to maximise data throughput in optical communications. It describes methods to analytically calculate the information-theoretical loss and the gradient of this loss as a function of the input constellation shape. The gradients of the mutual information (MI) and generalised mutual information (GMI) are critical to the optimisation of geometrically-shaped constellations. The analytically derived gradients of the achievable information rate metrics with respect to the input constellation are presented. The proposed method allows for improved design of higher cardinality and higher-dimensional constellations for optimising both linear and nonlinear fibre transmission throughput. Near-capacity achieving constellations with up to 8192 points for both 2 and 4 dimensions are presented. In the best case, a GMI value within 0.06&#x00A0;b/2Dsymbol of the additive white Gaussian noise channel (AWGN) capacity was achieved. Additionally, a design algorithm reducing the design computation time from days to minutes is introduced, allowing for the design of optimised constellations for both linear AWGN and nonlinear fibre channels over a wide range of signal-to-noise ratio values.

Mixed integer (non)linear approaches for the satellite constellation design problem

Mixed integer (non)linear approaches for the satellite constellation design problem

Simulation study on inclined orbit constellation of high-resolution electrooptical sensors for enhanced imaging efficiency in region of interest

Traditionally, high-resolution electrooptical (EO) sensors are placed in Sun-synchronous orbits (SSO) as they enable consistent solar illumination during imaging and near-global coverage for various remote sensing applications. However, these sensors inherently offer limited swath coverage resulting in poorer imaging efficiency and often require a large number of satellites in constellation for improving revisit time over region of interest (RoI). Compared with constellation of satellites in SSO, a smaller number of satellites in lower inclination orbits can provide significant advantage in terms of imaging efficiency in the tropical and near-tropical RoIs, which is desirable for many civilian and strategic applications. In this work, detailed analytical simulations have been performed for inclined orbit constellation of high-resolution EO sensors, and higher imaging efficiency has been demonstrated against SSO constellation. Rigorous mathematical models are developed to enable optimization of constellation design with proper fine-tuning of orbital parameters to maximize imaging efficiency in the RoI, and the model output is validated through STK simulation. For quantitative evaluation of imaging efficiency, two figures of merits, namely, average number of access per day and number of days with no access, have been estimated for various design cases. This study shows significant improvements in imaging efficiency parameters up to a factor of 3 in RoI as compared with traditional SSO constellation. This study is generic in nature and is applicable for any inclination angles and latitudes in the tropical and near tropical RoIs. This study can significantly aid in design of satellite constellations for future remote sensing missions.

Optimization of satellite resource scheduling under regional target coverage conditions

Abstract This study presented a mathematical description of an arbitrary shape area, and after analyzing the characteristics of the near-polar orbital co-ground trajectory constellation that satisfies the revisit interval constraint, an optimization model of the orbital parameters design of reference satellites in regional coverage constellations was constructed. Then based on the designed area covering the constellation of common ground trajectories, a simple and effective two-pulse maneuvering scheme was adopted for the needs of sudden tasks, and an existing satellite scheduling optimization model using the golden section method to constrain the boundary of substellar point coverage was constructed. Finally, the optimal design of regional coverage constellations and existing satellite dispatches was carried out for the sea areas with the most frequent tropical cyclone activities in the northwest Pacific Ocean, and the simulation results verified the effectiveness of the proposed optimization model and have certain practical use value.

Optimization of constellation deployment using on-board propulsion and Earth nodal regression

Constellation deployment using on-board propulsion is a cost-effective way for distributing multiple satellites into different orbital planes using a minimal number of launches. This paper focuses on the extension of previous studies based on analytical formulations of the problem into a more general numerically-based one, which can be applied to both electric and chemical propulsion systems. Additionally, the formulation is not restricted to in-plane maneuvers only, taking full advantage of the increased mobility capabilities of satellites equipped with high-efficiency propulsion systems. Two deployment methods are analyzed: the first is based on moving the satellites from the injection to the operational orbit sequentially with a properly timed delay between each maneuver so that the difference in nodal regression causes the accumulation of a given spacing; the second is built upon the parallel transfer of satellites into so called “drift” orbits which, once again, exploiting the differential nodal drift, can be used to accumulate orbital plane spacing until a required value is met, and the satellites can be finally moved into their operational orbits. A multi-objective optimization based on the high-fidelity numerical computation of maneuvers using a feedback control law coupled with a genetic algorithm is proposed, presenting a framework capable of generating optimal solutions with respect to total constellation propellant mass needs and deployment time. An example of application based on the FORMOSAT-3/COSMIC mission is presented. The results highlight the potential of the optimization routine which is intended to be applied systematically by mission designers to generate solutions for the deployment problem within the context of constellation design. Some important and un-explored properties of the problem, such as, launcher-related injection constraints, the selection of a suitable propulsion technology and the effects of atmospheric drag are analyzed. The results show the effect of these properties on the optimality of the solutions, and highlight the advantage of a mixed in-plane/out-of-plane maneuver approach.

Multi-Objective Evolutionary formulations for design of hybrid Earth observing constellations

With the recent advances in satellite miniaturization, communication and information technologies, and the advent of affordable small satellite launch services, there has been a paradigm shift in space exploration missions involving the transition from monolithic architectures formed by a large satellite to the concept of Distributed Spacecraft Missions (DSM), which fly multiple simpler and less costly satellites to offer increased capabilities such as better temporal, spatial, and angular sampling. Despite the potential to provide higher science return and novel data products, the orbit selection problem for Earth Observation DSMs requires a much more complex constellation design process, which involves several interrelated design variables and conflicting objectives. Because of this, prior work has focused mostly on relatively simple DSM architectures consisting of a single type of constellation, such as homogeneous Walker constellations. This paper presents a novel evolutionary formulation (i.e., chromosome and operators) in the context of Multi-Objective Evolutionary Algorithms (MOEA) that allows for the exploration of large tradespaces of non-Walker hybrid satellite constellations with diversity of orbital parameters. The idea behind this new formulation is that it allows to search through the space of different types of constellations – such as Walker formations, Sun-synchronous trains and string-of-pearls among others – and combinations thereof. This type of hybrid constellations have not been studied in detail. The methodology presented in this paper helps overcome the combinatorial explosion resulting when opening up the design space to include non-symmetrical configurations and relaxing constraints in the values of some orbital parameters (e.g. choosing a common altitude or inclination for all satellites forming the constellation). The proposed formulation is compared with a state-of-the-art evolutionary formulation using a variable-length chromosome in 5 different problems including the observation of symmetrical, asymmetrical, connected and disconnected regions of interest. Results show that the proposed formulations achieve better convergence and convergence rate than the state-of-the-art. The proposed method can reduce the effort required to design a problem formulation for each problem instance, while also reducing the risk of missing potentially good architectures due to formulations that are too restrictive and rely too much on previous experience and expertise.

Configuration design of hybrid constellations with synchronous orbital precession based on rapid coverage analysis

This paper mainly deals with the configuration design of hybrid constellations for Earth discontinuous coverage. Firstly, a general design model of the hybrid constellation with synchronous orbital precession and multiple repeating ground tracks is developed. Then, to cope with the massive coverage calculation during the constellation design process, an analytical method for rapid coverage analysis of hybrid constellations is proposed. Finally, numerical examples are carried out, and several hybrid constellation design cases are proposed. Results indicate that the proposed coverage analysis method is demonstrated to be of high precision, and the designed hybrid constellations can achieve superior coverage performance compared with conventional Walker constellations. This research can be conducive to hybrid constellations design and Earth discontinuous coverage analysis.