Performance Of Constellations Research Articles

Massive MIMO uplink and downlink joint representation based on couple dictionary learning

AbstractThe challenge of jointly representing both the uplink (UL) and downlink (DL) in massive multiple input multiple output (MIMO) systems have been tackled. Considering the angular reciprocity, a couple dictionary learning (CDL) support to enhance performance and address high complexity has been introduced. This approach minimizes the number of pilots and improves accuracy. Currently, accuracy analysis of UL/DL representation primarily relies on simulation. To bridge this gap, a proportion factor (PF) operator is proposed for CDL to assess accuracy. Specifically, a qualitative analysis formula is provided for accuracy and an optimal upper bound is established. Through theoretical proof, it is demonstrated that the accuracy of CDL for representation is mainly influenced by the cross‐correlation between the pilot matrix and the dictionary matrix. Inspired by PF operator, an optimal couple dictionary learning (OCDL) algorithm using singular value decomposition (SVD) is introduced to obtain dictionary updating, aiming at high‐precision representation. By establishing normalized mean squared error (NMSE), successful representation ratio, bit error rate (BER), and constellation performance, an OCDL algorithm that outperforms existing methods is showcased and channel representation accuracy is enhanced significantly.

Research on Design and Staged Deployment of LEO Navigation Constellation for MEO Navigation Satellite Failure

Low Earth orbit (LEO) satellites have unique advantages in navigation because of their high signal intensity and rapid geometric changes in a short period. In order to solve the problem of constellation performance degradation after a potential failure pertaining one or more medium Earth orbit (MEO) navigation satellites, this paper designs the LEO navigation constellation and considers the task requirements of different stages of constellation deployment. Firstly, the LEO navigation constellation is designed by a non-dominated sorting genetic algorithm II (NSGA-II). The average position dilution of precision (PDOP) is 1.676, which is an improvement compared to the average PDOP offered by the four traditional GNSS. Secondly, the staged deployment of constellation takes into account the degradation of constellation performance caused by the failure of MEO navigation satellites, and the Monte Carlo method is used to analyze the case of three simultaneous satellite failures. The results show that a single satellite failure within each orbital plane and adjacent satellites with close phase separation has a great impact on the performance of the MEO navigation constellation. On this basis, a staged deployment strategy was adopted in order to balance cost, risk, and performance. The three phases deploy 66, 156, and 288 satellites, respectively; as a make-up constellation under contingencies, a navigation enhancement constellation, and an independent navigation constellation, the deployment of the staged sub-constellations meets the mission requirements. The constellation design and staged deployment method proposed in this paper can provide reference for the future study of LEO navigation constellations.

Cislunar [formula omitted] and [formula omitted] axial orbits and their applications

Cislunar L4 or L5 axial orbit families are continuous asymmetrical periodic orbits from the figure-8 orbit around L4 or L5 Lagrange point of the Earth–Moon system to the halo-family around the Moon. They provide special locations of lunar relay satellites for the lunar south pole due to their offset locations. In this paper, we investigate the orbital characters and applications of cislunar L4 and L5 axial orbits. A construction method of cislunar L4 and L5 axial orbit families is proposed according to their topological feature in the torus space. Then, lunar relay performances, including coverage and eclipse, are analyzed for different cislunar L4 and L5 axial orbits. Numerical computation indicates that 3:1 resonant L4 and L5 axial orbits are the optimal options in terms of the stability, coverage and eclipse avoidance. Lunar relay performances of a two-satellite constellation deployed in these orbits are compared with that in a near rectilinear halo orbit (NRHO). Numerical results show that the constellation of axial orbits can provide longer contact duration to the lunar equator and southern hemisphere than that of the NRHO. Finally, a station-keeping strategy and a transfer design of cislunar L4 and L5 axial orbits are developed, and their fuel costs are studied.

16QAM optical signal generation scheme based on weighted optimal Euclidean distance.

A two-dimensional signal constellation scheme for binary uniform memoryless source transmission in optical fiber channels is studied in this paper. In geometric shaping (GS), optimization algorithms are usually used to change the overall position of constellation points while maintaining the probability of constellation points unchanged. Different optimization functions are used to allocate the position of constellation symbols, thereby improving constellation performance. A 16 quadrature amplitude modulation (QAM) optical signal generation scheme based on weighted optimal Euclidean distance is proposed in this paper. In order to obtain the best constellation diagram and increase the shaping gain, the weighted optimal Euclidean distance that can minimize the bit error rate (BER) over multiple iterative optimizations is used as the objective function. On the one hand, the proposed 16QAM optical signal generation scheme based on weighted optimal Euclidean distance always outperforms the uniform square 16QAM and the uniform circle 16QAM schemes in the back to back (BTB) transmission. On the other hand, after analyzing the simulation demonstration in a 50GBaud coherent optical communication system over 3000km, results demonstrate that the optical signal to noise ratio (OSNR) performance of this system is better than that of the uniform square 16QAM and the uniform circle 16QAM, which is improved by 0.52dB and 0.85dB, respectively. In addition, the proposed 16QAM system increases the transmission distance by 989km and 741km, respectively, compared to the other two systems. The performance confirms that the proposed novel 16QAM scheme, to the best of our knowledge, can effectively improve the reliability and transmission distance. Therefore, the proposed scheme has a certain development prospect in the future long-distance transmission of high-speed optical fiber communication.

Low orbit regional enhanced navigation constellation for BDS3 design based on Bayesian optimization algorithm

The application of Low Earth Orbit (LEO) satellite navigation can enhance geometric structure, increase observations and contribute to navigation and positioning. To improve the performance of the navigation constellation in China, this study proposes an optimized method of LEO-enhanced navigation constellation for BDS based on Bayesian optimization algorithm. In this paper, four different optimal LEO constellation configurations are designed, and their enhancements to BDS3 navigation performance are analyzed, including Geometric Dilution of Precision (GDOP), the numbers of visible satellites, and the rapid convergence of precision point positioning (PPP). Additionally, the enhancement advantages in China compared to other regions are further discussed. The results demonstrate that regional enhanced constellations with 70, 72, 80, and 81 satellites at an altitude of 1000 km can significantly improve the navigation performance of the navigation constellation. Globally, the addition of optimized LEO constellations has reduced the hybrid constellation GDOP by 19.0 %, 18.3 %, 19.9 %, and 20.3 %. Similar results can be obtained using the genetic algorithm (GA), but the computational efficiency of Bayesian optimization algorithm is 53.9 % higher than that of the genetic algorithm. The number of visible satellites of enhanced constellations in China has increased by more than four on average, which is better than that in other regions. In the PPP experiment, the convergence time of the stations in China and other regions is shortened by 83.0 % and 76.2 %, respectively, and the navigation performance of hybrid constellations in China is better.

Three-dimensional geometrically shaped constellation based on regular octahedron cells for IM/DD system

A three-dimensional (3D) constellation based on geometric shaping (GS) and probabilistic shaping (PS) is proposed for an intensity modulation/direct detection (IM/DD) system. The GS of 3D constellation is based on regular octahedron cells, and combined with PS using Huffman coding, the constellation figure of merit (CFM) and bit error rate (BER) performance of 3D constellation can be significantly improved. Results demonstrate that proposed 19-ary 3D constellation achieves a 2.2 dB receiver sensitivity gain compared with traditional 16-ary 3D constellation at the BER of 3.8 × 10-3. Moreover, the probabilistically shaped 19-ary 3D constellation exhibits a BER that is reduced by around one order of magnitude compared with the non-shaped 19-ary 3D constellation for the same transmission distance. In addition, the proposed 19-ary 3D constellation exhibits superior performance in terms of transmission distance and data rate compared with traditional 16-ary 3D constellation and GS 16-ary 3D constellation.

Optimizing the probability mass function of complex modulated signals through adaptive channel characterization.

We propose a probability mass function (PMF) optimization scheme for quadrature amplitude modulation (QAM) signals by considering the parametric characteristic of the training sequence. The training sequence for optimization is mapped in standard Maxwell-Boltzmann (M-B) distribution, and the considered characterizing parameters incorporate either the noise variance or the error matrix of the received symbols. The proposed PMF optimization is based on independent reallocation within each constellation ring, generating new distribution with almost the same entropy and transmitted power as the original distribution. This reallocation mechanism is model-free and iterative-free with very low computational complexity. By characterizing the channel in terms of constellation performance asymmetry, PMF reallocation can be effectively implemented to supplement the existing equalization algorithm. The effectiveness of this approach is experimentally verified in a 40-km transmission system with 24 Gbaud 64-QAM signals under three different scenarios. Through PMF reallocation, we achieve generalized mutual information (GMI) improvement of ∼0.06 and throughput improvement of ∼1.5 Gbit/s before forward error correction in comparison with the standard M-B distribution. The proposed mechanism provides a solution to obtain the optimal PMF in practical communication channels, which suffer from various types of noises and distortions.

Analysis performance of navigation constellation satellite failure and enhancement of LEO navigation

The stable operation of navigation satellite constellation is related to national economy and national defense security. The failure of any one or two satellites has little impact on the overall performance of the global navigation satellite constellation, and the availability of the navigation constellation decreases with the increase of the number of failed satellites. First, a typical medium earth orbit Walker-δ 24/3/1 constellation configuration was designed. Second, the service performance of the navigation constellation under different failure modes was analyzed. The weaknesses of the constellation were identified in combination with the availability data of the navigation constellation. Then, the overall performance of the navigation constellation after the low earth orbit satellite constellation compensates for the failure of the medium earth orbit satellite constellation is analyzed. The simulation results show that the failure of 5 global navigation satellites will reduce the availability of navigation constellation to 71%, and the hybrid navigation constellation can recover the availability to more than 97%. The orbital altitude and inclination of low orbit satellites affect the overall performance of the hybrid navigation constellation. The research results can provide reference for the demonstration of hybrid navigation constellation scheme.

Investigation of the Standalone and Combined Performance of IRNSS and QZSS Constellations over the Asia–Pacific Region

Investigation of the Standalone and Combined Performance of IRNSS and QZSS Constellations over the Asia–Pacific Region

Multi-Objective Optimization of an Intelligent Soil-Moisture-Monitoring Satellite Constellation

In early satellite mission design, requirements are not yet fixed, cost is sometimes negotiable, and designs are relatively unconstrained. During this period of design freedom, multi-objective optimization can provide a useful lens into the design space by showing theoretical performance limits and illuminating design tradeoffs. This work optimizes a radar constellation for a potential soil moisture mission. Several different optimization cases with different variables are considered and contrasted. The optimization of the instrument and constellation parameters is considered jointly and separately to better understand the effect of coupling on the optimization performance. A science-driven optimization based on soil moisture retrieval error is compared with a performance-metric-driven optimization. Pareto analysis and association rule mining are performed on the generated designs to provide insight into driving features. Design recommendations are made for several cost caps. Results show that optimization that considers the instrument and constellation design together find superior revisit metrics than treating instrument and constellation separately. The use of the science value metric as an optimization objective shows that while cost may always be increased to improve instrument and constellation performance, the difference in science value may be negligible. These findings can inform tradespace exploration studies for similar problems.

An Analytic Approach for Modeling Uplink Performance of Mega Constellations

In the mega constellation, hundreds of satellites are launched into space to provide global coverage and high-quality service. The number of served user terminals (UTs) can be large-scale under such a dense distribution of satellites, which may lead to severe intra-constellation interference in uplink communications. Hence, it is quite necessary to analyze the intra-constellation interference and deduce analytical expressions of uplink performance in mega constellations to provide design principles for the constellation construction. In this paper, we investigate the uplink performance of mega constellations in terms of outage probability (OP) and ergodic capacity (EC) with actual antenna patterns under the poisson point process constellation model. The expressions that reveal the relationships between the uplink performance and network parameters are derived, by which the constellation scale that satisfies the demand of EC can be obtained. The accuracy of the analytical results is verified through extensive simulations. Our results indicate that the EC first increases but then diminishes as the scale increases if there is enough UTs to be served, which may provide an insight on the scale construction of a mega constellation.

Investigating Performance of BDS-2+3 Dual-Frequency Absolute Positioning With Broadcast Ephemerides, RTS and Final MGEX Products

BDS-3 was formally put into service on July 31, 2020, and now along with BDS-2 provides the positioning, navigation and timing services. In this contribution, different techniques of dual-frequency absolute positioning using the fully serviceable BDS-2+3 constellation are evaluated and compared to the positioning performance of GPS constellation. The accuracy of BDS-3 broadcast ephemerides is significantly higher than that of BDS-2 and is comparable to that of GPS, while BDS-3 International GNSS Service (IGS) Real-Time Service (RTS) products are not as good as GPS at this stage. The static Single Point Positioning (SPP) using BDS-2+3 pseudoranges based on broadcast ephemerides attains the positioning accuracy of 0.743/0.601/1.021 m (95%) and 0.453/0.365/0.566 m (68%) in east/north/up components, while its positioning accuracy is 1.210/1.097/2.447 m (95%) and 0.660/0.586/1.264 m (68%) in kinematic mode. BDS-2+3 Precise Point Positioning (PPP) using pseudoranges with carrier-phase observations based on broadcast ephemerides is able to achieve a positioning accuracy of 0.239/0.174/0.529 m (95%) and 0.115/0.096/0.296 m (68%) in static mode, and 0.636/0.486/1.108 m (95%) and 0.304/0.242/0.556 m (68%) in kinematic mode. BDS-2+3 PPP based on final Multi-GNSS Experiment (MGEX) product can obtain the positioning accuracy of centimeter to millimeter in static mode and the centimeter-level positioning accuracy in kinematic mode. The experiment results show that the positioning performances of BDS-2+3 using broadcast ephemerides and final MGEX products are both comparable to those of GPS. However, due to the poor quality and incomeless of BDS IGS RTS product, BDS-2+3 SPP and PPP based on IGS RTS product obtain the poor positioning accuracies in both static and kinematic modes, which are obviously worse than the counterparts of GPS. Another remarkable result can be obtained that BDS-2+3 achieves a better positioning performance in Asia-Pacific region at higher cut-off elevations as compared to GPS positioning.

Communication-Aware Orbit Design for Small Spacecraft Swarms Around Small Bodies

Exploration of small Solar System bodies has traditionally been performed by monolithic spacecraft carrying several science instruments. However, instruments often cannot be operated simultaneously due to requirements including viewing angle, illumination, power, and data constraints. This has motivated interest in architectures in which a swarm of small spacecraft, each carrying one instrument, studies a small body after being deployed by a carrier spacecraft; such architectures hold promise to yield significant improvements in mission efficiency, increased data quality, and reduced mission duration. A key difficulty is the selection of orbits for the spacecraft, which must satisfy not only instrument requirements but also communication and data storage constraints. To address this, we propose a novel gradient-based optimization algorithm that simultaneously optimizes spacecraft orbits, observations, and communications; the approach captures instrument requirements, communication bandwidth, and memory usage, and it accommodates irregular gravity field models and surface geometries. Numerical simulations of a six-spacecraft swarm studying the 433 Eros asteroid show that the approach results in a 67.9% increase in data returned as compared to a communication-agnostic approach. Collectively, these results enable system designers to quickly assess the end-to-end performance of multispacecraft constellations, and represent a first step toward communication-aware design of multispacecraft missions for small Solar System body exploration.

Using a Multiobjective Genetic Algorithm to Design Satellite Constellations for Recovering Earth System Mass Change

The Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) provided twenty years of data on Earth’s time-varying gravity field. Due to their design, GRACE and GRACE-FO are inherently limited in their spatiotemporal coverage, limiting their resolution to a few hundred kilometers and temporally to roughly monthly solutions. To increase the global spatiotemporal resolution and allow for the determination of submonthly time-varying gravity field signals, a constellation of GRACE-type satellite pairs is a possible path forward. Advances in small form factor instrumentation for small satellites have become progressively inexpensive, reliable, and of higher quality. This leads us to consider that a constellation of GRACE-type small satellites could be part of future gravimetric satellite missions. In this work, we investigate the viability and limitations of a genetic-algorithm-based optimization and its objective function to generate satellite constellations to recover daily Earth system mass changes. The developed approach is used to create satellite constellations that are optimally designed to recover gravity variations of sufficient resolution at a range of temporal frequencies (i.e., daily to monthly). We analyze a constellation’s performance using a combination of observability in space, accounting for directionality, and homogeneity in time. This allows us to navigate through a vast search space in a relatively short period of time and estimate the relative performance of constellations to each other. Using evolutionary theory, we converge towards a set of optimally selected orbits. The characteristics of the designed constellations have been validated using high-fidelity numerical simulations. We summarize these results and discuss their implications for possible future constellations of small GRACE-like satellite pairs. The resulting constellations have an inherently improved spatiotemporal performance, which reduces temporal aliasing errors and allows the characterization of daily mass-change effects.

Cooperation in Space: HAPS-Aided Optical Inter-Satellite Connectivity With Opportunistic Scheduling

Issues with tracking, precision pointing, and Doppler shift are the major sources of performance loss in laser inter-satellite communication that can severely decrease the coverage and overall performance of satellite constellations. As a solution to these problems, we propose a cooperation strategy in which a high altitude platform station (HAPS) staying at a quasi-stationary position contributes to the inter-satellite connectivity. In this setup, the HAPS node uses two different scheduling approaches: one that relies on the zenith angle; the other on instantaneous signal-to-noise ratio. To quantify the performance of the proposed scheme, overall outage probabilities for the two scheduling methods are obtained. In addition, guidelines for the design of practical inter-satellite networks are provided.

From the Editors of the Special Issue on Multiplatform and Multifunctional RF Systems

The idea for this Special Issue on Multiplatform and Multifunctional RF Systems [(MPRFS) and (MFRFS)] was conceived in 2020 on the strength of a very successful workshop on Multiplatform RF Systems organized by the European Defence Agency (EDA). The editors were further motivated by the realization that modern platforms such as fighter jets, drones, reconnaissance aircraft, frigates, destroyers, and submarines have limited real estate for the inclusion of even more sensors—giving rise to the field of MFRFS. MFRFS represents a research and technology endeavor to realize multiple RF functions such as radar, electronic attack (EA), electronic support (ES), and communications (Comms) in a platform– sensor suite through the sharing of hardware architectures. There is no standard definition for MFRFS, but one interpretation is the use of active electronically scanned array (AESA) antennas for radar, EA, ES, and Comms so that the overall number of antennas distributed over a given platform may be reduced. There are, of course, other valid interpretations not predicated on the use of ASEAs, but rather aim to consolidate multiple functions into one suite of common hardware. The concept of MPRFS is based on the controlled utilization of RF systems that are available within an interconnected and spatially dislocated multiplatform constellation. Individual platforms may be strategically positioned and managed to improve constellation performance in complex operational environments. MPRFS and MFRFS are areas of active research and this is set to intensify in the coming years. We, as guest editors, are pleased to publish this first special issue dedicated to the field of MPRFS and MFRFS and, as the field matures, we are confident that future special issues will follow. This special issue comprises four interesting contributions. Each is briefly summarized.

Uplink Interference and Performance Analysis for Megasatellite Constellation

Satellite communications play an important role in future Internet of Things (IoT) networks, and megasatellite constellations can further provide global coverage and high-quality services for IoT communications. In the megaconstellation, large-scale satellites are launched to enhance the capacity. However, the dense distribution of satellites brings intraconstellation interference, limiting the performance. In order to evaluate the restriction of interference caused by system parameters, such as the scale of constellation or the frequency reuse factor, we investigate uplink intraconstellation interference and performance of the megasatellite constellation. First, a multibeam polar constellation with uplink spatial frequency reuse is assumed. Then, the interference model is constructed considering the antenna gain of interfering user terminals and multibeam satellites, where the details of the satellite-fixed frequency reuse scheme and coordinates of co-frequency cells are provided. To evaluate the performance, expressions of outage probability, ergodic capacity, and sum ergodic capacity are driven. The analytical results disclose the impact of system design on the performance, and the accuracy of analysis results is obtained through extensive simulation evaluation. The results show that sum ergodic capacity achieves highest in the case of full frequency reuse for the frequency-limited constellation system, and it gets a linear growth at first but then keeps flat with a trend of fluctuating downward as the scale increases; therefore, the impact of the scale should be considered when constructing megaconstellations.

Sampling Analysis and Processing Approach for Distributed SAR Constellations With Along-Track Baselines

In the constant strive for improving the capacity of next-generation spaceborne SARs while containing the increase in system complexity, distributed along-track constellations operated below Nyquist appear as one of the most promising solutions for delivering metric resolution imagery over swaths of hundreds of kilometers. In the operation of multistatic SAR constellations, however, sampling singularities typically result in dramatic noise scaling and the impossibility to recover the entire Doppler bandwidth unambiguously. We investigate in this article the likelihood of these singularities in the case of along-track distributed constellations and justify the use of irregular sampling schemes to reduce the percentage of invalid samples of an acquisition. This article also presents a bistatic polychromatic reconstruction algorithm, which is used for the evaluation of the performance of along-track distributed constellations. With all these elements, the performance of along-track multistatic systems is assessed by means of a Monte Carlo analysis and conclusions on the scaling numbers of the constellations are drawn. Based on the performance investigations, an exemplary distributed L-band SAR constellation is proposed as a corollary of this article.

Impacts of Orbital and Constellation Parameters on the Number and Spatiotemporal Coverage of LEO-LEO Occultation Events

The development of small-satellite technologies allows the low Earth orbit intersatellite link (LEO-LEO) occultation method to observe the Earth’s atmosphere with global coverage and acceptable costs using electromagnetic signals, in which the L/X/K/M band and short-wave infrared band signals have been well demonstrated to be suitable. We hence need to investigate the impacts of orbital and constellation parameters on the number and spatiotemporal distribution of LEO-LEO occultation events for best-possible LEO-LEO occultation mission design and optimization at the targeted mission size. In this study, firstly, an occultation events location simulation model accounting for the right ascension of the ascending node (RAAN) precession was set up and the concept of a time-dependent global coverage fraction of occultation events was defined. Secondly, numerical experiments were designed to investigate the orbital parameters’ impacts and to assess the performance of LEO-LEO occultation constellations, in which the Earth is divided into 5° × 5° latitude and longitude cells. Finally, the number, timeliness, and global coverage fraction of occultation events for two-orbit and multi-orbit LEO-LEO constellations were calculated and analyzed. The results show that: ① the orbit inclination and RAAN are the main impacting parameters followed by orbital height, while the RAAN precession is a relevant modulation factor; ② co-planar counter-rotating receiving and transmitting satellite orbits are confirmed to be ideal for a two-satellite LEO-LEO constellation; ③ polar and near-polar orbit constellations most readily achieve global coverage of occultation events; near-equator orbit constellations with supplementary receiving and transmitting satellite orbit planes also readily form the occultation event geometry, though the occultation events are mainly distributed over low and low-to-middle latitude zones; and ④ a well-designed larger LEO-LEO occultation constellation, composed of 36–72 satellites, can meet the basic requirements of global numerical weather prediction for occultation numbers and timeliness, yielding 23,000–38,000 occultation events per day and achieving 100% global coverage in 12–18 h.

Satellite Availability and Service Performance Evaluation for Next-Generation GNSS, RNSS and LEO Augmentation Constellation

Positioning accuracy is affected by the combined effect of user range errors and the geometric distribution of satellites. Dilution of precision (DOP) is defined as the geometric strength of visible satellites. DOP is calculated based on the satellite broadcast or precise ephemerides. However, because the modernization program of next-generation navigation satellite systems is still under construction, there is a lack of real ephemerides to assess the performance of next-generation constellations. Without requiring real ephemerides, we describe a method to estimate satellite visibility and DOP. The improvement of four next-generation Global Navigation Satellite Systems (four-GNSS-NG), compared to the navigation constellations that are currently in operation (four-GNSS), is statistically analyzed. The augmentation of the full constellation the Quasi-Zenith Satellite System (7-QZSS) and the Navigation with Indian Constellation (11-NavIC) for regional users and the low Earth orbit (LEO) constellation enhancing four-GNSS performance are also analyzed based on this method. The results indicate that the average number visible satellites of the four-GNSS-NG will reach 44.86, and the average geometry DOP (GDOP) will be 1.19, which is an improvement of 17.3% and 7.8%, respectively. With the augmentation of the 120-satellite mixed-orbit LEO constellation, the multi-GNSS visible satellites will increase by 5 to 8 at all latitudes, while the GDOP will be reduced by 6.2% on average. Adding 7-QZSS and 11-NavIC to the four-GNSS-NG, 37.51 to 71.58 satellites are available on global scales. The average position DOP (PDOP), horizontal DOP (HDOP), vertical DOP (VDOP), and time DOP (TDOP) are reduced to 0.82, 0.46, 0.67 and 0.44, respectively.