Constellation Rotation Research Articles

A method for estimating the rotation errors of BDS broadcast ephemeris using global satellite laser ranging data

Abstract The BeiDou-3 Navigation Satellite System (BDS-3) generates navigation messages from a regional ground tracking network and inter-satellite links, relying on predicted station coordinates and Earth rotation parameters (ERPs). These procedures, however, may lead to orientation errors in the broadcast ephemeris, termed constellation rotation errors. Traditionally, these errors are monitored through Helmert transformation analysis comparing broadcast and post-processed orbits, a method that highlights discrepancies between the global navigation satellite system (GNSS) terrestrial reference frame (TRF) and the International TRF (ITRF) but suffers from a two-week evaluation delay. This study proposes a near real-time approach for estimating constellation rotation errors using high-precision satellite laser ranging (SLR) data, representing the difference between GNSS TRF and ITRF through the International laser ranging service TRF. The impact of SLR data quantity and distribution on rotation estimation accuracy is investigated, and the effectiveness of this method on BDS-3 orbits with ERP-induced orientation deficiencies is validated. Results show that the root mean square of broadcast orbit errors and the orbit user ranging error reduce from 0.8/0.7/0.2 m to 0.1/0.1/0.1 m, respectively. This demonstrates the method’s capability for real-time monitoring and correcting orientation errors within BDS-3 navigation messages.

Performance comparison of orbit and clock augmentation corrections from PPP-B2b, HAS and CLAS

Precise Point Positioning (PPP) augmentation corrections can enhance the accuracy of Global Navigation Satellite System (GNSS) positioning. Three prominent PPP augmentation services: the third generation of BeiDou Navigation Satellite System (BDS-3) PPP-B2b, Europe's Galileo High Accuracy Service (HAS) and Quasi-Zenith Satellite System (QZSS) Centimeter Level Augmentation Service (CLAS), are evaluated and compared, contributing to the optimal utilization of these services. Based on a 25-day dataset in March 2023, all the three services have made significant improvements in GPS orbit accuracy compared to the broadcast ephemeris. Galileo HAS achieved the highest three-dimension (3D) orbit accuracy for both GPS and Galileo (10.5 and 10.4 cm), followed by CLAS (48.1 and 16.3 cm) and PPP-B2b (GPS: 73.0 cm, BDS-3: 44.6 cm). This distinct performance of PPP-B2b orbits is found for the first time to be related to the large constellation rotation errors, which accounts for roughly half of the orbit errors of along and cross components. Regarding clock errors, PPP-B2b and HAS enhanced GPS clock accuracy to 0.20 ns (70 %) and 0.17 ns (74 %), respectively, over the broadcast clock (0.66 ns), while CLAS shows a much smaller improvement. Moderate correlations of 0.3–0.8 between orbit and clock errors are observed for the three augmentation corrections. For signal in space ranging error (SISRE), HAS (GPS:5.5 cm, Galileo:4.9 cm) outperforms PPP-B2b (GPS:14.3 cm, BDS-3:8.9 cm) and CLAS (GPS:23.6 cm, Galileo:13.7 cm). The 2-hourly kinematic positioning results with an accuracy of better than 20 cm (95th percentile) for the horizontal and vertical component, could be achieved for both PPP-B2b and HAS within 20 min within their service area. It is not recommended rely solely on the orbit/clock/code bias of CLAS for precise positioning, as the positioning accuracy is influenced by the SISRE. PPP-RTK of CLAS achieves horizontal 10 cm (95th percentile) and rapid convergence of mostly less than a minute by incorporating phase bias and atmospheric corrections.

A new SLM scheme based on constellation rotation for PAPR reduction

A new SLM scheme based on constellation rotation for PAPR reduction

Digital Video Broadcasting T2 Lite Performance Evaluation Based on Rotated Constellation Rates

DVB-T2 offers the best levels of efficiency, reliability, and flexibility of any digital terrestrial broadcast technology now available. It provides the most up-to-date coding and modulation techniques to make the valuable terrestrial spectrum extremely effectively usable for many types of transmission. The mobile configuration of DVBT2 also known as T2-Lite, employs a constrained set of possible modes that are suited for movable transmission and reduce the demands placed on the receiver. This study compares the T2-Lite system's performance before and after using constellation rotation and cyclic Quadrature (Q) delay methods among different types of constellations, coding rates, and fading channels. Results show a significant improvement in T2-Lite system performance while using a rotating constellation in a bad fading environment. Moreover, the utilization of this technique enhances DVB-T2 Lite gain. All simulation of system components and channels were carried out in MATLAB R2021a software.

High security optical OFDM transmission scheme with four-dimensional region joint encryption based on power division multiplexing.

In this paper, a high security chaotic encryption scheme for orthogonal frequency division multiplexing (OFDM) transmission system is proposed by using power division multiplexing (PDM) technology and four-dimensional region joint encryption. The scheme uses PDM to realize simultaneous transmission of multiple user information, which can achieve a good compromise among system capacity, spectral efficiency and user fairness. In addition, bit cycle encryption, constellation rotation disturbance (CRD) and region joint constellation disturbance (RJCD) are used to realize four-dimensional region joint encryption, effectively improving the physical layer security. The masking factor is generated by the mapping of two-level chaotic systems, which can enhance the nonlinear dynamics and improve the sensitivity of encrypted system. A 11.76 Gb/s OFDM signal transmission over 25 km standard single-mode fiber (SSMF) is experimentally demonstrated. At the forward-error correction (FEC) bit error rate (BER) limit -3.8×10-3, the proposed receiver optical power based on quadrature phase shift keying (QPSK) without encryption, QPSK with encryption, variant-8quadrature amplitude modulation (V-8QAM) without encryption and V-8QAM with encryption are about -13.5dBm, -13.6dBm, -12.2dBm, and -12.1dBm. The key space is up to 10128. The results show that this scheme not only improves the security of the system and the ability to resist attackers, but also improves the system capacity and has the potential to serve more users. It has a good application prospect in the future optical network.

CG-SCMA Codebook Design Based on Maximized Euclidian Distance

Sparse code multiple access (SCMA) is a multi-dimensional codebook based on a class of non-orthogonal multiple access (NOMA) technologies enabling the delivery of non-orthogonal resource elements to numerous users in 5G wireless communications without increasing complexity. This paper proposes a computer-generated sparse code multiple access (CG-SCMA) technique, where the minimum Euclidian distance (MED) of a star 16-point quadrature amplitude modulation is maximized by CG-SCMA, thus creating a complex SCMA codebook based on optimizing the difference between the first and other radiuses over rotated constellations. To specify the most suitable values for this constellation, it is divided into four sub-constellations using trellis coded modulation (TCM) in an effort to optimize MED. The new codebook has four sub-constellations with MED values of 3.85, 2.26, 2.26, and 3.85, respectively. Application of the message passing algorithm (MPA) ensures low complexity of the decoding process.

Design Low Complexity SCMA Codebook Using Arnold’s Cat Map

In 5G wireless communications, sparse code multiple access (SCMA) – a multi-dimensional codebook based on a specific category of the non-orthogonal multiple access (NOMA) technique - enables many users to share non-orthogonal resource components with a low level of detection complexity. The multi-dimensional SCMA (MD-SCMA) codebook design presented in this study is based on the constellation rotation and interleaving method. Initially, a subset of the lattice Z 2 is used to form the mother constellation’s initial dimension. The first dimension is then rotated to produce other dimensions. Additionally, interleaving is employed for even dimensions to enhance fading channel performance. Arnold’s chaotic cat map is proposed as the interleaving method to reduce computational complexity. Performance of the SCMA codebook based on interleaving is evaluated by comparing it with selected codebooks for SCMA multiplexing. The metrics used for performance evaluation purposes include bit error rate (BER), peak to average power ratio (PAPR), and minimum Euclidean distance (MED), as well as complexity. The results demonstrate that the suggested codebook with chaotic interleaving offers performance that is equivalent to that of the conventional codebook based on interleaving. It is characterized by lower MED and higher BER compared to computer-generated and 16-star QAM codebook design approaches, but its complexity is lower than that of the conventional codebook based on interleaving.

Performance-Enhanced Three-Dimensional Trellis Coded Modulation Based on Four-Winged Fractional-Order Chaotic Encryption For Physical Layer Security

In this paper, an encrypted three-dimensional (3D) trellis-coded modulation (TCM) based on mapping by set-partitioning (MSP) of 3D constellation is proposed, for highly reliable and secure short-reach transmission. 3D-TCM encoder encryption and 3D constellation rotation are realized with the implementation of a 4D four-winged fractional-order chaotic (FWFC) system and MSP of 3D constellation, the suggested approach demonstrates higher coding gain and chaotic encryption. A 35 Gb/s (5 Gb/s × 7) encrypted 3D-TCM-32CAP signal transmission over ∼2 km seven-core fiber is experimentally demonstrated. The results show that the encrypted 3D-TCM-32CAP obtains a 2.9 dB and 3.8 dB gain in receiver sensitivity at a bit error rate (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> under the same bit rate, when compared with conventional 2D-TCM-32CAP and 3D-32CAP, respectively. Furthermore, a handsome key space of the proposed scheme is obtained ∼2.205 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">160</sup> , which is large enough to effectively guard against malicious attacks from illegal optical network units. In a nutshell, the experimental results indicate the proposed encrypted 3D-TCM-32CAP scheme combines the superiority of BER and security performance.

Modulation and coding scheme in SCMA communication system

Communication networks of future generations should provide a high level of spectral efficiency. The multiple access method is one of the technologies that directly affect this parameter. During the discussion of fifth-generation communication networks, a new approach to designing the non-orthogonal multiple access was proposed. One of the implementation techniques of this approach is sparse code multiple access. In the article, we consider this method and propose an approach to the development of a modulation code scheme to evaluate the sparse code multiple access performance and efficiency under transmission conditions close to reality. The approach is based on a similar modulation code scheme of existing communication systems. To form sparse code multiple access symbols, a codebook based on the mother constellation rotation and interleaving method is considered. We also introduce a modulation code scheme table for SCMA communication systems and evaluate their spectral efficiency.

Demonstration of Spatial Modulation Using a Novel Active Transmitter Detection Scheme with Signal Space Diversity in Optical Wireless Communications.

Line-of-sight (LOS) indoor optical wireless communications (OWC) enable a high data rate transmission while potentially suffering from optical channel obstructions. Additional LOS links using diversity techniques can tackle the received signal performance degradation, where channel gains often differ in multiple LOS channels. In this paper, a novel active transmitter detection scheme in spatial modulation (SM) is proposed to be incorporated with signal space diversity (SSD) technique to enable an increased OWC system throughput with an improved bit-error-rate (BER). This transmitter detection scheme is composed of a signal pre-distortion technique at the transmitter and a power-based statistical detection method at the receiver, which can address the problem of power-based transmitter detection in SM using carrierless amplitude and phase modulation waveforms with numerous signal levels. Experimental results show that, with the proposed transmitter detection scheme, SSD can be effectively provided with ~0.61 dB signal-to-noise-ratio (SNR) improvement. Additionally, an improved data rate ~7.5 Gbit/s is expected due to effective transmitter detection in SM. The SSD performances at different constellation rotation angles and under different channel gain distributions are also investigated, respectively. The proposed scheme provides a practical solution to implement power-based SM and thus aids the SSD realization for improving system performance.

A Comprehensive Technique to Design SCMA Codebooks

Sparse code multiple access (SCMA) is a potential candidate for improving spectral efficiency through overloading over resources. This letter proposes a comprehensive approach to achieve near-optimal SCMA codebooks designs for 150% and 200% overloading factors under various channel environments. This approach is based on a novel diversity analysis framework presented in this letter. Following this diversity analysis for the Rayleigh fading channel, we formulate a new key performance indicator (KPI) of the average symbol error rate (SER). The SER performance of an SCMA codebook is sensitive to KPIs. Thus, a suitable selection of the KPIs can improve performance. The proposed codebook design technique involves constellation rotation and dimensional permutation to optimize the KPIs. The proposed method can yield an SCMA codebook, which works equally well for uplink (UL) and downlink (DL) Rayleigh fading channels. This aspect of the proposed method eliminates the requirement of different designs for UL and DL. The SER is calculated through extensive Monte-Carlo simulations for all the proposed codebooks (with varying factors of overloading and alphabet sizes). The proposed codebooks outperform the state-of-the-art SCMA codebooks.

Research on the Rotational Correction of Distributed Autonomous Orbit Determination in the Satellite Navigation Constellation

The autonomous orbit determination of the navigation constellation uses only bidirectional ranging data of the inter-satellite link for data processing. The lack of space-time benchmark information related to the Earth inevitably causes overall rotational uncertainty in the constellation, leading to a decrease in orbit accuracy and affecting user positioning accuracy. This study (1) introduces a method for rotation correction in distributed autonomous orbit determination based on inter-satellite bidirectional ranging; (2) conducts constellation autonomous orbit determination and time synchronization processing experiments based on inter-satellite ranging data for the 24 medium Earth orbit (MEO) satellites in the Beidou-3 global satellite navigation system (BDS-3); and (3) makes comparative analyses on the accuracy of autonomous orbit determination based on three rotation correction cases, including a no-rotation-correction case, independent satellite constraints case, and global satellite constraints case. The experimental results are described as follows. For the no-rotation-correction case, the prediction error of the orbital inclination angle (iot, i) for the entire constellation on the 30th day was 2.11 × 10−7/rad, the prediction error of the right ascension of the ascending point (Omega, Ω) was 2.25 × 10−7/rad, and the average root mean square (RMS) of the user range error (URE) for the entire constellation orbit was 1.41 m. In the autonomous orbit determination experiment with independent constraints on satellites, the prediction error of i for the entire constellation on the 30th day was 5.43 × 10−7/rad, the prediction error of Ω was 2.03 × 10−7/rad, and the average RMS of the orbital URE for the entire constellation was 1.09 m. In the autonomous orbit determination experiment with global satellite constraints, the prediction error of i for the entire constellation on the 30th day was 5.31 × 10−7/rad, the prediction error of Ω was 1.95 × 10−7/rad, and the RMS of the orbital URE for the entire constellation was 0.94 m. According to the analysis of the above experimental results, compared with the autonomous orbit determination under the no-rotation-correction case, the adoption of an algorithm for independent satellite constraints to correct the overall constellation rotation weakens the constellation rotation influence; however, it may destroy the overall constellation configuration, which affects the stability of autonomous orbit determination. Finally, the algorithm based on global satellite constraints both impairs the influence of constellation rotation and maintains the overall constellation configuration.

Optimal Rotated QPSK Constellation for a Reliable SOMA Powerline Communication System in Nakagami-m Noise Environment

An <inline-formula> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula>-branch receive diversity powerline communication (PLC) system with two users and the transmitter employing a power-domain non-orthogonal multiple access (PD-NOMA) along with a rotated quadrature phase-shift keying (QPSK) modulation scheme, generally known as semi-orthogonal multiple access (SOMA) for data transmission is considered in this paper. The rotation of the data constellation and a proposed pre-processing at the receiver end for each user eliminate the usage of the additional successive-interference cancellation (SIC) hardware generally used in PD-NOMA PLC systems. Furthermore, optimal receiver structures are proposed using which closed-form expressions of the symbol error probability (SEP) are derived for the users using a characteristic function (c.f.) approach. The optimal rotation of the QPSK constellation minimizing the obtained SEP of the system is also derived. The diversity order of the system and the optimal angle of rotation at high average signal-to-noise ratio (SNR) values are found to be dependent only on the number of diversity branches. Moreover, the general dependence of the optimal rotation angle on various system parameters is corroborated by numerical results which provide various insights into the design of a reliable and energy-efficient PD-SOMA PLC system without the use of SIC hardware. The optimal rotation angle of the QPSK constellation also leads to novel optimal constellations for the users which are different than the conventional constellation utilized for data transmission in digital communication systems.

Adaptive Modulation SCMA Codebook Design Based on Constellation Rotation

Sparse Code Multiple Access (SCMA) is one of the competitive nonorthogonal multiple access (NOMA) techniques for the fifth-generation (5G) communication system. The SCMA codebook design is particularly important for SCMA systems. However, according to the results of our investigation of as many literature as possible, there is no research on adaptive modulation SCMA at present. Also, there is no systematic study concerning adaptive modulation SCMA codebook optimization. In this paper, an adaptive modulation SCMA transmission mechanism in different fading channels is proposed. Then, we optimize the adaptive modulation SCMA codebook design based on constellation rotation (AMSCR) for each adaptive mode including different modulation methods. The codebook optimization criterion is to maximize the minimum Euclidean distance between joint codewords. Since the space of the set of joint codewords is too large, the calculation of the minimum Euclidean distance has become an NP-hard problem. We use a genetic algorithm to solve this problem. As compared with the traditional SCMA codebook, the proposed AMSCR has better bit error rate performance in Gaussian channel and Rayleigh channel. The adaptive modulation strategy can maximize the throughput and has the best throughput performance compared with the traditional SCMA system and adaptive modulation SCMA system using traditional codebook.

A Phase Noise Resistant Constellation Rotation Method and Its Experimental Validation for NOMA Wi-Fi

Non-orthogonal multiple access (NOMA) is a well-accepted technology for future Wi-Fi systems to improve spectral efficiency. NOMA allows an access point (AP) to simultaneously serve multiple devices by splitting the transmit power between them. Using the superposition coding the AP combines signals of different frames with predefined power weights. However, as it is already known, the phase noise caused by hardware imperfections limits the performance of NOMA transmissions. The paper proposes a practical, easy-to-implement, and backward-compatible method to rotate the constellation of the low power signal in order to make it more robust to the phase noise. A mathematical model is developed to find such a rotation angle that minimizes the bit error rate (BER) of the low power frame. A new NOMA Wi-Fi prototype testbed is developed with the new feature of constellation rotation ability, which is used to validate the performance of our proposed method. Many experimental results show the proposed constellation rotation approach significantly decreases the BER in high signal-to-noise scenarios.

Sparse Superimposed Coding for Short-Packet URLLC

Sparse vector coding (SVC) is emerging as a key enabler for short packet ultra-reliable and low latency communications (URLLC), since it displays good block error rate (BLER) performance and can achieve low transmission latency. In this paper, we propose a SVC-based sparse superimposed transmission (SVC-ST) coding scheme to further enhance the BLER performance of SVC scheme. At the encoding side, a portion of transmission bits is represented by non-zero position indices of sparse vector. The remaining bits are equally split into multiple streams and then mapped into the non-zero positions of sparse vector via quadrature amplitude modulation (QAM) with constellation rotation (CR). We afterwards adopt the multipath matching pursuit-based soft decoding (MMP-SD) to recover the transmission packet. The BLER and bit error rate (BER) analysis of SVC-ST scheme demonstrate the validity and rationality of our study. Moreover, we find from the simulation results that the proposed SVC-ST scheme outperforms SVC and its enhanced version (ESVC) schemes in terms of BLER and latency performance.

Performance Analysis of Uplink NOMA With Constellation–Rotated STLC for IoT Networks

We investigate the uplink non-orthogonal multiple access (NOMA)-based Internet-of-Things (IoT) networks, where each IoT device (station: STA) equipped with a single antenna exploits the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">constellation-rotated</i> space-time line code (CR-STLC) to send signals to an access point (AP) equipped with two receive antennas. The AP decodes the signals transmitted from the STAs with the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">optimal</i> joint maximum-likelihood (JML) detector. As a main result, we mathematically analyze both the bit-error-rate (BER) performance and the spatial diversity order of each STA in the two-user uplink CR-STLC NOMA system. In particular, it is shown that the two-user uplink CR-STLC NOMA system achieves the optimal diversity order regardless of the constellation rotation angle in the high signal-to-noise ratio (SNR) regime. We also consider two different rotation angle optimization techniques (dynamic rotation & fixed rotation) to improve the BER performance in the practical SNR regime, and found that the fixed rotation approach is simple but yields almost the same performance as the dynamic approach. Finally, we show that the uplink CR-STLC NOMA system achieves the spatial diversity order of 1 even when more than two STAs send packets simultaneously. It is worth noting that all STAs obtain an improved spatial diversity gain compared to that without constellation rotation.

Optical Wireless Communications Using Signal Space Diversity with Spatial Modulation

A signal space diversity (SSD) scheme was proposed to be incorporated with spatial modulation (SM) in an intensity-modulation/direct-detection-based multiple-input-single-output (MISO) indoor optical wireless communication (OWC) system to improve bit-error-rate (BER) performance and system throughput. SSD was realized via signal constellation rotation and diversity interleaving using different channel gains to improve the BER. With SM incorporated, the MISO-OWC system throughput increased. Theoretical BER expressions of the SSD scheme were established for the first time by investigating the distance of neighboring constellation symbols upon maximum-likelihood detection. Such BER expressions were further verified by numerical results. The results showed that, except for the slightly-lower-accuracy performance brought by comparable distances of neighboring constellation symbols in cases of low signal-to-noise ratios, these BER expressions were accurate in most scenarios. Moreover, theoretical investigations of channel gain distributions were performed at different signal constellation rotation angles to show the capability of the SSD scheme to improve the BER. The results showed that a significantly improved BER by two orders of magnitude could be achieved using a reasonably high channel-gain ratio and a larger constellation rotation angle. The SSD-SM scheme provides a promising option to achieve transmitter diversity with an enhanced throughput in high-speed indoor OWC systems.

Symbol-Level Precoding With Constellation Rotation in the Finite Block Length Regime

This letter tackles the problem of optimizing the parameters of a symbol-level precoder for downlink multi-antenna multi-user systems in the finite block length regime. Symbol-level precoding (SLP) is a non-linear technique for multi-user wireless networks, which exploits constructive interference among co-channel links. Current SLP designs, however, implicitly assume asymptotically infinite blocks, since they do not take into account that the design rules for finite and especially short blocks might significantly differ. This letter fills this gap by introducing a novel SLP design based on discrete constellation rotations. The rotations are the added degree of freedom that can be optimized for every block to be transmitted, for instance, to save transmit power. Numerical evaluations of the proposed method indicate substantial power savings, which might be over 99% compared to the traditional SLP, at the expense of a single additional pilot symbol per block for constellation de-rotation.

Signal Space Diversity for Improving the Reliability Performance of OFDM with Subcarrier Power Modulation

As the demand for higher data rates continues to increase exponentially, there is a shift towards exploring contemporary techniques that are likely to offer higher spectral efficiency. A new modulation technique termed as orthogonal frequency division multiplexing with sub‐carrier power modulation (OFDM‐SPM) has recently been introduced. It is an original technique that is still largely under-explored and aims at transmitting more bits per sub‐carrier by manipulating the power of the sub‐carriers in an OFDM block, in addition to those bits that are usually transmitted by conventional modulation schemes such as M-PSK. During the investigation and theoretical testing stages, it was found that the additional data stream conveyed by subcarriers' power has higher bit error rate (BER) performance compared to the data stream conveyed by conventional modulation schemes. To overcome this shortfall, signal space diversity (SSD) along with coordinate interleaving is proposed in this work to be integrated with OFDM‐SPM to help improve the overall BER performance. By doing so, it is shown that a BER performance of 10-3 can be obtained at SNR of 15 dB, which means achieving an improvement of more than 5 dB compared to the case of using OFDM‐SPM without SSD. Furthermore, the performance results of OFDM‐SPM‐SSD is compared with those of OFDM‐SPM with maximal ratio combining (MRC) and the obtained results show that OFDM‐SPM‐SSD offers superior performance. Additionally, a study of the effect of the constellation rotation on OFDM‐SPM is provided and an in‐depth analysis is also carried out for different power polices of sub‐carrier power modulation with regards to two main performance metrics; namely BER and the throughput. Simulation results show that SSD provides a considerable improvement in the BER over both plain OFDM‐SPM and OFDM‐SPM‐MRC. The analysis also reveal that when considering the different power policies of SPM, the BER results are optimum in the case of using power‐reassignment policy.