Non-uniform Constellation Research Articles

Hybrid-Mux Signal Structure and Resource Allocation for In-Band Distribution Link and ITND Transmission in SFN Environment

This paper investigates the multiplexing and resource allocation to improve the spectrum efficiency and reduce demultiplexing complexity and latency in the wireless in-band distribution link (IDL) and inter-tower networks and datacasting (ITND) for terrestrial broadcasting systems. A novel Hybrid-Mux technology is proposed, which combines orthogonal multiplexing (TDM/FDM), non-orthogonal multiplexing (NOM, or LDM), and hierarchical modulation (HM) with the non-uniform constellation (NUC). Hybrid-Mux technology can achieve high spectrum efficiency, low complexity, and low latency to provide versatile services of mobile/fixed broadcast services, inter-tower communication networks and datacasting, as well as the in-band distribution link to support SFN operation. Two Hybrid-Mux signal structures with 2-layer and 3-layer power-based non-orthogonal multiplexing of different broadcast and network data services are introduced. The throughput optimization of each Hybrid-Mux structure is formulated and resolved under the constraint of ITND and IDL data capacity, SNR requirement, and optimized NUC HM. Simulation results show that, by properly implementing resource allocation and constellation design, the proposed 3-layer Hybrid-Mux structures can achieve higher capacity than the simple 2-layer Hybrid-Mux structure, while the demodulation and demultiplexing complexity is not much increased. A 2-tier ITND service is proposed. It consists of a robust control and datacasting (ITCD) tier and a high data rate intertower networking (ITCN) link. This design can increase the total aggregated system data rate substantively. MIMO structures supporting ITND and IDL transmission are also proposed to further improve the spectrum efficiency.

Enhanced Nonuniform Constellations for High-Capacity Communications With Low-Complexity Demappers

Non-uniform constellations (NUCs) successfully utilize geometrical shaping to approach the Shannon capacity, but increase demapping complexity. In this paper, enhanced non-uniform constellations for low-complexity and high-capacity communications are investigated and addressed in two steps: low-complexity demappers for fixed constellations and the constrained design of enhanced NUCs. First, simplified demappers for NUCs are studied, and modified virtual point searching (VPS)-based demappers are proposed. Theoretical analysis and numerical results show that the proposed modified VPS-based demappers reduce demapping complexity with negligible performance degradation. Secondly, two shaping constraint schemes are proposed to NUC design for the purpose of low complexity and high capacity. NUCs optimized under the proposed constraints outperform the uniform constellations, and the proposed demappers have good applicability to the optimized NUCs. The proposed NUC design constraint schemes and simplified demappers enable solutions to achieve low-complexity high-capacity communication.

An Improved SIC-Based Detection Scheme for Non-Uniform Constellations in ATSC 3.0 MIMO

This paper presents an alternative approach to real-valued signal representation and proposes an improved successive interference cancellation (SIC)-based detection scheme using the alternative signal representation for non-uniform constellations (NUCs) in Advanced Television Systems Committee (ATSC) 3.0. Since I/Q polarization interleaving in ATSC 3.0 multiple-input multiple-output (MIMO) precoding performs a non-linear operation, it makes it difficult to use conventional suboptimal detection schemes based on interference cancellation. Therefore, the alternative signal representation is designed to easily apply various suboptimal detection schemes. Further, to obtain more robustness and lower complexity, a suboptimal detection scheme based on the alternative signal representation and interference cancellation with QR decomposition is proposed. The proposed detection scheme exploits the structural properties of NUCs and jointly detects the real and imaginary parts as a block. In addition, by considering one or more candidate symbols in the interference cancellation for the proposed detection scheme, the performance and the complexity are trade-offs according to the number of the considering candidate symbols. Simulation results show that the proposed detection scheme with a slight increase of the complexity significantly outperforms a linear detection under fixed and mobile channels.

Low‐complexity demapping algorithm for two‐dimensional non‐uniform constellations in ATSC 3.0

The Advanced Television Systems Committee (ATSC) finalized its next-generation digital terrestrial broadcast standard in 2016, known as ATSC 3.0. In order to enhance spectral efficiency, the standard employs two-dimensional non-uniform constellations (2D-NUCs) for signal mapping. As a result, a 2D demapper, with computational complexity much higher than one-dimensional (1D) demappers, has to be designed for the receiver. In this paper, a suboptimal low-complexity 2D-demapping method is proposed for ATSC 3.0. The proposed method takes advantage of the 2D-NUC's feature that constellation points with same most significant bits tend to locate in the same subregion. Simulation results show that compared with the conventional Max-Log-MAP 2D demapping, the proposed method achieves at least 74 % complexity reduction with negligible performance loss. Moreover, compared with another 2D demapper specially designed for ATSC 3.0, the proposed method dispenses with high-complexity exponential and logarithmic operations at a small performance cost of at most 0.14 dB.

A Universal Low-Complexity Demapping Algorithm for Non-Uniform Constellations

A non-uniform constellation (NUC) can effectively reduce the gap between bit-interleaved coded modulation (BICM) capacity and Shannon capacity, which has been utilized in recent wireless broadcasting systems. However, the soft demapping algorithm needs a lot of Euclidean distance (ED) calculations and comparisons, which brings great demapping complexity to NUC. A universal low-complexity NUC demapping algorithm is proposed in this paper, which creates subsets based on the quadrant of the two-dimensional NUC (2D-NUC) received symbol or the sign of the in-phase (I)/quadrature (Q) component of the one-dimensional NUC (1D-NUC) received symbol. ED calculations and comparisons are only carried out on the constellation points contained in subsets. To further reduce the number of constellation points contained in subsets, the proposed algorithm takes advantage of the condensation property of NUC and regards a constellation cluster containing several constellation points as a virtual point. Analysis and simulation results show that, compared with the Max-Log-MAP algorithm, the proposed algorithm can greatly reduce the demapping complexity of NUC with negligible performance loss.

NUC Optimization-Aided Hierarchical Modulation to Achieve Comparable Capacity as Layered Division Multiplexing

This article investigates the non-uniform constellation (NUC) optimization adapted for Hierarchical modulation (HM) without using Successive Interference Cancellation (SIC). This approach is promising to reduce system demod/decode delay in comparison to Layered Division Multiplexing (LDM). By maximizing the constellation constrained capacity of Enhanced Layer (EL) service in HM, while the capacity of Core Layer (CL) service are approximately the same in HM and LDM, the capacity achieved by HM using NUCs is comparable to LDM. Particle Swarm Optimization (PSO) algorithm is used to resolve this problem. To accelerate the optimization, initial constellation is selected from regular NUCs or the combination of CL and EL constellations of LDM in ATSC 3.0. The results imply that under certain capacity demands, especially when there is a large difference between the SNR thresholds of CL and EL or the power ratio of CL to EL is high (for example, 10 dB or higher), HM, with lower delay compared to LDM, can achieve the capacity comparable or even better than LDM with the help of NUCs. Even if the power ratio of CL to EL is relatively low (for example, 3 dB), the capacity loss can be reduced with properly designed NUCs and the SNR threshold loss of EL can be approximately 0.4 dB with respect to LDM. However, LDM is still superior to HM when the difference between the SNR thresholds of CL and EL is relatively low.

Backward Compatible Low-Complexity Demapping Algorithms for Two-Dimensional Non-Uniform Constellations in ATSC 3.0

Non-uniform constellation (NUC) is an advanced technology in digital terrestrial television broadcasting (DTTB) systems to reduce the shapping gap of BICM capacity to Shannon theoretical limit and provide performance gain. Two-dimensional NUC (2D-NUC) is a kind of NUC providing more gain but bringing higher demapping complexity at the receiver, which hinders its application prospects, especially in power limited systems. This paper proposes three novel demapping algorithms with reduced complexity for low to medium code rate 2D-NUCs in Advanced Television Systems Committee 3rd Generation (ATSC 3.0) standard. The proposed algorithms are based on the introduction of virtual points, the strategy of condensed symbols reduction and some reasonable approximations. There is a trade-off between the demapping complexity and performance. These three algorithms have different degrees of reduction in complexity and performance degradation, so they accommodate for different practical requirements. Theoretical analysis and simulation results are also given in this paper to prove the efficiency of the proposed demapping algorithms with reduced complexity.

Enhancements on Coding and Modulation Schemes for LTE-Based 5G Terrestrial Broadcast System

Broadcasting and broadband network is moving towards integration and LTE-based 5G terrestrial broadcast is now researched in Release 16 in Third Generation Partnership Project (3GPP) standardization meetings. However, the work scope of LTE-based 5G terrestrial broadcast focuses on specifying new numerologies and some minor improvement on cell acquisition subframe, which is insufficient. In this paper, limitations in coding and modulation schemes of LTE-based 5G terrestrial broadcast system, e.g., Turbo codes and Quadrature Amplitude Modulation (QAM), are detailedly analyzed. To further enhance the spectrum efficiency of LTE-based 5G terrestrial broadcast system, LDPC (Low Density Parity Check) codes from 5G new radio (NR) standard and newly designed non-uniform constellations (NUCs) are adopted in this paper to replace Turbo codes and QAM respectively. Extensive simulations and complexity analysis show that the proposed LDPC coding and NUC modulation scheme, either standalone or combined, can provide significant performance gain over Additive White Gaussian Noise (AWGN) and Tapped Delayline (TDL) channels, without additional complexity. To summarize, this paper investigates the weakness of the coding and modulation schemes in current systems and provides potential alternatives for the enhanced future broadcast in 3GPP standard.

Low-Complexity Non-uniform Constellation Demapping Algorithm for Broadcasting System

Low-Complexity Non-uniform Constellation Demapping Algorithm for Broadcasting System

Joint Design for Modulation and Constellation Labels in Multiuser Superposition Transmission

Hierarchical modulation (HM), a promising non-orthogonal multiple access scheme, is able to provide different levels of protection for data streams and achieve a larger rate region that cannot be realized by traditional orthogonal schemes. In this paper, we propose a novel HM system with non-uniform constellation inputs and analytically derive the bit-interleaved coded modulation (BICM)-capacity for each hierarchical layer. Different from the power optimization method for the superimposed uniform constellation, we directly optimize the constellation positions in conjunction with the optimal binary labels design for HM in additive white Gaussian noise channels. For maximizing the BICM-capacity, a fairness balanced criteria is developed for the HM system by considering both power constraints and QoS constraints. Multi-start interior-point algorithm is then proposed to carry out the constellation optimization problems, and the corresponding methods are also proposed to reduce optimization complexity. Numerical results verify the performance gains of optimized HM compared with the optimized quadrature amplitude modulation based HM and other orthogonal transmission methods.

Low Complexity Adaptive Demapper for 2-D Non-Uniform Constellations

In this paper, a novel demapper for 2-D non-uniform constellations (2D-NUCs) is proposed, exploiting the characteristics of these constellations. It represents the combination of two underlying demapping techniques targeting the ATSC 3.0 compliant OFDM transceiver. On the one hand, for low code rates, we define a metric to perform condensed demapping. On the other hand, for high code rates, adaptive sub-region demapping is proposed. In this paper, a combination of both demapping methods is designed showing comparable performance to the classical ML demapper. The gap does not exceed 0.1 dB for all code rates of the ATSC 3.0 standard. Higher complexity reduction, from 79.2% to 95.4%, than state of art 2D-NUC demappers is obtained for 2D-256NUCs. These results are validated for ideal and non-ideal channel state information over additive white noise Gaussian and Rayleigh independently and identically distributed channels. Results are extended to 2D-1kNUCs and 2D-4kNUCs showing demapping complexity reduction from 96% to 99.7% with a negligible impact on performance.

The Joint Impact of Fading Severity, Irregular Constellation, and Non-Gaussian Noise on Signal Space Diversity-Based Relaying Networks

This work focuses on the interplay between rotation angle, transmit power, fading severity, and noise impairment severity in signal space diversity-based three time-slot decode-and-forward two-way relaying networks. Specifically, we develop a joint design for rotation angle selection and transmit power allocation, while taking into account the performance impact of fading severities on the channels and noise impairment severities on the receivers. To model different severities of fading and noise impairment, Nakagami distribution and additive non-Gaussian noise are used respectively. The objective in doing so is to promote the reliable reception of end-sources, while satisfying individual and total power budgets as well as average error probability. To this end, we start by deriving average error probabilities of end-sources for non-uniform constellations, which capture all possible signal constellations produced by using various rotation angles. Next, we formulate the joint design problem in an optimization form. Unfortunately, the resulting formulation is a non-convex optimization. To find the solution, we resort to numerical optimization. The numerical results not only validate the derived error probability expressions, but also demonstrate the efficacy of the proposed framework and provide useful insights on the interaction between rotation angle, transmit power, fading severities of the channels, and noise impairment severities at the end-sources.

TomoSAR Imaging for the Study of Forested Areas: A Virtual Adaptive Beamforming Approach

Among the objectives of the upcoming space missions Tandem-L and BIOMASS, is the 3-D representation of the global forest structure via synthetic aperture radar (SAR) tomography (TomoSAR). To achieve such a goal, modern approaches suggest solving the TomoSAR inverse problems by exploiting polarimetric diversity and structural model properties of the different scattering mechanisms. This way, the related tomographic imaging problems are treated in descriptive regularization settings, applying modern non-parametric spatial spectral analysis (SSA) techniques. Nonetheless, the achievable resolution of the commonly performed SSA-based estimators highly depends on the span of the tomographic aperture; furthermore, irregular sampling and non-uniform constellations sacrifice the attainable resolution, introduce artifacts and increase ambiguity. Overcoming these drawbacks, in this paper, we address a new multi-stage iterative technique for feature-enhanced TomoSAR imaging that aggregates the virtual adaptive beamforming (VAB)-based SSA approach, with the wavelet domain thresholding (WDT) regularization framework, which we refer to as WAVAB (WDT-refined VAB). First, high resolution imagery is recovered applying the descriptive experiment design regularization (DEDR)-inspired reconstructive processing. Next, the additional resolution enhancement with suppression of artifacts is performed, via the WDT-based sparsity promoting refinement in the wavelet transform (WT) domain. Additionally, incorporation of the sum of Kronecker products (SKP) decomposition technique at the pre-processing stage, improves ground and canopy separation and allows for the utilization of different better adapted TomoSAR imaging techniques, on the ground and canopy structural components, separately. The feature enhancing capabilities of the novel robust WAVAB TomoSAR imaging technique are corroborated through the processing of airborne data of the German Aerospace Center (DLR), providing detailed volume height profiles reconstruction, as an alternative to the competing non-parametric SSA-based methods.

Signal constellations employing multiplicative groups of Gaussian and Eisenstein integers for Enhanced Spatial Modulation

In this paper, we propose two new signal constellation designs employing Gaussian and Eisenstein Integers for Enhanced Spatial Modulation (ESM). ESM is a novel technique which was propounded by Cheng et al. The advantage of ESM over other Spatial Modulation (SM) schemes lies in its ability to enhance spectral efficiency while keeping the energy efficiency intact. This is done by activating either one or two antennas judiciously depending upon the required trade-off. In ESM, information radiated from the antennas depends upon index of the active transmit antenna combination(s) and also on the set of constellation points chosen, which may include points from multiple constellations. In this paper, we propose signal constellations based on multiplicative groups of Gaussian and Eisenstein integers. The set comprising of Gaussian and Eisenstein integers serves as primary and secondary constellation points for Gaussian Enhanced Spatial Modulation (GESM) scheme. The secondary constellation points are deduced from a single geometric interpolation from the primary constellation points. The Monte Carlo simulation results indicate that the proposed nonuniform constellations achieve impressive SNR gains compared to conventional constellation points used in the design of ESM. This new design has been described for MIMO employing 4 × 4 and 8 × 8 antenna configurations with only two active antennas. Furthermore, a closed form expression for the pairwise error probability (PEP) for the GESM scheme has been deduced. The PEP is utilized to determine the upper bound on the average bit error probability (ABEP). Our simulations indicate that the proposed GESM from Gaussian and Eisenstein integers scheme outperforms all the other variants of SM including conventional ESM by at least 2.5 dB at an average bit error ratio (ABER) of 10−5. Close correspondence between the theoretical analysis and the Monte Carlo simulation results are observed.

A Spectrally Efficient Signal Space Diversity-Based Two-Way Relaying System

This work proposes a new transmission scheme for multirelay two-way relaying systems, where two end- sources communicate with each other via a set of relays. In the proposed scheme, we consider signal space diversity and time division broadcast protocol jointly to increase spectral efficiency without sacrificing the system reliability. The idea behind this consideration is that original data symbols are rotated before transmission, and then the in-phase and quadrature components of these rotated symbols are transmitted through the cooperation of the end-sources and the relays. By doing so, the end-sources exchange four symbols over three time slots instead of two, i.e., doubling the number of transmitted symbols. In addition, relay selection is incorporated into this scheme to achieve a further increase in spectral efficiency. For relay selection, two different strategies are discussed: reactive and proactive relay selections. These strategies differ depending on whether relay selection is performed after or before the start of transmission. Specifically, for each relay-selection strategy, we first obtain a closed-form expression for the end-to-end (E2E) error probability with an arbitrary constellation, which accounts for all the resulting nonuniform constellation cases due to constellation rotation. Subsequently, with the derived expressions, we then formulate an optimization problem that considers the joint optimization of the rotation angle and the transmit powers at the end-sources and the relays. The objective of the optimization problem is to minimize the E2E error probability of one of the end-sources, while satisfying a set of total and individual transmit power constraints and a predefined threshold for the E2E error probability of the other end-source. Numerical results verify the theoretical analysis, and show that the scheme proposed herein provides not only higher spectral efficiency, but also more reliable transmission.

MIMO Sphere Decoding With Successive Interference Cancellation for Two-Dimensional Non-Uniform Constellations

Non-uniform constellations (NUCs) have been introduced to improve the performance of quadrature amplitude modulation constellations. 1D-NUCs keep the squared shape, while 2D-NUCs break that constraint to provide robustness. An impending problem with multiple-input multiple-output (MIMO) is the optimum demapping complexity, which grows exponentially with the number of antennas and the constellation order. Some well-known sub-optimum MIMO demappers, such as soft fixed-complexity sphere decoders (SFSD), can reduce that complexity. However, SFSD demappers do not work with the 2D-NUCs, since they perform a quantization step in separated I/Q components. In this letter, we provide an efficient solution for the 2D-NUCs based on Voronoi regions. Both complexity implications and SNR performance are also analyzed.

Optimization and Performance of Non-Uniform Rotated Constellations With Multi-RF Transmission Techniques

Non-Uniform Constellations (NUC) have been introduced in ATSC 3.0 (Advanced Television Systems Committee - Third Generation) as one of the main novelties to improve the performance compared to uniform Quadrature Amplitude Modulation (QAM) constellations. NUCs are optimized by means of signal geometrical shaping, considering the signal-to-noise ratio (SNR) and the channel model. ATSC 3.0 implements two types of NUC, depending on the number of real-valued dimensions in which they are optimized: 1D-NUC and 2D-NUC. However, the gain of NUCs becomes almost non-existent at high SNRs, especially when optimizing for fading channels. In that particular case, Rotated Constellations (RC) can be used to further improve the overall system performance. RCs may become especially effective when using multi-radio frequency (multi-RF) SNR averaging techniques such as Channel Bonding (CB) or Time-Frequency Slicing (TFS), where in-phase (I) and quadrature (Q) components are transmitted in different RF channels. 2D-NUCs can be rotated without increasing the demapping complexity, since a 2D-demapper is also needed. In this paper, we propose an optimization method designed for rotated 2D-NUCs, in which the rotation angle is considered as an additional variable, together with the symbol positions. The SNR gain obtained in fading channels is also provided for three different use cases: single-RF transmissions, CB with 2 RF channels as adopted in ATSC 3.0, and extension of multi-RF techniques to 4 RF channels.

Low-Complexity Demapping Algorithm for Two-Dimensional Non-Uniform Constellations

Non-uniform constellations (NUCs) have been recently introduced in digital broadcasting systems to close the remaining gap to the unconstrained Shannon theoretical limit. Compared to uniform quadrature amplitude modulation (QAM) constellations, NUCs provide a signal-to-noise ratio (SNR) gain (i.e., a reduction in the required SNR), especially for high-order constellations. One-dimensional NUCs (1D-NUC) have a squared shape with non-uniform distance between the constellation symbols. Since the I and Q components remain as two independent signals, a 1D-demapper as for uniform QAM constellations is feasible. Two-dimensional NUCs (2D-NUC) provide a better performance than 1D-NUCs, since they are designed by relaxing the square shape constraint, with arbitrary shape along the complex plane. However, the main drawback of 2D-NUCs is the higher complexity at the receiver, since a 2D-demapper is needed. In this paper, we propose a demapping algorithm that reduces from 69% to 93% the number of required distances when using 2D-NUCs. The algorithm discards or replicates those constellation symbols that provide scarce information, with a performance degradation lower to 0.1 dB compared to the optimal maximum likelihood demapper.

Low Complexity Max-log LLR Computation for Nonuniform PAM Constellations

In this letter, we derive a low-complexity method for demodulating nonuniform PAM signals. With uniform Gray-coded M-PAM constellations, the reflective symmetry can be exploited to demodulate the signals with low complexity. However with nonuniform constellations, this symmetry is lost and more complicated computations are required. We derive an analytic expression for the max-log LLR functions and show that they are piecewise linear functions. Based on this, we devise a demodulation algorithm that has complexity $\mathcal{O} \left(\log_2 M \right)$ as opposed to $\mathcal{O} \left(M \right)$ for the exhaustive search. We also present an approximation with reduced complexity and only modest performance degradation.

Non-Uniform Constellations for ATSC 3.0

This paper introduces the concept of a non-uniform constellation (NUC) in contrast to conventional uniform quadrature-amplitude modulation (QAM) constellations. Such constellations provide additional shaping gain, which allows reception at lower signal-to-noise ratios. ATSC3.0 will be the first major broadcasting standard, which completely uses NUCs due to their outstanding properties. We will consider different kinds of NUCs and describe their performance: 2-D NUCs provide more shaping gain at the cost of higher demapping complexity, while 1-D NUCs allow low-complexity demapping at slightly lower shaping gains. These NUCs are well suited for very large constellations sizes, such as 1k and 4k QAM.