Constellation Size Research Articles

Novel Modulation Recognition for WFRFT-Based System Using 4th-Order Cumulants

We present a novel modulation recognition for weighted-type fractional Fourier transform (WFRFT)-based systems using the fourth-order cumulants. First, the constellation characteristics of the basic digital modulations ASK, PSK, and QAM are analyzed, and the corresponding relationships between the neighboring constellation points’ distance and the constellation size are deduced. Second, the closed-form expressions of the fourth-order cumulants ( $C_{42}$ ) for the WFRFT-based systems with ASK, PSK, and QAM are derived. Finally, through the first- and second-order derivatives of the $C_{42}$ , we prove that the optimal WFRFT order $\alpha _{r}$ can be obtained through the minimization of the $C_{42}$ . The simulation results show that the novel recognition for the WFRFT-based system is feasible and can reach an accuracy of almost 90% when energy per bit-to-noise power spectrum density ratio ( ${E_{\text {b}}}/{N_{0}}$ ) is greater than 6.

Neural Network-Based Fading Channel Prediction: A Comprehensive Overview

By adapting transmission parameters such as the constellation size, coding rate, and transmit power to instantaneous channel conditions, adaptive wireless communications can potentially achieve great performance. To realize this potential, accurate channel state information (CSI) is required at the transmitter. However, unless the mobile speed is very low, the obtained CSI quickly becomes outdated due to the rapid channel variation caused by multi-path fading. Since outdated CSI has a severely negative impact on a wide variety of adaptive transmission systems, prediction of future channel samples is of great importance. The traditional stochastic methods, modeling a time-varying channel as an autoregressive process or as a set of propagation parameters, suffer from marginal prediction accuracy or unaffordable complexity. Taking advantage of its capability on time-series prediction, applying a recurrent neural network (RNN) to conduct channel prediction gained much attention from both academia and industry recently. The aim of this article is to provide a comprehensive overview so as to shed light on the state of the art in this field. Starting from a review on two model-based approaches, the basic structure of a recurrent neural network, its training method, RNN-based predictors, and a prediction-aided system, are presented. Moreover, the complexity and performance of predictors are comparatively illustrated by numerical results.

A Comparison of CP-OFDM, PCC-OFDM and UFMC for 5G Uplink Communications

Polynomial-cancellation-coded orthogonal frequency division multiplexing (PCC-OFDM) is a form of OFDM that has waveforms which are very well localized in both the time and frequency domains and so it is ideally suited for use in the 5G network. This paper analyzes the performance of PCC-OFDM in the uplink of a multiuser system using orthogonal frequency division multiple access (OFDMA) and compares it with conventional cyclic prefix OFDM (CP-OFDM), and universal filtered multicarrier (UFMC). PCC-OFDM is shown to be very much less sensitive to time and frequency offsets than either CP-OFDM or UFMC. For a given constellation size, PCC-OFDM in additive white Gaussian noise (AWGN) requires 3 dB lower signal-to-noise ratio (SNR) for a given bit-error-rate, and the SNR advantage of PCC-OFDM increases rapidly when there are timing and/or frequency offsets. For PCC-OFDM no frequency guard-band is required between different OFDMA users. PCC-OFDM is completely compatible with CP-OFDM and adds negligible complexity and latency, because it uses a simple mapping of data onto pairs of subcarriers at the transmitter, and a simple weighting-and-adding of pairs of subcarriers at the receiver. The weighting-and-adding step, which has been omitted in some of the literature, is shown to contribute substantially to the SNR advantage of PCC-OFDM. A disadvantage of PCC-OFDM (without overlapping) is the potential reduction in spectral efficiency because subcarriers are modulated in pairs, but this reduction is more than regained because no guard band is required and because, for a given channel, larger constellations can be used.

Comparison of DCO-OFDM, ADO-OFDM, HDC-OFDM and HNC-OFDM for Optical Wireless Communications

Abstract This paper presents a new form of orthogonal frequency division multiplexing (OFDM) termed as hybrid noise cancelled asymmetrically clipped optical OFDM (HNC-OFDM) for optical wireless communication. This HNC-OFDM is formed by combining the concepts of noise cancelled asymmetrically clipped optical OFDM and DC biased optical OFDM (DCO-OFDM). HNC-OFDM has the same bit error rate (BER) performance and dimming flexibility but less complexity compared to the recently developed hybrid diversity combined OFDM. The optimum DC bias level for HNC-OFDM, DCO-OFDM and asymmetrically clipped DC biased optical OFDM is shown to depend on the target BER, the constellation size, the received signal to noise power ratio, the proportion of DCO-OFDM element, the link type, equalization, etc. Simulations results show that with an optimum bias, HNC-OFDM can outperform others in an average power limited channel, while DCO-OFDM is a better choice for a peak power limited channel.

Opportunistic Group Antenna Selection in Spatial Modulation Systems

This paper proposes an opportunistic spatial modulation (OSM) scheme where the transmit antennas are divided into $K\geq 1 $ equal groups, and the best antenna from each group is selected to form a $K$ transmit antenna subset for implementing spatial modulation (SM). Thus, the activation of one antenna from the subset to transmit one of the $M$ -ary modulation symbols achieves a data rate of $\log _{2} (K) +\log _{2} (M)$ bits per channel use. Notably, special cases of OSM include conventional SM and pure single transmit antenna selection. To characterize and comparatively evaluate OSM, we first consider phase-shift keying modulation and derive a closed-form, improved union-bound of symbol error probability (SEP) with a single-antenna receiver. Explicit expressions for the SEP in the high signal-to-noise ratio regime are also presented. Extensions to quadrature amplitude modulation analysis and simulations of multiple-antenna reception case are also provided. Simulation results corroborate the analytical results and reveal the interesting interplay between the signal and spatial constellation diagrams. For a given number of transmit antennas and targeted data rate, asymptotically, the SEP can be minimized by using only one antenna group and the largest size of signal constellation, as this configuration achieves the full-diversity order.

A simple low-complexity algorithm for generalized spatial modulation

Generalized spatial modulation (GSM) is an extension of spatial modulation which is significant for the next generation communication systems. Optimal detection process for the GSM is the maximum-likelihood (ML) detection which jointly detects the antenna combinations and transmitted symbols. However, the receiver is much more complicated than SM due to inter-antenna interference and/or increased number of combinations. Therefore, the computational complexity of the ML detection grows with the number of transmit antennas and the signal constellation size. In this letter, we introduce a novel and simple detection algorithm which uses sub-optimal method based on the least squares solution to detect likely antenna combinations. Once the antenna indices are detected, ML detection is utilized to identify the transmitted symbols. For obtaining near-ML performance while keeping lower complexity than ML detection, sphere decoding is applied. Our proposed algorithm reduces the search complexity while achieving a near optimum solution. Computer simulation results show that the proposed algorithm performs close to the optimal (ML) detection resulting in a significant reduction of computational complexity.

3-D Polarized Modulation: System Analysis and Performance

In this paper we present a novel modulation technique for dual polarization communication systems, which reduces the error rate compared with the existent schemes. This modulation places the symbols in a 3D constellation, rather than the classic approach of 2D. Adjusting the phase of these symbols depending on the information bits, we are able to increase the bit rate. Hence, the proposed scheme conveys information by selecting both polarization state and the phase of radiated electromagnetic wave. We also analyse the performance of 3D Polarized Modulation (PMod) for different constellation sizes and we obtain a curve of rate adaptation. Finally, we compare the proposed 3D PMod with other existing schemes such as single polarization Phase Shift Keying (PSK) and double polarization Vertical Bell Laboratories Layer Space-Time (V-BLAST), both carrying the same number of information bits. The results show that 3D PMod always outperforms all other schemes, except for low order modulation. Therefore, we can conclude that 3D PMod is an excellent candidate for medium and high modulation order transmissions.

Bit-Metric Decoding of Non-Binary LDPC Codes With Probabilistic Amplitude Shaping

A new approach for combining non-binary low-density parity-check (NB-LDPC) codes with higher-order modulation and probabilistic amplitude shaping (PAS) is presented. Instead of symbol-metric decoding (SMD), a bit-metric decoder (BMD) is used so that matching the field order of the non-binary code to the constellation size is not needed, which increases the flexibility of the coding scheme. Information rates, density evolution thresholds and finite-length simulations show that the flexibility comes at no loss of performance if PAS is used.

Low-Complexity Near-ML Detection Algorithms for NR-STAR-MQAM Spatial Modulation

In this study, the authors propose two low-complexity near-maximum-likelihood (ML) detection algorithms for spatial modulation (SM) systems, employing the new multiple-ring star-M-ary quadrature amplitude modulation (NR-STAR-MQAM) constellation. The proposed detectors exploit the specific orientation of NR-STAR-MQAM, in order to avoid searching across all constellation points. As a result, the computational complexity is independent of both the constellation size and the number of rings presented in NR-STAR-MQAM. In addition, these detectors are generalized and can be applied to the entire star-MQAM family. The Monte Carlo simulation results demonstrate that the proposed detection algorithms achieve the same average bit error rate (ABER) as ML detection for SM but at a much lower computational complexity. For example, in a 4 × 4, 2R-STAR-16QAM aided SM system, the proposed optimal and sub-optimal detectors achieve an 88.8% and 90.5% reduction in computational complexity, respectively, compared to the ML detector. Furthermore, the simulation results are supported by a closed-form union-bound theoretical ABER expression.

Frequency-Domain Hybrid Modulation Formats for High Bit-Rate Flexibility and Nonlinear Robustness

Since the deployment of the first commercial polarization-multiplexed (PM) QPSK 100G systems, the evolution of coherent optical communications in the last decade has been largely dominated by single-carrier quadrature amplitude modulation (QAM) based modulation of increasing constellation size. However, as the data traffic becomes more dynamic and heterogeneous, an efficient use of the optical link requires more flexible modulation schemes, capable of adapting data-rate and distance with fine granularity. While typical multi-carrier modulation schemes composed of hundreds of subcarriers may be inadequate for optical transmission, namely due its high peak-to-average power ratio and increased nonlinearity penalties, it has been recently shown that few-carrier modulation (with symbol rate in the order of 2–4 GBaud) can provide an increased robustness to nonlinear propagation impairments. In this paper, we exploit the concept of frequency-domain hybrid modulation formats (FDHMF) based on electronic subcarrier multiplexing with the use of different QAM formats on each subcarrier to simultaneously enhance the data-rate flexibility and the nonlinear propagation performance of the optical link. In addition, by properly designing the FDHMF signal, an increased tolerance against optical filtering can also be achieved. Using the enhanced Gaussian noise model, we report a comprehensive theoretical study on the performance of FDHMF, considering independent- and joint-subcarrier forward-error correction strategies, optimization of power ratio between subcarriers, and corresponding impact of fiber nonlinearities. These theoretical insights are then validated by a broad range of wavelength-division multiplexing experiments with per-channel bit-rates in the range of 150G to 250G. The obtained results demonstrate that FDHMF is an effective solution for the implementation of flexible transponders capable of adapting the data rate to the lightpath quality of transmission: An enabling technology for the introduction of future elastic optical networks.

Paraunitary-Based Boolean Generator for QAM Complementary Sequences of Length <inline-formula> <tex-math notation="LaTeX">$2^{K}$ </tex-math> </inline-formula>

A Boolean generator for a large number of standard complementary QAM sequences of length $2^{K}$ is proposed. This Boolean generator is derived from the authors’ earlier paraunitary generator, which is based on matrix multiplications. Both generators are based on unitary matrices. In contrast to previous Boolean QAM algorithms which represent complementary sequences as a weighted sum, our algorithm has a multiplicative form. Any element of a sequence can be generated efficiently by indexing the entries of unitary matrices with the binary representation of the discrete time index (which is easily implemented as a binary counter). Our 1Qum (based on one QAM unitary matrix) and 2Qum (based on two QAM unitary matrices) algorithms generate generalized Case I – III sequences and generalized Case IV and V sequences, respectively, as specified by Liu et al. in 2013, in addition to many new 2Qum sequences. The ratio of the numbers of sequences that are generated by our new construction and the previous construction increases with the constellation size. For example, for a 1024-QAM sequence of length 1024, this ratio is 4.4. However, if we compare only 2Qum sequences to Case IV and V sequences, this ratio is 267.

Low-Complexity Decoder Based on Conditional ML for QOSTBC

In this letter, we present a new decoder for quasi-orthogonal space-time block code (QOSTBC) based on conditional maximum-likelihood (ML) decoder. The proposed decoder results in the decoding complexity of $\mathcal {O}(L^{1})$ , where $L$ is the constellation size. In addition, by decomposing the real and imaginary components of the received signals, we further reduce the complexity of the decoder. Unlike many of previous decoders proposed for QOSTBC, our decoder is compatible with any complex-valued constellation such as quadrature amplitude modulation. Furthermore, the advantage of the proposed decoder with respect to other decoders is analyzed in terms of preprocessing and detection complexity. The simulation results show the identical bit error rate performance of the proposed and conventional ML decoder.

Constellational Interdependence, Trust, and Cooperation in Supply-Chain Alliance Social Dilemmas

In their article about why supply chain alliances struggle to create value, McCarter and Northcraft (2007) observe that, as a collective action, supply chain alliances are social dilemmas, and McCarter and Northcraft point to the supply chain alliance structure as a culprit that undermines trust and subsequent cooperation among partners. An untested supply chain alliance structure of their model is constellational interdependence - or the number of independent supply chain alliances partners are involved in. We test predictions presented in the model about constellational interdependence with data from the experimental laboratory. Congruent with the model’s predictions, we find: (1) a partner’s contribution to a supply chain alliance decreases as the number of separate supply chain alliances their partners are engaged in increases; (2) trust among supply chain alliance partners decrease as the number of separate supply chain alliances those partners are engaged in increases; and (3) trust mediates the relationship between the size of the supply chain alliance constellation and partner contributions. In extending the model, we also find that constellation interdependence can benefit supply chain alliance cooperation when there are asymmetrical benefits among supply chain alliance partnerships.

Performance analysis of shadowed-Rice fading channel with cooperative spectrum sensing

ABSTRACTIn this paper, the performance analysis of wireless communication system over shadowed-Rice (SR) composite fading channel has been investigated and analysed. The unified analytical expressions of the average symbol error probability (ASEP) for several coherent and non-coherent modulation schemes separately with different constellation sizes are derived for composite fading channel under two different fade mitigation methods, with maximal ratio combining (MRC) microdiversity (Method 1) and MRC applied over the composite fading channel (Method 2). Furthermore, an asymptotic analysis is carried out and a closed-form expression of the ASEP with Method 2 is presented. Analytical expressions of the corresponding average probability of energy detection (PD) are formulated for both the methods. Finally, the derived PD expression is utilised to analyse the performance of cooperative system assuming erroneous feedback channel. Analysis of optimisation of detection threshold as well as number of cognitive users to minimise the total error rate is also carried out. The closed-form expressions are validated by comparing them with exact numerical results and Monte Carlo simulation.

M-PAM Joint Optimal Waveform Design for Multiuser VLC Systems Over ISI Channels

Visible light communication is a candidate technique to provide high-speed data transmissions. This paper proposes a joint optimal waveform design algorithm for visible light communication systems using $M$ -ary pulse amplitude modulation to support multiple users. Transmitted waveforms and minimum mean squared error filters are jointly optimized to minimize the intersymbol and multiple access interferences. Based on different channel conditions, the designed waveforms and modulation constellation sizes can be adaptively adjusted to guarantee the highest bit rates. Channel uncertainty is also considered in this paper. Compared with optical code division multiple access and time division multiple access, the algorithm proposed can provide higher bit rates. In addition, the proposed algorithm can flexibly adjust the illumination level by changing the optimization constraints. An offline waveform design algorithm is then proposed to diminish the optimization computation time. A waveform lookup table can be established offline in advance, and the proper waveforms can be selected from the table based on the actual channel gains in real time. The performance of the offline algorithm can be estimated by using the channel uncertainty model.

Simplicity-based recovery of finite-alphabet signals for large-scale MIMO systems

In this paper, we consider the problem of finite-alphabet source separation in both determined and underdetermined large-scale systems. First, we address the noiseless case and we propose a linear criterion based on ℓ1-minimization combined with box constraints. We investigate also the system conditions that ensure successful recovery. Next, we apply the approach to the noisy massive MIMO transmission and we propose a quadratic criterion-based detector. Simulation results show the efficiency of the proposed detection methods for various QAM modulations and MIMO configurations. We mention that there is no change in the computational complexity when the constellation size increases. Moreover, the proposed method outperforms the classical Minimum Mean Square Error (MMSE)-based detection algorithms.

How Many Signals Can Be Sent in a Multi-Cell Massive MIMO System

In this letter, we study how large the signal constellation can be under pilot contamination in a multi-cell massive multiple-input multiple-output uplink system. Specifically, based on an equivalent transmit–receive signal model, we observe that the transmitted signals by all users in different cells are compacted into a low-dimensional space when they arrive at the target base station. Then, the equivalent model reveals that the size of constellations used by all users is limited by a parameter, which is related to the large-scale fading factors only. We find that when the size of the signal constellation is smaller than the parameter, the error probability goes to zero. Otherwise, an error floor occurs regardless of the number of antennas and the pilot signal to noise ratio. Our simulations results validate the proposed analytical results.

Large MIMO Detection Schemes Based on Channel Puncturing: Performance and Complexity Analysis

A family of low-complexity detection schemes based on channel matrix puncturing targeted for large multiple-input multiple-output (MIMO) systems is proposed. It is well known that the computational cost of MIMO detection based on QR decomposition is directly proportional to the number of non-zero entries involved in back-substitution and slicing operations in the triangularized channel matrix, which can be too high for low-latency applications involving large MIMO dimensions. By systematically puncturing the channel to have a specific structure, it is demonstrated that the detection process can be accelerated by employing standard schemes, such as chase detection, list detection, nulling-and-cancellation detection, and sub-space detection on the transformed matrix. The performance of these schemes is characterized and analyzed mathematically, and bounds on the achievable diversity gain and probability of bit error are derived. Surprisingly, it is shown that puncturing does not negatively impact the receive diversity gain in hard-output detectors. The analysis is extended to soft-output detection when computing per-layer bit log-likelihood ratios; it is shown that significant performance gains are attainable by ordering the layer of interest to be at the root when puncturing the channel. Simulations of coded and uncoded scenarios certify that the proposed schemes scale up efficiently both in the number of antennas and constellation size, as well as in the presence of correlated channels. In particular, soft-output per-layer sub-space detection is shown to achieve a 2.5 dB signal-to-noise ratio gain at 10−4 bit error rate in 256-quadratic-amplitude modulation $16\times 16$ MIMO, while saving 77% of nulling-and-cancellation computations.

Time-Modulated FD-MIMO Array for Integrated Radar and Communication Systems

In this letter, we explore time-modulated frequency diverse multiple-input–multiple-output (TMFD-MIMO) array for integrated radar and communications, where the communication information bits are embedded via spread sequence technique during each radar pulse. Orthogonal waveforms are adopted in the TMFD-MIMO array for radar functionality, and a switching time-modulation scheme is applied according to the information bits, i.e., binary phase-shift keying (BPSK) associated spreading sequences. Thus, the number of embedded information bits during each radar pulse equals the number of spread sequences. In doing so, the communication receiver interprets the bits associated with a particular waveform as binary information with prior knowledge of the spread sequences. When compared with existing radar-communications, the achievable data rate is then proportionally increased with the pulse repetition frequency, spreading sequence, and size of the BPSK constellation. Moreover, satisfactory probability of target resolution and signal-to-interference-plus-noise ratio for radar functionality and symbol error rate for communication functionality are achieved.

Sensitivity analysis of launch activities in Low Earth Orbit

This work aims to investigate the response of the low Earth orbit environment to the change in number and distribution of new launches and to understand the effects of the size and post-mission lifetime of a large constellation of spacecraft. The analysis presented in this paper were carried out using MISSD, Model for Investigating control Strategies for Space Debris, a multi-shell, and multi-species source-sink statistical model able to simulate the injection, removal and interaction of six type of objects up to an altitude of 2000 km. The results suggest that multiple regions experience a sensible increment in the orbital density when slightly increasing the launch activity for the next 200 years. Recently, many private companies expressed their interest in putting large constellations of satellites at 1100–1300 km altitude. However, results show that the launch of just six additional spacecraft per year in this region increased the spatial density by an amount equal to the projection over 200 years of today's most crowded region. Results also show that the increase in the orbital population and collision risk caused by the presence of large constellations could be mitigated using a high level of post-mission disposal compliance, reliable deorbit mechanisms and reducing thepost-mission lifetime to 5 years.