Constellation Symbols Research Articles

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.

OFDM-Based Generalized Optical MIMO

The combination of multiple-input multiple-output (MIMO) transmission and orthogonal frequency division multiplexing (OFDM) modulation has been shown to be an effective way to substantially enhance the capacity of bandlimited optical wireless communication (OWC) systems. In this paper, we propose four OFDM-based generalized optical MIMO (GO-MIMO) techniques for intensity-modulation and direct-detection OWC systems, including OFDM-based frequency-domain generalized spatial modulation (FD-GSM), frequency-domain generalized spatial multiplexing (FD-GSMP), time-domain generalized spatial modulation (TD-GSM) and time-domain generalized spatial multiplexing (TD-GSMP). For OFDM-based FD-GSM and FD-GSMP, spatial mapping is performed in the frequency domain, while it is carried out in the time domain for OFDM-based TD-GSM and TD-GSMP. To efficiently estimate both spatial and constellation symbols in each OFDM-based GO-MIMO technique, a corresponding maximum-likelihood (ML) detection algorithm is designed. Extensive simulations are conducted to evaluate and compare the performance of OFDM-based GO-MIMO techniques under various MIMO settings in a typical indoor environment. Simulation results demonstrate that there exists an optimal GO-MIMO technique to achieve a target spectral efficiency for a given receiver location, and the obtained optimal GO-MIMO technique is also related to the specific location of the receiver.

Full-Duplex Quadrature Spatial Modulation for Multi-Antenna Systems

Devices with full-duplex (FD) radios are able to transmit and receive at the same time without requiring orthogonal resources, thereby creating strong self-interference (SI) that results from their own transmissions. Spatial modulation (SM), on the other hand, is a multi-antenna scheme that activates only one transmit antenna to send a data symbol, where the index of the activated antenna depends on the input bits. In this manner, additional data can be conveyed implicitly via the selection of the active transmit antenna. Quadrature spatial modulation (QSM) is a variant of SM, in which the quadrature components of the constellation symbol are separately modulated on the indices of the transmit antenna, leading to an increase in the data rate by implicitly encoding on the spatial domain. This article provides an overview of the research activity on FD-SM and proposes a novel FD-QSM scheme that exploits multiple antennas to achieve antenna cancellation at the receiving side to mitigate the SI signal. Assuming active cancellation mechanisms are also in place, the performance of FD-QSM is studied in the presence of residual SI (RSI). The results reveal that FD-QSM can provide more than 40 percent capacity gain over its half-duplex (HD) counterpart in the presence of strong RSI and roughly the same gain over HD spatial multiplexing (SMX)-based multiple-input-multiple-output (MIMO) systems with moderate RSI. When applied to the downlink of a cellular network, FD-QSM provides 2dB gain over FD-SM and 5dB gain over FD-MIMO, operating at the same spectral efficiency, while huge gains are observed when FD-QSM is applied to non-orthogonal multiple access (NOMA)-aided FD relay network.

Joint-Mapping Orthogonal Frequency Division Multiplexing With Subcarrier Number Modulation

Orthogonal frequency division multiplexing with subcarrier number modulation (OFDM-SNM) has been recently proposed to improve the spectral efficiency (SE) of the traditional OFDM system. In this paper, we propose a joint-mapping OFDM-SNM (JM-OFDM-SNM) scheme to transmit the signal vector with a constant length of information bits by jointly considering the subcarrier activation patterns and constellation symbols. A low-complexity detection scheme based on log-likelihood ratio criterion is proposed to relieve the high computational complexity of the maximum-likelihood detection at the cost of a negligible performance loss. Upper-bounded bit error rate (BER) and lower-bounded achievable rate are both derived in closed-form to evaluate the performance of JM-OFDM-SNM. To suit different application scenarios, we further propose two enhanced schemes, named adaptive JM-OFDM-SNM (AJM-OFDM-SNM) and JM-OFDM with in-phase/quadrature SNM (JM-OFDM-IQ-SNM), where the former adjusts the constellation orders for different numbers of active subcarriers, and the latter extends the indexing to in-phase and quadrature domains. Simulation results corroborate the tightness of the derived BER expression in the high signal-to-noise ratio region and show that (A)JM-OFDM-SNM improves the performance of OFDM-SNM, while both AJM-OFDM-SNM and JM-OFDM-IQ-SNM schemes perform better than JM-OFDM-SNM at the same SE.

Smart Detection Using the Cascaded Artificial Neural Network for OFDM With Subcarrier Number Modulation

Since the proposal of orthogonal frequency-division multiplexing with subcarrier number modulation (OFDM-SNM), the high detection complexity of this novel modulation scheme becomes a major issue degrading its applicability in practice. To provide an easy-to-implement and low-complexity solution to the detection of the OFDM-SNM signal, we design a cascaded artificial neural network (CANN) at the OFDM-SNM receiver to decouple the detection of subcarrier number pattern (SNP) and constellation symbols on the active subcarriers. This is the first time that the CANN design is introduced to assist in detecting parallel signals. Numerical simulations verify the effectiveness and efficiency of the proposed smart detection scheme and show that the CANN based smart detection with adequate training can yield comparable error performance to the optimal maximum-likelihood detection at much lower complexity.

Robust Symbol Detection in Large-Scale Overloaded NOMA Systems

We a framework for the design of low-complexity and high-performance receivers for multidimensional overloaded non-orthogonal multiple access (NOMA) systems. The framework is built upon a novel compressed sensing (CS) regularized maximum likelihood (ML) formulation of the discrete-input detection problem, in which the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -norm is introduced to enforce adherence of the solution to the prescribed discrete symbol constellation. Unlike much of preceding literature,.g., (Assaf et al., 2020, Yeom et al., 2019, Nagahara, 2015, Naderpour and Bizaki, 2020, Hayakawa and Hayashi, 2017, Hayakawa and Hayashi, 2018, and Zeng et al., 2020), the method is not relaxed into the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm, but rather approximated with a continuous and asymptotically exact expression without resorting to parallel interference cancellation (PIC). The objective function of the resulting formulation is thus a sum of concave-over-convex ratios, which is then tightly convexified via the quadratic transform (QT), such that its solution can be obtained via the iteration of a simple closed-form expression that closely resembles that of the classic zero-forcing (ZF) receiver, making the method particularly suitable to large-scale set-ups. By further transforming the aforementioned problem into a quadratically constrained quadratic program with one convex constraint (QCQP-1), the optimal regularization parameter to be used at each step of the iterative algorithm is then shown to be the largest generalized eigenvalue of a pair of matrices which are given in closed-form. The method so obtained, referred to as the Iterative Discrete Least Square (IDLS), is then extended to address several factors of practical relevance, such as noisy conditions, imperfect channel state information (CSI), and hardware impairments, thus yielding the Robust IDLS algorithm. Simulation results show that the proposed art significantly outperforms both classic receivers, such as the linear minimum mean square error (LMMSE), and recent CS-based state-of-the-art (SotA) alternatives, such as the sum-of-absolute-values (SOAV) and the sum of complex sparse regularizers (SCSR) detectors. It is also shown via simulations that the technique can be integrated with existing iterative detection-and-decoding (IDD) methods, resulting in accelerated convergence.

Virtual Spatial Channel Number and Index Modulation

This paper proposes a novel precoding‐aided and efficient data transmission scheme called virtual spatial channel number and index modulation (VS‐CNIM), which conveys extra data by changing both the number and index of active virtual parallel channels of multiple‐input multiple‐output (MIMO) channels, obtained through the singular value decomposition (SVD) in each time slot. Unlike the conventional virtual spatial modulation (VSM), where extra data bits are transmitted only using index of active virtual parallel channels, the VS‐CNIM scheme, depending on incoming information bits, transmits extra bits utilizing both the number and indices of active parallel channels along the bits carried by M‐ary constellation symbols. Therefore, VS‐CNIM provides significantly superior spectral efficiency (SE) compared to VSM. Considering the influence of imperfect channel estimation, a closed‐form upper bound is derived on average bit error probability (ABEP). The asymptotic performance is also analyzed, which gives the coding gain and diversity order and describes error floor under the consideration of perfect and imperfect channel estimation, respectively. Monte Carlo simulations exhibit that the VS‐CNIM scheme achieves considerably better error performance and high SE than precoding‐aided SM (PSM) and VSM schemes.

Index Modulation Aided Uplink NOMA for Massive Machine Type Communications

Single-carrier frequency-division multiple access (SC-FDMA) based index modulation (IM), referred here as SC-IM, allows users to implicitly transmit a part of their data bits by switching on some of their allocated subcarriers, followed by ${M}$ -ary constellation symbols transmission over the activated subcarriers. This sparse use of subcarriers provides better energy efficiency and error rate. Using these benefits, this letter exploits SC-IM with uplink power domain non-orthogonal multiple access (NOMA), where all users with the same allocated subcarrier set can simultaneously transmit their SC-IM data with different power levels, which are exploited by the receiver to perform multi-user detection. Performance of the proposed technique is analyzed and compared with conventional NOMA. It is shown that the proposed scheme can achieve energy efficient massive connectivity, which is a primary requirement for massive machine-type communications.

Binary MIMO Detection via Homotopy Optimization and Its Deep Adaptation

In this paper we consider maximum-likelihood (ML) MIMO detection under one-bit quantized observations and binary symbol constellations. This problem is motivated by the recent interest in adopting coarse quantization in massive MIMO systems--as an effective way to scale down the hardware complexity and energy consumption. Classical MIMO detection techniques consider unquantized observations, and many of them are not applicable to the one-bit MIMO case. We develop a new non-convex optimization algorithm for the one-bit ML MIMO detection problem, using a strategy called homotopy optimization. The idea is to transform the ML problem into a sequence of approximate problems, from easy (convex) to hard (close to ML), and with each problem being a gradual modification of its previous. Then, our attempt is to iteratively trace the solution path of these approximate problems. This homotopy algorithm is well suited to the application of deep unfolding, a recently popular approach for turning certain model-based algorithms into data-driven, and performance enhanced, ones. While our initial focus is on one-bit MIMO detection, the proposed technique also applies naturally to the classical unquantized MIMO detection. We performed extensive simulations and show that the proposed homotopy algorithms, both non-deep and deep, have satisfactory bit-error probability performance compared to many state-of-the-art algorithms. Also, the deep homotopy algorithm has attractively low computational complexity.

Spherical Quasi-Physical Model-Based Color-Shift Keying for Visible Light Communication

In this paper, the new family of spherical color-shift keying (SCSK) constellations is proposed for visible light communication (VLC) systems. Specifically, the constant-intensity constraint (CIC) for conventional color-shift keying (CSK) schemes, which originates from the requirement of non-flickering illumination, confines the constellation symbols on a two-dimensional (2D) plane of the three-dimensional (3D) intensity space. To fully utilize the potential degree of freedom offered by the 3D intensity space, we propose to expand the envelope of CSK constellations by replacing the constant intensity with a new spherical intensity constraint, aiming to maximize the minimum Euclidean distance (MED). More explicitly, we design the robust SCSK constellations with and without white color balance (CB), respectively. Particularly, we transform the constellation design problem to the so-called spherical circle packing (SCP) problem, which is resolved based on the spherical quasi-physical (SQP) model. Then, we propose the so-called spherical heuristic quasi-physical algorithm (SHQPA) integrating the binary search algorithm (BSA) and the configuration update algorithms (CUA) to obtain the optimal SCSK constellations. Furthermore, we also study the corresponding bit-to-symbol mapping rules for the generated SCSK constellations. Simulation results show that the new family of SCSK constellations outperforms the conventional CSK counterparts.

Spectrum Resource Allocation Based on Cooperative NOMA With Index Modulation

In this paper, two novel spectrum resource allocation schemes, based on orthogonal frequency division multiplexing with index modulation (OFDM-IM) and dual-mode OFDM-IM, are proposed for a three-node cooperative non-orthogonal multiple access (C-NOMA) system. In the first scheme, we allocate IM bits to serve the cell-edge user, and save the transmit power to assist the delivery of constellation symbols. Alternatively, constrained by the spectral efficiency (SE), the rest information bits of the cell-edge user can be carried by the conventional signal constellation. In the second scheme, to further eliminate the interference between users and boost the SE, different modulation modes (Mode I and Mode II) are employed to distinguish the subcarriers of the cell-center and cell-edge users, and to encode the incoming bit stream from these users, respectively. Furthermore, we consider two different detectors for the cell-edge user, i.e., the optimal/suboptimal maximum-likelihood detectors. Asymptotically tight bounds on the bit error rate of the above-mentioned users are derived in closed-form. Finally, simulation results verify the theoretical analysis and show that the proposed schemes have the potential to outperform C-NOMA.

Block Deep Neural Network-Based Signal Detector for Generalized Spatial Modulation

Generalized Spatial Modulation (GSM) is being considered for high capacity and energy-efficient networks of the future. However, signal detection due to inter channel interference among the active antennas is a challenge in GSM systems and is the focus of this letter. Specifically, we explore the feasibility of using deep neural networks (DNN) for signal detection in GSM. In particular, we propose a block DNN (B-DNN) based architecture, where the active antennas and their transmitted constellation symbols are detected by smaller sub-DNNs. After N-ordinary DNN detection, the Euclidean distance-based soft constellation algorithm is implemented. The proposed B-DNN detector achieves a BER performance that is superior to traditional block zero-forcing (B-ZF) and block minimum mean-squared error (B-MMSE) detection schemes and similar to that of classical maximum likelihood (ML) detector. Further, the proposed method requires less computation time and is more accurate than alternative conventional numerical methods.

Coded OFDM-IM with iterative detection☆

Coded Orthogonal frequency division multiplexing with index modulation (OFDM-IM) has been proposed, where channel coding and soft decision are employed to exploit the multipath diversity for the information conveyed by the constellation symbols. However, the performance of coded OFDM-IM is dependent on the detection performance of subcarrier activation pattern (SAP) and the diversity order of the SAPs requires further investigation. In this paper, a lower-bound of LLR detector is derived to show that the maximum achievable diversity order is the minimum Hamming distance between the SAPs for the LLR detector. Based on the analyses, iterative detection is proposed to improve the performance of coded OFDM-IM, where information-assisted LLR detector is proposed to improve the detection performance of SAP by using the soft information of the constellation symbols. Simulation results are provided to corroborate the diversity analyses and show the advantage of the coded OFDM-IM with iterative detection.

Timing Modulation for Macro-Scale Molecular Communication

In this letter, we propose a novel communication scheme for macro-scale molecular timing channels (MTCs), where the information carrier is the release time of the molecules. Next, the symbol constellation, receiver’s sampling time, and receiver’s decision rule are designed and analyzed. We further propose a computationally simple yet optimal receiver. Our numerical results show that macro-scale MTC is an approach for achieving ultra-reliable molecular communication.

Noncoherent Detection for Improving the Spectral Efficiency of OFDM-IM Systems

Today, Orthogonal Frequency Division Multiplexing (OFDM) is the most preferred and commonly used scheme for all communication systems. A new multicarrier technique called OFDM with Index Modulation (OFDM-IM) has been developed recently where the indices of the active subcarriers are used to transmit information in addition to the constellation symbols. In this article, system models of OFDM-IM and the two generalized schemes of OFDM-IM called OFDM with Generalized Index Modulation 1 (OFDM-GIM1) and OFDM with Generalized Index Modulation 2 (OFDM-GIM2) are studied. Here, noncoherent detection has been introduced for the two generalized schemes—OFDM-GIM1 and OFDM-GIM2 with the need for increasing the spectral efficiency. The probability of index error (Pie) is derived for OFDM-IM, OFDM-GIM1 and OFDM-GIM2. The developed noncoherent generalized schemes have reduced Pie and better performance with minimum Signal-to-Noise Ratio (SNR). This is clear from the simulation results that OFDM-GIM1 has less Pie than the other OFDM-IM schemes and it is around 10−1 when the required SNR is low about 8 dB.

Quadrature spatial modulation with space‐time block‐coded CPM MIMO system

AbstractQuadrature spatial modulation (QSM) is recently regarded as a technique to combat inter‐channel interference (ICI) for future wireless systems. In this paper, we consider a system of QSM combining space time block codes (STBC) and continuous phase modulation (CPM). In the system, the spatial constellation symbols are not expanded by two in‐phase and quadrature components, but represented by two STBC symbols. Moreover, we employ K‐means clustering algorithm to decrease the correlation of two transmit antennas. Then in the system, the bit error ratio (BER) performances are derived and evaluated for CPM and linear modulations (PSK, QAM). It is demonstrated that the proposed system has the advantages of BER performance and power spectrum density compared to its counterpart with linear modulations or without K‐means clustering of antennas.

On Orthogonal Coding-Based Modulation

In this letter, we propose a new orthogonal coding-based modulation (OCBM) scheme, in which all available transmitting subcarriers and antennas are activated at a time instant to transmit the data constellation symbols, and the indices of the activated subcarriers and antennas are also harnessed to carry information bits. Our OCBM especially addresses a novel scheme in spatial modulation (SM) domain via employing virtual subarray, and improves the spectral efficiency compared with the existing orthogonal frequency division multiplexing (OFDM)-spread spectrum (SS), index modulation (IM)-OFDM-SS and IM-OFDM based SM (the number of transmit antennas is more than 2). In addition, our investigated detection scheme of the OCBM reduces the complexity of the receiver design by using the unique behavior of the orthogonal code, especially for the detection of the transmitted antenna index bits. Our simulated experiments have been carried out to test the performance of the proposed scheme, and demonstrate the benefits of our suggested approach.

A Compressive Sensing Assisted Massive SM-VBLAST System: Error Probability and Capacity Analysis

The concept of massive spatial modulation (SM) assisted vertical bell labs space-time (V-BLAST) (SM-VBLAST) system [1] is proposed, where SM symbols (instead of conventional constellation symbols) are mapped onto the VBLAST structure. We show that the proposed SM-VBLAST is a promising massive multiple input multiple output (MIMO) candidate owing to its high throughput and low number of radio frequency (RF) chains used at the transmitter. For the generalized massive SM-VBLAST systems, we first derive both the upper bounds of the average bit error probability (ABEP) and the lower bounds of the ergodic capacity. Then, we develop an efficient error correction mechanism (ECM) assisted compressive sensing (CS) detector whose performance tends to achieve that of the maximum likelihood (ML) detector. Our simulations indicate that the proposed ECM-CS detector is suitable both for massive SM-MIMO based point-to-point and for uplink communications at the cost of a slightly higher complexity than that of the compressive sampling matching pursuit (CoSaMP) based detector in the high SNR region.

Design of Wavelet-Encoded Symbol Constellations for Cyclostationary Spectrum Sensing

In mobile communication systems, the signals propagate through multipath over time-varying channels, which are subject to distortion caused by fading and Doppler shifts. In order to minimize such distortions, coding techniques and transmission diversity can be employed, e.g., wavelet coding. In this work, the wavelet coding is investigated in scenarios of cognitive radio systems with dynamic spectrum access. Cognitive radio systems with dynamic spectrum access should be able to sense unoccupied frequency bands for opportunistic transmissions, as well as detect the presence of primary users when they occupy their licensed spectrum. Therefore, an essential element for the accurate operation of cognitive radio systems encoded by wavelet coding is the ability to sense the signals encoded by this technique. It is effectively demonstrated that the possibility of sensing such signals is associated with a suitable design of the signal constellation used in the modulation of the coded symbols. The constellation design of these is performed via genetic algorithms using a multiobjective optimization approach. The developed system is evaluated according to the robustness to time-varying flat fading through a bit error probability (BER) versus Eb/N0 analysis. The spectral sensing ability is also addressed employing the cyclostationary analysis. The results denote the feasibility of using wavelet coding in radio scenarios with dynamic spectrum access, with good performance in terms of BER and signal detection rates.

Cube-Split: A Structured Grassmannian Constellation for Non-Coherent SIMO Communications

In this paper, we propose a practical structured constellation for non-coherent communication with a single transmit antenna over Rayleigh flat and block fading channel without instantaneous channel state information. The constellation symbols belong to the Grassmannian of lines and are defined up to a complex scaling. The constellation is generated by partitioning the Grassmannian of lines into a collection of bent hypercubes and defining a mapping onto each of these bent hypercubes such that the resulting symbols are approximately uniformly distributed on the Grassmannian. With a reasonable choice of parameters, this so-called cube-split constellation has higher packing efficiency, represented by the minimum distance, than the existing structured constellations. Furthermore, exploiting the constellation structure, we propose low-complexity greedy symbol decoder and log-likelihood ratio computation, as well as an efficient way to associate it to a multilevel code with multistage decoding. Numerical results show that the performance of the cube-split constellation is close to that of a numerically optimized constellation and better than other structured constellations. It also outperforms a coherent pilot-based scheme in terms of error probability and achievable data rate in the regime of short coherence time and large constellation size.