16-ary Modulation Research Articles

Analysis and Design of QC-LDPC Coded BICM Ensembles Based on RCA Density Evolution

This paper presents density evolution (DE) techniques based on reciprocal channel approximation (RCA) for general bit-interleaved coded modulation (BICM) systems. The original RCA-based DE (RCA-DE) technique is implemented under the assumption of binary-input additive white Gaussian noise channels (BI-AWGNCs). In BICM systems, however, <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>-ary modulation schemes are generally used, and they can be regarded as to be a parallel transmission of <inline-formula> <tex-math notation="LaTeX">$\log _{2} M$ </tex-math></inline-formula> bits. Thus, <inline-formula> <tex-math notation="LaTeX">$\log _{2} M$ </tex-math></inline-formula> separate bit-level channels, which are not Gaussian equivalent, need to be considered. In order to extend the conventional RCA-DE technique to BICM systems, we first establish a model of protograph BICM ensembles. Two methods are developed based on the bit error rate (BER) and the BICM capacity in order to find a corresponding BI-AWGNC that models each of the bit-level channels. Using these methods, we implement the protograph RCA-DE technique for BICM systems and show that it achieves an accurate estimation. As a practical application of the proposed RCA-DE method, we design bit interleavers in order to achieve better BICM performance in the 3GPP New Radio (NR) LDPC coding system. Numerical results show that performance gain of up to 0.3 dB is consistently achieved over a wide range of parameter values.

An Intelligent Detection Based on Deep Learning for Multilevel Code Shifted Differential Chaos Shift Keying System With M-ary Modulation

Multilevel code shifted M-ary differential chaos shift keying (MCS-MDCSK) system provides higher data rate chaotic information transmission by applying multilevel code shifting aided M-ary modulation. However, the real-valued chaotic sequences induce interferences to signals while higher-order modulation shortens the Euclidean distance between adjacent symbols, thereby leading to performance degradation. To improve the bit-error rate (BER) performances, we propose an intelligent detector to achieve the joint demodulation and de-spreading at the receiver. In this design, we construct the recursive long short-term memory (LSTM) unit to extract features from the correlated chaotic modulated signals. Then we concatenate the LSTM unit with multiple full connection layers (FCLs) and compose the deep neural network (DNN) to recover the information. Owing to the serial concatenated LSTM-aided DNN, the intelligent detector can learn the joint chaotic modulation and spreading pattern, and achieve the joint demodulation and de-spreading. Consequently, larger performance gain can be attained and the reliability performances will be improved. Simulation results validate the proposed design. Moreover, for practical systems undergoing multiplicative fading, the intelligent MCS-MDCSK detector exhibits better BER performances than the benchmark systems.

Partially Information Coupled Bit-Interleaved Polar Coded Modulation

In this paper, we propose partially information coupled bit-interleaved polar coded modulation (PIC-BIPCM), which is a class of spatially coupled polar coding schemes designed for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{Q}$ </tex-math></inline-formula> -ary modulations. Specifically, we consider PIC-BIPCM schemes respectively constructed with three BIPCM schemes: direct BIPCM, punctured BIPCM, and multi-kernel BIPCM. We analyze the error performance of the proposed PIC-BIPCM over the binary erasure channel (BEC) via density evolution. With the analysis as a guideline, we jointly design the positions of coupled bits and the modulation bit-mapper by taking into account the partial polarization of finite length polar codes as well as the unequal error protection of high order modulations. Simulation results demonstrate significant performance improvement of the proposed PIC-BIPCM over the uncoupled BIPCM on both BEC and AWGN channels.

Moment-Generating Function Based Symbol Error Probability Comparison of M-ary Modulation Techniques in Fading Environment

This paper analyses and compare Symbol Error Probability (SEP) of M-ary modulation in different fading environment. Maximal ratio combining (MRC) technique with N branch receiver diversity is taken into consideration for the analysis. Expression for probability of symbol error for M-ary frequency shift keying/M-ary phase shift keying/M-ary differential phase shift key/and M-Level Quadrature Amplitude Modulation are obtained through moment-generating function (MGF) approach. Conventional integration process has probability of uncertainty and erroneousness because of composite mathematical calculations and infinite integration bounds. MGF method is used to avoid complex numerical computation for calculation of SEP. Comparison of SEP for diverse values of Rician factor “K”, Nakagami-M factor, modulation order “M” and diversity order “N” has been carried out.

Energy Efficient Parallel Concatenated Index Modulation and $M$-ary PSK Aided OFDM-DCSK Communications With QoS Consideration

In this paper, we propose a parallel concatenated index modulation and $M$ -ary phase shift keying (MPSK) to integrate with carrier interferometry (CI) codes into the orthogonal frequency division multiplex (OFDM) differential chaotic shift keying (DCSK) communication system. Our objective is to meet different quality of service (QoS) user demands while achieving higher energy efficiency and retaining reliable communications with low peak-to-average power ratio (PAPR). In our design, one input bit set is modulated by the index of the CI codes matrix whose rows are rotated circularly, another bit set is mapped to the MPSK symbols to realize the $M$ -ary modulation. Subsequently, the resultant MPSK symbols are modulated by reference chaotic sequences and spread by the information-bearing rotated CI codes matrix at the transmitter. After the OFDM modulations, the information bearing symbols are transmitted over multiple subcarriers. At the receiver, after the non-coherent chaotic correlation demodulation, the maximum likelihood detection method is firstly applied to attain the estimates of the index modulated bit set, which are then used to recover the phases of chaotic sequences for further evaluation of another MPSK modulated symbols. Since no additional energy is required while more bits can be transmitted via the $M$ -ary modulation and index modulation, the energy efficiency can be improved. In addition, thanks to the orthogonality of the CI codes matrix and the spreading in the frequency domain, the PAPR could be suppressed and reliability performances can be improved. Then theoretical analysis is conducted and simulation results validate the theoretical analysis. Moreover, the results demonstrate the superior bit error rate (BER) performances to benchmarks and flexible data rate could be provided for user terminals via different combinations of the index modulation and the $M$ -ary modulation.

The $\alpha$-$\mathcal {F}$ Composite Fading Distribution: Statistical Characterization and Applications

In this paper, the $\alpha$ - $\mathcal {F}$ composite fading distribution is introduced. It is worth highlighting that the $\alpha$ - $\mathcal {F}$ distribution offers more flexibility as it includes the composite $\mathcal {F}$ and the $\alpha$ - $\mu$ distributions, and their inclusive ones, as special cases. Moreover, unlike the composite $\mathcal {F}$ and the $\alpha$ - $\mu$ distributions, the $\alpha$ - $\mathcal {F}$ distribution jointly considers two important effects, namely the shadowing and the non-linearity of the propagation medium. Novel exact closed-form expressions for the probability density function (PDF), cumulative density function (CDF), moment-generating function, and higher order moments of the instantaneous signal-to-noise ratio are derived. The PDF and CDF are then employed to analyze the performance of a wireless communication system. To this end, we derive closed-form expressions for the outage probability, average channel capacity, and average bit error rate for binary coherent and non-coherent modulation schemes as well as for $M$ -ary modulation schemes. The analytical results are verified through numerical and Monte-Carlo simulations. The results demonstrate that the system performance improves as the non-linearity of the propagation medium and (or) the multipath parameter increase(s). Additionally, the system performance improves as the shadowing parameter increases. To demonstrate practical applications of the $\alpha$ - $\mathcal {F}$ distribution, we apply it to realistic channel measurements obtained for two different wireless emerging applications, namely underwater acoustic and device-to-device communications. The results demonstrate that the PDF of the $\alpha$ - $\mathcal {F}$ distribution provide a good fit to the measured data PDFs compared with other well-known distributions, namely $\mathcal {K}$ , $\kappa$ - $\mu$ shadowed, and $\alpha$ - $\mu$ distributions.

Convolutional Polar Coded Modulation

$2^m$-ary modulation creates $m$ bit channels which are neither independent nor identical, and this causes problems when applying polar coding because polar codes are designed for independent identical channels. Different from the existing multi-level coding (MLC) and bit-interleaved coded modulation (BICM) schemes, this paper provides a convolutional polar coded modulation (CPCM) method that preserves the low-complexity nature of BICM while offering improved spectral efficiency. Numerical results are given to show the good performance of the proposed method.

LLR Approximation for Fading Channels Using a Bayesian Approach

This letter investigates on the derivation of good log likelihood ratio (LLR) approximations under uncorrelated fading channels with partial statistical channel state information (CSI) at the receiver. While previous works focused mainly on solutions exploiting full statistical CSI over the normalized Rayleigh fading channel, in this letter, a Bayesian approach based on conjugate prior analysis is proposed to derive LLR values that only uses moments of order one and two associated with the random fading coefficients. The proposed approach is shown to be a more robust method compared to the best existing approximations, since it can be performed independently of the fading channel distribution and, in most cases, at a lower complexity. Results are validated for both binary and $M$ -ary modulations over different uncorrelated fading channels.

Dual-Hop Relaying Communications Over Fisher-Snedecor F-Fading Channels

In this paper, we present a comprehensive framework for the performance analysis of dual-hop relaying communications with variable gain amplify-and-forward (AF) relays and operating in the presence of both multipath fading and shadowing, modeled by the Fisher-Snedecor $\mathcal {F}$ -distribution. Novel closed-form expressions for the probability density function (PDF) and the cumulative distribution function (CDF) of the end-to-end signal-to-noise ratio (SNR) of the considered system subject to hardware impairments are first derived. Single-integral expressions for the numerical evaluation of the $n$ -th moment of the end-to-end SNR, the outage probability (OP), the ergodic capacity under different adaptive transmission schemes, the effective capacity and the average bit error rate (ABER) of $M$ -ary modulation schemes are further presented. The proposed analytical expressions are valid for most of the well-known fading distributions, provided that the moment generating function (MGF) of the inverse SNR of each hop is readily available. For the special case of ideal hardware, it is shown that the above performance metrics can be expressed in closed-form. It is worth pointing out that the proposed analysis is valid even when the destination node is equipped with multiple antennas and maximal ratio combining (MRC) is employed. The correctness of the proposed mathematical analysis is validated through extensive numerically evaluated results accompanied with Monte-Carlo simulations.

Multicarrier $M$ -Ary Orthogonal Chaotic Vector Shift Keying With Index Modulation for High Data Rate Transmission

A new multicarrier $M$ -ary orthogonal chaotic vector shift keying with index modulation (MC-MOCVSK-IM) is presented in this paper. In this design, information bits are conveyed not only by the multiple groups of $M$ -ary information bearing signals, but also by the specific indices of the selected reference signals which depend on the incoming mapped bits. Benefiting from the favorable features of multicarrier modulation, $M$ -ary modulation and index modulation, MC-MOCVSK-IM system is capable to offer higher energy efficiency and spectral efficiency at some expense of hardware complexity. In addition, the analytical bit error rate (BER) expressions of MC-MOCVSK-IM system are derived over additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels. The BER performance comparison between MC-MOCVSK-IM system and other non-coherent chaotic communication systems is carried out to highlight the superiority of MC-MOCVSK-IM system in terms of BER performance. Considering the dramatically increased demand for high-data-rate transmission and the harsh environment of future wireless communication, MC-MOCVSK-IM system shows strong robustness and offers competitive solutions for high-data-rate non-coherent chaotic communication systems.

Capacity and Error Probability Analysis of Neuro-Spike Communication Exploiting Temporal Modulation

In this paper, we consider a neuro-spike communication system between two neurons where nano-machines are used to enhance ability of neurons. Nano-machines can be employed for stimulation tasks when neurons have lost their ability to communicate. In the assumed system, information is conveyed via the time intervals between the input spikes train. For efficiency evaluation of temporal coding, we model the neuro-spike communication system by an additive Gamma noise channel. We present this model by considering different time distortion factors in the neuro-spike system. Then, we derive upper and lower bounds on the channel capacity. We analyze the channel capacity bounds as functions of the time intervals between the input spikes and the firing threshold of the target neuron. Moreover, we propose maximum likelihood and maximum a posteriori receivers and derive the resulting bit error probability when the system uses binary modulation. In addition, we obtain an upper bound for this error probability. Then, we extend this upper bound to the symbol error probability of the $T$ -ary modulations. Simulation results show that this upper bound is tight. The derived results show that temporal coding has a higher efficiency than spike rate coding in terms of achievable data rate.

Low-Resolution Quantization in Phase Modulated Systems: Optimum Detectors and Error Rate Analysis

This paper studies optimum detectors and error rate analysis for wireless systems with low-resolution quantizers in the presence of fading and noise. A universal lower bound on the average symbol error probability ( $\mathsf {SEP}$ ), correct for all $M$ -ary modulation schemes, is obtained when the number of quantization bits is not enough to resolve $M$ signal points. In the special case of $M$ -ary phase shift keying ( $M$ -PSK), the maximum likelihood detector is derived. Utilizing the structure of the derived detector, a general average $\mathsf {SEP}$ expression for $M$ -PSK modulation with $n$ -bit quantization is obtained when the wireless channel is subject to fading with a circularly-symmetric distribution. For the Nakagami- $m$ fading, it is shown that a transceiver architecture with $n$ -bit quantization is asymptotically optimum in terms of communication reliability if $n \geq \log _{2}M +1$ . That is, the decay exponent for the average $\mathsf {SEP}$ is the same and equal to $m$ with infinite-bit and $n$ -bit quantizers for $n\geq \log _{2}M+1$ . On the other hand, it is only equal to $\frac {1}2$ and 0 for $n = \log _{2}M$ and $n , respectively. An extensive simulation study is performed to illustrate the accuracy of the derived results, energy efficiency gains obtained by means of low-resolution quantizers, performance comparison of phase modulated systems with independent in-phase and quadrature channel quantization and robustness of the derived results under channel estimation errors.

Cooperative Time Successive SSK-M-ary Modulation for Decode-and-Forward Relay Systems

Space shift keying (SSK) is a single radio frequency (RF) chain multiple-input multiple-output (MIMO) scheme that uses the index of transmit antennas for information transmission. Time successive SSK- $ M$ -ary modulation (TSSM) and multi RF chain TSSM (MRF-TSSM) are recent MIMO techniques that achieve second order transmit diversity. We propose two cooperative relaying systems to attain distributed diversity in addition to transmit diversity of TSSM and MRF-TSSM. Cooperative-TSSM-1 (Coop-TSSM-1) uses multibranch relaying where TSSM is used in orthogonal time slots during the cooperative phase. Coop-TSSM-2 maps symbols to lower order constellations at multiple relays for simultaneous transmission of information using MRF-TSSM. We consider Decode-and-forward (DF) relaying where relays that correctly detect symbols forward it. We analyze the average number of relays that participate in cooperation, the end-to-end performance using a tight upper bound on the bit error rate (BER) and the asymptotic BER expressions to analyze diversity orders of both cooperative systems. We validate all analyzes using simulation results. From the analysis and results we show that Coop-TSSM-1 achieves better diversity order compared to Coop-TSSM-2 at the cost of higher number of time slots for completing the cooperative phase. Further in Coop-TSSM-2, results indicate that different constellation mappings used in MRF-TSSM during cooperative phase impact the BER performance. By applying spatial modulation based transmit diversity and $M$ -ary Modulation systems in the cooperative setups of Coop-TSSM schemes, performance comparison is given which highlights the significance of Coop-TSSM schemes.

Polarity-Header Optical OFDM for Visible Light Communication Systems

Orthogonal frequency division multiplexing (OFDM) is a candidate modulation technique to achieve high-speed data transmission in visible light communication systems that provide both illumination and downlink data transmission. This paper proposes a method called polarity-header optical OFDM (PHO-OFDM) specially designed to account for the nonlinear response of the LED transmitters. To make the transmitted signal positive, as required for intensity modulation and direct detection systems, a signal header containing the sign information of the bipolar OFDM signal is transmitted followed by the amplitude of the signal. The binary sign information can be encoded and transmitted via a few samples using $M$ -ary pulse-amplitude modulation. The amplitude of the OFDM signal that is larger than the maximum LED power is sent in a subsequent frame to reduce the nonlinear distortion due to peak-power clipping. Furthermore, illumination requirements are taken into account, and their effects on the system performance are discussed. This paper also considers the overhead cost of adding a cyclic prefix to minimize intersymbol interference in dispersive channels. Compared with state-of-the-art optical OFDM techniques, the proposed PHO-OFDM achieves a better BER performance and higher data throughput, and provides a larger illumination flexibility.

Coded Modulation for 100G Coherent EPON

Geometrically shaped (GS) 8-, 16, and 32- ary modulation formats are investigated for use in coherent passive optical networks. The modulation formats are designed to improve receiver sensitivity when paired with a binary, soft-decision forward error correction code (SD-FEC), such as a low density parity check (LDPC). Herein we consider the LDPC code specified in the draft 50G EPON standard, and show how this type of code can be particularly advantageous in a coherent transmission system. A receiver sensitivity of $-$ 26.7 dBm is achieved at a post-FEC bit error rate below 3.8 $\times 10^{-6}$ for a polarization-scrambled 32- ary GS modulation format at 25 GBd, received using a single-polarization, phase-diverse coherent receiver. This yielded a bit rate of 100 Gbit/s, net of coding and pilot overhead. This modulation format was shown to perform equally well in transmission, with no observed dispersion penalty after 80 km standard single mode fiber. Finally, this modulation format was received, at a reduced data rate of 50 Gbit/s, using a heterodyne coherent receiver based on a single balanced photodiode. The receiver sensitivity for this simplified receiver configuration was $-$ 28.5 dBm, yielding a power budget of 34.2 dB.

A Multilevel Code Shifted Differential Chaos Shift Keying System With $M$ -ary Modulation

In this brief, a multilevel code shifted differential chaos shift keying system with ${M}$ -ary modulation (MCS-MDCSK) is proposed, which is a hybrid of the ${M}$ -ary modulation and multilevel code shifted differential chaos shift keying. In the proposed system, since the reference signal and a number of different information bearing signals which can carry ${M}$ -ary constellation symbols are transmitted in the same slot, the spectral efficiency of MCS-MDCSK system is enhanced significantly. By combining with ${M}$ -ary modulation, MCS-MDCSK system makes great progress in pursuit of higher data rate. Moreover, we derive the analytical bit-error-rate (BER) for the proposed system over the additive white Gaussian noise and multipath Rayleigh fading channels, and we verify our theoretical derivations by simulations. Finally, the BER performance of the proposed system is compared with other non-coherent chaotic modulation systems and MCS-MDCSK system is found to be superior and competitive.

Symbol-Level Stochastic Chase Decoding of Reed-Solomon and BCH Codes

This paper proposes the symbol-level-stochastic Chase decoding algorithm (S-SCA) for the Reed–Solomon (RS) and Bose–Chaudhuri–Hocquenghem (BCH) codes, which is a soft-input soft-output (SISO) decoder. By the efficient usage of void space between constellation points for $q$ -ary modulations and using soft information at the input of the decoder, the S-SCA is capable of outperforming conventional symbol-level-Chase algorithm (S-CA) with a less computational cost. Since the S-SCA starts with the randomized generation of likely test-vectors, it reduces the complexity to polynomial order and also it does not need to find the least reliable symbols to generate test-vectors. The symbol-level-search bitwise-transmission stochastic Chase algorithm (SSBT-SCA) is also introduced for RS codes over binary phase shift keying (BPSK) transmission that is capable of generating symbol-level test-vectors with reduced complexity and to better mitigate burst errors. Simulation results show that by increasing the number of test-vectors, the performance of the algorithm can asymptotically approach the maximum-likelihood (ML) bound. The S-SCA provides near 2 dB decoding gain in comparison with S-CA for a (31, 25) RS code using 32-QAM, when 1024 test-vectors are used. Furthermore, the algorithm provides near 3 dB additional gain with 1024 test-vectors compared with S-CA that uses 65536 iterations when a (255, 239) RS code is used in an additive white Gaussian noise (AWGN) channel. For the Rayleigh fading channel and the same code, the algorithm provides more than 5 dB gain. Furthermore, for (63, 57) BCH codes and 8-PSK modulation, the proposed algorithm provides 3 dB gain with less complexity.

An $M$ -Ary Orthogonal Multilevel Differential Chaos Shift Keying System With Code Index Modulation

In this paper, an $M$ -ary orthogonal multilevel differential chaos shift keying system with code index modulation (CIM-OM-MDCSK) is proposed. In the proposed system, the multiple information bearing signals are modulated by the selected Walsh codes with specific indices and the $M$ -ary information signals which are composed of modulated bits, chaotic signals, and their Hilbert transform. Since the reference signal along with the information bearing signals are overlapping in time domain and orthogonal in code domain by using Walsh code sequences, the spectral efficiency of the CIM-OM-MDCSK system is improved largely. By combining the $M$ -ary modulation, orthogonal multilevel modulation, and code index modulation, the proposed CIM-OM-MDCSK system can achieve high data rate and superior bit error rate (BER) performance compared to its rivals. Moreover, we derive the BER expressions of the proposed system over additive white Gaussian noise and multipath Rayleigh fading channels. Finally, we make a performance comparison between the proposed system and other state-of-the-art non-coherent chaotic communication systems. The results confirm the competitive benefits of the proposed system.

Energy-Reliability Aware Link Optimization for Battery-Powered IoT Devices With Nonideal Power Amplifiers

In this paper, we study cross-layer optimization of low-power wireless links for reliability-aware applications while considering both the constraints and the nonideal characteristics of the hardware in Internet-of-Things (IoT) devices. Specifically, we define an energy consumption (EC) model that captures the energy cost—of transceiver circuitry, power amplifier (PA), packet error statistics, packet overhead, etc.—in delivering a useful data bit. We derive the EC models for an ideal and two realistic nonlinear PA models. To incorporate packet error statistics, we develop a simple, in the form of elementary functions, and accurate closed-form packet error rate approximation in Rayleigh block-fading. Using the EC models, we derive energy-optimal yet reliability and hardware compliant conditions for limiting unconstrained optimal signal-to-noise ratio (SNR), and payload size. Together with these conditions, we develop a semi-analytic algorithm for resource-constrained IoT devices to jointly optimize parameters on physical (modulation size, SNR) and medium access control (payload size and the number of retransmissions) layers in relation to link distance. Our results show that despite reliability constraints, the common notion—higher-order ${M}$ -ary modulations are energy optimal for short-range communication—prevails, and can provide up to 180% lifetime extension as compared to often used OQPSK modulation in IoT devices. However, the reliability constraints reduce both their range and the energy efficiency, while nonideal traditional PA reduces the range further by 50% and diminishes the energy gains unless a better PA is used.

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.