Modulation Alphabet Research Articles

Optimized Multi-Primary Modulation for Visible Light Communication

Multi-primary modulation scheme has the potential to provide robust visible light communication links and mitigate any color fluctuations by providing identical chromaticity modulation alphabets. This work describes constellation optimization technique for multi-primary modulation (MPM), which shows that using different power levels for the primary lights can lead to obtain the same color and, furthermore, enhance the Euclidean distances between data symbols in the multi-dimensional color space. The bit error rate performances of the optimized MPM and the original non-optimized MPM schemes are evaluated considering indoor optical wireless channel models with additive white Gaussian noise. The results show that the optimized MPM provides better spectral efficiency and outperforms the original non-optimized MPM scheme by achieving up to 3.5 dB Signal-to-noise ratio gain for the same spectral efficiency and, therefore, opens doors for implementation of robust visible light communication links exploiting multi-color light sources.

Demonstration of a quantum advantage by a joint detection receiver for optical communication using quantum belief propagation on a trapped-ion device

Demonstrations of quantum advantage have largely focused on computational speedups and on quantum simulation of many-body physics, limited by fidelity and capability of current devices. Discriminating laser-pulse-modulated classical-communication codewords at the minimum allowable probability of error using universal-quantum processing presents a promising parallel direction, one that is of both fundamental importance in quantum state discrimination, as well as of technological relevance in deep-space laser communications. Here we present an experimental realization of a quantum joint detection receiver for binary phase shift keying modulated codewords of a 3-bit linear tree code using a recently-proposed quantum algorithm: belief propagation with quantum messages. The receiver, translated to a quantum circuit, was experimentally implemented on a trapped-ion device -- the recently released Honeywell LT-1.0 system using ${}^{171}Yb+ $ ions, which possesses all-to-all connectivity and mid-circuit measurement capabilities that are essential to this demonstration. We conclusively realize a previously postulated but hitherto not-demonstrated joint quantum detection scheme, and provide an experimental framework that surpasses the quantum limit on the minimum average decoding error probability associated with pulse-by-pulse detection in the low mean photon number limit. The full joint-detection scheme bridges across photonic and trapped-ion based quantum information science, mapping the photonic coherent states of the modulation alphabet onto inner product-preserving states of single-ion qubits. Looking ahead, our work opens new avenues in hybrid realizations of quantum-enhanced receivers with applications in astronomy and emerging space-based platforms.

A Message Passing-Assisted Iterative Noise Cancellation Method for Clipped OTFS-BFDM Systems.

Compared with orthogonal frequency division multiplexing (OFDM) systems, orthogonal time frequency space systems based on bi-orthogonal frequency division multiplexing (OTFS-BFDM) have lower out-of-band emission (OOBE) and better robustness to high-mobility scenarios, but suffer from a higher peak-to-average ratio (PAPR) in large data packets. In this paper, one-iteration clipping and filtering (OCF) is adopted to reduce the PAPR of OTFS-BFDM signals. However, the extra noise introduced by the clipping process, i.e., clipping noise, will distort the desired signal and increase the bit error rate (BER). We propose a message passing (MP)-assisted iterative cancellation (MP-AIC) method to cancel the clipping noise based on the traditional MP decoding at the receiver, which incorporates with the (OCF) at the transmitter to keep the sparsity of the effective channel matrix. The main idea of MP-AIC is to extract the residual signal fed to the MP detector by iteratively constructing reference clipping noise at the receiver. During each iteration, the variance of residual signal and channel noise are taken as input parameters of MP decoding to improve the BER. Moreover, the convergence probability of the modulation alphabet after MP decoding in the current iteration is used as the initial probability of MP decoding in the next iteration to accelerate the convergence rate of MP decoding. Simulation results show that the proposed MP-AIC method significantly improves MP-decoding accuracy while accelerating the BER convergence in the clipped OTFS-BFDM system. In the clipped OTFS-BFDM system with rectangular pulse shaping, the BER of MP-AIC with two iterations can be reduced by 72% more than that without clipping noise cancellation.

Jointly increasing modulation cardinality and controlling beam diameter in LG-OAM free-space optical communication using convolutional neural network

Modulation alphabets using sets of simple superposed and multiplexed superposed orbital angular momentum in a Laguerre–Gauss laser beam over free-space turbulence channel are tested for shift keying demodulation using a convolutional neural network. Simulation results show similar performance in both cases. Moreover, the results suggest a criterion of alphabet formation and bit mapping, leading to a lower topological charge strategy to jointly increase alphabet cardinality and control beam diameter for transmission.

Enhanced Propriety-Based I/Q Imbalance Compensation in LTE/NR Receivers

In mobile communications, radio-frequency receivers are mainly implemented using the direct-conversion architecture. A critical aspect in the design of this receiver type is the matching between the analog in-phase (I) and quadrature (Q) paths. Any gain or phase imbalance generates image components in the baseband, which distort the desired receive signal. Many digital solutions for online compensation of this effect have been proposed in the literature. A common statistical measure that is used by non-data-aided algorithms is the so-called propriety of the receive signal. This concept is suitable for most communication signals, but fails, for instance, in case of the real-valued binary phase-shift keying (BPSK) modulation. In this work, we provide a thorough statistical analysis of Long-Term Evolution (LTE) and New Radio (NR) up- and downlink sequences, which allows us to extend a propriety-based estimator to improper alphabets. This algorithm employs the method of moments. We show that the observed signal statistics can be altered by omitting a predefined set of samples. In a second step, we prove that this concept substantially enhances the imbalance compensation also for proper quadrature amplitude modulation (QAM) alphabets. All theoretical results are supported by simulations to evaluate the actual performance gains in practical scenarios. Depending on the resource block allocation and the noise levels, we obtain double-digit improvements of the image rejection ratio, while reducing the computational effort by about 6.6% compared to the standard moment-based I/Q imbalance estimator.

Two approaches to the extension problem for arbitrary weights over finite module alphabets

The extension problem underlies notions of code equivalence. Two approaches to the extension problem are described. One is a matrix approach that reduces the general problem for weights to one for symmetrized weight compositions. The other is a monoid algebra approach that reframes the extension problem in terms of modules over the monoid algebra determined by the multiplicative monoid of a finite ring.

Space-Frequency Increment Index Modulation Approach for Fifth Generation and Beyond Wireless Communication Systems

Unlike the classical modulation, for instance, quadrature amplitude modulation (QAM) and others, where bits are transmitted via symbols particularly from modulation alphabets, in index modulation (IM), extra information bits can be conveyed via the indices of a particular transmit entities during the transmission process. Transmit antenna elements are example of transmit entities in multi-antenna systems which can be used to convey extra information bits. Recently, frequency diverse array (FDA), as a new type of transmit antenna array which differs from the traditional phased-array has been proposed in the literature. In FDA, the element indices has small frequency increment across them. In this paper, space-frequency increment IM is proposed. The proposed scheme utilizes the indices of the activated transmit FDA antennas and their respective corresponding frequency increments $\Delta f$ to convey additional information bits. The proposed scheme is inspired by the principle of quadrature spatial modulation (QSM) and no additional antenna activation is required. Compared with spatial modulation (SM) and QSM, it is shown that, the proposed scheme achieved higher spectral efficiency. Further, the average bit error rate (ABER), secrecy sum rate (SSR) and system capacity are derived and evaluated. Moreover, a low-complexity decoding algorithm is examined. Finally, via numerical results, the proposed scheme shows to be better than the comparative alternatives (QSM/SM), and may offer promising properties in various contexts.

On Channel Codes for Short Underwater Messages

Acoustic underwater communication is a challenging task. For a reliable transmission, not only good channel estimation and equalization, but also strong error correcting codes are needed. In this paper, we present the results of the coding competition “Wanted: Best channel codes for short underwater messages” as well as our own findings on the influence of the modulation alphabet size in the example of non-binary polar codes. Furthermore, the proposals of the competition are compared to other commonly used channel codes.

Low Complexity Iterative Receiver With Lossless Information Transfer for Non-Binary LDPC Coded PDMA System

In this work, we first proposed a non-binary low-density parity-check (NB-LDPC) coded pattern division multiple access (PDMA) scheme with the order of the Galois field equal to the size of modulation alphabet which can avoid the symbol-to-bit or bit-to-symbol probability conversion between the detector and decoder as in binary coded system. Specifically, we considered a 4-ary LDPC over Galois field (GF(4)-LDPC) coded PDMA system with quadrature phase shift keying (QPSK) modulation. At the receiver side, Gaussian approximation based message passing (GAMP) detection algorithm instead of standard message passing (SMP) is employed to achieve a tradeoff between the computational complexity and the detection performance. When iterative detection and decoding (IDD) algorithm is used, the symbol-wise extrinsic information of the detector and GF(4)-LDPC decoder can be exchanged without information loss. At last, we proposed a symbol-wise EXIT (S-EXIT) based iterative optimization algorithm to improve the system performance. Both the S-EXIT chart based analysis and numerical simulation results show the validity of the proposed scheme above.

Nonlinearity Mitigation in WDM Systems: Models, Strategies, and Achievable Rates

After reviewing models and mitigation strategies for interchannel nonlinear interference (NLI), we focus on the frequency-resolved logarithmic perturbation model to study the coherence properties of NLI. Based on this study, we devise an NLI mitigation strategy which exploits the synergic effect of phase and polarization noise compensation (PPN) and subcarrier multiplexing with symbol-rate optimization. This synergy persists even for high-order modulation alphabets and Gaussian symbols. A particle method for the computation of the resulting achievable information rate and spectral efficiency (SE) is presented and employed to lower-bound the channel capacity. The dependence of the SE on the link length, amplifier spacing, and presence or absence of inline dispersion compensation is studied. Single-polarization and dual-polarization scenarios with either independent or joint processing of the two polarizations are considered. Numerical results show that, in links with ideal distributed amplification, an SE gain of about 1 bit/s/Hz/polarization can be obtained (or, in alternative, the system reach can be doubled at a given SE) with respect to single-carrier systems without PPN mitigation. The gain is lower with lumped amplification, increases with the number of spans, decreases with the span length, and is further reduced by in-line dispersion compensation. For instance, considering a dispersion-unmanaged link with lumped amplification and an amplifier spacing of 60 km, the SE after 80 spans can be be increased from 4.5 to 4.8 bit/s/Hz/polarization, or the reach raised up to 100 spans (+25%) for a fixed SE.

Capacity and Achievable Rate Regions for Linear Network Coding Over Ring Alphabets

The rate of a network code is the ratio of the block size of the network’s messages to that of its edge codewords. We compare the linear capacities and achievable rate regions of networks using finite field alphabets to the more general cases of arbitrary ring and module alphabets. For non-commutative rings, two-sided linearity is allowed. Specifically, we prove the following for directed acyclic networks. First, the linear rate region and the linear capacity of any network over a finite field depend only on the characteristic of the field. Furthermore, any two fields with different characteristics yield different linear capacities for at least one network. Second, whenever the characteristic of a given finite field divides the size of a given finite ring, each network’s linear rate region over the ring is contained in its linear rate region over the field. Thus, any network’s linear capacity over a field is at least its linear capacity over any other ring of the same size. An analogous result also holds for linear network codes over module alphabets. Third, whenever the characteristic of a given finite field does not divide the size of a given finite ring, there is some network whose linear capacity over the ring is strictly greater than its linear capacity over the field. Thus, for any finite field, there always exist rings over which some networks have higher linear capacities than over the field.

Spectrally Augmented Hartley Transform Precoded Asymmetrically Clipped Optical OFDM for VLC

In this letter, layered discrete Hartley transform (DHT)-spread asymmetrically clipped optical-orthogonal frequency division multiplexing (LDHTS-ACO-OFDM) is presented; it uses DHT for multiplexing/demultiplexing and pulse-amplitude modulation (PAM) alphabets. LDHTS-ACO-OFDM yields several concrete enhancements over classical layered asymmetrically clipped O-OFDM (LACO-OFDM), such as low peak-to-average power ratio (PAPR), lower computational complexity, improved bit error rate (BER), and lower optical power penalty in a dispersive channel. Besides, LDHTS-ACO-OFDM augments the spectral efficiency relative to DHTS-ACO-OFDM with each addition of layer and ousts the inefficient bandwidth utilization limitation of DHTS-ACO-OFDM.

Nonlinear frequency division multiplexing with b-modulation: shifting the energy barrier.

The recently proposed b-modulation method for nonlinear Fourier transform-based fiber-optic transmission offers explicit control over the duration of the generated pulses and therewith solves a longstanding practical problem. The currently used b-modulation however suffers from a fundamental energy barrier. There is a limit to the energy of the pulses, in normalized units, that can be generated. In this paper, we discuss how the energy barrier can be shifted by proper design of the carrier waveform and the modulation alphabet. In an experiment, it is found that the improved b-modulator achieves both a higher Q-factor and a further reach than a comparable conventional b-modulator. Furthermore, it performs significantly better than conventional approaches that modulate the reflection coefficient.

Contender waveforms for Low-Power Wide-Area networks in a scheduled 4G OFDM framework

When designing new solutions for Low-Power Wide-Area (LPWA) networks, coexistence and integration into existing 4G frameworks should be considered to ease the deployment procedure and reduce costs. In a previous work, Turbo-FSK was proposed as a potential physical layer for LPWA networks. With its constant envelope and high energy efficiency, the scheme is a serious contender for this type of networks. We propose to study the system in the Orthogonal Frequency Division Multiplexing (OFDM) framework, currently used by existing cellular networks and also considered for the recently standardized Narrow-Band IoT (NB-IoT). Several extensions of the Turbo-FSK scheme are presented. A hybrid modulation alphabet, combining orthogonal with linear modulations, is introduced, and the substitution of Frequency Shift Keying (FSK) modulation for another orthogonal modulation based on Zadoff-Chu (ZC) sequences is considered. Simulations are run under various conditions including Rayleigh fading channel with mobility, demonstrating that the Turbo-FSK scheme is able to achieve performance close to the Turbo Coded Orthogonal Frequency Division Multiplexing (TC-OFDM) when a low rate is considered. When considering hybridation of the alphabet, limitations appear for higher data rate, which can be overcome by changing the orthogonal alphabet. The study of the variation of the envelope of the compared solutions emphasizes the crucial trade-off between performance and efficiency of the power amplifier (PA), a main concern for low-power applications. While using the proposed solutions, we demonstrate that energy consumption can be reduced by up to a factor of 2.5.

A MAP-Based Layered Detection Algorithm and Outage Analysis Over MIMO Channels

Efficient symbol detection algorithms carry critical importance for achieving the spatial multiplexing gains promised by multi-input multi-output (MIMO) systems. In this paper, we consider a maximum a posteriori probability (MAP)-based symbol detection algorithm, called M-BLAST, over uncoded quasi-static MIMO channels. Relying on the successive interference cancellation (SIC) receiver, the M-BLAST algorithm offers a superior error performance over its predecessor V-BLAST with a signal-to-noise ratio (SNR) gain of as large as 2 dB under various settings of recent interest. Performance analysis of the M-BLAST algorithm is very complicated since the proposed detection order depends on the decision errors dynamically, which makes an already complex analysis of the conventional ordered SIC receivers even more difficult. To this end, a rigorous analytical framework is proposed to analyze the outage behavior of the M-BLAST algorithm over binary complex alphabets and two transmitting antennas, which has a potential to be generalized to multiple transmitting antennas and multidimensional constellation sets. The numerical results show a very good match between the analytical and simulation data under various SNR values and modulation alphabets.

End-to-End Error-Correcting Codes on Networks With Worst-Case Bit Errors

In highly dynamic wireless networks, communications face several challenges. In the first place, noise levels between nodes might be difficult to predict a priori . Besides, a Byzantine attacker hidden in the network, with knowledge of the network topology and observation of all transmissions, can choose arbitrary locations to inject corrupted packets. Considering that transmissions are usually in bits and hardware in wireless networks usually use modulation schemes with the size of modulation alphabet being powers of two, e.g. BPSK, QPSK, 16-QAM, 64-QAM, and so on, to address the above problem, we study coding for networks experiencing worst case bit errors, and with network codes over binary extension fields. We demonstrate that in this setup prior network error-correcting schemes can be arbitrarily far from achieving the optimal network throughput. A new transform metric for errors under the considered model is proposed. Using this metric, we replicate many of the classical results from coding theory. Specifically, new Hamming-type , Plotkin-type , and Elias-Bassalygo-type upper bounds on the network capacity are derived. A commensurate lower bound is shown based on Gilbert–Varshamov (GV)-type codes for error-correction. The GV codes used to attain the lower bound can be non-coherent, that is, they require neither prior knowledge of the network topology nor network coding kernels. We also propose a computationally efficient concatenation scheme. The rate achieved by our concatenated codes is characterized by a Zyablov-type lower bound. We provide a generalized minimum-distance decoding algorithm which decodes up to half the minimum distance of the concatenated codes. The end-to-end nature of our design enables our codes to be overlaid on the classical distributed random linear network codes. The other advantage of the end-to-end strategy over the link-by-link error-correction is that it reduces the computational cost at the internal nodes for performing error-correction.

A Low-Complexity Maximum-Likelihood Detector for Differential Media-Based Modulation

Media-based modulation (MBM) uses radio frequency mirrors at the transmit antenna in order to create different channel fade realizations based on their ON/OFF status. These complex fade realizations constitute the channel modulation alphabet. This channel modulation alphabet has to be estimated a priori at the receiver for detection. In this letter, we present a differential MBM (DMBM) scheme which does not require estimation of channel modulation alphabet at the receiver for detection. Consecutive MBM blocks are differentially encoded. We propose a low-complexity maximum-likelihood detection algorithm for DMBM. Simulation results show that the DMBM has only about 2–4 dB performance loss compared with MBM with perfect knowledge of the channel alphabet.

Improved sparse multiuser detection based on modulation-alphabets exploitation

In this paper, we focus on sporadic random-access communications and consider compressed-sensing (CS) techniques to perform the multiuser detection (MUD). Since all the users do not necessarily transmit information, MUD consists in detecting the transmitting users (activity detection) and their corresponding transmitted data (data detection). The main results presented here rely on the exploitation of the user signal alphabet knowledge within the detection step. To this aim, several modifications of the group orthogonal matching pursuit (GOMP) algorithm were proposed, differing in the way the modulation alphabet knowledge is considered within the detection stage. These modifications can be extended to any greedy-based CS-MUD. To overcome the error floor occurring at high SNR with a higher number of active users, we then propose an iterative ℓ1 minimization-based MUD algorithm that alternates between activity and data detection. Compared to the existing GOMP-based CS-MUD, the proposed modified GOMP algorithms exhibit a significant gain with almost the same complexity. The iterative ℓ1 minimization-based MUD algorithm has a higher complexity but outperforms all the others without any observed error-floor.

Capacity of optical communications over a lossy bosonic channel with a receiver employing the most general coherent electro-optic feedback control

We study the problem of designing optical receivers to discriminate between multiple coherent states using coherent processing receivers---i.e., one that uses arbitrary coherent feedback control and quantum-noise-limited direct detection---which was shown by Dolinar to achieve the minimum error probability in discriminating any two coherent states. We first derive and re-interpret Dolinar's binary-hypothesis minimum-probability-of-error receiver as the one that optimizes the information efficiency at each time instant, based on recursive Bayesian updates within the receiver. Using this viewpoint, we propose a natural generalization of Dolinar's receiver design to discriminate $M$ coherent states each of which could now be a codeword, i.e., a sequence of $N$ coherent states each drawn from a modulation alphabet. We analyze the channel capacity of the pure-loss optical channel with a general coherent-processing receiver in the low-photon number regime and compare it with the capacity achievable with direct detection and the Holevo limit (achieving the latter would require a quantum joint-detection receiver). We show compelling evidence that despite the optimal performance of Dolinar's receiver for the binary coherent-state hypothesis test (either in error probability or mutual information), the asymptotic communication rate achievable by such a coherent-processing receiver is only as good as direct detection. This suggests that in the infinitely-long codeword limit, all potential benefits of coherent processing at the receiver can be obtained by designing a good code and direct detection, with no feedback within the receiver.

On Media-Based Modulation Using RF Mirrors

Media-based modulation (MBM) is a recently proposed modulation scheme which uses radio frequency (RF) mirrors at the transmit antenna(s) in order to create different channel fade realizations based on their ON/OFF status. These complex fade realizations constitute the modulation alphabet. MBM has the advantage of increased spectral efficiency and performance. In this paper, we investigate the performance of some physical layer techniques when applied to MBM. Particularly, we study the performance of $i)$ MBM with generalized spatial modulation (GSM), $ii)$ MBM with mirror activation pattern (MAP) selection based on an Euclidean distance (ED) based metric, and $iii)$ MBM with feedback based phase compensation and constellation rotation. Our results show that, for the same spectral efficiency, GSM-MBM can achieve better performance compared to MIMO-MBM. Also, it is found that MBM with ED-based MAP selection results in improved bit error performance, and that phase compensation and MBM constellation rotation increases the ED between the MBM constellation points and improves the performance significantly. We also analyze the diversity orders achieved by the ED-based MAP selection scheme and the phase compensation and constellation rotation (PC-CR) scheme. The diversity orders predicted by the analysis are validated through simulations.