Constellation Shaping Research Articles

Adaptive Turbo Equalization for Probabilistic Constellation Shaped Underwater Acoustic Communications

To increase the spectral efficiency of the underwater acoustic (UWA) communication system, the high order quadrature amplitude modulations (QAM) are deployed. Recently, the probabilistic constellation shaping (PCS) has been a novel technology to improve the spectral efficiency. The PCS with high-order QAM is introduced into the UWA communication system. A turbo equalization scheme with PCS was proposed to cancel the severe inter-symbol interference (ISI). The non-zero a priori information is available for the equalizer and decoder before turbo iteration. A priori hard decision approach is proposed to improve the detection performance and the equalizer convergence speed. At the initial turbo iteration, the relation between the a priori information and the probability of the amplitude of 16QAM symbols in one dimension is given. The simulation results verified the efficiency of the proposed method, and compared to the uniform distribution (UD), the PCS-16QAM had a significant improvement of the bit error rate (BER) performance with PCS-adaptive turbo equalization (PCS-ATEQ). The UWA communication experiments further verified the performance superiority of the proposed method.

2048-QAM transmission at 15 GBd over 100 km using geometric constellation shaping.

We experimentally investigated a pilot-aided digital signal processing (DSP) chain in combination with high-order geometric constellation shaping to increase the achievable information rates (AIRs) in standard intradyne coherent transmission systems. We show that the AIR of our system at 15 GBd was maximised using geometrically-shaped (GS) 2048 quadrature amplitude modulation (QAM), reaching 18.0 b/4D-symbol in back-to-back transmission and 16.9 b/4D-symbol after transmission through 100 km of a single-mode fibre after subtracting the pilot overhead (OH). This represents the highest-order GS format demonstrated to date, supporting the highest AIR of any standard intradyne system using conventional optics and 8-bit electronics. Detailed characterisation of the DSP, transceiver performance, and transmission modelling has also been carried out to provide insight into sources of impairments and directions for further improvement.

Does Probabilistic Constellation Shaping Benefit IM-DD Systems Without Optical Amplifiers?

Probabilistic constellation shaping (PCS) has been widely applied to amplified coherent optical transmissions owing to its shaping gain over the uniform signaling and fine-granularity rate adaptation to the underlying fiber channel condition. These merits stimulate the study of PCS for short-reach applications dominated by intensity modulation (IM) - direct detection (DD) systems. As commercial IM-DD systems typically do not employ optical amplification to save the cost and power consumption, they are no longer subject to an average power constraint (APC) but a peak power constraint (PPC), which poses unique challenges to take full advantages of PCS. This paper provides a comprehensive investigation of PCS in IM-DD systems without optical amplifiers. In particular, we reveal when the transmitter enhances the peak-to-average power ratio of the signal, a PPC system can be partially or even fully converted to an APC system in which the classical PCS offers its merits. The findings are verified through an IM-DD experiment using 4- and 8-ary pulse amplitude modulations.

Optimizing Probabilistic Constellation Shaping for Amplifier-Less Coherent Optical Links

Coherent optical systems for short-reach links have seen a boost in their popularity with the standardization of 400ZR. These systems need to be cost and power-efficient, while coping with the ever increase in traffic demand. The use of probabilistic constellation shaping (PCS) can help meet these demands, since it reduces the gap to the channel capacity. However, studies concerning PCS typically include optical amplification; therefore, its gain in amplifier-less systems has been somewhat uncertain. In this work, we focus on an amplifier-less coherent optical link employing PCS, reducing both power consumption and system complexity due to the removal of the amplifier. We employ PCS for different modulation orders and bit rates, while optimizing several key parameters such as the FEC coding overhead, modulation depth and clipping. With this comprehensive study, we demonstrate by system simulation and experimental validation that PCS is beneficial even for amplifier-less systems, since it introduces residual gains while allowing higher flexibility in defining the net bit rate in a system with fixed baud rate.

Fast‐adaptive weighted constellation designs based on hybrid constellation shaping for long‐haul optical fiber communication systems

AbstractA novel fast‐adaptive weighted hybrid‐shaped M‐ary quadrature amplitude modulation (HS‐MQAM) format is proposed in this paper. By introducing a fast‐adaptive weighting factor array related to geometric shaping and probabilistic shaping, the non‐linear impairment is mitigated and the bit error rate (BER) and mutual information (MI) performances are further improved. The simulation results show that the proposed HS‐61QAM outperforms both geometric‐shaped 61 quadrature amplitude modulation (GS‐61QAM) and regular 64QAM, and has more obvious advantages in the long‐haul optical transmission system. For a 120‐Gb/s optical communication system over 10 × 75 km fiber transmission link, compared with GS‐61QAM and regular 64QAM, the proposed approach can achieve about 4.2 and 8 dB OSNR gain at the BER of 10−2, and 0.21 and 0.55 bits/symbol MI gain at the OSNR of 22 dB.

Trellis Shaping for Fiber Nonlinearity Mitigation in Coherent Optical OFDM Systems

In this article, trellis shaping technique is numerically and experimentally investigated to improve the performance of optical orthogonal frequency division multiplexing (OFDM) signal. Different from other constellation shaping techniques, trellis shaping can be designed to reduce the correlation value of OFDM data sequence and average power simultaneously in one OFDM symbol. It means that optical OFDM signals generated by trellis shaping can improve the performance under both linear and nonlinear channels. For comparison with trellis shaping technique, we also consider optimal Maxwell–Boltzmann (MB) shaping and uniform signaling techniques at spectral efficiency (SE) of 10 and 14 bits/4D-sym. Numerical simulations show that trellis shaping can provide certain shaping gain over uniform signaling under linear additive white Gaussian noise (AWGN) channel. The fiber transmission results indicate that OFDM signals with trellis shaping have higher effective signal-to-noise ratio (SNR) than those with MB shaping and uniform signaling. It means that trellis shaping technique has the ability to mitigate the fiber nonlinear noise. Considering both linear and nonlinear noise in the fiber link, trellis shaping can extend the transmission distance by $\sim$ 110 km and $\sim$ 200 km over MB shaping and uniform signaling at SE of 10 bits/4D-sym. At SE of 14 bits/4D-sym, trellis shaping provides similar performance as MB shaping but $\sim$ 120-km extension reach in comparison with uniform signaling. The performances of OFDM signals with trellis shaping, MB shaping and uniform signaling are also experimentally investigated in a four-channel wavelength division multiplexing (WDM) fiber transmission systems. The experimental results show that trellis shaping can also mitigate the nonlinear distortions induced by the clipping effects at the transmitter side. Compared with MB shaping, trellis shaping extends the transmission reach by $\sim$ 240 km and $\sim$ 90 km at SE of 10 and 14 bits/4D-sym, respectively.

200 Gbit/s Photonics-Aided MMW PS-OFDM Signals Transmission at W-Band Enabled by Hybrid Time-Frequency Domain Equalization

Millimeter-wave (MMW) transmission has the advantage of larger available bandwidth compared with traditional wireless communications. Compared with the electrical algorithms, photonics-aided MMW signals generation can support a large modulation bandwidth and is regarded as a potential candidate for future RoF link. In this experiment, we demonstrate a W-band (75 GHz ~ 110 GHz) photonics-aided MMW communication system. To overcome the high-frequency power loss induced by the limited bandwidth of photoelectric devices, we adopt orthogonal frequency division multiplexing (OFDM) signal with hybrid quadrature amplitude modulation (QAM) formats. Moreover, the probabilistic constellation shaping (PCS) technique is used to further improve the system capacity. In the offline digital signal processing (DSP), a time-domain Volterra series based nonlinear equalizer with I/Q multiple input multiple output (MIMO) structure can compensate for the nonlinearity during the fiber and wireless transmission. Finally, a hybrid time-frequency domain least mean square (LMS) equalizer is proposed to eliminate the crosstalk in the adjacent OFDM symbols and subcarriers. With the aid of advanced modulation and hybrid time-frequency domain equalization, 30 Gbaud OFDM MMW signals with hybrid PS-512QAM and PS-128QAM at 92.5 GHz can be successfully transmitted over 1-m wireless link, whose raw transmission rate is 208.4 Gbit/s. It is worth noting that the hybrid time-frequency domain LMS equalizer can increase the maximal AIR to 178.8 Gbit/s.

Huffman-Coded Sphere Shaping for Extended-Reach Single-Span Links

Huffman-coded sphere shaping (HCSS) is an algorithm for finite-length probabilistic constellation shaping, which provides nearly optimal energy efficiency at low implementation complexity. In this paper, we experimentally study the nonlinear performance of HCSS employing dual-polarization 64-ary quadrature amplitude modulation (DP-64QAM) in an extended-reach single-span link comprising 200 km of standard single-mode fiber (SSMF). We investigate the effects of shaping sequence length, dimensionality of symbol mapping, and shaping rate. We determine that the naive approach of Maxwell–Boltzmann distribution matching — which is optimal in the additive white Gaussian noise channel — provides a maximum achievable information rate (AIR) gain of 0.18 bits/4D-symbol with respect to uniform signaling at optimum launch power in the infinite length regime. Conversely, HCSS can achieve a gain of 0.37 bits/4D-symbol over uniform signaling using amplitude sequence length of 32, which may be implemented without multiplications, using integer comparison and addition operations only. Coded system performance, with a net data rate of approximately 425 Gb/s for both shaped and uniform inputs, is also analyzed.

Performance-Enhanced DMT System With Joint Precoding and Probabilistic Constellation Shaping

The promising solution for short-reach optical communication, discrete multitone (DMT) system suffer from high peak-to-average power ratio (PAPR). It is easy for the DMT signal to enter the nonlinear region of the components in the systems, which distorts the signal and limits the modulation efficiency. It is well-known that the precoding technique can suppress the PAPR of DMT without loss of spectral efficiency. We found that, in the I/Q plane, the nonlinear distortion clusters in the constellation points with higher power due to the joint precoding and inverse fast Fourier transform. The principle of this phenomenon has been studied. To cope with the specially distributed nonlinear distortions induced by precoding, we adopted the probabilistic constellation shaping (PCS) technique to reduce the probability of constellation points with high power, resulting in the overall performance improvement. Joint precoding and PCS significantly improve the resistance to nonlinear distortions for DMT systems. Simulations and experiments of 16-QAM and 64-QAM DMT transmission systems were conducted to evaluate the performance. The experimental results show that at the NGMI threshold of 0.92, up to 4 dB enhancement of the receiver sensitivity has been achieved by the proposed scheme when 4-GBd 64-QAM signals are transmitted.

A novel four dimensional constellation shaping with non-uniform signaling for long-haul fiber-optic communication

In this paper, a new four-dimensional (4D) constellation shaping scheme is proposed for long-haul fiber-optic system to approach the optimal performance. The scheme designs a non-uniform signaling for 4D 80-ary multisphere distribution (4D-80MD) constellation by combining constellation shaping of four dimensions with pragmatic low density parity check (LDPC) code modulation. Additionally, the design of multisphere distribution is introduced based on a bounded-energy enumerative amplitude trellis. The proposed 4D-80MD constellation has the same spectral efficiency (SE) as the conventional polarization-multiplexed 8-ary quadrature-amplitude modulation (PM-8QAM). We study the efficiency of 4D-80MD, combined with bit-interleaved coded-modulation with iterative decoding, and demonstrate in back-to-back system that the proposed 4D-80MD outperforms PM-8QAM about 1 dB For a long-haul optical fiber system, the optimized 4D-80MD is able to achieve a reach improvement of up to 21%. The results also show increased rates and reduced non-linear noise compared with 2D shaped signal with the same SE.

Circularly Symmetric Companding Quantization-Inspired Hybrid Constellation Shaping for APSK Modulation to Increase Power Efficiency in Gaussian-Noise-Limited Channel

In this paper we address hybrid probabilistic-geometric constellation shaping (HCS) of amplitude phase shift keying (APSK) constellation based on the reversed model of optimal companding quantization for circularly symmetric sources with the goal to increase the constellation power efficiency in Gaussian-noise-limited channel. To empirically optimize the proposed APSK constellation such that a symbol-error rate (SER) reaches its minimum under given constraints with respect to signal-to-noise ratio (SNR) and the prior probabilities of constellation points, for various settings of constellation parameters, we investigate SER dependence on SNR and determine the constellation parameters achieving minimum SER. The SER dependence on SNR we estimate theoretically by deriving approximate formula for SER of uncoded APSK constellation in Gaussian-noise-limited channel and practically by performing simulation. The obtained results are well-matched verifying the accuracy of approximate SER formula. The results also show that our APSK constellation outperforms some previous APSK and M-ary QAM constellations in terms of power efficiency. Thus, for SER equal to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> the gain in power efficiency amounts up to 2.35 dB, 2.23dB and 1.64 dB compared with the maximum mutual information-optimized 4+12-APSK, 4+12+16-APSK and 4+12+20+28-APSK constellations, respectively. This means that by employing APSK constellation we propose instead the traditional APSK constellations the transmitted signal power can be reduced by a third enabling lower power consumption. The improved power efficiency of our APSK constellation makes it suitable for application in power-limited communications such as fiber-optic communications, satellite communications, power-line communications, and multiple-input multiple-output wireless transmissions.

АНАЛИЗ ПАРАМЕТРИЧЕСКОЙ ЧУВСТВИТЕЛЬНОСТИ СПОСОБА ОПТИМИЗАЦИИ СТРУКТУРЫ СПЕКТРАЛЬНО-ЭФФЕКТИВНЫХ РАДИОСИГНАЛОВ

Currently, increasing the speed of information transmission in wireless communication networks is a topical issue. The growing demand for spectral efficiency in radio communication systems gives rise to the introduction of signals with amplitude-phase modulation. Despite all its advantages, signals with vector modulation are characterized by a change in the envelope, which makes it impossible to use highly efficient nonlinear power amplifiers. Energy efficiency is clearly a critical factor in portable radio communications systems, where power supplies are often used in small packages, and the presence of energy losses due to heat dissipation is a significant drawback that requires additional cooling systems. In this connection, when developing modern radio communications, radio engineers are faced with the contradictory task of achieving maximum energy and spectral efficiency. One of the approaches to reduce nonlinear distortion of vector modulation is the use linearization schemes for nonlinear power amplifiers. This work is devoted to increasing the energy and spectral efficiency of signals with amplitude-phase modulation. The article discusses the restrictions imposed on the input signals for the method for optimizing of structure of spectrally effective radio signals with vector modulation, the formation of the output signal, the influence of phase shifters phase imbalance on p/2, the index of balance modulation, and the analysis of parametric sensitivity. The possibility of using quadrature modulators to form components with phase modulation and constant envelope is considered. This method was simulated and the effect of phase imbalance on the shape of the output signal constellation was revealed.

Complex signal constellations in cumulantsbased AMC: Statistics and performance

In this paper various complex signal constellations are considered in the context of Automatic Modulation Classification (AMC) based on a higher-order normalized cumulants value. Most of the constellations have been addressed so far with fourth-order cumulants as AMC features only. The goal of this paper is to provide comparable values of sixth-order cumulants' statistics for complex signal constellations as well, while resolving ambiguity in constellation shapes addressed at the same time and directing towards the criterion for estimation of expected classification performance.

Rate Adaptability Using LUT-Based Distribution Matching for Probabilistic Constellation Shaping

We investigate the flexibility of a LUT-based hierarchical DM for Probabilistic Constellation Shaping providing flexible net bit rates. Using a fixed parallelized input and output LUT-based architecture, including a flexible strategy to organize the input bits in each LUT, the proposed scheme shows an efficient performance in terms of rate loss vs. complexity, resulting in a DM solution to enable flexible bit rates with improved channel transmission. We use an 800G example design with soft-decision FEC to discuss the optimization strategy and to demonstrate the flexibility of the proposed method, enabling a high granularity bit rate operation in the range of 160 to 800Gb/s with a rate loss always below 0.14bits/symbol.

FPGA Implementation of Rate-Adaptable Prefix-Free Code Distribution Matching for Probabilistic Constellation Shaping

In this work, we implement a rate-adaptable (RA) prefix-free code distribution matching (PCDM) encoder in a field-programmable gate array (FPGA). The implemented RA-PCDM encoder supports a wide range of information rates from 1.6 to 4.8 bit/symbol with fine granularity of 0.2 bit/symbol in probabilistic constellation shaping (PCS) systems. The shaping performance of the implemented RA-PCDM is within 0.55 dB of the theoretical limit. Massively parallel encoding of RA-PCDM is demonstrated using a sliding window processor, in a universal architecture for all PCDM codebooks. Given that the procedure and complexity of RA-PCDM decoding is almost the same as those of RA-PCDM encoding, it is shown that the RA-PCDM uses substantially less hardware area than a traditional rate adaptation scheme based on low-density parity-check (LDPC) codes, while offering finer rate granularity and shaping gain. The RA-PCDM is therefore a practical PCS technology that enables high-throughput optical communications to approach channel capacity more closely at a lower cost than RA-LDPC.

Probabilistic Shaping for the Optical Phase Conjugation Channel

Probabilistic constellation shaping is studied and developed for optical phase conjugation (OPC)-based nonlinearity compensation of Kerr nonlinearities in optical fiber links. The mid-link OPC scenario is considered for dispersion compensated systems. It is demonstrated in simulations and experimentally that transmission strategies optimal for classical additive white Gaussian noise (AWGN) channels can be sub-optimal for these systems without nonlinearity compensation. On the contrary, when nonlinearity compensation is applied with mid-link OPC, the channel noise is demonstrated to be Gaussian and AWGN-like transmission strategies thus remain effective. A channel-agnostic probability mass function (PMF) optimization algorithm is proposed for the input constellation in order to further improve the shaping gains in both scenarios. Operating arbitrary PMFs on arbitrary channels is enabled by a channel-agnostic digital signal processing (DSP) chain. After ≈2000 km of transmission, mid-link OPC is demonstrated to provide ≈1 dB of gain in effective SNR, which translates to ≈0.4 bits/QAM symbol of gain in achievable information rate. The gain is then increased by an extra 0.2 bits/QAM symbol by applying probabilistic shaping.

A Note on Probabilistic and Geometric Shaping for the AWGN Channel

When considering coded modulation schemes for the AWGN channel, two main practical limitations prevent achieving channel capacity, namely the need to use a finite constellation and coding inefficiencies. Constellation shaping was given new impetus in recent works by Bocherer et al. , which combined probabilistically shaped ASK constellations with LDPC coding. One open question is how far their results are from optimal solutions based on the use of finite constellations. We investigate this issue and show through experimental analysis that most of the loss is due to inefficient coding design and little benefits should be expected by adding two-dimensional geometric shaping.

16-QAM probabilistic constellation shaping by adaptively modifying the distribution of transmitted symbols based on errors at the receiver.

We simulate and experimentally demonstrate a feedback-based probabilistic constellation shaping (FB-PCS) of a 10 Gbaud 16-ary quadrature amplitude modulation (16-QAM) signal. Our approach is to adaptively modify the distribution of transmitted symbols based on errors at the receiver, and assumptions about the channel model are not required. Specifically, the error feedback enables solving an optimization problem to find the distribution that maximizes the mutual information between the input and output of the channel without knowledge of the channel itself. A known training sequence with uniform distribution is transmitted, and the errors at each constellation point are counted at the receiver. This information is relayed to the transmitter, which then updates the data constellation with a new probability distribution such that constellation points with more errors are used less frequently. We examine four different system scenarios in simulation and one scenario in experiment. In simulation, we find that FB-PCS (a) reduces the number of errors when compared to uniform shaping for the four scenarios, and (b) reduces symbol error rate (SER) by approximately an order of magnitude or has similar SER compared to conventional Maxwell-Boltzmann (M-B) shaping. Moreover, we demonstrate that FB-PCS can lead to an SER reduction of ∼50%.

Trainable Communication Systems: Concepts and Prototype

We consider a trainable point-to-point communication system, where both transmitter and receiver are implemented as neural networks (NNs), and demonstrate that training on the bit-wise mutual information (BMI) allows seamless integration with practical bit-metric decoding (BMD) receivers, as well as joint optimization of constellation shaping and labeling. Moreover, we present a fully differentiable neural iterative demapping and decoding (IDD) structure which achieves significant gains on additive white Gaussian noise (AWGN) channels using a standard 802.11n low-density parity-check (LDPC) code. The strength of this approach is that it can be applied to arbitrary channels without any modifications. Going one step further, we show that careful code design can lead to further performance improvements. Lastly, we show the viability of the proposed system through implementation on software-defined radios (SDRs) and training of the end-to-end system on the actual wireless channel. Experimental results reveal that the proposed method enables significant gains compared to conventional techniques.

Optimization of Probabilistic Shaping for Nonlinear Fiber Channels with Non-Gaussian Noise.

Probabilistic constellation shaping is investigated in the context of nonlinear fiber optic communication channels. Based on a general framework, different link types are considered—1. dispersion-managed channels, 2. unrepeatered transmission channels and 3. ideal distributed Raman amplified channels. These channels exhibit nonlinear effects to a degree that conventional probabilistic constellation shaping strategies for the additive white Gaussian (AWGN) noise channel are suboptimal. A channel-agnostic optimization strategy is used to optimize the constellation probability mass functions (PMFs) for the channels in use. Optimized PMFs are obtained, which balance the effects of additive amplified spontaneous emission noise and nonlinear interference. The obtained PMFs cannot be modeled by the conventional Maxwell-Boltzmann PMFs and outperform optimal choices of these in all the investigated channels. Suboptimal choices of constellation shapes are associated with increased nonlinear effects in the form of non-Gaussian noise. For dispersion-managed channels, a reach gain in 2 spans is seen and across the three channel types, gains of >0.1 bits/symbol over unshaped quadrature-amplitude modulation (QAM) are seen using channel-optimized probablistic shaping.