Quadrature Amplitude Modulation Signals Research Articles

Experimental demonstration of flexible information rate PON beyond 100 Gb/s with rate-compatible LDPC codes

The applications of rate-compatible low-density parity-check (RC-LDPC) codes are investigated for a 16 quadrature amplitude modulation (16QAM) signal and coherent detection system. With rate-compatible signals, we can provide the flexible net data rate between 135.5 Gb/s and 169.7 Gb/s in a passive optical network (PON) link. Based on the LDPC codes defined in the IEEE 802.3ca standard, we construct two sets of RC-LDPC codes with a fixed and variable information bit length. Since the puncturing operation may degrade the performance of LDPC codes, we apply the protograph-based extrinsic information transfer (PEXIT) technique to optimize the puncturing positions to mitigate the degradation. Additionally, we explore four low-complexity LDPC decoding algorithms (min sum, offset min sum, variable weight min sum, and relaxed min sum with 2 nd min emulation) to investigate the relationship between the computational complexity and decoding performance. Simulation results indicate that the constructed codewords exhibit good performance in the waterfall region across a range of code rates. Finally, we conduct an experimental setup in a dual-polarization 25 GBaud 16QAM coherent PON to verify the effectiveness of the constructed LDPC codes with four decoding algorithms. The experimental results show maximal 4.8 dB receiver sensitivity differences, which demonstrate the feasibility of the method for constructing RC-LDPC codes in future high-speed flexible coherent PON.

Dual high-order QAM-modulated mm-wave signal transmission in the Q-band enabled by simple IM/DD architecture and bandpass delta-sigma modulation.

The intensity-modulation (IM)/direct-detection (DD) systems have been proven effective and low-cost due to their simple system architecture. However, the Mach-Zehnder modulator (MZM) of the IM/DD systems only reserves its driving signal intensity. Therefore, the IM/DD systems are generally unable to transmit vector signals and have a restricted spectrum efficiency and channel capacity. Similarly, the radio-over-fiber (RoF) transmission systems based on IM/DD are limited by their simple architecture and generally cannot transmit high-order quadrature amplitude modulation (QAM) signals, which hinders the improvement of their spectrum efficiency. To address the challenges, we propose a novel, to the best of our knowledge, scheme to simultaneously transmit the dual independent high-order QAM-modulated millimeter-wave (mm-wave) signals in the RoF system with a simple IM/DD architecture, enabled by precoding-based optical carrier suppression (OCS) modulation and bandpass delta-sigma modulation (BP-DSM). The dual independent signals can carry different information, which increases channel capacity and improves spectrum efficiency and system flexibility. Based on our proposed scheme, we experimentally demonstrate the dual 512-QAM mm-wave signal transmission in the Q-band (33-50 GHz) under three different scenarios: 1) dual single-carrier (SC) signal transmission, 2) dual orthogonal-frequency-division-multiplexing (OFDM) signal transmission, and 3) hybrid SC and OFDM signal transmission. We achieve high-fidelity transmission of dual 512-QAM vector signals over a 5 km single-mode fiber (SMF) and a 1-m single-input single-output (SISO) wireless link operating in the Q-band, with the bit error rates (BERs) of all three scenarios below the hard decision forward error correction (HD-FEC) threshold of 3.8 × 10-3. To the best of our knowledge, this is the first time dual high-order QAM-modulated mm-wave signal transmission has been achieved in a RoF system with a simple IM/DD architecture.

Fiber-optic parametric amplifier-based all-optical format conversion enabling optical networks interconnection with different modulation formats

A fiber-optic parametric amplifier (FOPA)-based all-optical format conversion (AOFC) scheme is proposed and numerically simulated to achieve optical networks interconnection with different modulation formats. In this scheme, the power transfer function (PTF) and the relative phase shift (RPS) functions between the input and output optical signals for the single-pump FOPA are derived and numerically analyzed. For the input 20 Gbps bipolar 4-ary pulse amplitude modulation (PAM4) signal, it can be converted into a BPSK signal (BPSK1) based on the power saturation characteristic of the PTF. By adjusting the input power of the input PAM4 signal, it can also be converted into a level-swapping PAM4 signal based on the single-pump FOPA. When the level-swapping PAM4 signal is sent into the single-pump FOPA with suitable power again, another BPSK signal (BPSK2) could also be generated. When the PAM4-to-BPSK format converter based on the single-pump FOPA is combined with the dual-pump FOPA (namely phase-sensitive amplifier, PSA), the 16-ary quadrature amplitude modulation (16QAM) signal can also be de-aggregated into four BPSK signals or two quadrature phase shift keying (QPSK) signals. The constellation diagrams, the power waveforms, the error vector magnitude (EVM) and the bit error rate (BER) of the relevant optical signals are measured to evaluate the scheme performance. The scheme can be deployed at the optical gateway to realize optical networks interconnection using different modulation formats.

Online digital compensation of pump dithering induced phase and amplitude distortions in transmission links with cascaded fibre-optical parametric amplifiers

We present an advanced online digital signal processing (DSP) method for correcting the phase and amplitude distortions caused by the phase modulation of the pump source and its interaction with the dispersive fibre channel in transmission systems using cascaded fibre-optical parametric amplifiers. The proposed algorithm is numerically demonstrated to achieve significant (up to 3.7 dB for a four-tone pump-phase modulation scheme) Q2-factor performance improvement over conventional DSP in 16 quadrature-amplitude modulation signal transmission.

Robust multimodulus blind equalization algorithm for multilevel QAM signals in impulsive noise

As a blind equalization algorithm, the fractional lower-order statistics based multimodulus algorithm (FLOS-MMA) is suitable for equalizing multilevel quadrature amplitude modulation (QAM) signals in impulsive noise. However, the equalization performance of FLOS-MMA is severely degraded in strong impulsive noise because the first-order gradient of the cost function constrains the ability of FLOS to suppress large outliers in the equalizer output signal and is sensitive to large outliers in the equalizer input signal. To enhance the robustness of multimodulus blind equalization algorithm against impulsive noise, a FLOS based momentum fractional-order multimodulus algorithm (FLOS-MFOMMA) is proposed in this paper. The proposed algorithm mitigates the adverse effects of impulsive noise on the updating of equalizer coefficients by utilizing the fractional-order gradient and accelerates the convergence speed by incorporating a momentum term. Then, the steady-state excess mean square error and the computational complexity of FLOS-MFOMMA are analyzed theoretically. Finally, numerical simulations, for equalizing 16-QAM signals under impulsive noise environments, show that the proposed algorithm is superior to FLOS-MMA in terms of robustness and convergence speed.

Hierarchical blind phase search for correcting imperfect phase rotation in QAM signals synthesized via optical coherent superposition.

Coherent superposition has been proposed to synthesize high-order quadrature amplitude modulation (QAM) by coherently superposing low-order QAMs in the optical domain. These approaches could effectively relax the digital-to-analog converter resolution and reduce the complexity of the driving electronics. However, in the superposition process, imperfect phase rotations (IPRs) in low-order QAMs will be transferred to the resultant high-order QAM. Importantly, the induced IPR cannot be compensated for by conventional linear equalizers and carrier recovery methods. To combat the induced IPR, herein, we propose a hierarchical blind phase search (HBPS) algorithm to compensate for the IPRs in synthesized high-order QAMs. The proposed HBPS can match the generation mechanism of the IPRs in coherent superposition, by tracing back and estimating the IPR in the QPSK-like constellation of each hierarchy and finally correcting the induced IPRs. Simulation and experimental results verify that this algorithm could effectively compensate for the IPR in the resultant 16-QAMs synthesized using coherent superposition approaches. The proposed HBPS shows significant optical signal-to-noise ratio (OSNR) gains compared to the conventional blind phase search (BPS) method for high-order QAMs coherently superposed using optical signal processing (OSP) and tandem modulators (TMs). Specifically, at the BER of 2.4e-2, the HBPS achieves a 1.5-dB OSNR sensitivity enhancement over the BPS in either OSP or TMs-based schemes, even with an imperfection rotation of up to 20∘.

Influence of quadrature transformation imbalance on the noise immunity of signal reception with amplitude-phase shift keying

Objectives. At the present time, amplitude-phase shift keyed (APSK) signals are actively used in satellite communication systems. In particular, they are applied in systems which operate in a limited radio frequency spectrum with increased data transmission quality requirements. Such systems use multi-channel type receivers with maximum likelihood decision on the received symbol (correlation receiver) or quadrature type receivers. The noise immunity of these receivers is directly dependent on the quality of the formation of reference oscillations. These oscillations are reference signals for correlation receivers and in-phase and quadrature components for quadrature receivers. The aim of the work is to analyze the influence of the amplitude and phase parameter spread of the in-phase and quadrature channels on the noise immunity of receiving APSK signals with a circular shape of the signal constellation.Methods. Methods of statistical radio engineering, theory of optimal signal reception, and computer simulation are used.Results. The study established the characteristics of noise immunity of the APSK signal reception depending on the spread of parameters of the quadrature converter. The theoretical calculations were confirmed by the results of modeling the transmission of APSK signals in a Gaussian communication channel. A comparison with systems using quadrature amplitude modulation (QAM) was carried out, in order to assess system stability in the presence of spread parameters among other similar systems.Conclusions. The studies enabled us to conclude that an imbalance of the quadrature reference oscillations can lead to a significant decrease in the noise immunity of radio systems using APSK signals. The minimum energy loss due to imbalance of quadrature reference oscillations is achieved when the imbalance value is less than 10% in amplitude and 2°–3° in phase. The amplitude imbalance of quadrature reference oscillations when receiving QAM signals is more pronounced than in the case of APSK signals. The phase imbalance affects approximately the same.

Geometrically Shaped Odd-Bit QAM Constellations Suitable for Principal Component-Based Phase Estimation

For high-speed optical communication systems, laser phase noise (LPN) stands as a pivotal factor influencing the quality of the received signal. Therefore, the employment of a highly accurate carrier phase recovery (CPR) algorithm at the receiving end is indispensable to ensure the reliability of transmission. While a CPR algorithm called principal component-based phase estimation (PCPE) has been proven to be capable of achieving low-complexity and high-performance phase recovery for even-bit quadrature amplitude modulation (QAM) (i.e., square QAM) signals, it is not compatible with traditional cross-shaped odd-bit QAM signals. To circumvent this problem, a signal constellation design scheme based on geometric shaping (GS) is proposed. The pair-wise optimization (PO) algorithm is used to optimize the constellation structure of 32QAM and 128QAM signals in order to obtain results that are compatible with the PCPE algorithm. Monte Carlo simulation results reveal that for odd-bit QAM signals utilizing PCPE for phase recovery, the proposed GS constellations enhance the mutual information (MI) performance across the entire measured signal-to-noise (SNR) range. Moreover, compared with regular 32QAM and 128QAM constellations using the well-known blind phase search (BPS) algorithm, the proposed GS and PCPE scheme can achieve SNR gains of 1.10 dB and 2.59 dB, respectively, when considering the 20% soft-decision forward error correction (SD-FEC) overhead. Verification through commercial simulation software corroborates these findings, demonstrating that the proposed GS constellations are particularly suitable for the PCPE algorithm, especially under conditions of high optical signal-to-noise ratio (OSNR). To the best of our knowledge, this is the first time that the incompatibility between the PCPE algorithm and odd-bit QAM signals has been investigated, and the proposed GS scheme has broadened the application scope of the low-complexity CPR algorithm.

Coherent optical transmitter IQ imbalance mitigation with embedded carrier phase and frequency offset estimation.

We present a 4×4 real-valued channel equalizer with embedded phase estimator, designed for carrier phase and frequency offset estimation and compensation in coherent optical communications with in-phase/quadrature (IQ) impairments. These impairments include IQ timing skew, gain imbalance, and quadrature phase errors at the transmitter side. To achieve adaptive control of the equalizer's filter coefficients, we employ the decision-directed least mean square (DD-LMS) algorithm. This algorithm minimizes the error between the filter outputs and the desired signals in a symbol-by-symbol manner, resulting in faster channel coefficients adaptation speed. Simulation results for a 60 GBaud polarization-multiplexing 16 quadrature amplitude modulation (PM-16QAM) signal demonstrate that our proposed equalizer outperforms a 2×2 cascaded multi modulus algorithm-based (CMMA-based) equalizer, a 2×2 complex-valued method based on the DD-LMS algorithm, and the 4×4 real-valued equalizer without embedded frequency offset estimation (FOE), when the transmitter IQ impairments exist. Experimental validation is also conducted for the 60 GBaud PM-16QAM and 45 GBaud PM-64QAM signals. Similar to the simulation results, our experiments show that the proposed 4×4 real-valued equalizer with embedded FOE can achieve effective SNR penalties of less than 0.41 dB at 7 ps skew, 1.33 dB at 3.5 dB gain imbalance, and 1.64 dB at the bias voltage shift of 0.5 V for the 60 GBaud PM-16QAM signal. Finally, our experimental results confirm the effectiveness of our proposed method in carrier phase estimation as well as the frequency offset compensation, when compared with 4×4 real-valued equalizer without embedded FOE.

Simulation-Enhanced MQAM Modulation Identification in Communication Systems: A Subtractive Clustering-Based PSO-FCM Algorithm Study

Signal modulation recognition is often reliant on clustering algorithms. The fuzzy c-means (FCM) algorithm, which is commonly used for such tasks, often converges to local optima. This presents a challenge, particularly in low-signal-to-noise-ratio (SNR) environments. We propose an enhanced FCM algorithm that incorporates particle swarm optimization (PSO) to improve the accuracy of recognizing M-ary quadrature amplitude modulation (MQAM) signal orders. The process is a two-step clustering process. First, the constellation diagram of the received signal is used by a subtractive clustering algorithm based on SNR to figure out the initial number of clustering centers. The PSO-FCM algorithm then refines these centers to improve precision. Accurate signal classification and identification are achieved by evaluating the relative sizes of the radii around the cluster centers within the MQAM constellation diagram and determining the modulation order. The results indicate that the SC-based PSO-FCM algorithm outperforms the conventional FCM in clustering effectiveness, notably enhancing modulation recognition rates in low-SNR conditions, when evaluated against a variety of QAM signals ranging from 4QAM to 64QAM.

Research Progress on Carrier-Free Phase-Retrieval Receivers

In order to deal with the chromatic dispersion-induced power fading issue for short-reach direct-detection optical fiber communication applications, such as the ever-increasing data-center interconnections (DCIs), optical filed recovery is intensively being under investigation. To date, various direct detection schemes capable of optical field recovery have been proposed, including the Kramers–Kronig (KK) receiver, asymmetric self-coherence detection (ASCD) receiver, carrier-assisted differential detection receiver (CADD), Stokes vector receiver (SVR), and carrier-free phase-retrieval (CF-PR) receiver. Among those, the CF-PR receiver attracts lots of research attention because it can circumvent the requirement of a strong continuous-wave (CW) optical carrier for the beating with the signal. Generally, the CF-PR receiver consists of only two single-ended photodiodes (PDs) and one dispersive element, for the field recovery of the quadrature amplitude modulation (QAM) signals. Based on the theoretical and experimental studies reported so far, this paper reviews the latest progress of CF-PR receivers designed for high-speed optical short-reach transmission links.

Reconfigurable all-optical pattern recognition for PSK and QAM signals in high-speed optoelectronic firewalls.

In the fifth generation fixed networks (F5G) era, full-fiber-connected optical networks support emerging bandwidth-hungry services. However, optical networks are vulnerable to attack by tapping or other methods, which has been paid more and more attention in modern optical infrastructure. Therefore, high-speed optoelectronic firewalls appear as one of the promising technologies to guarantee security. The most significant and challenging component of a high-speed optoelectronic firewall is all-optical pattern recognition, especially for more advanced high-order modulation formats such as phase shift keying (PSK) or quadrature amplitude modulation (QAM) to satisfy efficient enhanced fixed broadband in F5G. In this paper, what we believe to be a novel reconfigurable all-optical pattern recognition system for PSK and QAM signals is proposed with two implementation architectures. The proposed system mainly consists of a generalized XNOR (GXNOR) and a recirculating loop. The two implementation architectures are precisely two realization methods of the GXNOR part. One employs two cascaded IQ Mach-Zehnder modulators and the other is implemented by the four-wave mixing. The numerical simulation results demonstrate that the two implementation architectures can both achieve all-optical pattern recognition for the reconfigurable high-order modulation formats of QPSK, 8PSK, and 16QAM with the recorded baud rate of 260GBaud.

Performance of quantum-dash mode-locked lasers (QD-MLLDs) for high-capacity coherent optical communications.

We investigate the capabilities and limitations of quantum-dash mode-locked lasers (QD-MLLDs) as optical frequency comb sources in coherent optical communication systems. We demonstrate that QD-MLLDs are on par with conventional single-wavelength narrow linewidth laser sources and can support high symbol rates and modulation formats. We manage to transmit 64 quadrature amplitude modulation (QAM) signals up to 80 GBd over 80 km of standard single-mode fiber (SSMF), which highlights the distinctive phase noise performance of the QD-MLLD. Using a 38.5 GHz (6 dB bandwidth) silicon photonic (SiP) modulator, we achieve a maximum symbol rate of 104 GBd with 16QAM signaling and a maximum net rate of 416 Gb/s per carrier in a single polarization setup and after 80 km-SSMF transmission. We also compare QD-MLLD performance with commercial narrow-linewidth integrable tunable laser assemblies (ITLAs) and explore their potential for use as local oscillators (LOs) and signal carriers. The QD-MLLD has 45 comb lines usable for transmission at a frequency spacing of 25 GHz, and an RF linewidth of 35 kHz.

214.7 Tbit/s S, C, and L-band transmission over 50 km SSMF based on silicon photonic integrated transceivers

We experimentally demonstrate a 214.7 Tbit/s generalized mutual information (GMI) estimated throughput by ultra-wideband wavelength division multiplexing (WDM) transmission in standard single-mode fiber (SSMF). With 50-GHz grid, 396 transmission channels are used to deliver 49 GBaud probabilistically constellation-shaped (PCS) 256 quadrature amplitude modulation (QAM) and PCS-64QAM signals. Silicon photonic integrated transceiver is employed to complete electro-optic and optic-electro conversion of the modulated signals. S, C, and L-band rare-earth-doped amplifiers enable the 19.8 THz bandwidth WDM transmission without the assistance of distributed Raman amplification. The measured data rate shows great potential for Silicon photonic devices deployed in ultra-wideband WDM transmission.

Gain of Spatial Diversity with Conjoint Signals in Arbitrarily Correlated Rayleigh Fading Channels

Coding gains for arbitrarily correlated signals in a spatial diversity system with conjoint signals are presented in this study. The basic form of the proposed signal synthesizer evenly produces phase changes in the output signals. The mixer is an orthogonal transformation matrix, which is energy preserving and blind to the channel correlation matrix. The idea is to synthesize additional conjoint signal copies from the received signals that would be received if there were more antennas. However, these conjoint signals contain a level of correlation with the received signals. With the assumption of flat Rayleigh fading channels, simulation results for symbol error probability (SEP) are presented for different numbers of receive branches and varying correlation conditions. It is shown that under binary phase shift keying (BPSK), the synthesizer achieves decorrelation coding gains of about 1 dB when selection combining (SC) or equal gain combining (EGC) is used. The synthesizer’s performance across M-ary quadrature amplitude modulation (MQAM) signals is also tested. In addition, analytical frameworks are derived for BPSK and MQAM, which are tightly bound by the Monte Carlo simulation results obtained using Matlab. The correlation analysis is performed for different numbers of antennas and varied antenna spacings.

23.1-Gb/s 135-GHz Wireless Transmission Over 4.6-Km and Effect of Rain Attenuation

In this article, we have experimentally demonstrated a fiber-wireless-integration <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$D$</tex-math> </inline-formula> -band (110–170 GHz) transmission system. To extend the wireless transmission distance while maintaining the wireless bit rate as high as possible, we designed high-gain lens horn antenna modules consisting of a pair of dielectric plano-convex lenses and horn antennas for long-haul wireless links. In addition, we employ the Volterra nonlinear equalization (VNE) algorithm based on the multiple-input–multiple-output (MIMO) structure to precisely compensate for the in-phase/quadrature (I/Q) imbalance and nonlinear impairment of quadrature amplitude modulation (QAM) signals mainly caused by photoelectric (O-E) conversion and electric-photo (E-O) conversion. Meanwhile, one of the methods adopted in our experiment to decrease the influence of nonlinearity on high-order QAM signals is coupling the high-order modulation format with the probabilistic shaping (PS) technology. As a result of outdoor field experimental verification, the demonstration at 135 GHz carrier with a net rate of 23.1 Gb/s over 10 km optic-fiber and 4.6 km wireless transmission distance has been successfully carried out. It is, as we know, the first time that a record-breaking product of net bit rate and wireless transmission distance, i.e., 23.1 Gb/s <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times$</tex-math> </inline-formula> 4.6 km <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$=$</tex-math> </inline-formula> 106.3 Gb/s <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\cdot$</tex-math> </inline-formula> km, has been accomplished based on a fiber-wireless-integration system. Also, for the first time, we have measured the effect of rain attenuation for the 135 GHz millimeter-wave (mm-wave) wireless link and established more accurate rainfall models for the Shanghai region of China by comparing them with multiple rainfall models. This work can be used as a complement to the International Telecommunication Union-Radiocommunication sector (ITU-R) recommendations.

Optical link encoding based simultaneous correction for crosstalk and nonlinearity in multi-site optical converged networks.

This paper reports a correction scheme to address the problem of modulation nonlinearity and optical switch crosstalk simultaneously for the multi-site optical converged network. Based on the optical link encoding and exclusive-or operation for the received signal, the present spectrum usage can be obtained among the confusion with interferences containing the modulated harmonic distortion and the crosstalk leakage from other sites. The proof-of-concept experiment is performed on various interferences involving the linear frequency modulated (LFM) waveform and the quadrature amplitude modulation (QAM) signal. The corrected spectrum has realized an improved signal-to-noise ratio (SNR) of over 22 dB compared to the uncorrected counterpart. Furthermore, it consistently maintains a superior SNR, surpassing the single impairment-corrected scenario by an impressive margin of at least 15.9 dB. Besides, the implementation would not introduce additional noise, making the corrected result agree well with the ideal case. Without any increase in hardware complexity, the presented scheme provides an effective technique to meet the correction challenge of large-scale and complicated optical networks with multiple optoelectronic devices.

Closed‐form expression of long‐range modulated massive multiple‐input multiple‐output fractional Fourier transform‐orthogonal frequency division multiplexing system under two‐wave with diffuse power fading channel

SummaryIn this paper, the massive multiple‐input multiple‐output fractional Fourier transform‐based orthogonal frequency division multiplexing (MIMO FrFT‐OFDM) system is investigated using the Long Range (LoRa) modulation technique. The conventional system relies on quadrature amplitude modulated (QAM) modulation technology; high‐power amplifiers are needed to transmit the QAM signal. The LoRa modulation technique produces long‐range and low power signals. The two‐wave with diffused power (TWDP) fading channel is used to examine the system's performance. The expression of the bit‐error rate (BER) of the proposed system is also represented in a unique closed form. The proposed system is applied to a state‐of‐the art hospital, one of the Internet of Things (IoT) applications. As the problem of heart stroke is common, it needs to be monitored every second. The electrocardiogram (ECG) data are used to evaluate how well the proposed system is working. Using the proposed model, the physicians get the patient's ECG data while moving in the hospital, getting it at a high data rate, at a low cost because of the extended battery life, a long range, and a low BER. The data considered are from the MIT‐BIH Arrhythmia Database. The result displays that the proposed model achieves a BER of at 10 dB of signal‐to‐noise ratio (SNR), and the conventional model achieves the same BER at 15 dB of SNR. The BER performance of the proposed system is improved by nearly 5 dB.

Detecting Massive MIMO-QAM Signal via ℓ2-Box ADMM Approach

In this letter, we develop two efficient detectors for the massive multiple-input multiple-output (MIMO) system with quadrature amplitude modulation (QAM) signal based on the ℓ2-box intersection technique and the alternating direction method of multipliers (ADMM) approach. Specifically, the first one called ADMM-1 has theoretically-guaranteed convergence under mild conditions, and the second one called ADMM-2 owns cheaper computational complexity. Moreover, all variables are solved analytically in the detection procedure. Simulation results demonstrate the effectiveness of the proposed ℓ2-box ADMM detectors in comparison with the state-of-the-art methods.

Optimizing the probability mass function of complex modulated signals through adaptive channel characterization.

We propose a probability mass function (PMF) optimization scheme for quadrature amplitude modulation (QAM) signals by considering the parametric characteristic of the training sequence. The training sequence for optimization is mapped in standard Maxwell-Boltzmann (M-B) distribution, and the considered characterizing parameters incorporate either the noise variance or the error matrix of the received symbols. The proposed PMF optimization is based on independent reallocation within each constellation ring, generating new distribution with almost the same entropy and transmitted power as the original distribution. This reallocation mechanism is model-free and iterative-free with very low computational complexity. By characterizing the channel in terms of constellation performance asymmetry, PMF reallocation can be effectively implemented to supplement the existing equalization algorithm. The effectiveness of this approach is experimentally verified in a 40-km transmission system with 24 Gbaud 64-QAM signals under three different scenarios. Through PMF reallocation, we achieve generalized mutual information (GMI) improvement of ∼0.06 and throughput improvement of ∼1.5 Gbit/s before forward error correction in comparison with the standard M-B distribution. The proposed mechanism provides a solution to obtain the optimal PMF in practical communication channels, which suffer from various types of noises and distortions.