QAM Systems Research Articles

Blind Equalization for QAM System in the Presence of Impulsive Noise

Blind Equalization for QAM System in the Presence of Impulsive Noise

Joint Optimization of Probabilistic Shaping and Geometric Shaping for Faster-than-Nyquist Signaling

Abstract We propose a joint optimization algorithm of probabilistic shaping and geometric shaping for faster-than-Nyquist (FTN) signaling. The theoretical analysis and bit error performance both represent that the FTN probabilistic-geometric shaping method is superior to the conventional Nyquist regular QAM system. When spectral efficiency (SE) is 3.077 bits/s/Hz, the proposed 16QAM FTN probabilistic-geometric shaping scheme can obtain 1.65 dB theoretical gain compared to the conventional Nyquist regular 16QAM system, while the simulation gain is 2.90 dB with spectral efficiency at 3.077 bits/s/Hz. The proposed 16QAM FTN probabilistic-geometric shaping scheme can obtain 1.63 dB theoretical gain compared to the conventional FTN regular 16QAM system, while the simulation gain is 3.28 dB with spectral efficiency at 3.282 bits/s/Hz. Therefore, the proposed method is reliable, which can be regarded as a potential scheme for the 6G communications.

Joint equalization of RSOP and PMD fused probability-aware with square-root cubature Kalman filter for the PDM PCS-64QAM system under extreme scenarios.

Extreme scenario of lightning strikes would generate ultra-fast rotation of state-of-polarization (RSOP) up to 5.1 Mrad/s and large polarization mode dispersion (PMD) in optical ground wire (OPGW). Unfortunately, the conventional multiple modulus algorithm (MMA) cannot equalize these polarization impairments in polarization division multiplexing (PDM) probabilistic constellation shaping (PCS)-64QAM system. Moreover, due to unavoidable linearization errors and higher modulation order, the extended Kalman filter based on measurement equations of concatenated multiplication (EKF-CM) is highly unstable and fails under such scenarios. To address the above issues, we have proposed a joint equalization scheme of PMD and RSOP, which fuses probability-aware with square-root cubature Kalman filter (PA-SCKF). Firstly, according to the characteristic that the amplitude of PCS signals obeys mixed Rician distribution, the scheme combines maximum a posteriori criterion to obtain the optimal radius of constellation ring which the received symbol belongs to, for the sake of calculating the innovations of SCKF. Secondly, it performs joint equalization of PMD and RSOP impairments based on SCKF and time-frequency conversion architecture. 28GBaud PDM PCS-64QAM simulation results demonstrate that our scheme can jointly equalize maximum impairments of 8.34 Mrad/s RSOP and 90ps DGD under entropy of 4.5bits/symbol. Additionally, only 0.9 dB OSNR penalty is obtained after joint equalization of 6 Mrad/s RSOP with 70ps DGD impairments. Even under entropy of 5.5bit/symbol, it can still jointly equalize impairments of 6.05 Mrad/s RSOP with 60ps DGD. Furthermore, 16GBaud PCS-64QAM experimental results indicate that the maximum joint equalization performances of PA-SCKF scheme under entropy of 4.5bit/symbol and 5bit/symbol are 17 Mrad/s RSOP with 52ps DGD, and 9 Mrad/s RSOP with 52ps DGD, respectively. These results manifest that our PA-SCKF scheme outperforms both MMA and EKF-CM schemes. Importantly, its complexity is on an order of O(Llog2 L), which is comparable to that of EKF-CM scheme.

16QAM optical signal generation scheme based on weighted optimal Euclidean distance.

A two-dimensional signal constellation scheme for binary uniform memoryless source transmission in optical fiber channels is studied in this paper. In geometric shaping (GS), optimization algorithms are usually used to change the overall position of constellation points while maintaining the probability of constellation points unchanged. Different optimization functions are used to allocate the position of constellation symbols, thereby improving constellation performance. A 16 quadrature amplitude modulation (QAM) optical signal generation scheme based on weighted optimal Euclidean distance is proposed in this paper. In order to obtain the best constellation diagram and increase the shaping gain, the weighted optimal Euclidean distance that can minimize the bit error rate (BER) over multiple iterative optimizations is used as the objective function. On the one hand, the proposed 16QAM optical signal generation scheme based on weighted optimal Euclidean distance always outperforms the uniform square 16QAM and the uniform circle 16QAM schemes in the back to back (BTB) transmission. On the other hand, after analyzing the simulation demonstration in a 50GBaud coherent optical communication system over 3000km, results demonstrate that the optical signal to noise ratio (OSNR) performance of this system is better than that of the uniform square 16QAM and the uniform circle 16QAM, which is improved by 0.52dB and 0.85dB, respectively. In addition, the proposed 16QAM system increases the transmission distance by 989km and 741km, respectively, compared to the other two systems. The performance confirms that the proposed novel 16QAM scheme, to the best of our knowledge, can effectively improve the reliability and transmission distance. Therefore, the proposed scheme has a certain development prospect in the future long-distance transmission of high-speed optical fiber communication.

64-QAM WDM-MDM Coherent Transmission System Based on LSTM Nonlinear Equalization

64-QAM WDM-MDM Coherent Transmission System Based on LSTM Nonlinear Equalization

A nonbinary LDPC-coded product distribution matching probabilistic shaping scheme for high order modulation

In this paper, a non-binary low-density parity-check (LDPC)-coded low complexity product distribution matching (PDM) probabilistic shaping (PS) scheme for high-order modulation is proposed. Compared with conventional non-binary LDPC-coded regular quadrature amplitude modulation (QAM) schemes, the proposed non-binary LDPC-coded low complexity PDM-PS QAM scheme can obtain shaping gain, as evidenced through theoretical average mutual information and simulated error performance analyses. When the spectral efficiency is 4.5 bits/s/Hz, compared with the regular 64QAM system, the proposed 64QAM PDM-PS system can obtain 0.26 dB theoretical energy gain, while its simulated error performance is 0.30 dB. When the spectral efficiency is 6.0 bits/s/Hz, compared with the regular 256QAM system, the proposed 256QAM PDM-PS system can obtain 0.73 dB theoretical energy gain, while its simulated error performance is 0.93 dB. Compared with the conventional non-binary LDPC-coded PS QAM scheme, the proposed non-binary LDPC-coded PDM-PS QAM scheme can reduce the computational complexity by 33.1% and 49.7% under 64QAM and 256QAM, respectively, with acceptable error performance loss. The information-theoretic and error performance analyses both indicate the effectiveness and reliability of the proposed scheme.

Swarm Intelligence Based MMSE Frequency Domain Equalization for MIMO Systems

The automatic upgradation of equalizer weights in channel equalization demands a low-complexity, highly accurate estimation of recovery at the minimum possible time. The low-complexity frequency domain equalization improves the minimum mean square error (MMSE) of the equalization process. Adding the superiority of particle swarm optimization (PSO) to the equalizer coefficient selection process enhances the MMSE. This work proposes frequency-domain channel equalization along with a modified PSO (MPSO) as an adaptive algorithm for equalizer weight selection in MIMO systems. The simulation results validate the performance with the time domain linear and decision feedback equalizer structures for BPSK and QAM systems. The parameters are carefully selected by analyzing MMSE thoroughly under timevarying channel conditions.

Low-disturbance automatic bias point control for optical IQ modulator using digital chaotic waveform as dither signals.

A low-disturbance automatic bias point control (ABC) method for optical in-phase and quadrature modulators (IQM) is proposed using digital chaotic waveform as dither signals. Two distinct chaotic signals, each with unique initial values, are introduced to the direct current (DC) port of IQM in conjunction with a DC voltage. Due to the robust autocorrelation performance and exceptionally low cross-correlation of chaotic signals, the proposed scheme is capable of mitigating the impact of low-frequency interference, signal-signal beat interference, and high-power RF-induced noise on transmitted signals. In addition, due to the broadwidth of chaotic signals, their power is distributed across a broad frequency range, resulting in a significant reduction in power spectral density (PSD). Compared to the conventional single-tone dither-based ABC method, the proposed scheme exhibits a reduction in peak power of the output chaotic signal by over 24.1 dB, thereby minimizing disturbance to the transmitted signal while maintaining superior accuracy and stability for ABC. The performance of ABC methods, based on single-tone and chaotic signal dithering, are experimentally evaluated in both 40Gbaud 16QAM and 20Gbaud 64QAM transmission systems. The results indicate that the utilization of chaotic dither signals leads to a reduction in measured bit error rate (BER) for 40Gbaud 16QAM and 20Gbaud 64QAM signals, with respective decreases from 2.48% to 1.26% and from 5.31% to 3.35% when the received optical power is -27dBm.

Impact of resampling interpolation FIR filter in the practical Kramers-Kronig receiver.

The practical Kramers-Kronig (KK) receiver has been a competitive receiving technique in the data-center, medium reach, and even long-haul metropolitan networks. Nevertheless, an extra digital resampling operation is required at both ends of the KK field reconstruction algorithm due to the spectrum broadening caused by adopting the nonlinear function. Generally, the digital resampling function can be implemented by using linear interpolation (LI-ITP), the Lagrange cubic interpolation (LC-ITP), the spline cubic interpolation (SC-ITP), time-domain anti-aliasing finite impulse response (FIR) filter method (TD-FRM) scheme, and fast Fourier transform (FFT)-based scheme. However, the performance and the computational complexity analysis of different resampling interpolation schemes in the KK receiver have not been thoroughly investigated yet. Different from the interpolation schemes of conventional coherent detection, the interpolation function of the KK system is followed by the nonlinear operation, which will broaden the spectrum significantly. Due to the frequency-domain transfer function of different interpolation schemes, the broadened spectrum will have a potential spectrum aliasing, which will cause serious inter-symbol interference (ISI) and further impair the KK phase retrieval performance. We experimentally investigate the performance of different interpolation schemes under different digital up-sampling rates (i.e. the computational complexity) as well as the cut-off frequency, the tap number of the anti-aliasing filter, and the shape factor of the TD-FRM scheme in a 112-Gbit/s SSB DD 16-QAM system over 1920-km Raman amplification (RFA)-based standard single-mode fiber (SSMF). The experimental results involve that the TD-FRM scheme outperforms other interpolation schemes and the complexity is reduced by at least 49.6%. In fiber transmission results, take 20% soft decision-forward error correction (SD-FEC) of 2×10-2 as the threshold, the LI-ITP and LC-ITP schemes only reach 720-km while others can reach up to 1440-km.

Error performance analysis of generalized quadrature spatial modulation using H-8QAM

Motivated to enhance the error performance (EP) of generalised complex quadrature spatial modulation (GCQSM) systems, this study proposes a scheme that builds on GCQSM and uses hexagonal quadrature amplitude modulation (H-QAM) constellations which have the advantages of a maximised Euclidean distance with relatively low peak-to-average power ratio, compared to conventional QAM (C-QAM) systems. This in turn, leads to an enhancement of the EP of GCQSM schemes. The proposed scheme utilises a rotated hexagonal 8QAM (H-8QAM) set. Thus, the proposed scheme is herein named; Generalised QSM using H-8QAM (GQSM-H-8QAM). In this study, the EP of the proposed GQSM-H-8QAM scheme is investigated over Rayleigh frequency flat-fading channels with additive white Gaussian noise. Additionally, a theoretical average bit error probability (ABEP) expression of the GQSM-H-8QAM scheme is formulated and validated using Monte Carlo simulations. Compared to simulation results, the ABEP proves to be increasingly tight at high signal-to-noise ratio values. Obtained simulation results also show an improvement in the EP of the GQSM-H-8QAM scheme over various SM schemes like GCQSM, C-QSM and conventional-generalized spatial modulation (C-GSM), at the same spectral efficiency (SE). An improvement in the EP of 0.61 dB with SE of 8 bits/s/Hz is seen in 4times 4 GQSM-H-8QAM over 4times 4 GCQSM using C-8QAM, 2.58 dB over 4times 4 C-QSM-C-64QAM and a gain of 4.85 dB over 4times 4 C-GSM-C-64QAM.

Low Complexity, Pairwise Layered Tabu Search for Large Scale MIMO Detection

This paper presents a low complexity pairwise layered tabu search based detection algorithm for a large-scale multiple-input multiple-output system. The proposed algorithm can compute two layers simultaneously and reduce the effective number of tabu searches. An efficient Gram matrix and matched filtered output update strategy is developed to reuse the computations from past visited layers. Also, a precomputation technique is adapted to reduce the redundancy in computation within tabu search iterations. Complexity analysis shows that the upper bound of initialization complexity in the proposed algorithm reduces from \(O(N_t^4)\) to \(O(N_t^3)\). The detection performance of the proposed detector is almost the same as the conventional complex version of LTS for 64QAM and 16QAM modulations. However, the proposed detector outperforms the conventional system for 4QAM modulation, especially in \(16 \times 16\) and \(8 \times 8\) MIMO. Simulation results show that the percent of complexity reduction in the proposed method is approximately 75% for \(64 \times 64\), 64QAM and 85% for \(64 \times 64\) 16QAM systems to achieve a BER of \(10^{-3}\). Moreover, we have proposed three layer-wise iteration allocation strategies that can further reduce the upper bound of complexity with minor degradation in detection performance.

A 4 × 210 Gbps high-speed optical wireless system in medium earth orbit (MEO) using matched filters and digital signal processing

Abstract In this work, a high-speed optical wireless system is realized to cater to the bandwidth demands of data services in inter-satellite by using 4 × 210 Gbps capacity enabled by dual-polarization (DP) 128-Quadrature amplitude modulation (QAM) at 25 GHz channel spacing and artificial intelligence (AI). For nonlinear compensation, equalization, normalization, and interference reduction, digital signal processing (DSP), and matched filters are included in the receiver. Results are analyzed by considering error vector magnitude (EVM), Q-factor, and BER at different link lengths. Moreover, two polarizations such as horizontal and vertical polarizations are investigated separately to find out optimal polarization state. Further comparison of the proposed DP-128 QAM is performed with quadrature phase-shift keying (QPSK)and results revealed that the QAM system carrying different states of polarization (SOPs) successfully covered 17,500 km at 125 Gbps and offered enhanced performance as compared to the conventional QPSK and QAM modulations due to narrow carrier spectrum (27 symbols).

High receiver skew-tolerant and hardware-efficient clock recovery for short-reach coherent transmission.

The performance of the high-baud-rate and high-order-modulation-format short-reach coherent transmission systems is sensitive to the in-phase and quadrature (IQ) skew. The conventional receiver IQ skew compensation schemes based on adaptive equalizers (AEQs) suffer from the IQ skew enhanced timing jitter incurred by the clock recovery algorithm (CRA), resulting in a serious sensitivity degradation. In this paper, we first propose a novel multiplication-free timing phase error detector (TPED) with the gain insensitive to the receiver IQ skew and the capability to deal with the complex-valued Nyquist signal with an arbitrary roll-off factor and its real-valued IQ tributaries. Based on the TPED, we then propose a new all-digital feedback CRA able to compensate for the receiver IQ skew. With the novel CRA, the IQ skew enhanced timing jitter is eliminated and the receiver sensitivity can be improved by more than 1 dB for the 61 GBaud dual-polarization Nyquist 16QAM system for an IQ skew of 5 ps. Furthermore, the proposed CRA can reduce the computation complexity of the AEQ by more than 25% compared with the existing schemes by relieving the AEQ from IQ skew compensation. Both numerical simulations and experiments are carried out to validate the advantages of the proposed algorithms. The high-skew-tolerant and low-complexity CRA is a strong candidate for the power-sensitive high-speed short-reach coherent transmission systems.

Performance investigation of the probability-aided maximum likelihood sequence detector for a probabilistic shaped 16-QAM system.

In this paper, for the first time, a probability-aided maximum-likelihood sequence detector (PMLSD) is experimentally investigated through a 64-GBaud probabilistic shaped 16-ary quadrature amplitude modulation (PS-16QAM) transmission experiment. In order to relax the impacts of PS technology on the decision module, a PMLSD decision scheme is investigated by modifying the decision criterion of maximum-likelihood sequence detector (MLSD) correctly. Meanwhile, a symbol-wise probability-aided maximum a posteriori probability (PMAP) scheme is also demonstrated for comparison. The results show that the PMLSD scheme outperforms the direct decision scheme about 1.0-dB optical signal to noise ratio (OSNR) sensitivity. Compared with symbol-wise PMAP scheme, PMLSD scheme can effectively relax the impacts of PS technology on the decision module and a more than 0.8-dB improvement in terms of OSNR sensitivity in back-to-back (B2B) case is obtained. Finally, we successfully transmit the PS-16QAM signals over a 2400-km fiber link with a bit error ratio (BER) lower than 1.00×10-3 by adopting the PMLSD scheme.

Cost-effective and robust DSP scheme for a short-reach coherent system in the presence of transmitter IQ skew and chromatic dispersion.

A cost-effective and robust digital signal processing (DSP) scheme is proposed and demonstrated experimentally in a coherent 61 GBaud PDM 16QAM system. In our scheme, multi-stage DSP blocks are used to deal with channel effects, transceiver in-phase and quadrature (IQ) skew, and phase noise. A 4×4 real-valued multiple-input multiple-output (RV-MIMO) with N1 taps is for polarization recovery and receiver IQ skew calibration. After frequency offset compensation, two 2×2 RV-MIMO with N2 taps are used to compensate for chromatic dispersion (CD), inter-symbol interference, transmitter IQ skew, and phase noise. Finally, the residual phase noise is eliminated by the maximum likelihood (ML) estimator. The experimental results indicate that the proposed scheme provides better received optical power sensitivity and CD tolerance than the existing simplified DSP schemes. In addition, the proposed scheme can tolerate transmitter IQ skew up to 7 ps in a 10 km case, which outperforms both simplified and conventional DSP schemes. Meanwhile, the proposed scheme can keep the same transceiver IQ skew and CD tolerance and has reduced complexity by 25% after 10 km links, compared to 4×4 RV-MIMO followed by a transmitter skew compensator. To the best of our knowledge, the proposed scheme is the most cost-effective solution for a high baud rate datacenter interconnects where transmitter IQ skew and CD have to be dealt with.

Mitigation of nonlinear phase noise in single-channel coherent 16-QAM systems employing logistic regression

We propose and analyze a classifier based on logistic regression (LR) to mitigate the impact of nonlinear phase noise (NPN) caused by Kerr-induced self-phase-modulation in digital coherent systems with single-channel unrepeated links. Simulation results reveal that the proposed approach reduces the bit error ratio (BER) in a 100-km-long 16 quadrature amplitude modulation (16-QAM) system operating at 56-Gbps. Thus, the BER is reduced from 6.88 × 10−4 when using maximum likelihood to 4.27 × 10−4 after applying the LR-based classification, representing an increase of 0.36 dB in the effective Q-factor. This performance enhancement is achieved with only 624 operations per symbol, which can be easily parallelized into 16 lines of 39 operations.

Transmission of a 112-Gbit/s 16-QAM over a 1440-km SSMF with parallel Kramers-Kronig receivers enabled by an overlap approach and bandwidth compensation.

We investigate the parallelized performance of the conventional Kramers-Kronig (KK) and without the digital up-sampling KK (WDU-KK) receivers in a 112-Gbit/s 16-ary quadrature amplitude modulation (16-QAM) system over a 1440-km standard single-mode fiber (SSMF). A joint overlap approach and bandwidth compensation filter (OLA-BC) architecture is presented to mitigate the edge effect caused by the Hilbert transform and the Gibbs phenomenon induced by the FIR filter, respectively. Moreover, the computational complexity of the OLA-BC based parallelized KK/WDU-KK receiver is also discussed. Parallelized KK/WDU-KK receivers based on the presented OLA-BC architecture can effectively mitigate the edge effect and the Gibbs phenomenon together with more than two orders of magnitude improvement in terms of bit-error-ratio (BER) compared with parallelized KK/WDU-KK receivers without OLA-BC receivers in back-to-back (B2B) case. Finally, we successfully transmit the 16-QAM signals over 960-km SSMF with a BER lower than 7% hard-decision forward error correction (HD-FEC) threshold (3.8 × 10-3) and 1440-km SSMF with a BER lower than 20% soft-decision FEC (SD-FEC) threshold (2 × 10-2).

Performance Analysis of All-optical PPM-mQAM Communication Systems

Increasing the spectral efficiency of transmission has increased interests in hybrid optical communication systems. However, these systems suffer from the nonlinear fiber impairments that produce nonlinear phase noise (NPN). In this paper, we investigate all-optical coding m-ary quadrature amplitude modulation (mQAM) by pulse position modulation (PPM) in a single channel optical communication system to increase the transmission capacity and reduce the NPN. The system performance that optically modulates the data by hybrid PPM-mQAM format is numerically investigated by simulation. The results show that the transmission capacity is duplicated and NPN is significantly moderated when PPM-4QAM and PPM-16QAM are used. At bit error rate (BER) of 10−4, the transmission distances of PPM-4QAM is increased by about 33%, in comparison to 4QAM system. In addition, the required optical signal-to-noise ratios (OSNRs) for achieving BER of 1×10−4 are decreased by 4.7 dB and 7.5 dB for the PPM-4QAM and PPM-16QAM schemes, respectively.

Reduced sampling rate Kalman filters for carrier phase and frequency offset tracking in 200\xa0Gbps 16 QAM coherent communication system

We propose 1 state and 2 state multi-step Kalman filters (MKFs) to estimate and compensate CFO, LPN and NLPN in long-haul coherent fiber-optic communication systems. The proposed filters generate state estimates once every m symbols and therefore operate at a reduced sampling rate compared to conventional KFs that perform symbol by symbol processing. No computations are performed to obtain phase estimates of the intermediate m-1 samples; instead, the present and previous estimates are averaged and used to derotate the intermediate m-1 samples which are then demodulated to recover the transmitted symbols. This reduces the computational load on the receiver DSP. Further, in order to improve estimation accuracy, we adaptively vary the process noise covariance Q. Simulation results of 200 Gbps PDM 16 QAM system over 12 spans shows that the proposed 1 state MKF can reduce the sampling rate requirement by a factor of m = 20 with Q-factor degradation of 1.32 dB compared to single-step KF at linewidth of 100 kHz. The 2 state MKF tracks PN and CFO with a maximum step size of m=10 for a CFO of 100 MHz at linewidth of 100 kHz. We also study the dynamic performance of the proposed algorithms by applying step change to CFO. The 2 state MKF with adaptive Q is able to track a step change of 400 MHz of CFO with m = 1 and 3 with high estimation accuracy but slower convergence time compared to the non-adaptive 2 state MKF. Finally, we study the computational requirements of the proposed MKFs and show that they offer significant reduction in computations compared to single-step KF thus making the proposed filters suitable for hardware implementation.

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.