Maximum Likelihood Sequence Detection Research Articles

Practical Considerations in Direct Detection Under Tukey Signalling

The deliberate introduction of controlled intersymbol interference (ISI) in Tukey signalling enables the recovery of signal amplitude and (in part) signal phase under direct detection, giving rise to significant data rate improvements compared to intensity modulation with direct detection (IMDD). The use of an integrate-and-dump detector makes precise waveform shaping unnecessary, thereby equipping the scheme with a high degree of robustness to nonlinear signal distortions introduced by practical modulators. Signal sequences drawn from star quadrature amplitude modulation (SQAM) formats admit an efficient trellis description that facilitates codebook design and low-complexity near maximum-likelihood sequence detection in the presence of both shot noise and thermal noise. Under the practical (though suboptimal) allocation of a 50% duty cycle between ISI-free and ISI-present signalling segments, at a symbol rate of 50 Gbaud and a launch power of -10 dBm the Tukey scheme has a maximum theoretically achievable throughput of 200 Gb/s with an (8,4)-SQAM constellation, while an IMDD scheme achieves about 145 Gb/s using PAM-8. Note that the two mentioned constellations have the same number of magnitude levels and the difference in throughput is resulting from exploiting phase information under using a complex-valued signal constellation.

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.

High-Dimensional Feature Based Non-Coherent Detection for Multi-Intensity Modulated Ultraviolet Communications

Ultraviolet communication (UVC) has been regarded as a promising supplement for overloaded conventional wireless communications. One challenge lies in the communication deterioration caused by the UV-photon scattering induced inter-symbol-interference (ISI), which will be even worse when encountering multilevel pulse amplitude modulation (multi-PAM) symbols. To address this ISI, traditional coherent detection methods (e.g., maximum-likelihood sequence detection, MLSD) require high computational complexities for UV channel estimation and sequential detection space formation, thereby making them less attractive. Current non-coherent detection, which simply combines the ISI-insensitive UV signal features (e.g., the rising edge) into a one-dimensional (1D) metric, cannot guarantee reliable communication accuracy. In this work, a novel high-dimensional (HD) non-coherent detection scheme is proposed, leveraging a HD construction of the ISI-insensitive UV signal features. By doing so, we transform the ISI caused sequential detection into an ISI-released HD detection framework, which avoids complex channel estimation and sequential detection space computation. Then, to compute the detection surface, a UV feature based unsupervised learning approach is designed. We deduce the theoretical bit error rate (BER), and prove that the proposed HD non-coherent detection method has a lower BER than that of the current 1D non-coherent scheme. Simulation results validate our results, and more importantly, demonstrate a BER that approaches that of the state-of-the-art coherent MLSD ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$&lt; $</tex-math></inline-formula> 1 dB in SNR at BER = <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$4.5\times 10^{-3}$</tex-math></inline-formula> , the 7% overhead forward-error-correction limit), and also a reduction of computational complexity by at least two orders of magnitude.

Cross Domain Iterative Detection for Orthogonal Time Frequency Space Modulation

Recently proposed orthogonal time frequency space (OTFS) modulation has been considered as a promising candidate for accommodating various emerging communication and sensing applications in high-mobility environments. In this paper, we propose a novel cross domain iterative detection algorithm to enhance the error performance of OTFS modulation. Different from conventional OTFS detection methods, the proposed algorithm applies basic estimation/detection approaches to both the time domain and delay-Doppler (DD) domain and iteratively updates the extrinsic information from two domains with the unitary transformation. In doing so, the proposed algorithm exploits the time domain channel sparsity and the DD domain symbol constellation constraints. We evaluate the estimation/detection error variance in each domain for each iteration and derive the state evolution to investigate the detection error performance. We show that the performance gain due to iterations comes from the non-Gaussian constellation constraint in the DD domain. More importantly, we prove that the proposed algorithm can indeed converge and, in the convergence, the proposed algorithm can achieve almost the same error performance as the maximum-likelihood sequence detection even in the presence of fractional Doppler shifts. Furthermore, the computational complexity associated with the domain transformation is low, thanks to the structure of the discrete Fourier transform (DFT) kernel. Simulation results are consistent with our analysis and demonstrate a significant performance improvement compared to conventional OTFS detection methods.

Sub-sampling generation of ultra-high baud rate PAM/QAM signals via high-order partial response narrowing

Ultra-high baud rate signal generation and detection is of great importance for future intra-data-center interconnect (intra-DCI). In this work, based on a single digital-to-analog convertor (DAC) with 120GSa/s sampling rate, we experimentally demonstrate sub-sampling generation of pulse amplitude modulation (PAM) signals by using high-order partial response narrowing (HPRN) scheme. High-order partial response is utilized to concentrate most of the signal energy into the Nyquist region of DAC sampling rate. A digital brick-wall filter is then employed to avoid spectral overlap by removing the out-of-band components in the frequency domain. The manually induced inter-symbol interference (ISI) can be eliminated by maximum likelihood sequence detection (MLSD) at the receiver. In the experiment, 210Gbaud on-off keying (OOK) signal can be successfully generated and transmitted over 500m standard single-mode fiber (SSMF) with bit-error rate (BER) below the 20% hard-decision forward error correction (HD-FEC) threshold of 1.5×10−2, achieving sub-sampling rate of 0.571. For high-order modulation formats, 217.5Gb/s (145Gbaud) PAM-3 BTB generation and 256Gb/s (128Gbaud) PAM-4 500m transmission are also realized, respectively. Furthermore, for coherent detection systems, 160Gbaud quadrature phase shift keying (QPSK) signal generation is demonstrated by applying HPRN on the in-phase and quadrature components separately, and using carrier phase recovery including pilot symbol group-based coarse estimation and shaped constellation-based blind phase search (BPS) algorithm. The results reveal that the HPRN scheme can extend the usage of DAC at the expense of higher optical signal-to-noise ratio (OSNR) for 200G high-speed optical links and beyond.

Simplified Receivers for Generic Binary Single Side Band CPM Using PAM Decomposition

This paper investigated the pulse amplitude modulation (PAM) decomposition of a class of continuous phase modulation (CPM) signal, which has the property to be a single-side band. We used the PAM decomposition as a convenient solution to provide a large reduced complexity trellis detection to approach the theoretical optimal performance. Moreover, we developed an algorithm to obtain the necessary PAM pulses to approach the optimal performance bound using suboptimal receivers. The algorithm is generic; it can provide the results for any parameter combinations. The proposed demodulation system exhibits excellent performance with minimal complexity with respect to the maximum likelihood sequence detection (MLSD) optimal receiver.

A Demodulation Method Using a Gaussian Mixture Model For Unsynchronous Optical Camera Communication With on-off Keying

We consider optical camera communication (OCC) between a camera receiver with optical lenses and distributed transmitters. This article investigates the features of an OCC system when the periods of reception and transmission are slightly different from each other. We describe a received light signal model for the OCC system with on-off keying and regard the received signals generated from a probability distribution of a Gaussian mixture model. We obtain the parameters of the probability distributions by applying a variational Bayesian inference method and utilize them for channel estimation. In addition, we define cost functions and minimize them to demodulate the transmitted bit sequences. The demodulation procedure uses a maximum-likelihood sequence detection method, which can be implemented by the Viterbi algorithm and estimates a synchronization parameter by minimizing the cost functions. Our new demodulation method requires neither synchronization devices nor training sequences for estimating the parameters. Moreover, the receiver does not need the precise transmission period, which is difficult to know in advance in practical situations because of the frequency tolerance of the clock generator in the transmitter. To validate our developed method, we conducted numerical simulations and compared the results with those from an oracle estimator that knows the parameters other than the bit sequence in advance. We also experimented in a real setup situation, and the results show the efficiency of our developed method.

Fractionally Spaced Equalization and Decision Feedback Sequence Detection for Diffusive MC

In this letter, we consider diffusive molecular communication (MC) systems affected by signal-dependent diffusive noise, inter-symbol interference, and external noise. We design linear and nonlinear fractionally-spaced equalization schemes and a detection scheme which combines decision feedback and sequence detection (DFSD). In contrast to the symbol-rate equalization schemes in the MC literature, the proposed equalization and detection schemes exploit multiple samples of the received signal per symbol interval to achieve lower bit error rates (BERs) than existing schemes. The proposed DFSD scheme achieves a BER which is very close to that achieved by maximum likelihood sequence detection, but with lower computational complexity.

Non-Coherent Detection for Ultraviolet Communications With Inter-Symbol Interference

Ultraviolet communication (UVC) serves as a promising supplement to share the responsibility for the overloads in conventional wireless communication systems. One difficulty lies in how to address the inter-symbol-interference (ISI) from the strong scattering nature and the time-varying channel response. This is more challenging for the energy-constrained scenarios (e.g., underwater UV), as existing coherent schemes (i.e., requiring exact channel information for signal detection) become less attractive given the computational and storaging complexity for repeated time-varying channel estimation and statistical signal detection. In this work, a novel non-coherent paradigm is proposed, via the exploration of the UV signal features that are insensitive to the ISI. By optimally weighting and combining the extracted features to minimize the bit error rate (BER), the optimally-weighted non-coherent detection (OWNCD) is proposed, which converts the signal detection with ISI into a binary detection framework, with a heuristic weight updating approach for time-varying channel. As such, the proposed OWNCD avoids the complex channel estimation and guarantees the detection accuracy. Compared to the state-of-the-art coherent maximum likelihood sequence detection (MLSD) in the cases of static and time-varying channel response, the proposed OWNCD can gain $\sim$ 1 dB and $\sim$ 8 dB in signal-to-noise-ratio (SNR) at the 7 $\%$ overhead forward-error-correction (FEC) limit (BER of $4.5\times 10^{-3}$ ), respectively, and can also reduce the computational complexity by 4 order of magnitude.

Bidirectional Viterbi decoding algorithm for OvTDM

Overlapped time domain multiplexing (OvTDM) is an innovative encoding scheme that can obtain high spectral efficiency. However, the intentional inter-symbol interference (ISI) caused by OvTDM will make the decoding process more complex. The computational complexity of maximum likelihood sequence detection increases exponentially with the growth of spectral efficiency in OvTDM. As a consequence of high complexity, the decoding effort for a given spectral efficiency may occasionally exceed the physical limitations of the decoder, leading inevitably to buffer overflows and information erasures. In this paper, we propose a bidirectional Viterbi algorithm (BVA) based on the bidirectional sequence decoding for OvTDM. With the BVA, the decoding operation starts simultaneously from the both ends of the corresponding trellis and stops at the middle of trellis. The simulation results show that compared with Viterbi algorithm (VA), the decoding time of BVA can be reduced by about half. And the memory space of two decoders in BVA are about half of that in VA, which means that the BVA has lower memory requirements for decoder. And the decoding performance of BVA is almost the same as VA.

Low-complexity equalization scheme for suppressing FFE-enhanced in-band noise and ISI in 100 Gbps PAM4 optical IMDD system.

The commonly used feed-forward equalizer (FFE) in an intensity modulation and direct-detection (IMDD) system is seriously restrained by the enhanced in-band noise in the high-frequency region. In this Letter, a low-complexity equalization scheme including FFE, post-filter (PF), and a newly designed interference cancellation (IC) algorithm is proposed to cope with the FFE-enhanced noise and serious inter-symbol interference (ISI) simultaneously. In our experiment, the achieved bit error rate value of 100 Gb/s optical double-sideband (ODSB) four-level pulse amplitude modulation (PAM4) signal transmission over 10 km standard single-mode fiber (SSMF) can go below the 20% overhead soft-decision forward error correction threshold of ${2.7} \times {{10}^{ - 2}}$2.7×10-2 when the FFE is replaced by the proposed equalizer. Even a 100 Gb/s optical single-sideband (OSSB) PAM4 signal can be successfully transmitted over 80 km SSMF. The results show that the proposed ${\rm FFE}+{\rm PF}+{\rm IC}$FFE+PF+IC algorithm can effectively suppress the FFE-enhanced noise and ISI with a quite low increase in complexity. Moreover, compared to the joint FFE, PF, and maximum likelihood sequence detection (MLSD) algorithm, the proposed ${\rm FFE}+{\rm PF}+{\rm IC}$FFE+PF+IC algorithm has 1.2 dB and 0.4 dB power penalties after 10 km SSMF in ODSB and 80 km SSMF in OSSB cases, respectively. However, the complexity of this IC algorithm is approximately 3% that of the MLSD.

A decoding method based on RNN for OvTDM

Overlapped X domain multiplexing (OvXDM) is a promising encoding technique to obtain high spectral efficiency by utilizing Inter-Symbol Interference (ISI). However, the computational complexity of Maximum Likelihood Sequence Detection (MLSD) increases exponentially with the growth of spectral efficiency in OvXDM, which is unbearable for practical implementations. This paper proposes an OvTDM decoding method based on Recurrent Neural Network (RNN) to realize fast decoding of OvTDM system, which has lower decoding complexity than the traditional fast decoding method. The paper derives the mathematical model of the OvTDM decoder based on RNN and constructs the decoder model. And we compare the performance of the proposed decoding method with the MLSD algorithm and the Fano algorithm. It's verified that the proposed decoding method exhibits a higher performance than the traditional fast decoding algorithm, especially for the scenarios of a high overlapped multiplexing coefficient.

Notice of Violation of IEEE Publication Principles: Channel Equalization and Data Detection of OVFDM Under Fading Channel

Obtaining high spectral efficiency by overlapping and weighting multiplexing waveforms, OVFDM (Overlapped Frequency Division Multiplexing) system is considered to be a promising multi-carrier technology in future communication networks. Limited by the non-orthogonality between subcarriers, OVFDM systems usually use MLSD (Maximum Likelihood Sequence Detection) algorithm for decoding, which brings high computational complexity and thus limits the applying of OVFDM system in engineering. In this paper, a ZP (Zero-padding) - OVFDM architecture is proposed and the architecture can benefit from frequency diversity. Meanwhile, compared with the MLSD algorithm, the proposed MAP (Maximum A Posteriori) -based Viterbi decoding algorithm has better performance and requires much less computation by evaluating the likelihood of each detection and discarding the least possible ones based on the MAP criterion. The numerical results show that OVFDM can provide superior performance over OFDM on frequency selective fading channels.

240 Gbit/s Silicon Photonic Mach-Zehnder Modulator Enabled by Two 2.3-Vpp Drivers

We recently reported for the first time 200 Gbit/s/ $\lambda$ net rate data transmission with a single silicon photonic modulator in an intensity modulation direct detection link. Our demonstration relied on an in-house designed, O-band segmented-electrode MZM. In this article, we detail the optimization of the modulator driving scheme, bandwidth/efficiency trade-off and modulation format enabling this result. We use two single-ended RF signals, each having 2.3-Vpp amplitude only, to drive two 1.5-mm modulator segments and transmit data at 80 Gbaud PAM-8 (240 Gbit/s) across 2 km under the 20% soft-decision forward error correction BER threshold of 2E-02. We further decrease the BER using maximum likelihood sequence detection (MLSD), and discuss the related implications. Additionally, we present the system margins regarding modulator drive voltage, received optical power and equalizer taps. At 240 Gbit/s line rate, the modulator energy consumption is only 73 fJ/bit at the SD-FEC threshold. We finally discuss practical implementation considerations for our system.

System Optimization of an All-Silicon IQ Modulator: Achieving 100-Gbaud Dual-Polarization 32QAM

We experimentally demonstrate the highest, to the best of our knowledge, reported net rate in a SiP IQ modulator. At 100 Gbaud 32QAM (quadrature amplitude modulation), and assuming 20% FEC (forward error correction) overhead, we achieved a dual polarization net rate of 833 Gb/s. This record was achieved by adapting digital signal processing to the challenging pattern dependent distortion encountered in the nonlinear and bandwidth limited regime. First the Mach Zehnder modulator (MZM) operating point (trading off modulation efficiency and 3 dB bandwidth) and linear compensation (electrical and optical) are jointly optimized. Next, the key application of nonlinear pre- and post-compensation are explored. We show that nonlinear processing at the transmitter, in our case an iterative learning control (ILC) method, is essential as post-processing alone could not achieve reliable communications at 100 Gbaud. Nonlinear post-compensation algorithms pushed the performance under the FEC threshold with the introduction of structured intersymbol interference in post processing and a simple one-step maximum likelihood sequence detector. We provide detailed descriptions of our methodology and results.

Sparse Bayesian Learning-Aided Joint Sparse Channel Estimation and ML Sequence Detection in Space-Time Trellis Coded MIMO-OFDM Systems

Sparse Bayesian learning (SBL)-based approximately sparse channel estimation schemes are conceived for space-time trellis coded (STTC) multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems relying on trellis-based encoding and decoding over the data subcarriers. First, a pilot-aided channel estimation scheme is developed employing the multiple response extension of SBL (MSBL) framework. Subsequently, a novel data-aided joint channel estimation and data decoding framework relying on optimal maximum likelihood sequence detection (MLSD) is intrinsically amalgamated with our powerful EM-based MSBL algorithm. Explicitly, an MSBL-based MIMO channel estimate is gleaned in the E-step followed by a novel modified path-metric-based Viterbi decoder in the M-step. Our theoretical analysis characterizes the performance of the proposed schemes in terms of the associated frame error rate (FER) upper bounds by explicitly considering the effect of estimation errors along with evaluating the product measure of the STTC under consideration. Finally, our simulation results are complemented by the Bayesian Cramer-Rao bound (BCRB), the associated complexity analysis and the performance of the proposed schemes for validating the theoretical bounds.

Toward Single Lane 200G Optical Interconnects With Silicon Photonic Modulator

In this work, based on a conventional silicon photonic travelling-wave Mach-Zehnder modulator (MZM) with a 3-dB bandwidth of 22.5 GHz, we experimentally demonstrate ultra-high speed optical interconnects with Nyquist shaped pulse amplitude modulation (PAM) signals. For bandwidth-limited systems, a two-tap digital post filter is employed to suppress the equalization-enhanced high frequency noise. The post filter induced inter-symbol interference (ISI) is subsequently eliminated by maximum likelihood sequence detection (MLSD). Enabled by the post filter and MLSD, we achieve 200 Gb/s (80 Gbaud) PAM-6 signal direct detection (DD) transmission over 1 km standard single-mode fiber (SSMF) with a bit-error rate (BER) below the 20% hard-decision forward error correction (HD-FEC) threshold of 1.5 × 10−2. For PAM-4 format, we successfully transmit 192 Gb/s (96 Gbaud) and 176 Gb/s (88 Gbaud) signals over 1 km and 2 km SSMF, respectively, with BERs lower than the 20% HD-FEC threshold. For PAM-8 format, 192 Gb/s (64 Gbaud) and 168 Gb/s (56 Gbaud) signals are generated at back-to-back (BTB) and transmitted over 1 km SSMF, respectively. To our best knowledge, we achieve the highest single lane bitrates ever reported for single polarization PAM-4/6/8 signal generation and DD transmission with all-silicon MZM. The flexible receiver-side digital signal processing (DSP) can significantly enhance the performance of silicon MZM, which provides a promising solution for future single lane 200 G data-center interconnects.

Hartley-Domain DD-FTN Algorithm for ACO-SCFDM in Optical-Wireless Communications

In this paper, we propose a Hartley-domain direct-detection faster-than-Nyquist (HD-DD-FTN) algorithm for asymmetrically clipped optical single-carrier frequency-division multiplexing (ACO-SCFDM) in optical-wireless communications (OWC). The HD-DD-FTN algorithm includes modified Hartley-domain equalization (HDE) and maximum likelihood sequence detection, which can simultaneously compensate serious high-frequency distortion and eliminate enhanced in-band noise for the bandwidth-limited OWC. Modified HDE can be implemented by real-valued operations, which is appropriate for dealing with real-valued signals. The simulation results show that ACO-SCFDM system using the HD-DD-FTN algorithm is more robust to inter-symbol interference than that using conventional HDE algorithm. Therefore, the bit error rate performance of the ACO-SCFDM system using HD-DD-FTN algorithm is better than that using the conventional HDE algorithm. In conclusion, the ACO-SCFDM system using the HD-DD-FTN algorithm shows great potential for bandwidth-limited OWC.

Joint FDE and MLSD Algorithm for 56-Gbit/s Optical FTN-PAM4 System Using 10G-Class Optics

In this paper, we propose a joint frequency-domain equalizer (FDE) and maximum likelihood sequence detection (MLSD) algorithm to eliminate the serious inter-symbol interference for 56-Gbit/s optical faster-than-Nyquist 4-level pulse-amplitude modulation (FTN-PAM4) system using 10 G-class optics. The simplified FDE structure is first designed to replace the feed-forward equalization (FFE) and post filter structure in conventional joint FFE, post filter and MLSD algorithm. In the joint algorithms, the simplified FDE structure has approximately $13\%$ and $1\%$ computational complexity compared to FFE with least-mean-square (FFE-LMS) adaptive algorithm and FFE with recursive-least-squares (FFE-RLS) adaptive algorithm, respectively. Therefore, the proposed joint FDE and MLSD algorithm has much lower computational complexity than the conventional joint FFE, post filter and MLSD algorithm. Meanwhile, the experimental results show that the performance of joint FDE and MLSD algorithm is better than that of joint FFE-LMS, post filter and MLSD algorithm, and is similar with that of joint FFE-RLS, post filter and MLSD algorithm. In conclusion, the proposed joint FDE and MLSD algorithm has both low computational complexity and excellent performance for optical FTN-PAM4 systems, which shows its potential for applications in low-cost and low-power short-reach optical interconnects.

Beyond 100G Single Sideband PAM-4 Transmission With Silicon Dual-Drive MZM

We experimentally demonstrate beyond 100G single sideband (SSB) 4-ary pulse amplitude modulation (PAM-4) signal generation with a silicon dual-drive Mach-Zehnder modulator (DD-MZM) operating at C-band. With Kramers-Kronig detection, a 128-Gb/s PAM-4 signal is transmitted over 80-km standard single mode fiber (SSMF) with a bit error rate (BER) below the 7% hard-decision forward error correction (HD-FEC) threshold of 3.8 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . In comparison, a 168-Gb/s PAM-4 signal is transmitted over 80-km SSMF with a BER below the 20% HD-FEC threshold of 1.5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> . A two-tap digital post filter and maximum likelihood sequence detection are applied to compensate for the limited system bandwidth. To the best of our knowledge, this letter reports the highest single-lane bitrate of 80-km SSB transmission with a DD-MZM and direct detection. It provides an attractive low-cost solution for inter-datacenter interconnection and metro-haul transmission.