Maximum Likelihood Sequence Estimation Research Articles

Modified DDFTN Algorithm for Band-Limited Short-Reach Optical Interconnects

Inter symbol interference (ISI) degrades the performance of intensity modulation and direct detection (IM/DD) transmission systems due to various transceiver and channel impairments. To overcome the ISI of IM/DD transmission systems, the direct detection faster than Nyquist (DDFTN) algorithm has been widely used. However, when a system is subjected to severe ISI, the performance of the conventional DDFTN algorithm is suboptimal. To further improve the performance of IM/DD transmission systems, a modified DDFTN algorithm is proposed. We add least squares (LS) channel estimation after the postfilter. The coefficients of maximum likelihood sequence estimation (MLSE) are close to the initial channel response with LS channel estimation. The performance of the conventional and modified DDFTN algorithms is compared for 112, 140, and 160 Gbit/s PAM4 signals over 2 km, 1 km, and 500 m standard single-mode fibers (SSMFs) in a 3 dB bandwidth, 19 GHz IM/DD system in the C band. For 140 Gbit/s signal transmission over 1 km, the modified DDFTN algorithm achieves the optimal receiver sensitivity of -1.5 dBm at a 7% forward error correction (FEC) threshold of 3.8E-3, which is better than the receiver sensitivity of -0.5 dBm achieved with the conventional DDFTN algorithm. Furthermore, for 160 Gbit/s signal transmission over 500 m, the modified DDFTN algorithm achieves the optimal receiver sensitivity of 1 dBm at 3.8E-3, which is also a superior result compared to the conventional DDFTN algorithm.

Low-complexity and low-latency equalization technique - probabilistic noise cancellation.

Both inside data centers (DCs) and in short optical links between data centers (DC campuses), intensity-modulation and direct-detection (IMDD) systems using four-level pulse amplitude modulation (PAM4) will dominate this decade due to low transceiver price and power consumption. The next DC transceiver generation based on 100 Gbaud PAM4 will require advanced digital signal processing (DSP) algorithms and more powerful forward error correction (FEC) codes. Because of bandwidth limitations, the conventional DC DSP based on a few-tap linear feed-forward equalizer (FFE) is likely to be upgraded to more complex but still low-complexity Volterra equalizers followed by a noise whitening filter and either a maximum likelihood sequence estimation (MLSE) or a maximum a posteriori probability (MAP) algorithm. However, stringent power consumption and latency requirements may limit the use of complex algorithms such as decision feedback equalizer (DFE) or MLSE/MAP in DC networks (DCN). In this paper, we introduce a low-complexity, low-latency algorithm based on a feedforward structure, yielding a performance between DFE and MLSE. We call the novel equalization algorithm probabilistic noise cancellation (PNC), since it weights noise patterns based on their probabilities in the presence of bandwidth limitations. The probabilistic weighting is efficiently exploited in correcting correlated errors caused by noise coloring in the FFE.

Collaborative FFE-assisted simplified soft-output MLSE with LDPC for high-speed IM-DD transmissions.

In this paper, we propose a feed-forward equalizer (FFE)-assisted simplified soft-output MLSE (sMLSE) by collaborating the maximum likelihood sequence estimation (MLSE) with soft-decision low-density-parity-check (LDPC) decoding. The simplified sMLSE results in undetermined log-likelihood ratio (LLR) magnitudes when the reserved level is less than or equal to the half of modulation order. This severely degrades the performance of soft-decision forward error correction (SD-FEC) decoding. In the FFE-assisted simplified sMLSE, we use the LLRs calculated from pre-set FFE to replace these undetermined LLRs of simplified sMLSE. Thus, the proposed method eliminates the SD-FEC decoding performance degradation resulted from simplification. We conduct experiments to transmit 184-Gb/s PAM-4 or 255-Gb/s PAM-8 signal in IM-DD system at C-band to evaluate the performance of the proposed sMLSE. The results show that the proposed sMLSE can effectively compensate for the degradation of LLR quality. For 255-Gb/s PAM-8 signal transmissions, the FFE-assisted simplified sMLSE achieves almost the same SD-FEC decoding performance as the conventional sMLSE but with 85% complexity reduction.

High-Quality and Low-Complexity Polar-Coded Radio-Wave Encrypted Modulation Utilizing Multipurpose Frozen Bits

In recent years, physical layer security (PLS), which utilizes the inherent randomness of wireless signals to perform encryption at the physical layer, has attracted attention. We propose chaos modulation as a PLS technique. In addition, a method for encryption using a special encoder of polar codes has been proposed (PLS-polar), in which PLS can be easily achieved by encrypting the frozen bits of a polar code. Previously, we proposed a chaos-modulated polar code transmission method that can achieve high-quality and improved-security transmission using frozen bit encryption in polar codes. However, in principle, chaos modulation requires maximum likelihood sequence estimation (MLSE) for demodulation, and a large number of candidates for MLSE causes characteristic degradation in the low signal-to-noise ratio region in chaos polar transmission. To address this problem, in this study, we propose a versatile frozen bit method for polar codes, in which the frozen bits are also used to reduce the number of MLSE candidates for chaos demodulation. The numerical results show that the proposed method shows a performance improvement by 1.7 dB at a block error rate of 10-3 with a code length of 512 and a code rate of 0.25 compared with that of conventional methods. We also show that the complexity of demodulation can be reduced to 1/16 of that of the conventional method without degrading computational security. Furthermore, we clarified the effective region of the proposed method when the code length and code rate were varied.

Suppressed Noise Enhancement Equalization Combined With Nonlinear-MLSE Techniques for Bandwidth-Limitation IM/DD System

Bandwidth limitation introduced inter-symbol interference (ISI) is the major impediment for high baud rate intensity modulation and direct detection (IM/DD) system with commercial devices. Least mean square (LMS) criterion based feedforward equalizer (FFE) is the most common method to eliminate ISI in single-carrier system. However, there is a tradeoff between the residual ISI and enhanced noise when the system bandwidth is severely limited. Although a post filter (PF) followed by maximum likelihood sequence estimation (MLSE) can suppress the enhanced noise effectively, the residual ISI left by post-FFE will degrade the system performance as the subsequent MLSE only handles ISI introduced by PF. In this paper, an adaptive partial response equalization realized by a channel-shortening filter (CSF) is investigated, which is combined with MLSE. As the target of CSF is a partial response signal with desired low-pass feature, the noise will not be enhanced in this scheme. And the residual ISI with determined response can be fully solved by MLSE. The performance of CSF based MLSE (CSF-MLSE) is evaluated and compared to PF based MLSE (PF-MLSE) in 60/70/75Gbaud four-level pulse amplitude modulation (PAM-4) system with 10-dB bandwidth of 16.2GHz. The experimental results show that CSF-MLSE has a better capability of ISI elimination compared to PF-MLSE. The bit error rate (BER) can be reduced from 7.4×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> to 4×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> and from 3×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> to 1×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> for 70Gbaud and 75Gbaud in optical back-to-back (OBTB) transmission. To further compensate the system nonlinear impairments, several nonlinear MLSE (NL-MLSE) techniques assisted by look-up table (LUT) or Volterra filter are proposed and investigated in this paper. The BER of 75Gbuad PAM-4 can be below 3×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> after using NL-MLSE schemes.

Enhanced Performance of Artificial-Neural-Network-Based Equalization for Short-Haul Fiber-Optic Communications

This work proposes an efficient and easy-to-implement single-layer artificial neural network (ANN)-based equalizer with improved compensation performance. The proposed equalizer is used for effectively mitigating the distortions induced in the short-haul fiber-optic communication systems based on intensity modulation and direct detection (IMDD). The compensation performance of the ANN equalizer is significantly improved, exploiting an introduced advanced training scheme. The efficiency and robustness of the proposed ANN equalizer are illustrated through 10- and 28-Gbaud short-reach optical-fiber communication systems. Compared to the efficient but computationally expensive maximum likelihood sequence estimator (MLSE), the proposed ANN equalizer not only significantly reduces its computational equalization cost and storage memory requirements, but it also outperforms its bit error rate performance.

High-Capacity IM-DD Transmission in O-Band Using Advanced Maximum Likelihood Sequence Estimation Methods

We propose advanced maximum likelihood sequence estimation (MLSE) methods for increasing the capacity of short-reach intensity-modulated direct detection (IM-DD) transmissions for economically realizing next generation Ethernet such as 800GbE or 1.6TbE. It is particularly important to conquer the traffic growth in data center networks, which has become a major issue. In this article, we introduce a method for reducing the complexity of the Viterbi algorithm, which is a problem in the actual implementation of MLSE, by using a penalty-less truncated trellis diagram with temporal decision results. Next, we introduce a method for improving the demodulation performance by precisely emulating the nonlinear response of the transmission system with low-cost devices using a nonlinear filter. Finally, we introduce a method for reducing the computational complexity with a decision feedback function. Transmission experiments in the O-band with transmission rates of 200 Gbps/lane or higher using each of the proposed methods are also presented. Finally, we present a 200Gbps/lane 4-LAN-WDM 800G 2km transmission experiment using a 4-channel LAN-WDM TOSA designed for 400G transmission.

Burst errors suppression for MLSE in high-speed IM/DD transmission systems using PAM.

Maximum likelihood sequence estimation (MLSE) is the optimal signal sequence detection that can remove the inter-symbol interference (ISI). However, we find that the MLSE causes burst consecutive errors alternating between +2 and -2 in M-ary pulse amplitude modulation (PAM-M) IM/DD systems with large ISI. In this paper, we propose to use precoding to suppress the burst consecutive errors resulted from MLSE. A 2 M modulo operation is employed to guarantee that the probability distribution as well as the peak-to-average power ratio (PAPR) of encoded signal remain unchanged. After the receiver-side MLSE, the decoding process that involves adding the current MLSE output to the previous one and applying a 2 M modulo is implemented to break the burst consecutive errors. We conduct experiments to transmit 112/150-Gb/s PAM-4 or beyond 200-Gb/s PAM-8 signals at C-band to investigate the performance of the proposed MLSE integrated with precoding. The results show that the precoding can break burst errors effectively. For 201-Gb/s PAM-8 signal transmission, the precoding MLSE can achieve 1.4-dB receiver sensitivity gain and reduce the maximum length of burst consecutive errors from 16 to 3.

Asymmetrically Clipped Optical Hadamard Coded Modulation (ACO-HCM)

In many optical wireless communications systems, power efficiency is paramount. In others, flexibility is important. To achieve these goals, this paper presents a novel transmission scheme dubbed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">asymmetrically clipped optical Hadamard coded modulation (ACO-HCM)</i> . ACO-HCM combines the characteristics of real-valued non-negative orthogonal frequency-division multiplexing (OFDM) and Hadamard coded modulation (HCM). Unlike OFDM, which is based on the Fourier transform and therefore delivers a continuous waveform, ACO-HCM provides a discrete set of amplitudes. This feature is desirable for nonlinear channels. Error probabilities are analytically calculated for a linear receiver similar to the decorrelation receiver in direct-sequence code-division multiple access (DS-CDMA). Maximum-likelihood sequence estimation is also investigated and shown to outperform the linear receiver, particularly in the presence of a time-dispersive channel. The peak-to-average power ratio of ACO-HCM is derived for the electrical as well as the optical domain in closed form.

Joint Linear and Nonlinear Equalization Based on Cascaded ANN-MLSE With a Modified Loss Function for PAM-4 Optical Transmission

High-speed optical transmission systems suffer from severe inter-symbol interferences (ISIs) and nonlinear distortions due to the limited bandwidth and the nonlinear response of optical and electrical components at the transceivers. Previous work has shown the benefits of applying maximum-likelihood sequence estimation (MLSE) to deal with the ISI and using the neural network-based equalizer (NNE) to mitigate strong nonlinearities. However, most of the NNE has a quasi-hard output as the training and validation loss continue to drop to an over-equalized state in which the quasi-hard output sequence loses the symbol-wise soft information of the signal and fails to obtain the BER performance gain from MLSE. In this work, we investigate the cascaded NNE and MLSE equalization scheme to deal with linear and nonlinear impairments. To solve the over-equalized problem, we propose a modified loss function (MLF) assisting NNE to achieve soft-out without entering into the over-equalized state. With the soft output after NNE, joint linear and nonlinear equalization can be realized by cascading the NNE with MLSE. Both numerical simulations and experimental demonstrations confirm the improved performance of our proposed method. With joint linear and nonlinear equalization, improved back-to-back (BtB) and fiber transmission performances of the 220-Gbps PAM-4 signal are demonstrated.

Demonstration of 200 Gbps PAM-4 transmission in a limited-bandwidth system using a two-tap THP with nonlinearity compensator

In this paper, we have proposed a digital signal processing (DSP) method for a 200 Gbps pulse-amplitude modulation level-4 (PAM-4) transmission in a bandwidth-limited system. To mitigate inter-symbol interferences (ISI) in the system and reduce the propagation of errors in the receiver, the Tomlinson-Harashima precoding (THP) technique was applied to the transmitter. For simplicity, the number of THP taps was limited to two (i.e., one coefficient to be optimized); the residual ISI resulting from the short tap was compensated for with a decision feedback equalizer (DFE). The performance of the proposed DSP was analyzed via experiments and simulations. Compared to conventional DSP techniques (such as DFE and the maximum likelihood sequence estimation (MLSE) without THP), the proposed DSP performs better within the limited-bandwidth region. As a result, the soft-decision forward error correction (SD-FEC) threshold (of 2 × 10−2) was satisfied even when the bandwidth fell to below 35% of the baud rate. To enhance this performance, post-filter and MLSE were additionally applied, after which its performance was investigated. In addition, the nonlinear characteristics of the components were alleviated by applying a pre-distortion technique to the THP using look-up tables; this further enhanced performance, lowering the SD-FEC threshold’s bandwidth to 32% of the baud rate.

Effects of acoustic nonlinearity on communication performance in soft tissues.

Acoustic communication has been gaining traction as an alternative communication method in nontraditional media, such as underwater or through tissue. Acoustic propagation is known to be a nonlinear phenomenon; nonlinear propagation of acoustic waves in soft tissues at biomedical frequencies and intensities has been widely demonstrated. However, the effects of acoustic nonlinearity on communication performance in biological tissues have not yet been examined. In this work, nonlinear propagation of a communication signal in soft tissues is analyzed. The relationship between communication parameters (signal amplitude, bandwidth, and center frequency) and nonlinear distortion of the communication signal propagating in soft tissues with different acoustic properties is investigated. Simulated experiments revealed that, unlike linear channels, bit error rates increase as signal amplitude and bandwidth increase. Linear and decision feedback equalizers fail to address the increased error rates. When tissue properties and transmission parameters can be estimated, receivers based on maximum likelihood sequence estimation approach the performance of an ideal receiver in an ideal additive white Gaussian noise channel.

LSTM Attention Neural-Network-Based Signal Detection for Hybrid Modulated Faster-Than-Nyquist Optical Wireless Communications.

In order to improve the accuracy of signal recovery after transmitting over atmospheric turbulence channel, a deep-learning-based signal detection method is proposed for a faster-than-Nyquist (FTN) hybrid modulated optical wireless communication (OWC) system. It takes advantage of the long short-term memory (LSTM) network in the recurrent neural network (RNN) to alleviate the interdependence problem of adjacent symbols. Moreover, an LSTM attention decoder is constructed by employing the attention mechanism, which can alleviate the shortcomings in conventional LSTM. The simulation results show that the bit error rate (BER) performance of the proposed LSTM attention neural network is 1 dB better than that of the back propagation (BP) neural network and outperforms by 2.5 dB when compared with the maximum likelihood sequence estimation (MLSE) detection method.

Improving the spectral efficiency of visible light communications by a super-Nyquist multi-band CAP modulation.

In this Letter, we propose a flexible bandwidth compression scheme for visible light communication (VLC) systems employing multi-band carrierless amplitude and phase (CAP) modulation. The scheme combines a narrow filtering for every subband at the transmitter and an N-symbol look-up-table (LUT) based maximum likelihood sequence estimation (MLSE) at the receiver. The N-symbol LUT is generated by recording pattern-dependent distortions induced by inter-symbol-interference (ISI), inter-band-interference (IBI), and the other channel effects upon the transmitted signal. The idea is experimentally demonstrated on a 1 m free space optical transmission platform. The results show that the proposed scheme can improve the subband overlap tolerance up to 42% in subband overlapping scenarios, that is, 3 bit/s/Hz, which is the highest spectral efficiency (SE) among the experimented schemes.

A Maximum-Likelihood-Based Two-User Receiver for LoRa Chirp Spread-Spectrum Modulation

Long Range (LoRa) is an emerging low-power wide-area network technology offering long-range wireless connectivity to Internet of Things (IoT) devices. For energy efficiency reasons, LoRa end nodes implement a nonslotted ALOHA multiple access scheme to transmit packets to the gateway. Due to the lack of synchronization between end nodes, collisions between uplink packets have been identified as the main obstacle to the scaling of dense LoRa networks. To tackle this issue, we present in this article a LoRa receiver that is capable of decoding colliding packets from two interfering end nodes. The proposed two-user detector is derived from the maximum-likelihood principle using a detailed model of two colliding LoRa packets. As the complexity of the maximum-likelihood sequence estimation is prohibitive, complexity-reduction techniques are introduced to enable practical implementations of the receiver. An in-depth performance analysis highlights that the proposed two-user detector inherently leverages the differences in received power, time offsets, and frequency offsets between the users to separate and demodulate their respective signals. To demonstrate the practicality of the proposed detector, an interference-robust synchronization algorithm is then designed and evaluated. Simulation results indicate that a LoRa receiver combining the proposed synchronization algorithm and two-user detector is capable of detecting and demodulating two interfering users with satisfactorily error rates.

Ambient Environmental Parameter Estimation for Reliable Diffusive Molecular Communications

Molecular communication is a promising communication technology that uses biomolecules such as proteins and ions to establish a communication link between nanoscale devices. In diffusive molecular communication, which uses diffusion characteristics of transfer molecules, the diffusion mechanism is mathematically derived as a Channel Impulse Response (CIR) to design an optimal detector structure. However, an ideal environment is assumed for deriving a CIR. Hence there is a concern that developed systems based on the derived CIR may not operate well in a realistic environment. In this study, based on the finite element method (FEM), we constructed a model of the environment with heterogeneous temperature distribution and actual volume of transmitting molecules to not only demodulate the bit information via maximum likelihood sequence estimation (MLSE) but also to estimate the temperature and volume of the transmitting molecules. Furthermore, in this study, we evaluated the performance of the MLSE method and investigated the effects of ambient environmental temperature distribution and volume of the transmitted molecules on diffusive molecular communication. The evaluation results demonstrated that the proposed method can improve the communication performance by approximately 9 dB by estimating the temperature and transmit molecule volume.

Complexity curtailed MLSE equalizer based on a compact look-up-table for C-band DSB IM/DD transmission.

Chromatic dispersion appears to be a major performance limiting problem in optical intensity modulation direct detection (IM/DD) transmission systems, especially for a double-sideband (DSB) signal. We propose a complexity-reduced look-up-table based maximum likelihood sequence estimation (LUT-MLSE) for DSB C-band IM/DD transmission based on pre-decision-assisted trellis compression and a path-decision-assisted Viterbi algorithm. To further compress the size of the LUT and reduce the length of the training sequence, we proposed a finite impulse response (FIR) and LUT hybrid channel model for the LUT-MLSE. For PAM-6 and PAM-4, the proposed methods can compress the size of the LUT into 1/6 and 1/4, and reduce the number of multipliers by 98.1% and 86.6% with slight performance degradation. We successfully demonstrate a 20-km 100-Gb/s PAM-6 and a 30-km 80-Gb/s PAM-4 C-band transmission over dispersion-uncompensated links.

A Mixed-Integer Solution for TDOA Based Direct Positioning of Digital Modulation Signal

This paper proposes a direct position determination (DPD) method for a digital modulation signal based on time difference of arrival (TDOA) measurements. Unlike the two-step positioning process, the measurements are used to directly estimate the source position. Fully utilizing information in a transmitted waveform can improve the accuracy of source localization in a single-step method. Based on maximum likelihood (ML) estimates, when the digital modulation scheme is known to the location system, an alternating iterative DPD method is developed to locate the emitter. The objective function of the proposed algorithm takes into account the source position and transmitted symbol sequence, which makes it a mixed-integer optimization problem. In particular, ML sequence estimation is adopted and the complex envelope is restored using a genetic algorithm. Then, based on Newton’s method, an alternating iterative algorithm is proposed to update the position and symbol sequence results. Compared with the existing DPD method, the proposed algorithm gives more accurate location results for unknown waveforms. In addition, the proposed algorithm can reach the Cramér-Rao bound (CRB) for known signal waveforms, as verified using comprehensive simulations.

Advanced nonlinearity equalizer with TC-NL-MLSE for transmitting beyond 200-Gb/s PAM-8 in IM/DD systems.

The severe band-limited effect resulted from the low-cost optical transceiver increases the channel memory length and the number of taps of the equalizers. Besides, the interaction of fiber dispersion and square-law detection introduce nonlinear distortions in intensity modulation and direct-detection (IM/DD) transmission systems. The serious band-limited effect and nonlinear distortions degrade the transmission performance and bring challenges to current equalizers for low-complexity implementation. In this paper, we propose a trellis-compression nonlinear maximum likelihood sequence estimation (TC-NL-MLSE) algorithm to compensate the linear and nonlinear distortions with lower complexity. In the TC-NL-MLSE, we introduce a polynomial nonlinear filter (PNLF) to partly compensate both the linear distortions and nonlinear distortions. Then, we establish a look-up-table (LUT) to calculate the nonlinear branch metric (BM). To simplify the calculation, two or three levels with the highest probabilities are selected according to decision thresholds for each symbol to compress the state-trellis graph (STG). This significantly reduces computational complexity on BM calculations especially for high-order modulations. We conduct experiments to transmit beyond the 200-Gb/s PAM-8 signal over 2-km standard single mode fiber (SSMF) at C-band. The TC-NL-MLSE outperforms the reduced-state MLSE with PNLF, and can reach the 7%-overhead hard-decision forward error correction threshold. Moreover, the TC-NL-MLSE reduces the complexity by 97% compared with standard LUT-MLSE, limiting the multipliers around 100 at the expense of only 0.2-dB receiver sensitivity penalty.

Decision region partition aided MLSE for O-band 65-Gbaud PAM-4 system over 40-km transmission with a severe bandwidth constraint.

Maximum likelihood sequence estimation (MLSE) is an optimal solution to realize sequence detection in the digital signal processing (DSP) of short reach O-band intensity modulation/direct detection (IM/DD) systems with bandwidth limitation. However, traditional MLSE requires relatively high computational complexity for short reach optical interconnect. Although the computational complexity of single-symbol sequence detection is quite low, the capability of combating with the inter symbol interference (ISI) is inadequate. To combine the low computational complexity of single-symbol sequence detection with the high reliability of multi-symbol sequence detection in MLSE, decision region partition aided MLSE (DRP-MLSE) is proposed and verified with 60-Gbaud and 65-Gbaud PAM-4 IM/DD systems over 40-km single-mode fiber (SMF) transmission. The experimental results show that the DRP-MLSE can realize similar performance of conventional MLSE with negligible penalty and significantly lower computational complexity.