Sequential Detection Algorithm Research Articles

Real-World Gait Detection Using a Wrist-Worn Inertial Sensor: Validation Study.

Wrist-worn inertial sensors are used in digital health for evaluating mobility in real-world environments. Preceding the estimation of spatiotemporal gait parameters within long-term recordings, gait detection is an important step to identify regions of interest where gait occurs, which requires robust algorithms due to the complexity of arm movements. While algorithms exist for other sensor positions, a comparative validation of algorithms applied to the wrist position on real-world data sets across different disease populations is missing. Furthermore, gait detection performance differences between the wrist and lower back position have not yet been explored but could yield valuable information regarding sensor position choice in clinical studies. The aim of this study was to validate gait sequence (GS) detection algorithms developed for the wrist position against reference data acquired in a real-world context. In addition, this study aimed to compare the performance of algorithms applied to the wrist position to those applied to lower back-worn inertial sensors. Participants with Parkinson disease, multiple sclerosis, proximal femoral fracture (hip fracture recovery), chronic obstructive pulmonary disease, and congestive heart failure and healthy older adults (N=83) were monitored for 2.5 hours in the real-world using inertial sensors on the wrist, lower back, and feet including pressure insoles and infrared distance sensors as reference. In total, 10 algorithms for wrist-based gait detection were validated against a multisensor reference system and compared to gait detection performance using lower back-worn inertial sensors. The best-performing GS detection algorithm for the wrist showed a mean (per disease group) sensitivity ranging between 0.55 (SD 0.29) and 0.81 (SD 0.09) and a mean (per disease group) specificity ranging between 0.95 (SD 0.06) and 0.98 (SD 0.02). The mean relative absolute error of estimated walking time ranged between 8.9% (SD 7.1%) and 32.7% (SD 19.2%) per disease group for this algorithm as compared to the reference system. Gait detection performance from the best algorithm applied to the wrist inertial sensors was lower than for the best algorithms applied to the lower back, which yielded mean sensitivity between 0.71 (SD 0.12) and 0.91 (SD 0.04), mean specificity between 0.96 (SD 0.03) and 0.99 (SD 0.01), and a mean relative absolute error of estimated walking time between 6.3% (SD 5.4%) and 23.5% (SD 13%). Performance was lower in disease groups with major gait impairments (eg, patients recovering from hip fracture) and for patients using bilateral walking aids. Algorithms applied to the wrist position can detect GSs with high performance in real-world environments. Those periods of interest in real-world recordings can facilitate gait parameter extraction and allow the quantification of gait duration distribution in everyday life. Our findings allow taking informed decisions on alternative positions for gait recording in clinical studies and public health. ISRCTN Registry 12246987; https://www.isrctn.com/ISRCTN12246987. RR2-10.1136/bmjopen-2021-050785.

Selected aspects of measurement data processing in electronic warfare devices

Electronic warfare (Polish acronym WRE ‒ walka radioelektroniczna) is a set of militaryactions based on the use of the electromagnetic spectrum and it includes:— reception and identification of electromagnetic emissions,— reducing the effectiveness of the enemy’s electronic devices,— enabling effective use of the spectrum by own forces.The task of the WRE in peacetime is to obtain information about radio-electronic devices, especiallyradars. These tasks are performed by ELINT (Electronic Intelligence) and/or ESM (Electronic WarfareSupport Measures) devices. They operate passively in the 0.5÷18 GHz band, their detection is difficultand the information they provide allows to detect a threat to own forces and to take appropriatecountermeasures. Radar recognition is a complex process that involves the following stages. The firststage: gathering measurements and their grouping into the so-called packets and graphical display ofthe received pulse trains. The measurements are represented by the so-called measurement vectors(descriptors) containing signal parameters, including the TOA (Time of Arrival) pulse with nanosecondaccuracy. The second stage: associating pulse packets with logical sources in order to obtainrepresentative data strings. This stage is signal sorting and deinterleaving. The third stage: estimationof the WS signal vector based on the associated pulse packets. The final stage of data processing is thecomparison of the obtained signal descriptor parameters WS with Database (BD) radar patterns. Thereconnaissance result allows for the assessment of the threat resulting from the operation of this radar.Radar recognition requires precise determination of many parameters of its signal. For pulsed radars,important parameters are the Pulse Repetition Interval (PRI) and the type of PRI modulation. Radarsare characterised by a high complexity of PRI changes. This provides great utility and makes it possibleto distinguish even radar units and changes in their locations. This allows for the detection and fullidentification of objects that use radars (e.g. ships) with the given object completely out of sight; it alsoallows to predict intentions of the target. The basic inter-pulse PRI modulations include: stagger, dwelland switch, jitter or sliding. PRI changes in radar signals may be periodic with long cycles, difficultto identify in cluttered conditions. Unfortunately, the received pulse trains are usually distorted. Thismakes the WS estimation process difficult ‒ especially in automatic mode. PRI analysis has receivedmuch attention in the literature. The methods are computationally complex and have numerouslimitations. This article presents ASWC algorithm (Sequential Cycle Detection Algorithm) of PRIproprietary, with relatively low computational complexity. Examples of test results confirming its higheffectiveness in automatic PRI analysis performed under interference conditions were also presented.Keywords: radars, electronic warfare, radar recognition, ELINT, ESM, pulse descriptor, PRI

Assessing real-world gait with digital technology? Validation, insights and recommendations from the Mobilise-D consortium

BackgroundAlthough digital mobility outcomes (DMOs) can be readily calculated from real-world data collected with wearable devices and ad-hoc algorithms, technical validation is still required. The aim of this paper is to comparatively assess and validate DMOs estimated using real-world gait data from six different cohorts, focusing on gait sequence detection, foot initial contact detection (ICD), cadence (CAD) and stride length (SL) estimates.MethodsTwenty healthy older adults, 20 people with Parkinson’s disease, 20 with multiple sclerosis, 19 with proximal femoral fracture, 17 with chronic obstructive pulmonary disease and 12 with congestive heart failure were monitored for 2.5 h in the real-world, using a single wearable device worn on the lower back. A reference system combining inertial modules with distance sensors and pressure insoles was used for comparison of DMOs from the single wearable device. We assessed and validated three algorithms for gait sequence detection, four for ICD, three for CAD and four for SL by concurrently comparing their performances (e.g., accuracy, specificity, sensitivity, absolute and relative errors). Additionally, the effects of walking bout (WB) speed and duration on algorithm performance were investigated.ResultsWe identified two cohort-specific top performing algorithms for gait sequence detection and CAD, and a single best for ICD and SL. Best gait sequence detection algorithms showed good performances (sensitivity > 0.73, positive predictive values > 0.75, specificity > 0.95, accuracy > 0.94). ICD and CAD algorithms presented excellent results, with sensitivity > 0.79, positive predictive values > 0.89 and relative errors < 11% for ICD and < 8.5% for CAD. The best identified SL algorithm showed lower performances than other DMOs (absolute error < 0.21 m). Lower performances across all DMOs were found for the cohort with most severe gait impairments (proximal femoral fracture).Algorithms’ performances were lower for short walking bouts; slower gait speeds (< 0.5 m/s) resulted in reduced performance of the CAD and SL algorithms.ConclusionsOverall, the identified algorithms enabled a robust estimation of key DMOs. Our findings showed that the choice of algorithm for estimation of gait sequence detection and CAD should be cohort-specific (e.g., slow walkers and with gait impairments). Short walking bout length and slow walking speed worsened algorithms’ performances.Trial registration ISRCTN – 12246987.

Toward Chaotic Secure Communications: An RIS Enabled M-Ary Differential Chaos Shift Keying System With Block Interleaving

Chaotic secure communication systems using chaotic waveforms as their spreading carriers can hide the transmitted information bits over a wide frequency range of chaotic waveform, which disguises the transmitted information waveform as noise. In this paper, a reconfigurable intelligent surface (RIS) enabled <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary differential chaos shift keying with block interleaving (RIS-MDCSK-BI) system is proposed for chaotic secure communications, where an RIS is deployed at the transmitter to assist communications and a pair of block interleaving patterns are used to interleave <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary information-bearing signals to enhance security performance. Moreover, we propose a chaotic merging sort algorithm to generate different block interleaving patterns, where these interleaving patterns are encrypted by using the non-periodic and noise-like properties of chaotic signals. To estimate information bits at the legitimate receiver, we propose a sequential detection algorithm and a joint detection algorithm. Then, theoretical bit error rate (BER) performances of the proposed RIS-MDCSK-BI system with the legitimate receiver and the eavesdropping receiver are derived. The security performance metrics, including information leakage and secrecy outage probability, are also analyzed. Monte Carlo simulations are performed to verify the superior BER performance and security performance of the proposed RIS-MDCSK-BI system compared to benchmark systems.

A sequential Bayesian changepoint detection procedure for aberrant behaviours in computerized testing.

Changepoints are abrupt variations in a sequence of data in statistical inference. In educational and psychological assessments, it is essential to properly differentiate examinees' aberrant behaviours from solution behaviour to ensure test reliability and validity. In this paper, we propose a sequential Bayesian changepoint detection algorithm to monitor the locations of changepoints for response times in real time and, subsequently, further identify types of aberrant behaviours in conjunction with response patterns. Two simulation studies were conducted to investigate the efficiency and accuracy of the proposed detection procedure in terms of identifying one or multiple changepoints at different locations. In addition to manipulating the number and locations of changepoints, two types of aberrant behaviours were also considered: rapid guessing behaviour and cheating behaviour. Simulation results indicate that ability estimates could be improved after removing responses from aberrant behaviours identified by our approach. Two empirical examples were analysed to illustrate the application of the proposed sequential Bayesian changepoint detection procedure.

Deep learning based sequence detection with natural redundancy for memory sources

AbstractThe current wireless communication system has higher performance demands for receivers. This paper considers exploiting the natural redundancy (NR) that is widely existed in the transmission sources to improve the receiver's performance of sequence detection. The type of NR discussed in this paper is the inherent redundancy in data caused by the correlation between symbols in the memory sources. Since the correlation between transmitted symbols is too challenging to obtain, deep learning (DL) is introduced into sequence detection, which has a powerful ability to extract complex patterns from data. Specifically, intended for a specific memory source that is convenient for performance analysis, namely the Markov source, an iterative sequence detection algorithm based on the long short‐term memory network is proposed. Simulation results demonstrate that the receiver's performance can be improved by exploiting the NR and the proposed DL‐based sequence detection scheme can obtain optimal bit error rate performance with blind state transition probability of the transmitted Markov source.

A data-driven deep learning network for massive MIMO detection with high-order QAM

Massive multiple-input multiple-output (MIMO) can provide higher spectral efficiency and energy efficiency compared to conventional MIMO systems. Unfortunately, as the numbers of modulation orders and antennas increase, the computational complexity of conventional symbol detection algorithms becomes unaffordable and their performance deteriorates. However, deep learning (DL) techniques can provide flexibility, nonlinearity and computational parallelism for massive MIMO detection to address these challenges. We propose an efficient data-driven detection network, i.e., accelerated multiuser interference cancellation network (AMIC-Net), for uplink massive MIMO systems. Specifically, we first introduce an extrapolation factor regarded as a learnable parameter into the multiuser interference cancellation (MIC) algorithm for iterative sequential detection (ISD) detector through extrapolation technique to enhance the convergence performance. Then we unfold the above accelerated iterative algorithm and adopt a sparsely connected approach, instead of fully connected, to obtain a relatively simple deep neural network (DNN) structure to enhance the detection performance through the data-driven DL approach. Furthermore, in order to accommodate communication scenarios with higher-order modulation, a novel activation function is proposed, which is composed of multiple softsign activation functions with additional learnable parameters to implement a multi-segment mapping of the set of constellation points with different modulations. Numerical results show that the proposed DL network can bring significant performance gain to ISD detector with various massive antenna settings and outperform the existing detectors with the same or lower computational complexity, especially in high-order QAM modulation scenarios.

Sequential Detection and Estimation of Multipath Channel Parameters Using Belief Propagation

This paper proposes a belief propagation (BP)-based algorithm for sequential detection and estimation of multipath component (MPC) parameters based on radio signals. Under dynamic channel conditions with moving transmitter/receiver, the number of MPCs, the MPC dispersion parameters, and the number of false alarm contributions are unknown and time-varying. We develop a Bayesian model for sequential detection and estimation of MPC dispersion parameters, and represent it by a factor graph enabling the use of BP for efficient computation of the marginal posterior distributions. At each time step, a snapshot-based parametric channel estimator provides parameter estimates of a set of MPCs which are used as noisy measurements by the proposed BP-based algorithm. It performs joint probabilistic data association, and estimation of the time-varying MPC parameters and the mean number of false alarm measurements, by means of the sum-product algorithm rules. The algorithm also exploits amplitude information enabling the reliable detection of "weak" MPCs with very low component signal-to-noise ratios (SNRs). The performance of the proposed algorithm compares well to state-of-the-art algorithms for high SNR MPCs, but it significantly outperforms them for medium or low SNR MPCs. Results using real radio measurements demonstrate the excellent performance of the proposed algorithm in realistic and challenging scenarios.

Sequential detection of a temporary change in multivariate time series

In this work, we aim to provide a new and efficient recursive detection method for temporarily monitored signals. Motivated by the case of the propagation of an event over a field of sensors, we assumed that the change in the statistical properties in the monitored signals can only be temporary. Unfortunately, to our best knowledge, existing recursive and simple detection techniques such as the ones based on the cumulative sum (CUSUM) do not consider the temporary aspect of the change in a multivariate time series. In this paper, we propose a novel simple and efficient sequential detection algorithm, named Temporary-Event-CUSUM (TE-CUSUM). By combining with a new adaptive way to aggregate local CUSUM variables from each data stream, we empirically show that the TE-CUSUM has a very good detection rate in the case of an event passing through a field of sensors in a very noisy environment.

Multistatic Noncoherent Linear Complexity Miller Sequence Detection For Gen2 RFID/IoT

Passive Gen2 radio frequency identification (RFID) tags work thanks to the utilization of line codes that balance their operation between two opposite states: absorbing RF (for energy harvesting) and reflecting RF (for backscattering/communications). Given the current RF harvesting technology, batteryless tags need to be located very close to an active illuminator in order to harvest sufficient energy and operate. To tackle this limitation, prior art has tried to bring the illuminator closer to the tags by designing proprietary illuminating architectures. Our solution comes in two parts. First, we offer a novel, Gen2-compliant, near-optimal, noncoherent sequence detection algorithm with linear complexity (in the sequence length) for Miller line codes. We leverage the robustness of this algorithm to overcome issues inherent in multistatic setups, such as carrier frequency offset. Second, we propose a modular multistatic architecture that makes use of low-cost commodity software defined radios (SDR) and omnipresent Ethernet infrastructure. Simulations and experimental results in a monostatic, bistatic, or multistatic SDR testbed with commercial RFIDs, corroborate the low-cost, real-time and near-optimal flavor of our solution.

Research on PDMA system based on complementary sequence and low complexity detection algorithm

With the intensive deployment of mobile networks and the vigorous development of new multimedia services, video has gradually become the mainstream of cultural consumption. The contradiction between the proliferation of video data services and the scarcity of spectrum resources has brought great challenges to the current network resource allocation. Non-orthogonal multiple access (NOMA) can be used to solve this problem by signal superposition and spectrum multiplexing to improve system access capability. As a new type of joint optimization design of transmitter and receiver side, PDMA has high research value. In this paper, a framework of PDMA video transmission system based on H.264 video compression coding (HVC-PDMA) is proposed. Poly complementary sequence (PCS) spread spectrum coding is performed on the transmission codebook in order to improve the transmission accuracy. Meanwhile, a low complexity serial sphere compensated Max-log MPA (SSCM-MPA) algorithm is proposed to reduce the complexity of the multi-user detection algorithm. Simulation results show that the PCS spread spectrum can improve system throughput and peak signal-to-noise ratio (PSNR) while reducing bit error rate (BER). SSCM-MPA algorithm can greatly reduce the complexity and improve the transmission efficiency.

Low-complexity interference cancellation algorithms for detection in media-based modulated uplink massive-MIMO systems

Media-based modulation (MBM) is a novel modulation technique that can improve the spectral efficiency of the existing wireless systems. In MBM, multiple radio frequency (RF) mirrors are placed near the transmit antenna(s) and are switched ON/OFF to create different channel fade realizations. In such systems, additional information is conveyed through the ON/OFF status of RF mirrors along with conventional modulation symbols. A challenging task at the receiver is to detect the transmitted information symbols and extract the additional information from the channel fade realization used for transmission. In this paper, we consider a massive MIMO (mMIMO) system where each user relies on MBM for transmitting information to the base station, and investigate the problem of symbol detection at the base station. First, we propose a mirror activation pattern (MAP) selection based modified iterative sequential detection algorithm. With the proposed algorithm, the most favorable MAP is selected, followed by the detection of symbol corresponding to the selected MAP. Each solution is subjected to the reliability check before getting the update. Next, we introduce a K favorable MAP search based iterative interference cancellation (KMAP-IIC) algorithm. In particular, a selection rule is introduced in KMAP-IIC for deciding the set of favorable MAPs over which iterative interference cancellation is performed, followed by a greedy update scheme for detecting the MBM symbols corresponding to each user. Simulation results show that the proposed detection algorithms exhibit superior performance-complexity trade-off over the existing detection techniques in MBM-mMIMO systems.

Sequential Attack Detection in Recommender Systems

Recommender systems are widely used in electronic commerce, social media and online streaming services to provide personalized recommendations to the users by exploiting past ratings and interactions. This paper considers the security aspect with quick and accurate detection of attacks by observing the newly created profiles sequentially to prevent the damage which may be incurred by the injection of new profiles with dishonest ratings. The proposed framework consists of a latent variable model, which is trained by a variational EM algorithm, followed by a sequential detection algorithm. The latent variable model generates homogeneous representations of the users given their rating history and mixed data-type attributes such as age and gender. The representations are then exploited to generate univariate statistics to be efficiently used in a CUSUM-like sequential detection algorithm that can quickly detect persistent attacks while maintaining low false alarm rates. We apply our proposed framework to three different real-world datasets and exhibit superior performance in comparison to the existing baseline algorithms for both attack profile and sequential detection. Furthermore, we demonstrate robustness to different attack strategies and configurations.

Detection of Unsupervised Standardized Gait Tests From Real-World Inertial Sensor Data in Parkinson's Disease.

Gait tests as part of home monitoring study protocols for patients with movement disorders may provide valuable standardized anchor-points for real-world gait analysis using inertial measurement units (IMUs). However, analyzing unsupervised gait tests relies on reliable test annotations by the patients requiring a potentially error-prone interaction with the recording system. To overcome this limitation, this work presents a novel algorithmic pipeline for the automated detection of unsupervised standardized gait tests from continuous real-world IMU data. In a study with twelve Parkinson's disease patients, we recorded real-world gait data over two weeks using foot-worn IMUs. During continuous daily recordings, the participants performed series of three consecutive 4×10 -Meters-Walking-Tests ( 4×10 MWTs) at different walking speeds, besides their usual daily-living activities. The algorithm first detected these gait test series using a gait sequence detection algorithm, a peak enhancement pipeline, and subsequence Dynamic Time Warping and then decomposed them into single 4×10 MWTs based on the walking speed. In the evaluation with 419 available gait test series, the detection reached an F1-score of 88.9% and the decomposition an F1-score of 94.0%. A concurrent validity evaluation revealed very good agreement between spatio-temporal gait parameters derived from manually labelled and automatically detected 4×10 MWTs. Our algorithm allows to remove the burden of system interaction from the patients and reduces the time for manual data annotation for researchers. The study contributes to an improved automated processing of real-world IMU gait data and enables a simple integration of standardized tests into continuous long-term recordings. This will help to bridge the gap between supervised and unsupervised gait assessment.

Fault tolerant control of islanded AC microgrids under sensor and communication link faults using online recursive reduced-order estimation

Cyber-Physical Systems (CPSs) have become an inseparable part of the new industrial era referred to as Industry 4.0 the quintessential example of which are smart grids. With a cyber communication level integrated with the physical components, besides considerable merits came along some reliability and security concerns. To address these issues, there ought to be a supervisory level monitoring and control system to identify any faults within the system and balance out their potential damaging impacts. In this paper, we consider fault tolerant control (FTC) problem in one of the building blocks of smart grids i.e. microgrids. The FTC method is based on online recursive reduced-order model estimation and Klaman Filter (KF) residual generation. Then, two-sided cumulative sum (CUSUM) sequential change detection algorithm is employed for sensor fault or communication link failure detection. Lastly, a fault-tolerant logic is constructed to switch between actual data and the internal model for the control system.

Comparative analysis of sequential community detection algorithms based on internal and external quality measure

Community detection is a dominant research field in social media mining. Numerous algorithms have been developed to detect community structure in network. Each of them focuses on different characteristic of data and generates different communities for same dataset. So cluster validation or comparative analysis of these algorithms is required to compare the efficiency of these algorithms. There are two known ways for cluster validation: Internal Quality Measure (IQM) and External Quality Measure (EQM). IQM evaluates the cluster without reference to external information while EQM requires already known clusters i.e. ground truth for comparison. Most of the researchers have compared Community Detection algorithms on the basis of either IQM or EQM but not both. In this paper, we have tried to compare nine existing sequential community detection algorithms on the basis of both IQM and EQM and we observed that overall performance of Louvain, Fastgreedy and Walktrap algorithm is more efficient than other algorithms. From this paper, researchers working in this area can get information about major sequential community detection algorithms and their efficiency on small real world datasets. They can incorporate the findings to develop more efficient algorithms.

2-D Channel Characterization of a Molecular Motor Signal

In this article, a two-dimensional channel characterization of a molecular motor signal in a diffusive fluid environment is provided by deriving the first hitting time probability density function of the motor signal to an absorbing lattice point. A temporal modulation scheme to establish communication between two nodes using the motor signal is also proposed. Detection of the motor signal is achieved by using the maximum likelihood detector with erasures for a negligible or no-interference scenario. On the other hand, for motor signal reception with inter-symbol interference, the reception process is modeled as a hidden Markov model, and a Viterbi sequence detection algorithm is devised for decoding the sequence of input Markov states. Efficient criteria to determine the memory length of a diffusive molecular communication (MC) system are defined, which address the problem of choosing a detector for a given MC system. It is demonstrated using numerical results that the hitting probability and, consequently, the error performance of the motor signal worsens with an increase in the unbound probability (ϵ/2). Furthermore, it is also quantitatively established, as to, why in nature directed signals are preferred for communication over purely random diffusive signals at larger distances.

Wishart-Based Adaptive Temporal Filtering of Polarimetric SAR Imagery

Temporal filtering for speckle reduction of polarimetric SARimages is described. The method is based on a sequential complex Wishart-based change detection algorithm which is applied to polarized SAR imagery, including the dual-polarization intensity data archived on the Google Earth Engine (GEE). Software for convenient application and analysis is presented. Results compare favorably with, and improve upon, standard spatial and temporal filters for speckle reduction.

Malicious User Detection for Cooperative Mobility Tracking in Autonomous Driving

The mobility status of self and surrounding vehicles provides important information to various tasks in autonomous driving (AD) and intelligent transportation system (ITS). Accordingly, a precise, stable, and robust mobility tracking framework is essential. Compared with self-tracking that relies only on mobility observations from onboard sensors [e.g., global positioning system (GPS), inertial measurement unit (IMU), and camera], cooperative tracking markedly increases the precision and reliability of the mobility information by integrating observations from roadside units (RSUs) and nearby vehicles through vehicle-to-everything (V2X) communications in the Internet of Vehicles (IoV). Nevertheless, cooperative tracking can be quite vulnerable if there are malicious users sending bogus observations in the cooperative network. In this article, we present a malicious user detection framework, which includes two sequential detection algorithms and a secure mobility data exchange and fusion model to detect and remove bogus mobility information and integrate proposed detection algorithms with previous data fusion algorithms, which secures the cooperative mobility tracking in AD, ITS. Simulations validate the effectiveness and robustness of the proposed framework under different types of attacks.

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.