Intersymbol Interference Research Articles

Low hardware-complexity IQ skew tolerant finite field and time domain hybrid adaptive equalization for 400G/800G-ZR coherent transmission

In 400G/800G-ZR transmission systems afflicted by substantial inter-symbol interference (ISI) stemming from chromatic dispersion (CD), frequency-domain adaptive equalizers (FD-AEQs) are preferred to time-domain AEQs (TD-AEQs) as the former have relatively lower computation load. However, the reliance of FD-AEQs on computationally expensive fast Fourier transform (FFT)/inverse fast Fourier transform (IFFT) operations poses a major obstacle in the development of low-power 400G/800G-ZR digital coherent transceivers. Furthermore, to mitigate the significant performance degradation due to receiver in-phase and quadrature (IQ) skew, the employment of twice the number of filters becomes imperative to enable individual adjustments of the I and Q tributaries, nearly doubling the number of necessary FFT/IFFT operations and computation load. This prohibitively high computation load poses a formidable obstacle to the realization of low-power and cost-effective transceivers. To address this issue, we introduce a novel low hardware-complexity IQ skew tolerant finite field (FF) and TD hybrid AEQ for 400G/800G-ZR coherent transmission. By optimizing the AEQ design and the Fermat number transform (FNT) based linear convolution scheme, the proposed hybrid AEQ can achieve a remarkable reduction in hardware complexity by more than 70%, compared with the existing IQ skew tolerant FD-AEQ, while preserving the same receiver sensitivity. Both numerical simulations and experiments demonstrate that the performance of the low complexity hybrid AEQ is the same as the FD-AEQ with much higher complexity. The proposed comprehensive and hardware efficient hybrid AEQ scheme is very appealing for 400G/800G-ZR coherent receivers which need to compensate for large ISI and IQ skew under stringent power constraints.

Enhanced Carrier Phase Recovery Using Dual Pilot Tones in Faster-than-Nyquist Optical Transmission Systems

Compared with high spectrum efficiency faster-than-Nyquist (FTN) backbone network, an enhanced carrier phase recovery based on dual pilot tones is more sensitive to capital cost in FTN metropolitan areas as well as inter-datacenter optical networks. The use of distributed feedback (DFB) lasers is a way to effectively reduce the cost. However, under high symbol rate FTN systems, equalization-enhanced phase noise (EEPN) induced by a DFB laser with large linewidth will significantly deteriorate the system performance. What is worse, in FTN systems, tight filtering introduces inter-symbol interference so severe that the carrier phase estimation (CPE) algorithm of the FTN systems is more sensitive to EEPN, thus it will lead to a more serious cycle slip problem. In this paper, an enhanced carrier phase recovery based on dual pilot tones is proposed to mitigate EEPN and suppress cycle slip, in which the chromatic dispersion (CD)-aware Tx and LO laser phase noise is estimated, respectively. Offline experiments results under 40 Gbaud polarization multiplexing (PM) 16-quadrature amplitude modulation (QAM) FTN wavelength division multiplexing (FTN-WDM) systems at 0.9 acceleration factor, 5 MHz laser linewidth, and 500 km transmission demonstrate that the proposed algorithm could bring about 0.65 dB improvement of the required SNR for the normalized generalized mutual information of 0.9 compared with the training sequence-based cycle slip suppression carrier phase estimation (TS-CSS) algorithm.

A Design of NLOS Communication Scheme Based on SC-FDE with Cyclic Suffix for UAV Payload Communication

Non-line-of-sight (NLOS) communication with severe loss always leads to performance degradation in unmanned aerial vehicle (UAV) payload communication. In this paper, a UAV NLOS communication scheme based on single-carrier frequency domain equalization with cyclic prefix and cyclic suffix (CP/CS-SC-FDE) is designed. First, the reasons behind the generation of later intersymbol interference (LISI) in UAV NLOS communication are investigated. Then, the frame structure of conventional single-carrier frequency domain equalization with cyclic prefix (CP-SC-FDE) is improved, and the UAV NLOS communication frame structure based on cyclic prefix (CP) and cyclic suffix (CS) is designed. Furthermore, a channel estimation algorithm applicable to this scheme is proposed. The numerical results show that this UAV communication scheme can eliminate intersymbol interference (ISI) in NLOS communication. Compared with the conventional CP-SC-FDE system, this scheme can achieve excellent performance in the Rayleigh channel and other standard NLOS channels. In the CP/CS-SC-FDE system, the BER result is similar to that under ideal synchronization.

Graphene Phase Modulators Operating in the Transparency Regime.

Next-generation data networks need to support Tb/s rates. In-phase and quadrature (IQ) modulation combine phase and intensity information to increase the density of encoded data, reduce overall power consumption by minimizing the number of channels, and increase noise tolerance. To reduce errors when decoding the received signal, intersymbol interference must be minimized. This is achieved with pure phase modulation, where the phase of the optical signal is controlled without changing its intensity. Phase modulators are characterized by the voltage required to achieve a π phase shift, Vπ, the device length, L, and their product, VπL. To reduce power consumption, IQ modulators are needed with <1 V drive voltages and compact (sub-cm) dimensions, which translate in VπL < 1Vcm. Si and LiNbO3 (LN) IQ modulators do not currently meet these requirements because VπL > 1Vcm. Here, we report a double single-layer graphene (SLG) Mach-Zehnder modulator (MZM) with pure phase modulation in the transparency regime, where optical losses are minimized and remain constant with increasing voltage. Our device has VπL ∼ 0.3Vcm, matching state-of-the-art SLG-based MZMs and plasmonic LN MZMs, but with pure phase modulation and low insertion loss (∼5 dB), essential for IQ modulation. Our VπL is ∼5 times lower than the lowest thin-film LN MZMs and ∼3 times lower than the lowest Si MZMs. This enables devices with complementary metal-oxide semiconductor compatible VπL (<1Vcm) and smaller footprint than LN or Si MZMs, improving circuit density and reducing power consumption by 1 order of magnitude.

A Hybrid Network Integrating MHSA and 1D CNN–Bi-LSTM for Interference Mitigation in Faster-than-Nyquist MIMO Optical Wireless Communications

To mitigate inter-symbol interference (ISI) caused by Faster-than-Nyquist (FTN) technology in a multiple input multiple output (MIMO) optical wireless communication (OWC) system, we propose an ISI cancellation algorithm that combines multi-head self-attention (MHSA), a one-dimensional convolutional neural network (1D CNN), and bi-directional long short-term memory (Bi-LSTM). This hybrid network extracts data features using 1D CNN and captures sequential information with Bi-LSTM, while incorporating MHSA to comprehensively reduce ISI. We analyze the impact of antenna numbers, acceleration factors, wavelength, and turbulence intensity on the system’s bit error rate (BER) performance. Additionally, we compare the waveform graphs and amplitude–frequency characteristics of FTN signals before and after processing, specifically comparing sampled values of four-pulse-amplitude modulation (4PAM) signals with those obtained after ISI cancellation. The simulation results demonstrate that within the Mazo limit for selecting acceleration factors, our proposal achieves a 7 dB improvement in BER compared to the conventional systems without deep learning (DL)-based ISI cancellation algorithms. Furthermore, compared to systems employing a point-by-point elimination adaptive pre-equalization algorithm, our proposal exhibits comparable BER performance to orthogonal transmission systems while reducing computational complexity by 31.15%.

Learning Gradient-Based Feed-Forward Equalizer for VCSELs

Vertical cavity surface-emitting laser (VCSEL)-based optical interconnects (OI) are crucial for high-speed data transmission in data centers, supercomputers, and vehicles, yet their performance is challenged by harsh and fluctuating thermal conditions. This paper addresses these challenges by integrating an ordinary differential equation (ODE) solver within the VCSEL communication chain, leveraging the adjoint method to enable effective gradient-based optimization of pre-equalizer weights. We propose a machine learning (ML) approach to optimize feed-forward equalizer (FFE) weights for VCSEL transceivers, which significantly enhances signal integrity by managing inter-symbol interference (ISI) and reducing the symbol error rate (SER).

Performance Analysis of Multiple-Input Multiple-Output Orthogonal Frequency Division Multiplexing System using Arithmetic Optimization Algorithm

This research aims to optimize the interference mitigation and improve system performance metrics, such as bit error rates, inter-carrier interference (ICI), and inter-symbol interference (ISI), by integrating the Redundant Discrete Wavelet Transform (RDWT) with the Arithmetic Optimization Algorithm (AOA). This will increase the spectral efficiency of MIMO-OFDM systems for ultra-high data rate (UHDR) transmission in 5G networks. The most important contribution of this study is the innovative combination of RDWT and AOA, which effectively addresses the down sampling issues in DWT-OFDM systems and significantly improves both error rates and data rates in high-speed wireless communication. Fifth-generation wireless networks require transmission at ultra-high data rates, which necessitates reducing ISI and ICI. Multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) is employed to achieve the UHDR. The bandwidth and orthogonality of DWT-OFDM (discrete wavelet transform-based OFDM) are increased; however system performance is degraded due to down sampling. The redundant discrete wavelet transform (RDWT) is proposed for eliminating down sampling complexities. Simulation results demonstrate that RDWT effectively lowers bit error rates, ICI, and ISI by increasing the carrier-to-interference power ratio (CIR). The Arithmetic Optimization Algorithm is used to optimize ICI cancellation weights, further enhancing spectrum efficiency. The proposed method is executed in MATLAB and achieves notable performance gains: up to 82.95% lower error rates and 39.88% higher data rates compared to the existing methods. Conclusion: The integration of RDWT with AOA represents a significant advancement in enhancing the spectral efficiency of MIMO-OFDM systems for UHDR transmission in 5G networks. The proposed method not only enhances system performance but also lays a foundation for future developments in high-speed wireless communication by addressing down sampling issues and optimizing interference mitigation.

Передача двоичных сообщений ортогонализованными частично перекрывающимися сигналами

Frequency efficiency, noise immunity and implementation complexity are the most important parameters for the transmission of binary messages. One of the directions for increasing frequency efficiency is the conscious or controlled introduction of intersymbol interference into the transmitted signal with an acceptable reduction in noise immunity and complication of implementation. The article analyzes the transmission of binary messages by orthogonalized narrow-band partially overlapping signals. The formation of the transmitted signal and processing of the received signal are considered. The probability of error when exposed to interference in the form of white noise is determined. The transmission noise immunity was assessed using simulation. The considered method of transmitting binary messages provides good frequency efficiency without the use of a spectrum shaper with high noise immunity.

The method of forming ensembles of complex signals based on multi-scale decomposition of time intervals at different levels of detail

This article addresses the challenges of forming signal ensembles in dynamic cognitive radio environments, focusing on the limitations of traditional methods. The study proposes a new approach based on multiscale time interval decomposition, which allows for the creation of signal ensembles at varying levels of temporal detail. The key innovation of this method is its ability to improve signal reproduction accuracy, reduce inter-symbol and inter-channel interference, and enhance the overall efficiency of data processing. The method's adaptability to changing environmental conditions is also a core advantage, enabling better use of bandwidth and reduced transmission delay. Through the decomposition of time intervals into coarse, intermediate, and fine levels, this method allows for the detailed analysis of short-term, medium-term, and long-term signal components. Experimental results demonstrate the superiority of this approach in terms of signal recovery accuracy, noise resilience, and processing speed. These findings highlight the potential for optimizing signal processing in cognitive radio networks, particularly in environments with high levels of noise and interference. Future research aims to integrate machine learning algorithms to further enhance adaptability in real-time scenarios.

Error performance analysis for OOK modulated optical camera communication systems

Integrating image sensors’ imaging capabilities into the receiver for visible light communication is a prominent characteristic of optical camera communication (OCC). However, the exposure effect during imaging distorts received waveforms and introduces inter-symbol interference (ISI), leading to decreased OCC reliability. This paper aims to provide an in-depth analysis of the impact of image sensor exposure effects on the error performance of OCC systems. Analytical expressions of the pixel signal-to-interference and noise ratio (PSINR) are derived using the pulse response function (PRF) for an on-off keying (OOK) modulated OCC system with varying exposure times. Furthermore, the bit error rate (BER) performance is evaluated analytically using PSINR, and a straightforward BER measurement scheme is proposed for experimental validation. Results from analyses and experiments conducted under different exposure times indicate that longer exposures lead to increased ISI and decreased PSINR, thereby increasing the error probability of data demodulation. Additionally, a combined impact of noise and exposure on OCC system reliability is observed, highlighting noise-limited and interference-limited characteristics under low and high signal-to-noise ratio (SNR) conditions, respectively. By utilizing PSINR as a bridge, this paper precisely analyzes OCC system reliability under exposure effects, laying a theoretical foundation for system design and optimization.

On the impact of interlayer misalignment for dual-layer data detection in three dimensional magnetic recording

Three-dimensional magnetic recording (3DMR) is a crucial technology for significantly increasing the storage capacity of hard disk drives (HDDs). However, the presence of inter-symbol interference (ISI), intertrack interference (ITI), and interlayer interference (ILI) poses significant challenges to the accurate detection of data stored on multiple layers. This study addresses the impact of interlayer misalignment on the bit error rate (BER) performance in 3DMR systems. We evaluate the performance based on a neural network estimator for reconstructing the top-layer read response signal using feedback from a Viterbi detector. This enables the separation of bottom-layer signals by subtraction from the mixed readback signal. We introduce a dual-layer partial response maximum likelihood (PRML) detector for simultaneous bit retrieval from both layers. Furthermore, we investigate methods of a per-layer binary classifier and a dual-layer four-class classifier based on neural networks. Our study demonstrates the BER performance of these detection schemes influenced by the interlayer misalignment, especially when the offset is 0, 10%, 50%, and 90% of the bit dimensions between the two layers. The results show that the neural network-based reconstruction and separation method achieves better bottom-layer BER performance under a slight interlayer misalignment. The BER performance benefits more from a mild downtrack offset than the crosstrack offset. The neural network-based separation detection and the dual-layer PRML achieve the lowest top-layer BER and the worst bottom-layer BER when the interlayer misalignment is half a bit.

Distortion-tolerant on–off keying preemphasis signal transmission for a 10 Gbps indoor visible light communications

Abstract The design and simulation of indoor visible light communication (VLC) system with preemphasis is proposed for 5 m transmission of signal at the data rate of 10 Gbps for receiving only applications like smart TV, smart speaker, and smart home appliance control. The preemphasis driver circuit is designed to reduce the intersymbol interference by pulse shaping the signal and transimpedance amplifier is used to amplify the signal for longer distance transmission. Intensity modulation at the sender side and direct detection at the receiver-side are adopted in this work for the improvement of the system’s overall performance and to decrease its implementation cost. The system performance is analyzed in terms of BER, data-rate, Q-factor, and eye diagrams. The setup is developed, which includes a nonreturn-to-zero (NRZ) generator, preemphasis driver, light-emitting-diode, VLC channel, and receiver with an avalanche photodiode and Gaussian LPF. At 10 Gbps data rate, the maximum transmission distance that can be obtained is 5 m with a BER of less than 10−31.

Low-complexity adaptive multipath interference and channel noise mitigation scheme based on optimized detection for bandwidth-limited IM/DD systems.

In this Letter, we propose a low-complexity adaptive multipath interference (MPI) and channel noise mitigation (AMCM) scheme in the receiver digital signal processing (DSP) for bandwidth-limited intensity modulation and direct detection (IM/DD) transmission systems. Following channel equalization, MPI and channel noise are distributed in the low- and high-frequency parts, respectively, and exhibit the characteristics of bandstop filtering. The proposed AMCM is designed based on optimized detection, which incorporates an adaptive bandpass filter (BPF) and a log-maximum a posteriori estimation with a lookup table-based fixed number of surviving states (LUT-based FS-MAP) decoder. The adaptive BPF is capable of mitigating the MPI and channel noise based on spectral distribution. Moreover, the LUT-based FS-MAP decoder can eliminate intersymbol interference (ISI) introduced by the BPF. The proposed AMCM is implemented in an O-band 56-Gbaud IM/DD optical 4-level pulse amplitude modulation (PAM-4) system with a 10.7-GHz bandwidth over a 10-km standard single-mode fiber with different linewidths. The results demonstrate that the proposed AMCM scheme can enhance signal-to-interference ratio (SIR) tolerance to 11 dB with only three real-valued multiplications per symbol, achieving a 7% hard-decision forward error correction threshold. To the best of our knowledge, for the first time, this represents the inaugural instance of optimized detection being employed for MPI mitigation.

Estimation of the Impulse Response of the AWGN Channel with ISI within an Iterative Equalization and Decoding System That Uses LDPC Codes.

In this paper, new schemes have been proposed for the estimation of the additive white Gaussian noise (AWGN) channel with intersymbol interference (ISI) in an iterative equalization and decoding system using low-density parity check (LDPC) codes. This article explores the use of the least squares algorithm in various scenarios. For example, the impulse response of the AWGN channel h was initially estimated using a training sequence. Subsequently, the impulse response was calculated based on the training sequence and then re-estimated once using the sequence estimated from the output of the LDPC decoder. Lastly, the impulse response was calculated based on the training sequence and re-estimated twice using the sequence estimated from the output of the LDPC decoder. Comparisons were made between the performances of the three mentioned situations, with the situation in which a perfect estimate of the impulse response of the channel is assumed. The performance analysis focused on how the bit error rate changes in relation to the signal-to-noise ratio. The BER performance comes close to the scenario of having a perfect estimate of the impulse response when the estimation is performed based on the training sequence and then re-estimated twice from the sequence obtained from the output of the LDPC decoder.

Frame-rate adaptive fractionally spaced equalization enabled high-throughput optical camera communication.

Optical camera communication (OCC) has garnered worldwide research attention, due to its immunity to electromagnetic interference (EMI) and efficient utilization of spectrum resources. However, the limited bandwidth of the OCC system and the timing offset of the camera result in low system throughput. To enhance the OCC throughput, we propose and experimentally demonstrate a frame-rate adaptive fractionally spaced equalization algorithm (FA-FSE) for the joint mitigation of severe inter-symbol interference (ISI) and timing offset arising in OCC. Experimental results validate its correct and power-efficient function, leading to a record aggregated throughput of 250.96 kbit/s, when the 8-level pulse amplitude modulation (PAM-8) signals are independently modulated to eight chip-on-board light emitting diode (COB-LED) light strips, while simultaneously received by a smartphone 10 cm away.

Artificial neural network-based sparse channel estimation for V2V communication systems

Abstract Artificial neural networks (ANNs) have gained a lot of attention from researchers in the past few years and have been employed on a large scale. They have also been gaining momentum in wireless communication systems. For efficient vehicle-to-vehicle (V2V) channel communication, a sparse multipath channel issue must be studied. To minimize the multipath effect, a time reversal (TR) operation and time division synchronization orthogonal frequency division multiplexing (TDS-OFDM) have been appealing because of their fast synchronization and active spectral efficiency. To improve the transceiver's execution in a frequency-selective fading channel environment, an OFDM system is used to reduce inter- symbol interference (ISI). Simultaneous Orthogonal Matching Pursuit (SOMP) channel state estimator algorithm suffer from high computational cost and high computational complexity. The ANN algorithm has better performance than SOMP algorithm. The proposed neural network technologies have lower complexity than the SOMP algorithm. The application of ANN is capable of solving complex problems, such as those encountered in image, signal processing and have been implemented for channel estimation in OFDM. The proposed ANN outperformed the SOMP algorithm with regard to signal compensation. Overall, the ANN algorithm achieved the best performance. This study proposes an ANN-based sparse channel state estimator. Regarding the bit error rate (BER) metric, the proposed estimator outperforms the channel estimation approach based on the SOMP. The simulation results confirm the efficacy of the proposed approach.

Pre-filters design for weighted sum rate maximization in multiuser time reversal downlink systems

In high-speed multiuser Time Reversal (TR) downlink systems, the transmission rate is degraded due to the presence of severe inter-user and inter-symbol interference. Moreover, maximizing the weighted sum rate in such systems is a critical objective, since the weighting factors represent the priority of different users in different applications. However, it faces significant challenges as it is an NP-hard and non-convex problem. In order to suppress these interferences and maximize the weighted sum rate, in this paper we present a novel approach for the joint design of the pre-filters. The proposed method applies successive convex approximation to transform the original problem into a Second-Order Cone Programming (SOCP) problem. Then, a low-complexity iterative algorithm is provided to effectively solve the resulting SOCP problem. According to the simulation results, the proposed method reaches a local optimum within a few iterations and demonstrates superior performance in terms of weighted sum rate compared to the current algorithm.

Performance Investigation of Joint LUT and GS Algorithm at the Transceiver for Nonlinear and CD Compensation

In order to meet the increasing requirements of speed and distance, an advanced digital signal processing (DSP) algorithm is preferred without changing the system structure in intensity modulation and the direct detection (IM/DD) system. As the transmission distance increases, the power fading induced by dispersion must be mitigated. In addition, linear and nonlinear inter symbol interference (ISI) introduced by bandwidth limitation and device imperfections becomes an obstacle to achieving higher capacity. The Gerchberg–Saxton (GS) algorithm was recently used to compensate for dispersion. In this paper, GS-based pre- and post-compensation schemes in the IM/DD system with nonlinearity were investigated. We investigated and compared the performance of the GS-based pre- and post-compensation algorithm in a 28 GB aud four-level pulse amplitude modulation (PAM-4) transmission over 40 km standard single-mode fiber (SSMF). The bit error rate (BER) achieved a threshold of 3.8 × 10−3 using look-up-table (LUT), FFE, and the GS-based pre-compensation algorithm without iterations. Turning to the GS-based post-compensation scheme, 80 iterations are needed. However, the demand for FFE is reduced. The algorithm selection depends on the tolerance of the transmitter or receiver complexity in specific scenarios. The joint LUT and GS-based pre-compensation algorithm may be a preferable approach in scenarios where a low-complexity receiver is desired.

Fractionally spaced nonlinear Tomlinson-Harashima precoding with weight clustering for C-band 100 Gbaud/λ PAM-4 transmission.

A nonlinear Tomlinson-Harashima precoding (NTHP) scheme has been verified for its capability to effectively address both the linear and nonlinear inter-symbol interferences (ISIs) arising in the intensity-modulation direct-detection (IM-DD) fiber optics transmission. Nevertheless, the application of the NTHP scheme may significantly increase the number of levels for the intensity modulated signals, resulting in the reduction of both eye width and receiver sensitivity. Here, we propose a fractionally spaced NTHP with a weight clustering (FS-NTHP-WC) scheme. Consequently, an accurate ISI feedback can be obtained to enlarge the eye width; meanwhile a hardware-efficient implementation without the equalization penalty can be achieved by weight clustering and pruning. When the C-band 100 Gbaud/λ PAM-4 signals are transmitted, our proposed FS-NTHP-WC scheme not only can achieve 0.25 dB and 0.5 dB gains of receiver sensitivity under back-to-back (B2B) and 2-km standard single-mode fiber (SSMF) transmission conditions, respectively, but can also cut down the computational complexity by 90% and 76% in terms of the number of multiplications and additions, respectively, in comparison with the NTHP scheme.

Performance Analysis and ISI Mitigation With Imperfect Transmitter in Molecular Communication.

In molecular communication (MC), molecules are released from the transmitter to convey information. This paper considers a realistic molecule shift keying (MoSK) scenario with two species of molecule in two reservoirs, where the molecules are harvested from the environment and placed into different reservoirs, which are purified by exchanging molecules between the reservoirs. This process consumes energy, and for a reasonable energy cost, the reservoirs cannot be pure; thus, our MoSK transmitter is imperfect, releasing mixtures of both molecules for every symbol, resulting in inter-symbol interference (ISI). To mitigate ISI, the properties of the receiver are analyzed and a detection method based on the ratio of different molecules is proposed. Theoretical and simulation results are provided, showing that with the increase of energy cost, the system achieves better performance. The good performance of the proposed detection scheme is also demonstrated.