Residual Intersymbol Interference Research Articles

Spatial diversity processing mechanism based on the distributed underwater acoustic communication system.

To address the problem of unreliable single-link underwater acoustic communication caused by large signal delays and strong multipath effects in shallow water environments, this paper proposes a distributed underwater acoustic diversity communication system (DUA-DCS). DUA-DCS employs a maneuverable distributed cross-medium buoy network to form multiple distributed, non-coherent, and parallel communication links. In the uplink, a receiving diversity processing mechanism of joint decision feedback equalizer embedded phase-locked loop and maximum signal-to-interference ratio combining (DFE-PLL-MSIRC) is proposed to achieve waveform-level diversity combining of underwater signals. A phase-locked loop module is embedded in each branch of the decision feedback equalizer to eliminate the residual frequency and phase errors after Doppler compensation. Meanwhile, the combining coefficients are determined based on the maximum signal-to-interference ratio criterion, taking into account the residual inter-symbol interference after equalization, resulting in efficient and accurate computation. Additionally, the combined decision values are fed back to the feedback filters in each branch to ensure more accurate feedback output. Simulation and lake experiment results demonstrate that, compared to the single-link communication system, DFE-PLL-MSIRC can achieve a diversity gain of more than 5.2 dB and obtain about 3 dB more diversity gain than the comparison algorithm. And the BER of DFE-PLL-MSIRC can be reduced by at least one order of magnitude, which is lower by at least 0.6 order of magnitude compared to the comparison algorithm. In the downlink, a transmitting diversity processing mechanism of complex orthogonal space-time block coding (COSTBC) is proposed. By utilizing a newly designed generalized complex orthogonal transmission matrix, complete transmission diversity can be achieved at the coding rate of 3/4. Compared to the single-link communication system, the system can achieve a diversity gain of more than 6 dB.

Adaptive Hybrid Iterative Linearization Algorithms for IM/DD Optical Transmission Systems

For optical field recovery and linear dispersion compensation, we propose a performance-enhanced linearization algorithm, termed adaptive hybrid multi-constraint iteration algorithm (MCIA), which does not require any physical modifications to standard configurations of intensity-modulation and direct-detection (IM/DD) transmission systems. To improve the sensitivity to the residual inter-symbol interference (ISI) effect, we introduce, after fiber backward-propagation, a linear feed-forward equalizer (FFE) pair into the proposed algorithm. To improve the sensitivity to fiber dispersion estimation errors, we utilize a two-stage dispersion estimator coupled with the G-S iteration. After 100-Gb/s PAM-4 signal transmissions over 400-km fibers, the simulation results show that the MCIA offers a 1.5-dB optical signal-to-noise ratio (OSNR) gain and a 1-dB optical power budget improvement compared with the decision-directed data-aided iterative algorithm (DD-DIA), for highly dispersive IM/DD transmissions. By performing adaptive dispersion estimation, the MCIA has higher tolerance to estimation errors in fiber length. Moreover, for cases subject to large dispersion, the usage of the embedded FFE pair not only desensitizes the MCIA on the limited bandwidth effect, but also accelerates the convergence performance for reaching lower BERs. We experimentally demonstrate that the proposed algorithm can support 150-Gb/s PAM-4 transmissions over 25-km standard single mode fibers (SSMF), where just a 7-tap FFE-pair is required. For 150 Gb/s transmissions, the tolerance to fiber length estimation error is increased from 0.9 km to 20 km.

A New Dual Mode Blind Equalization Method Based on Neighborhood Symbol‐Based Decision and Decision‐Directed Algorithm

AbstractIn this paper, a new dual mode blind equalization method using neighborhood symbol‐based decision and decision‐directed (NSBD‐DD) algorithm is proposed to equalize the satellite communication signals. The proposed algorithm adopts the combined cost function to employ the advantages of symbol decision algorithm and the decision‐directed algorithm, which can further improve the universality of the proposed algorithm. Compared with the conventional blind equalization algorithm, the compensation ability of intersymbol interference and convergence speed of the proposed algorithm can be improved simultaneously. To verify the performance of the proposed algorithm, the computer simulation is performed, and the simulation results show that the residual intersymbol interference of the 64QAM signals can be decreased to −50 dB under the satellite channel, which has 30 dB lower than multi‐modulus algorithm (MMA), 26 dB lower than NSBD algorithm, and 10 dB lower than SBD algorithm. And compared with SBD algorithm, the number of iterations required for the NSBD‐DD algorithm can be decreased from 8000 iterations to 6000 iterations, which convergence speed is increased by 25%. © 2023 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Gerchberg-Saxton Based FIR Filter for Electronic Dispersion Compensation in IM/DD Transmission Part II: Experimental Demonstration and Analysis

In this article, the first experimental demonstration of a non-iterative electronic dispersion compensation (EDC) solution implemented at the transmitter using a finite impulse response (FIR) filter optimized with the Gerchberg-Saxton (GS) algorithm, is presented, for intensity-modulation and direct-detection (IM/DD) systems. The theoretical framework and preliminary simulations have been presented in Part I of this work. Here, the performance is compared between the GS FIR filter and the iterative GS algorithm in 56-Gb/s on-off keying (OOK) transmissions over 80-km single mode fiber (SMF) with a post feed-forward equalizer (FFE) for combating residual inter-symbol interference. Furthermore, the influence of the pulse shape (raised cosine or rectangular) and modulation format (return-to-zero (RZ) or non-return-to-zero (NRZ)) on the measured bit error ratio (BER) is investigated, while changing the number of FIR taps, post-FFE taps, and post-FFE samples-per-symbol. It is shown that within the range of the target digital extinction ratios (DERs) for which the original iterative GS algorithm offers benefit, both analytical and numerical methods for calculating the optimum FIR taps, outlined in Part I, produce similar BER performance as predicted. Hence, the former method is extended, here, through a non-recursive frequency response formula, which offers insight into the action of the GS filter with different pulse shaping and enables the derivation of the explicit GS impulse response. It is also shown that rectangular RZ exploits the full benefit of GS filtering through a uniform spectrum, achieving BER < 3.8×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> , with a 641-tap <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> /2-spaced pre-EDC FIR filter and a 3-tap adaptive <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> -spaced post-FFE.

A 25Gb/s RX front-end with multi-stage linear equalizer and 3-tap speculative DFE in 65nm CMOS technology

This work proposes a RX front-end structure, which is used for channel equalization of 25Gb/s high-speed links. This design includes two parts, linear equalizer and decision feedback equalizer. Linear equalizer consists of the variable gain amplifier, the continuous-time linear equalizer and the output buffer, which provide 19dB peaking gain around the Nyquist frequency. The half-rate decision feedback equalizer with one speculative tap is cascaded after the buffer to eliminate residual inter-symbol interference. The circuit layout occupies an area of 0.005mm2 designed in 65nm CMOS, the power consumption of which is 96mW under 1.2V power supply. The design is used to equalize the FR-4 backplane channel, of which the insertion loss reaches 35dB at 12.5GHz. The result shows that both the voltage margin and time margin of the receiver signal reach 171mV and 0.61UI at the BER of 10-12, respectively.

Pulses With Minimum Residual Intersymbol Interference for Faster Than Nyquist Signaling

Faster than Nyquist signaling increases the spectral efficiency of pulse amplitude modulation by accepting intersymbol interference, where an equalizer is needed at the receiver. Since the complexity of an optimal equalizer increases exponentially with the number of the interfering symbols, practical truncated equalizers assume shorter memory. The power of the resulting residual interference depends on the transmit filter and limits the performance of truncated equalizers. In this paper, we use numerical optimizations and the prolate spheroidal wave functions to find optimal time-limited pulses that achieve minimum residual interference. Compared to root raised cosine pulses, the new pulses decrease the residual interference by an order of magnitude, for example, a decrease by 32 dB is achieved for an equalizer that considers four interfering symbols at 57% faster transmissions. As a proof of concept, for the 57% faster transmissions of binary symbols, we showed that using the new pulse with a 4-state equalizer has better bit error rate performance compared to using a root raised cosine pulse with a 128-state equalizer.

An Estimated δ-Based Iterative Block Decision Feedback Equalization in SC-FDE System

We provide a novel nonlinear frequency domain equalization algorithm for the frequency domain equalization of an SC-FDE system by improving the classical iterative block decision feedback equalization (IBDFE) algorithm and applying δ estimation to the improved algorithm. The improvement of the IBDFE algorithm is carried out by replacing the ZF equalization in the feedback branch with the MMSE equalization and eliminating the iteration of the correlation factor, thus reducing the noise error and the computational complexity of the original algorithm. δ estimation can estimate residual inter-symbol interference in the signal after MMSE equalization and reject it, thus further improving the equalization accuracy. The simulation results show that the performance of the novel algorithm is better than that of the IBDFE algorithm with similar complexity, or the complexity of the novel algorithm is lower than that of the IBDFE algorithm with similar performance.

The Residual ISI for Which the Convolutional Noise Probability Density Function Associated with the Blind Adaptive Deconvolution Problem Turns Approximately Gaussian.

In a blind adaptive deconvolution problem, the convolutional noise observed at the output of the deconvolution process, in addition to the required source signal, is—according to the literature—assumed to be a Gaussian process when the deconvolution process (the blind adaptive equalizer) is deep in its convergence state. Namely, when the convolutional noise sequence or, equivalently, the residual inter-symbol interference (ISI) is considered small. Up to now, no closed-form approximated expression is given for the residual ISI, where the Gaussian model can be used to describe the convolutional noise probability density function (pdf). In this paper, we use the Maximum Entropy density technique, Lagrange’s Integral method, and quasi-moment truncation technique to obtain an approximated closed-form equation for the residual ISI where the Gaussian model can be used to approximately describe the convolutional noise pdf. We will show, based on this approximated closed-form equation for the residual ISI, that the Gaussian model can be used to approximately describe the convolutional noise pdf just before the equalizer has converged, even at a residual ISI level where the “eye diagram” is still very closed, namely, where the residual ISI can not be considered as small.

4-bit DAC based 6.9Gb/s PAM-8 UOWC system using single-pixel mini-LED and digital pre-compensation.

Low-cost underwater wireless optical communication (UOWC) systems are attractive for high-speed connections among unmanned vehicles or devices in various underwater applications. Here we demonstrate a high-speed and low-cost UOWC system using a low-resolution digital to analog converter (DAC), a single-pixel mini-sized light-emitting diode (mini-LED), and digital pre-compensation (DPC). The enabled DPC scheme comprises digital pre-distortion (DPD), digital pre-emphasis (DPE), and digital resolution enhancer (DRE), which pre-compensate for mini-LED nonlinearity, the bandwidth limitation of the mini-LED and avalanche photodiode detector, and DAC resolution limitation, respectively. The simulation results show that the in-band signal-to-quantization noise ratio can be increased by 6.8 dB using DRE based on a 4-bit DAC. To further improve the system capacity, we tune the level of DPE in order to optimize the trade-off between the residual inter-symbol interference and signal-to-noise ratio. With the combination of optimized DPE and DRE, we obtain a 21.1% higher data rate compared with full DPE only and demonstrate the transmission of 6.9 Gb/s PAM-8 signal over a 2-m distance underwater based on a single-pixel mini-LED and 4-bit DAC. This paper reports a cost-effective UOWC system first using a low-resolution DAC and DPC, which offers a promising path toward low-cost underwater optical wireless networks.

Chirp-Like Polyphase Sequence Based Discrete Circulant Transform Spread OFDM for Bandwidth-Limited IM/DD Systems

We propose and investigate chirp-like polyphase sequence (CLPS) based discrete circulant transform spread (DCrT-S) OFDM in bandwidth-limited intensity-modulation and direct-detection systems. This scheme can control the distribution of residual inter-symbol interference (ISI) and inter-carrier interference (ICI) across subcarriers by adjusting the CLPS's parameters. We also propose a sparse CLPS (SCLPS) scheme, by inserting zeros between the elements of the CLPS, to further balance the effects of the ISI/ICI and the noise and improve the performance by optimizing both the CLPS's parameters and the sparsity. We reveal the optimal design rule of CLPS/SCLPS analytically and investigate the performance of the proposed schemes using two-parameter CLPS in ∼110-Gbit/s simulations and experiments. It is shown that the optimal parameter vector of the CLPS is a Zadoff-Chu sequence that spreads the ISI/ICI more evenly over subcarriers. The performance is further improved by optimizing the sparsity. The optimal CLPS and sparsity are insensitive to the received optical power, the system bandwidth, the length of cyclic prefix, the chirp parameter and the signal data rate, and so can be pre-set without channel information. Both CLPS- and SCLPS-based DCrT-S-OFDM outperform Nyquist PAM, conventional OFDM, discrete-Fourier-transform spread (DFT-S) OFDM, and orthogonal-circulant-transform precoded (OCT-P) OFDM. By using the proposed scheme, the data rate is enhanced by 6.7% and 3.2% compared to DFT-S-OFDM and OCT-P-OFDM at a bit error rate (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> , while the complexity is reduced to 57.9% of OCT-P-OFDM.

Accurate Statistical BER Analysis of DFE Error Propagation in the Presence of Residual ISI

This brief discusses the limitation of previously published statistical decision feedback equalizer (DFE) models when residual inter-symbol interference (ISI) is present and proposes a method that overcomes this limitation. The paper presents an accurate closed-form expression for the DFE with residual ISI and additive white Gaussian noise (AWGN). The analysis is extended to 4-level pulse amplitude modulation (PAM-4) to cover serial links of current interest. The results verify that the proposed model estimates an accurate bit error rate (BER).

A Novel Sum-Product Detection Algorithm for Faster-Than-Nyquist Signaling: A Deep Learning Approach

A deep learning assisted sum-product detection algorithm (DL-SPDA) for faster-than-Nyquist (FTN) signaling is proposed in this paper. The proposed detection algorithm works on a modified factor graph which concatenates a neural network function node to the variable nodes of the conventional FTN factor graph to approach the maximum a posterior probabilities (MAP) error performance. In specific, the neural network performs as a function node in the modified factor graph to deal with the residual intersymbol interference (ISI) that is not considered by the conventional detector with a limited complexity. We modify the updating rule in the conventional sum-product algorithm so that the neural network assisted detector can be complemented to a turbo equalization receiver. Furthermore, we propose a compatible training technique to improve the detection performance of the proposed DL-SPDA with turbo equalization. In particular, the neural network is optimized in terms of the mutual information between the transmitted sequence and the extrinsic information. We also investigate the maximum-likelihood bit error rate (BER) performance of a finite length coded FTN system. Simulation results show that the error performance of the proposed algorithm approaches the MAP performance, which is consistent with the analytical BER.

Experimental demonstration of pre-electronic dispersion compensation in IM/DD systems using an iterative algorithm.

To combat chromatic dispersion (CD) in intensity modulation and direct detection (IM/DD) systems, three chirp-free demonstrations are experimentally performed with an iterative pre-electronic dispersion compensation (pre-EDC) algorithm at the transmitter end, for 28 GBaud non-return-to-zero on-off keying (NRZ-OOK), 56 GBaud NRZ-OOK and 28 GBaud four-level pulse-amplitude-modulation (PAM-4) signals, over distances of 100 km, 50 km and 40 km of single mode fiber (SMF), respectively. The iterative pre-EDC algorithm is based on the Gerchberg-Saxton (GS) algorithm, which treats the unconstrained phase at the direct detection receiver as a degree of freedom. At the receiver side, only a linear fractionally-spaced (T/2) post-feed-forward equalizer (post-FFE) is employed to combat the residual inter-symbol interference (ISI). Experimental results show that the aforementioned three demonstrations can approach the forward error correction (FEC) bit error rate (BER) threshold of 3.8 × 10-3 with (15 pre-EDC iterations and 5-tap post-FFE), (30 pre-EDC iterations and 15-tap post-FFE), and (10 pre-EDC iterations and 25-tap post-FFE), respectively. The results indicate the applicability of the pre-EDC algorithm in high-capacity IM/DD systems for transmission distances below 100 km of SMF.

A Simple Two-Stage Equalizer for OTFS With Rectangular Windows

Orthogonal time-frequency space (OTFS) bears the potential to achieve excellent performance in high mobility scenarios. However, conventional linear equalizer performs poorly. In this letter, we propose a novel two-stage equalizer, wherein received signals are judiciously processed in two domains. First, in the time-frequency domain, a sliding window-assisted minimum mean square error (SW-MMSE) equalizer is proposed to restrict the inter-carrier interference effectively. Then in the second stage, a delay-doppler domain equalizer further mitigates the residual inter-symbol interference of the first stage. Our proposed two-stage equalizer enjoys low implementation complexity, and simulation validates its performance advantage over the conventional one-stage MMSE equalizer.

Compensation of Chromatic Dispersion and Nonlinear Phase Noise Using Iterative Soft Decision Feedback Equalizer for Coherent Optical FBMC/OQAM Systems

In this article, we propose an iterative soft decision feedback (ISDF) equalizer to compensate for the chromatic dispersion and nonlinear phase noise effects in 30-Gbaud coherent optical filter bank multicarrier with off-set quadrature amplitude modulation (FBMC/OQAM) system. Conventional optical FBMC/OQAM system usually uses a 1-tap zero-forcing equalizer per subcarrier to combat the inter-symbol interference (ISI) caused by the chromatic dispersion (CD) in optical fiber. However, residual ISI and inter-carrier interference (ICI) still remain in the system and have significant impact on the system performance. To overcome this problem, a new ISDF N-tap frequency sampling (FS) equalizer is proposed to jointly mitigate the residual ISI and ICI which permits a better trade-off between performance and complexity. Simulation results show that, the proposed technique is capable of suppressing the interference more effectively than using only 1-tap equalizer. The feedback branch of the proposed ISDF equalizer can be exploited further to compensate for the nonlinear effect of the optical fiber. With compensation of linear and nonlinear impairments the proposed technique acts as a backpropagation method for optical FBMC/OQAM system.

Iterative-Detection-Aided Tomlinson-Harashima Precoding for Faster-Than-Nyquist Signaling

Faster-than-Nyquist(FTN) is a promising technique due to higher spectral efficiency, but at a cost of introducing the inter-symbol interference (ISI) which usually requires the computationally demanding detection algorithms. In order to reduce the detection complexity at the receiver, in this paper, a novel Tomlinson-Harashima precoding (THP) scheme is proposed for FTN system. In the conventional THP (CTHP) scheme, the ISI introduced by time-packing can only be diminished from several preceding information symbols, which results in large residual ISI and an unattractive bit-error-rate (BER) performance. Moreover, due to the suboptimal receiver - a simple modulo operation which ignores the correlation between received symbols, CTHP faces obvious capacity loss and is ineffective to execute interference cancellation for FTNS. In this paper, residual ISI of FTNS in CTHP is formulated in detail and modeled mathematically. Further more, an improved THP method with an optimized receiver based on the soft interference cancelation (SIC) algorithm and iterative turbo process is proposed to combat residual ISI for FTNS. Computational complexity analysis and numerical simulation results show that the proposed scheme not only has inexpensive computational cost but also greatly outperforms CTHP and other cited schemes. Moreover, for moderate time-packing, it can approach the ISI-free BER performance boundary and is also competitive to the MAP equalization technique.

A 36 Gb/s wireline receiver with adaptive CTLE and 1-tap speculative DFE in 0.13 µm BiCMOS technology

This paper presents a 36 Gb/s receiver equalizer including an adaptive continuous time linear equalizer (CTLE), which is based on slope detection and a half-rate speculative decision feedback equalizer (DFE) in 0.13 µm BiCMOS technology for high speed serial link. The CTLE with middle frequency compensation can not only adjust the ratio of high frequency and low frequency components adaptively, but also provide a small amount of equalization to middle frequency range. A half-rate speculative DFE, which is connected to the back of the CTLE, can satisfy the time constraints and eliminate the residual inter-symbol interference. The chip area including pads is about 1.2 mm2 and the power consumption is about 750 mW under 3.3 V power supply. Measurement results show that the receiver chip can effectively equalize 24 dB loss at Nyquist frequency and a clear eye diagram can be captured at 36 Gb/s.

A Review on Training and Blind Equalization Algorithms for Wireless Communications

Every wireless communication system comes with an innate problem of multipath propagation, which results in spreading the resultant symbols on a time scale and thus causes the symbols to overlap and end up in Inter-symbol Interference (ISI). The overall signal is distorted and the receiver is unable to recover the original signal. ISI from the signal must be removed and the signal must be brought back to its original form as it was sent or as close to it as possible; and process of equalization is used in all wireless communication system for this purpose. Two types of equalization processes are common in modern wireless communication systems. Training based equalization requires the sender block of communication system to constantly send a pilot/training signal in order to update the receiver about the original signal. The receiver removes the ISI and extracts the unadulterated signal. The second equalization process is called blind equalization and it does not require any pilot signal. The receiver only needs to know the type of constellation scheme used in modulation and then the original signal is extracted based on that information. In this paper we have thoroughly reviewed four equalization algorithms, two from each type of equalization for 16-QAM constellation and 64-QAM constellation. We came up with constellation diagrams for each equalization algorithm and comparison of BER, residual ISI and MSE for 16-QAM and 64-QAM is done through simulations. In case of LMS and RLS algorithm for 16 QAM, the performance of RLS gets slightly better than LMS at 6 dB, however, at around 12–14 dB and onwards the BER of RLS leads and there is a significantly better BER than LMS. In future, we will compare these algorithms in order to figure out the best algorithms for the current and upcoming 5G and 6G communication technologies.

Rprop and improved Rprop+ based constant modulus type (RCMT) blind channel equalization algorithm for QAM signal

The aim of paper is to address the issues such as poor convergence, moderate BER, residual ISI associated with unsupervised (blind) weight adaptation technique employed for channel equalization. Two noble algorithms based on resilient back propagation framework have been proposed as solution for QAM signal. The widely accepted gradient descent based Constant Modulus algorithm suffers from poor convergence issues, high residual ISI and Moderate BER. Proposed solution assimilate Constant Modulus Algorithm (CMA) like error function into a general Rprop algorithm having two distinctive approaches of with/ without weight backtracking capability, taking into consideration of frequency selective nature of channels and additive gaussian noise. The algorithms exploit the advantage of Rprop mechanism, thus improving the convergence rate and have better ISI (inter symbol interference) suppression capability. Simulation of the proposed Rprop and improved Rprop+ based CM type (RCMT) algorithm proves their advantageously enhanced capabilities in terms of convergence, complexity, and residual ISI in comparison to the CMA and its variants. Proposed algorithm can also been used for M-PSK signal for which it shows similar performance.

Efficient Blind Adaptive CSE to Reduce Cyclic Prefix Length in Direct Detection Optical OFDM Systems

Abstract Direct detection optical orthogonal frequency division multiplexing (DDO-OFDM) systems for a long-reach of standard single mode fiber (SSMF) require a large length of cyclic prefix (CP) to avoid the inter-symbol interference (ISI) effect caused by group velocity dispersion (GVD). Unfortunately, this method is inefficient due to the energy wasted in CP samples. In order to reduce the CP length and to mitigate the residual ISI, a novel blind adaptive channel shortening equalizer (CSE) is proposed in this paper. Based on the orthogonality between subcarriers in the fast Fourier transform (FFT) property, the proposed algorithm attempts to minimize the sum-squared correlation (SSCM) between each sample located in a well-defined window to update the CSE coefficients. Thus, the combined channel-CSE response is shortened. Therefore, it can cancel the residual ISI effect due to the GVD and the short CP length. The performance of the system is evaluated on basis of bit error rate (BER) versus optical signal to noise ratio (OSNR) for different CP lengths. The simulation results validate the new algorithm SSCM and show that it can reduce the CP length with a much better system improvement than existing algorithms.