Intersymbol Interference Channels Research Articles

Study the BER Performance Comparison of MIMO Systems Using BPSK Modulation with ZF and MMSE Equalization

In the modern age, wireless communication is very helpful in various mobile antenna communication systems. In mobile communication systems, the transmission of data transfer rates is very high and it plays an important role in several services like video, top-quality audio, and mobile integrated service digital network. During the transmission of data at higher data transmission rates through the mobile radio channels, the channel impulse response can spread over many symbol periods as well as cause inter-symbol interference (ISI). Wireless transmission is suffering from fading and interference effects which may be combated with equalizer. Due to fading and interference, it creates a problem for signal recovery in wireless communication. The main objective of this paper is to analyze the different types of equalizers such as ZF and MMSE for BPSK modulation. The simulation result has been developed by using MATLAB toolbox version 2015a and a multi-tap ISI channel is considered. By analyzing the simulation result it shows that if the number of tap lengths is increasing, BER will decrease in ZF equalizer. And finally shows BER vs SNR comparison of two different types of an equalizer and is able to find out MMSE performance is better than ZF equalizer.

Unsupervised Linear and Nonlinear Channel Equalization and Decoding Using Variational Autoencoders

A new approach for blind channel equalization and decoding, variational inference, and variational autoencoders (VAEs) in particular, is introduced. We first consider the reconstruction of uncoded data symbols transmitted over a noisy linear intersymbol interference (ISI) channel, with an unknown impulse response, without using pilot symbols. We derive an approximate maximum likelihood estimate to the channel parameters and reconstruct the transmitted data. We demonstrate significant and consistent improvements in the error rate of the reconstructed symbols, compared to existing blind equalization methods such as constant modulus, thus enabling faster channel acquisition. The VAE equalizer uses a convolutional neural network with a small number of free parameters. These results are extended to blind equalization over a noisy nonlinear ISI channel with unknown parameters. We then consider coded communication using low-density parity-check (LDPC) codes transmitted over a noisy linear or nonlinear ISI channel. The goal is to reconstruct the transmitted message from the channel observations corresponding to a transmitted codeword, without using pilot symbols. We demonstrate improvements compared to the expectation maximization (EM) algorithm using turbo equalization. Furthermore, unlike EM, the computational complexity of our method does not have exponential dependence on the size of the channel impulse response.

Performance Analysis of ZF and MMSE channel equalizer for Butterworth and Chebyshev Low Pass Channels

Due to the high demand for information in the communication system needs a greater amount of data transmission on the current channels. The data flow rate on the existing channel is bounded because of the Inter Symbol Interference (ISI). To minimize the influence of ISI Channel equalizers are utilized. The Zero Forcing (ZF) & Minimum Mean Square Error (MMSE) equalizer is used to compare the eye diagrams before and after the equalizer in this paper. It shows that the equalizer reduce the ISI effectively and achieves the suitable performance.

Iterative Receiver Design for Probabilistic Constellation Shaping in ISI Channel

This paper investigates the receiver design for probabilistic constellation shaping signaling over inter-symbol interference channel. The key component performing the constellation shaping is an adjustable distribution matcher, and the probabilistic shaping system is capable to adapt to variable data rates by adjusting the distribution match rate rather than the modulation or coding mode. In this paper, we resort to distinct techniques to derive two iterative receivers operating in time domain. Shaped-BCJR is a trellis-based solution where forward/backward algorithm together with turbo iteration is used to compute the posteriori probability in which the nonuniform a priori symbol probability initializes the calculation. Another receiver is based on linear filtering where expectation propagation provides a Gaussian approximation of the posteriori probability of each symbol. This receiver structure is represented by a factor graph and we detail the derivation of messages exchanging between adjacent nodes. The Bayesian equalization in each EP iteration brings unacceptable computational burden. An efficient block-wise matrix inversion strategy is proposed to tackle this problem, significantly reducing the computational complexity with little performance loss. Simulation results show that the proposed algorithms remarkably outperform LMMSE solutions and traditional EP based algorithms. Proposed matrix inversion strategy can also be used to improve the performance of other filter-type solutions.

Information Rates of Energy Harvesting Communications With Intersymbol Interference

We consider energy harvesting communications over an intersymbol interference (ISI) channel corrupted by additive white Gaussian noise. We assume that the energy arrivals at the transmitter, which is equipped with a finite battery, are independent and identically distributed, and provide a method of computing achievable information rates with channel inputs selected from a finite alphabet. We illustrate the methodology via a set of examples quantifying the effects of energy arrival rates as well as battery capacity on the achievable information rates.

MMSE Equalization Based Performance of Chaotic Interleaving Scheme for Iterative IDMA System

Background: In this paper, a chaotic interleaving scheme is proposed for further performance improvement of Interleave Division Multiple Access (IDMA). Interleavers are used to generate permuted sequence of signals to be transmitted with optimum correlation. Methods: Random interleaving (RI) was the fundamental taxonomy and used to distinguish the different users in IDMA scheme. The logistic map based chaotic interleaving scheme is suggested for IDMA. The system is also combined with Minimum Mean Square Error (MMSE) equalizer to combat the effect of Inter Symbol Interference (ISI). Results: For the sake of simplicity, no pulse shaping is assumed at the transmitter and ISI channel is considered to be a fixed 3 tap channel. Simulations are performed in MATLAB. BPSK modulation is used. Furthermore, the results show that the IDMA with proposed logistic map based chaotic interleaver outperforms the traditional random interleaving scheme in terms of BER without the need of extra memory and computational complexity. Conclusion: The obtained results show the noticeable performance improvement of CI-IDMA with MMSE equalization in deep fading situations. Chaos based interleaver also offers other advantages such as less requirement of memory and small implementation complexity.

Dual Capacity Upper Bounds for Binary-Input Single-Tap ISI Channels

The capacity of noisy channels with memory and finite input has been difficult to characterize explicitly in many cases. In this paper, we consider single-tap binary-input Gaussian channels with inter-symbol interference (ISI). The dual capacity method is used to obtain upper bounds using Markov test distributions. The bound, expressed as a single-letter optimization problem, is solved numerically. For higher memory, the notion of cycle basis is used to provide an exponential reduction in the computational complexity of the optimization problem. Bounds were obtained for the important case of the dicode channel, and these are better than the previously known upper bounds and are close to achievable rates over a wide range of SNRs.

Gaussian Intersymbol Interference Channels With Mismatch

This paper considers the problem of channel coding over Gaussian intersymbol interference (ISI) channels with a given decoding rule. Specifically, it is assumed that the mismatched decoder has an incorrect assumption on the channel impulse response. The mismatch capacity is the highest achievable rate for a given decoding rule. The existing achievable rates for channels and decoding metrics with memory (as in our model) are currently available only in the form of multi-letter expressions that cannot be calculated. Consequently, they provide little insight on the mismatch problem. In this paper, we derive the computable formulas of achievable rates and discuss some implications of our results. Our achievable rates are based on two ensembles: the ensemble of codewords generated by an autoregressive process and the ensemble of codewords drawn uniformly over a “type class” of real-valued sequences. We provide a few numerical results of our achievable rates, as functions of the mismatched ISI parameters. Finally, we compare our results with universal decoders which are designed outside the true class of channels that we consider in this paper.

Blind MIMO Cooperative Jamming: Secrecy via ISI Heterogeneity Without CSIT

We investigate the secure degrees of freedom (SDoF) of the multiple-input multiple-output (MIMO) wiretap channel with intersymbol interference (ISI) in the presence of a multi-antenna cooperative jammer. We focus on the practically relevant setting with no channel state information at the transmitters (CSIT). More specifically, the legitimate transmitter and the cooperative jammer only have statistical knowledge of the channel in terms of the effective number of ISI channel taps, i.e., channel impulse response (CIR) lengths, toward the legitimate receiver and the eavesdropper. Our main contribution is to show that in the absence of CSIT, positive SDoF can be achieved by carefully exploiting: 1) the heterogeneity of the CIR lengths toward both receivers and 2) the relative number of antennas at the four terminals. To achieve secrecy, we propose a scheme in which the transmitter strategically sends a mixture of information and artificial noise symbols in a way that exploits the heterogeneity of CIR lengths. Additionally, the cooperative jammer transmits artificial noise symbols in a way that completely masks all the information symbols that are received at the eavesdropping node. Under the proposed scheme, positive SDoF can be achieved, even when the number of antennas at the legitimate receiver is less than the number of antennas at the eavesdropper.

Approximate MLSE Equalization of SOQPSK-TG in Aeronautical Telemetry

An approximate maximum likelihood sequence estimator (MLSE) equalizer for shaped offset QPSK, version TG (SOQPSK-TG) is derived based on the pulse amplitude modulation (PAM) approximation of SOQPSK-TG using the two principal PAM pulses. The resulting equalizer is a generalization of the equalizer based on the Ungerboeck observation model, where the generalization is to two parallel, cross-correlated symbol streams over parallel intersymbol interference channels. The bit error rate (BER) performance and computational complexity of the approximate MLSE equalizer operating over three example channels, motivated by multipath propagation in aeronautical telemetry and with increasing selectivity, are presented. The BER performance was evaluated using computer simulations and shown to be approximately 5–8 dB better than the best frequency-domain minimum mean-squared error (MMSE) equalizers published in the open literature. The computational complexity, measured by the number of real-valued multiplications, is comparable to that of the frequency-domain MMSE equalizers.

Tomlinson–Harashima precoding for transmitter‐side inter‐symbol interference cancellation in PSK modulation

Dirty paper coding (DPC) is a non-linear transmit scheme in presence of known interference, which is capacity achieving. Unfortunately, the implementation complexity of DPC is usually prohibitive. A sub-optimal yet practical method to implement DPC in inter-symbol interference channels is Tomlinson–Harashima precoding (THP). However, THP is not applicable to the constant-envelope phase shift keying (PSK) modulation. In this study, a modified Tomlinson–Harashima precoder is proposed to implement DPC for PSK modulation. The technique involves design of decision region at the receiver side and an algorithm to select the phase of transmitted symbol optimally at the transmitter side accordingly. Various patterns, namely, striped, checked, hexagonal, and radial are proposed and examined. Simulation results show that by using the proposed equaliser, the error floor is eliminated and significantly smaller bit-error rate is achieved. Numerical and simulation results show that the striped pattern outperforms other decision region designs. Moreover, its implementation and computational complexities is almost the same as the Tomlinson–Harashima precoder.

Low computationally complex recurrent neural network for high speed optical fiber transmission

The demand for high speed data transmission has increased rapidly over the past few years, leading to the development of the data center concept. Considering that vertical cavity surface emitting lasers (VCSELs) based optical interconnect is evolving to 100 Gb/s, relative intensity noise and mode partition noise are becoming significant, which cannot be equalized by conventional equalizers efficiently. On the other hand, optical fiber suffers from inter-symbol interference (ISI) and nonlinear channel response, making the equalization process even more challenging. Recently, several machine learning techniques have already been applied to recover signal from nonlinear distortions. However, previous experiments mainly focused on achieving low BER and have neglected the computational complexity. In this paper, we have designed a recurrent neural network (RNN) based equalizer. The equalizer is tested over a PAM-4 modulated VCSEL-MMF optical interconnect link, and shows BER performance improvement over equalizers based on ANN. A variant, Half-RNN, is also proposed and tested, whose computational complexity is 70% lower than ANN with similar BER performance. Our experiments provide guidance for designing neural network structure when using deep learning for equalization, justifying the significance of our work.

OFDM Signal Recovery in Deep Faded Erasure Channel

In high-speed digital wireless communication applications, the intersymbol interference channel may have spectral nulls or erasures, which may degrade the orthogonal frequency division multiplexing (OFDM) bit error rate (BER) performance. In this paper, we prove that the BER performance of the OFDM system is considerably refined if the erased symbols in erasure channel (or received symbols on the deep-faded subcarriers in Rayleigh fading channel) are estimated based on the rest symbols in each OFDM signal. Also, an oversampled OFDM scheme which is a particular form of the pre-coded OFDM schemes is considered to guarantee high enough sampling rate. Furthermore, a new iterative receiver is proposed for perfect symbol recovery. A comprehensive Monte Carlo simulation study is performed to validate the theoretical results and affirm the superior performance of the oversampled OFDM scheme with the iterative receiver, compared with the typical detector for the OFDM scheme.

Equalization in chaos-based communication systems using kernel adaptive filtering

Chaos-based communication systems have attracted attention of researchers in academy and industry in the last decades. A particular family of such systems has as basic idea to use the transmitted message to modify a known nonlinear chaotic signal generator (CSG). In the receiver, the knowledge of the employed nonlinear CSG in conjunction with chaotic synchronization permits to recover the original message. These systems are an alternative for spread spectrum communication with a possible increase in the security in the physical layer, since it is necessary to perfectly know the CSG in the receiver to decode the message. However, the lack of robustness of chaotic synchronization in relation to channel noise and intersymbol interference still poses a barrier for their practical use. The problem of equalization for such systems have been tackled for a while, and algorithms based on the normalized least-mean squares have presented auspicious results for linear channels. For nonlinear channels, Kernel Adaptive Filters (KAFs) have been used since they are able to solve nonlinear problems implicitly projecting the input vector into a larger dimension space, where they can be linearly solved. Therefore, in this paper, we propose the use of KAFs with two purposes: to equalize linear and nonlinear channels and, at the same time, decode the message without knowledge of the CSG in the receiver. Simulation results show that the proposed solution is able to perform these tasks.

A study of analog decision feedback equalization for ADC-Based serial link receivers

High-speed serial link receivers based on analog-to-digital converters (ADCs) provide better programmability with different channel characteristics and the possibility of employing powerful signal equalization techniques in the digital domain. However, complexity and power consumption are still major issues in adopting such receivers in high-speed applications when compared to traditional binary or mixed-signal approaches. Embedded decision feedback equalization (DFE) before ADC quantization can relax the design requirements of both the ADC and post-ADC digital processing. This paper studies the impact of embedded analog DFE on voltage margin improvement of an ADC-based receiver through worst-case analysis. An analytical expression for the link bit-error-rate (BER) with analog DFE is derived and validated through simulations. An empirical study is conducted that evaluates the achievable BER of embedded analog DFE as a function of the channel inter-symbol interference (ISI) and ADC resolution. A channel-dependent parameter is introduced and employed to quantify the BER improvement achieved by embedding analog DFE in a receiver. A prototype receiver with embedded DFE is designed and laid out in a 130 nm CMOS process and achieves 4.64-bits peak ENOB and 4.08 pJ/conv.-step FOM at a 1.6-GS/s sampling rate. The BER performance of the receiver over high-loss FR4 channels at 1.6 Gb/s is evaluated and used to validate the simulation results.

Random coding bound for channels with memory decoding function with partial overlapping. Part 2. Examples and Discussion

Introduction:Suboptimal random coding exponent Er*(R; ψ) for a wide class of finite-state channel models using a mismatched decoding function tp was obtained and presented in the first part of this work. We used tp function represented as a product of a posteriori probabilities of non-overlapped input subblocks of length 2B+1 relative to the overlapped output subblocks of length 2W+1. It has been shown that the computation of function Er*(R; ψ) is reduced to the calculation of the largest eigenvalue of a square non-negative matrix of an order depending on the B and W values.Purpose:Toillustrate the approach developed in the first part of this study with its application to various channel modelled as a probabilistic finite-state machine.Results:We consider channels with state transitions not depending on the input symbol (channels with freely evolving states), and channels with deterministic state transitions, in particular, intersymbol interference channels. We present and discuss numerical results of calculating this random coding exponent in a full range of code rates for some of channel models for which similar results were not obtained before. Practical computations were carried out for relatively small values of B and W. Nevertheless, even for small values of these parameters a good correspondence with some known results for optimal decoding was shown.

Non-Coherent Massive SIMO Systems in ISI Channels: Constellation Design and Performance Analysis

A massive single-input multiple-output (SIMO) system with a single transmit antenna and a large number of receive antennas in intersymbol interference (ISI) channels is considered. Contrast to existing energy detection (ED)-based non-coherent receiver where conventional pulse amplitude modulation (PAM) is employed, we propose a constellation design which minimizes the symbol-error rate (SER) with the knowledge of channel statistics. To make a comparison, we derive the SERs of the ED-based receiver with both the proposed constellation and PAM, namely $P_{e\_opt}$ and $P_{e\_pam}$. Specifically, asymptotic behaviors of the SER in regimes of a large number of receive antennas and high signal-to-noise ratio (SNR) are investigated. Analytical results demonstrate that the logarithms of both $P_{e\_opt}$ and $P_{e\_pam}$ decrease approximately linearly with the number of receive antennas, while $P_{e\_opt}$ degrades faster. It is also shown that the proposed design is of less cost, because compared with PAM, less antennas are required to achieve the same error rate.

Frequency Domain Equalization and Post Distortion for LED Communications With Orthogonal Polynomial Based Joint LED Nonlinearity and Channel Estimation

The light-emitting diode (LED) is the major source of nonlinearity in LED communications, and the nonlinearity needs to be effectively modeled and mitigated to avoid the degradation of communication performance. In indoor LED communications, multipath dispersion can lead to inter-symbol interference (ISI) at high data rates. In this paper, we jointly estimate the LED nonlinearity and ISI channel based on an orthogonal polynomial based technique. Then, frequency domain equalization and post-distortion are adopted to mitigate the ISI and nonlinearity. Simulation results are provided to demonstrate the effectiveness of the proposed technique.

Closed-Form Expressions for Channel Shortening Receivers Using $A\ Priori$ Information

Channel shortening has been studied in the context of intersymbol interference and multi-in multi-out channels as a means to compute a posteriori probabilities with a BCJR algorithm at a reduced computational complexity. This is done by considering an approximate channel response of reduced length. In a turbo receiver, soft a priori information can be linearly combined with the received sequence to form a new input to the BCJR trellis-based processing. In this letter, we provide closed-form expressions for the channel shortening filters using a generalized mutual information objective function. The proposed receiver allows a complexity reduction with respect to numerical optimization approaches which may also present stability, precision, and convergence issues.

Channel-Adaptive ADC and TDC for 28 Gb/s PAM-4 Digital Receiver

A low-power channel-adaptive 28 Gb/s PAM-4 receiver is presented utilizing a predictive analog-to-digital converter (ADC), a successive-approximation-register (SAR) time-to-digital converter (TDC), and a feed-forward equalizer (FFE) in the digital domain. The variable-resolution flash ADC takes advantage of the channel inter-symbol interference (ISI) and can achieve 5.5 bits resolution utilizing only 16 comparators. By reusing the comparators, the ADC can provide a programmable resolution from 2 to 5.5 bits consuming 40 to 90 mW, respectively. The SAR-TDC generates 5 bits timing information that includes 2 bits ISI and 3 bits timing error to achieve a low-latency and low-jitter timing recovery. Subsequently, a three-to-eight programmable tap FFE is used to equalize up to 30-dB loss achieving bit error rate lower than 10−8. FFE is implemented in a field-programmable gate array, and the first three taps are realized in a look-up table (LUT). An offline higher resolution ADC is used to generate the pre-computed values for the LUT. Measured power consumption is 130 mW (excluding digital signal processing) from a 1.2-V power supply with active chip area of 0.2025 mm2 in 65-nm technology. Due to programmability on the both ADC resolution and the number of FFE taps according to the channel loss, the receiver enables energy efficiency according to loss compensation.