Blind Equalization Research Articles

Modified Blind Equalization Algorithm Based on Cyclostationarity for Contaminated Reference Signal in Airborne PBR.

In airborne passive bistatic radar (PBR), the reference channel toward the opportunity illuminator is applied to receive the direct-path signal as the reference signal. In the actual scenario, the reference signal is contaminated by the multipath signals easily. Unlike the multipath signal in traditional ground PBR system, the multipath signal in the airborne PBR owns not only the time delay but also the Doppler frequency. The contaminated reference signal can cause the spatial-temporal clutter spectrum to expand and the false targets to appear. The performance of target detection is impacted severely. However, the existing blind equalization algorithm is unavailable for the contaminated reference signal in airborne PBR. In this paper, the modified blind equalization algorithm is proposed to suppress the needless multipath signal and restore the pure reference signal. Aiming at the Doppler frequency of multipath signal, the high-order moment information and the cyclostationarity of source signal are exploited to construct the new cost function for the phase constraint, and the complex value back propagation (BP) neural network is exploited to solve the constraint optimization problem for the better convergence. In final, the simulation experiments are conducted to prove the feasibility and superiority of proposed algorithm.

Collaborative Blind Equalization for Time-Varying OFDM Applications Enabled by Normalized Least Mean and Recursive Square Methodologies

In this work, a collaborative blind equalization method for the orthogonal frequency division multiplexing (OFDM) signals in time-varying channels is presented. Equalizers are eliminated the inter-symbol interference (ISI) in the received signals caused by channel distortions. The conventional adaptive equalization requires sending the training-sequences periodically to synthesize the channel model, which can only provide redundant information, and consequently decrease the channel utilization and complicate the system. To overcome this drawback, the blind equalization methods, which need not send the training-sequences periodically, is developed. However, the conventional blind equalization methods still suffer from various disadvantages. The normalized least mean square (NLMS) method is able to converge rapidly, whereas its equalization error is relatively large. The recursive least square (RLS) method has smaller steady-state error but low convergence rate, demanding massive training sequences. To further enhance the equalization performance of time-varying OFDM systems, which is typically with massive calculation, a collaborative blind equalization is proposed in this work, which is able to effectively combine the characteristics of the conventional NLMS and RLS methods together. The numerical simulations demonstrate the proposed LM-RS method can exhibit quite good performance. Particularly, as compared with the conventional NLMS and RLS methods, the proposed LM-RS method achieves smaller steady-state error and lower complexity, as well as similar convergence rate. All these results indicate that the proposed collaborative LM-RS blind equalization method is suitable for the OFDM transmission under the time-varying wireless application environments.

Modeling Binaural Unmasking of Speech Using a Blind Binaural Processing Stage.

The equalization cancellation model is often used to predict the binaural masking level difference. Previously its application to speech in noise has required separate knowledge about the speech and noise signals to maximize the signal-to-noise ratio (SNR). Here, a novel, blind equalization cancellation model is introduced that can use the mixed signals. This approach does not require any assumptions about particular sound source directions. It uses different strategies for positive and negative SNRs, with the switching between the two steered by a blind decision stage utilizing modulation cues. The output of the model is a single-channel signal with enhanced SNR, which we analyzed using the speech intelligibility index to compare speech intelligibility predictions. In a first experiment, the model was tested on experimental data obtained in a scenario with spatially separated target and masker signals. Predicted speech recognition thresholds were in good agreement with measured speech recognition thresholds with a root mean square error less than 1 dB. A second experiment investigated signals at positive SNRs, which was achieved using time compressed and low-pass filtered speech. The results demonstrated that binaural unmasking of speech occurs at positive SNRs and that the modulation-based switching strategy can predict the experimental results.

Research on Digital Simulation of Blind Equalization in Multipath Ground-to-Air Communication Channel

In ground-to-air communication, the inter-symbol interference caused by multipath effect is often the important cause of poor communication quality. Channel equalization technology can effectively solve the problem of inter-symbol interference in ground-to-air communication. Firstly, we theoretically analysed the multipath transmission channel of ground-to-air communication and did the simulation modeling work. Then, we selectively analysed the model structure, the principle of the process and the adopted key equalization algorithm. Based on the technology system and working parameters commonly used in ground-to-air communication, we simulated equalizing reception processing performance of the communication model in multipath channel and gave some simulation data. Experimental results showed that DD-LMS adaptive equalization technology can significantly improve the reception performance of the communication system in the ground-to-air communication system which is affected by multipath interference and it provides valuable reference for the evaluation of the multipath transmission performance of the ground-to-air communication system.

A Partial Amplify and Forward Cooperative Communication Strategy Based on Blind Signal Detection

Due to the great potential in extending propagation distance and enhancing the link reliability, amplify and forward (AF) cooperative communications have attracted much attention recently. However, the existing studies mainly focus on the energy consumption analysis and optimization, and also the channels used in communications are based on Rayleigh/Rician fading model, and/or it was usually supposed that the channel state information (CSI) is known or can be acquired by a training sequence. In this paper, blind signal detection for AF cooperative communication systems based on time division multiple access (TDMA) is studied, in which the channels are modeled as frequency selective fading and the CSI are unknown. A blind signal detection algorithm of partial amplify and forward (PAF) cooperative communication is proposed based on semidefinite relaxation (SDR). This method can recover the data without the training sequence and need not to implement blind equalization for the unknown channels. With the correlation between data of different links, the proposed method can obtain the optimal solution efficiently and achieve better performance of signal detection than the traditional algorithm. By simulations, the energy consumption efficiency as well as the overall system performance of the proposed strategy are verified.

Coordinate descent algorithms for phase retrieval

Phase retrieval aims at recovering a complex-valued signal using the magnitude-only measurements of its linear transformation, and has wide applicability in areas including astronomy, computational biology, crystallography, digital communications, electron microscopy, neutron radiography and optical imaging. However, phase recovery involves solving a system of quadratic equations or minimizing a multivariate fourth-order polynomial, indicating that it is a challenging nonconvex optimization problem. To tackle phase retrieval in an effective and efficient manner, we apply coordinate descent (CD) such that a single unknown is solved at each iteration while all other variables are kept fixed. As a result, only minimization of a univariate quartic polynomial is needed which is easily achieved by finding the closed-form roots of a cubic equation. Three computationally simple algorithms referred to as cyclic, randomized and greedy CDs, based on different updating rules, are devised. It is proved that the three CDs globally converge to a stationary point of the nonconvex problem, and specifically, the randomized CD locally converges to the global minimum and attains exact recovery at a geometric rate with high probability if the sample size is large enough. The cyclic and randomized CDs are also modified via minimization of the ℓ1-regularized quartic polynomial for phase retrieval of sparse signals. Furthermore, a novel application of the three CDs, namely, blind equalization in digital communications, is proposed. It is demonstrated that the CD methodology is superior to the state-of-the-art techniques in terms of computational efficiency and/or recovery performance.

Eigenvalue-Spread-Based Combination Rule for Distributed Blind Equalization in Networked System

Eigenvalue-Spread-Based Combination Rule for Distributed Blind Equalization in Networked System

A Concurrent Dual Mode Adaptive Switching Blind Equalization System in Impulse Noise

Due to the influence of various factors, the noise in actual digital communication system is non-Gaussian and always assumed to be impulse noise. But most blind equalization algorithms are mainly directed against Gaussian noise and the performance of common algorithms under impulse noise is poor. So, in this paper, we have studied the problem of channel equalization under impulse noise and improved the fractional lower order constant modulus algorithm(FLOM-CMA). Then, by convex combining with decision-directed least mean p norm(DD-LMP) algorithm, a new concurrent adaptive switching blind equalization system had been proposed here. The advantages of different modes are fully combined in our system by soft-switching, which is the FLOM mode is used to make the equalization process converge quickly, and then, after the eye map of signal is open, the joint parameter is gradually reduced to zero and our system adaptive switching to DD mode to improve its convergence accuracy. The excess mean square error(EMSE) of our system is analyzed, and several experiments have been simulated to prove that our system performs better than other traditional algorithms.

Blind Fractionally Spaced Channel Equalization for Shallow Water PPM Digital Communications Links.

Underwater acoustic digital communications suffer from inter-symbol interference deriving from signal distortions caused by the channel propagation. Facing such kind of impairment becomes particularly challenging when dealing with shallow water scenarios characterized by short channel coherence time and large delay spread caused by time-varying multipath effects. Channel equalization operated on the received signal represents a crucial issue in order to mitigate the effect of inter-symbol interference and improve the link reliability. In this direction, this contribution presents a preliminary performance analysis of acoustic digital links adopting pulse position modulation in severe multipath scenarios. First, we show how the spectral redundancy offered by pulse position modulated signals can be fruitfully exploited when using fractional sampling at the receiver side, which is an interesting approach rarely addressed by the current literature. In this context, a novel blind equalization scheme is devised. Specifically, the equalizer is blindly designed according to a suitably modified Bussgang scheme in which the zero-memory nonlinearity is replaced by a M-memory nonlinearity, M being the pulse position modulation order. Numerical results not only confirm the feasibility of the technique described here, but also assess the quality of its performance. An extension to a very interesting complex case is also provided.

Blind Equalization of Lung Crackle Sounds to Compensate Chest Attenuation.

Diseased lungs generate adventitious sounds that propagate through the thorax, reaching the surface where they may be heard or recorded. The attenuation imposed to the lung sounds by the thorax depends on the physical characteristics of each patient, hampering the analysis of quantitative indexes measured to assist the diagnosis of cardiorespiratory disorders. This work proposes the application of a blind equalizer (eigenvector algorithm - EVA) to reduce the effects of thorax attenuation on indexes measured from crackle sounds. Computer simulated crackles (acquired on the posterior chest wall after being applied to volunteer's mouth) and actual crackles belonging to a database were equalized. Quantitative indexes were measured from crackles before and after equalization. Comparison of indexes measured from simulated crackles reveals that the equalizer improves the results due to attenuation compensation and removal of Gaussian noise. Effects of equalization on indexes measured from actual crackles were qualitatively assessed. Results point out that blind equalization of crackles recorded on the thorax provides more consistent quantitative indexes to assist the diagnosis of different cardiorespiratory diseases.

Blind Equalization Based on Normalized Error in Wireless Sensor Networks

Blind Equalization Based on Normalized Error in Wireless Sensor Networks

Experimental demonstration of blind equalization for OFDM/OQAM-VLC system

Orthogonal frequency-division multiplexing/offset quadrature amplitude modulation (OFDM/OQAM) in direct-detection system obtains many benefits such as free of cyclic prefix (CP) and high side-lobe suppression ratio in comparison with CP-OFDM signal. Unfortunately, for OFDM/OQAM signal, it needs an extra interference cancellation process to eliminate the imaginary intrinsic interference (IMI) when using one-tap frequency equalization known as interference approximation method (IAM). Blind equalization without a pilot overhead for OFDM/OQAM signal is proposed and experimentally demonstrated in visible light communication (VLC) system with limited modulation bandwidth. Experimental results show that blind equalization for OFDM/OQAM-VLC can effectively eliminate the IMI effect and can exhibit better symbol error rate on different subcarriers. Furthermore, compared with conventional IAM, it exhibits 3.2 and 2.7 dB overall improvement in Q2-factor using blind equalization based on the constant modulus algorithm and constant norm algorithm, respectively. In addition, the system can achieve a total data rate of 3.96 Gb / s over 5-m free space link with a bit error rate lower than hard-decision forward error correction limit of 3.8 × 10 − 3.

Performance analysis of the multiuser Shalvi-Weinstein algorithm

Performance analyses of blind adaptive equalizers provide valuable insights on their behavior, thus being fundamental in the design process. In the literature, interesting theoretical results to predict the steady-state performance of well-known constant-modulus-based algorithms were obtained under rather idealized equalization conditions. In practice, however, the communication channel is often noisy and perfect equalization can be unachievable. In this paper, we employ a linear regression model, commonly used in supervised adaptive filtering, to consider imperfect equalization conditions in the steady-state analysis of constant-modulus-based algorithms. Due to the nonlinear nature of blind algorithms, this analysis extension is a rather challenging, but rewarding, task. In particular, we apply the extended analysis model to the multiuser Shalvi–Weinstein algorithm, chosen due to its inherent advantages in adaptive blind equalization, namely high convergence rate and numerical robustness. As a result, we obtain a theoretical expression for its excess mean-square error (EMSE) at steady state. Interestingly enough, the resulting EMSE expression allows for the identification of distinct performance degradation causes, such as effects due to high-order statistics of the transmitted constellation, imperfect equalization, and multiuser cross-correlation penalty. In spite of the many assumptions considered throughout the EMSE expression derivation, simulation results validate it under realistic operating conditions.

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.

Network Intrusion Feature Map Node Equalization Algorithm Based on Modified Variable Step-Size Constant Modulus

When the network is subject to intrusion and attack, the node output channel equalization will be affected, resulting in bit error and distortion in the output of network transmission symbols. In order to improve the anti-attack ability and equalization of network node, a network intrusion feature map node equalization algorithm based on modified variable step-size constant modulus blind equalization algorithm (MISO-VSS-MCMA) is proposed. In this algorithm, the node transmission channel model after network intrusion is constructed, and sequential processing is performed to intruded nodes with the variable structure feedback link control method. With diversity spread spectrum technology, the channel loss after network intrusion is compensated and the network intrusion map feature is extracted. According to the extracted feature amount, channel equalization processing is performed for the cost function with the MISO-VSS-MCMA method to reduce the damage of network intrusion to the channel. Simulation results show that in node transmission channel equalization after network intrusion, this algorithm can reduce the error bit rate of signal transmission in network, and provide a good ability of correcting phase deflection in the output constellation, thus avoiding the error bit distortion and channel damage caused by network intrusion to the signal with a good equalization effect. This algorithm provides stronger convergence and map concentration, which demonstrates that its anti-interference and signal recovery capabilities are better, so it improves the anti-attack ability of the network.

Joint blind equalization of CD and RSOP using a time-frequency domain Kalman filter structure in Stokes vector direct detection system.

We propose a joint blind equalization method for chromatic dispersion (CD) and ultra-fast rotation of state-of-polarization (RSOP) in a Stokes vector direct detection (SV-DD) system based on a new time-frequency domain Kalman filter structure. In an SV-DD system, the impairments induced by CD and RSOP possess a nonlinear form. Therefore, CD and RSOP cannot be treated sequentially, which causes difficulty in jointly equalizing these two impairments using an ordinary algorithm. The Kalman filter was proven to be effective in equalizing polarization effects in a coherent receiver. However, this approach has inherent limitations given that the Kalman filter was originally presented as a method implemented in the time domain whereas CD is eventually induced in the frequency domain. In this report, the proposed time-frequency domain Kalman filter can facilitate CD compensation in the frequency domain and RSOP equalization in the time domain by exploiting a sliding window structure. Both the CD compensation and the RSOP equalization are conducted in Stokes space when the proposed method is utilized, which is specially designed for an SV-DD system. The presented approach was checked using a 28 Gbaud 16-QAM SV-DD system simulation platform. The simulation results confirm that the method is very effective and has strong tolerance to CD (more than 2550 ps/nm, equivalent to a 150 km G. 652 fiber) combined with ultra-fast RSOP (up to 2 Mrad/s) for application in extreme polarization environments, like the transient lightning in a rainy day.

Convex Combination of SISO Equalization and Blind Source Separation for MIMO Blind Equalization

For Multiple-Input Multiple-Output (MIMO) system the received signal will suffer not only inter-symbol interference but also inter-antenna interference under frequency selective fading channel. This paper proposes a MIMO blind equalization algorithm consisting of the convex combination of Single-Input Single-Output (SISO) blind equalization algorithm and blind source separation (BSS). The main purpose of the SISO equalization algorithm is to convert the convolution channel into multiplicative channel, and the BSS algorithm is mainly used to separate the different sources. The SISO equalization algorithm used in the paper is the modified constant modulus algorithm (MCMA) because of its simplicity and effectiveness. The BSS algorithm is the constraint fitting probability density function algorithm (CFPA). The MIMO blind equalization algorithm is named as MCMA–CFPA. Moreover, a low complexity MCMA–CFPA and a dual mode algorithm based on soft switching are presented. Simulation results show that the proposed algorithms can simultaneously equalize and separate all transmission signals.

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.

CMA adaptive equalization in subspace pre-whitened blind receivers

In blind channel equalization, the use of whitening transformation (WT) preceding the constant modulus algorithm (CMA), referred to as the pre-whitened CMA, may accelerate the rate of convergence of using the CMA alone. In this work, we develop a novel subspace pre-whitened CMA (SP-CMA) using the subspace WT. By allowing the channel matrix to be non-square, this approach for the subspace WT offers greater flexibility in the design of the WT than the conventional per-whitened CMA does. The similarities and differences between the SP-CMA and the conventional CMA were first examined and analyzed in terms of their convergence behaviors from a theoretical viewpoint. The convergence behavior of the SP-CMA was analyzed under the whiteness assumption in which the input of the blind equalizer has been whitened beforehand by the subspace WT. The upper bound of the improvement in convergence of the SP-CMA over its CMA counterpart was developed. This analysis can be readily extended to other existing pre-whitened CMA schemes. Computer simulations using two highly dispersive multipath channels confirmed the superior convergence of the SP-CMA.

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.