Nonlinear Decision Feedback Research Articles

Adaptive two-stage nonlinear feedforward equalizer and decision feedback equalizer for a visible-light communication and ultra-large effective area pure silica fiber seamless integrated system

We proposed an adaptive two-stage nonlinear feedforward equalizer and decision feedback equalizer to minimize the negative influence of nonlinear distortions. A data rate of 960 Mbit/s is experimentally achieved on the guided visible-light transparent transmission over a 100-m ultra-large effective area pure silica fiber. The experimental results verified the effectiveness and improvement of the proposed method compared with the traditional feedforward post-equalizers.

Single-Carrier Frequency-Domain Equalization With Hybrid Decision Feedback Equalizer for Hammerstein Channels Containing Nonlinear Transmit Amplifier

We propose a nonlinear hybrid decision feedback equalizer (NHDFE) for single-carrier (SC) block transmission systems with nonlinear transmit high power amplifier (HPA), which significantly outperforms our previous nonlinear SC frequency-domain equalization (NFDE) design. To obtain the coefficients of the channel impulse response (CIR) as well as to estimate the nonlinear mapping and the inverse nonlinear mapping of the HPA, we adopt a complex-valued (CV) B-spline neural network approach. Specifically, we use a CV B-spline neural network to model the nonlinear HPA, and we develop an efficient alternating least squares scheme for estimating the parameters of the Hammerstein channel, including both the CIR coefficients and the parameters of the CV B-spline model. We also adopt another CV B-spline neural network to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can be estimated using the least squares algorithm based on the pseudo training data obtained as a natural byproduct of the Hammerstein channel identification. The effectiveness of our NHDFE design is demonstrated in a simulation study, which shows that the NHDFE achieves a signal-to-noise ratio gain of 4dB over the NFDE at the bit error rate level of $10^{-4}$ .

FEEDBACK EQUALIZER FOR VEHICULAR CHANNEL

Abstract In this fast moving world, the number of fatal accidents is increasing day by day and this leads to the requirement of the availability of the traffic condition and road conditions related data to the users. Therefore, to support Vehicle-to-vehicle (V2V) communication in high speed mobility condition, it is required to have reliable and secure of communication. Here, the performance of multiple input and multiple output (MIMO) system as a combination of nonlinear decision feedback receiver (DFE) have been investigated in V2V channel. In this paper, through the simulation, the results are presented to show the effect of the channel correlation coefficient and Doppler shift (Fd) (because of the relative velocity of the vehicle) over the performance of the MIMO system. As a counter measure of those problems nonlinear receivers have been formulated and analyzed.

Modified Nonlinear Decision Feedback Equalizer for Long-Haul Fiber-Optic Communications

In a long-haul optical fiber communication system, fiber attenuation, dispersion, and nonlinearity combined with nondeterministic noise from optical amplifiers used for periodic regeneration cause adverse effects on system performance. Several optical and electrical signal processing techniques have been proposed, and implemented to extract the transmitted data; some provide better performance than others, but at a cost of higher computational complexity. We present a modified nonlinear decision feedback equalizer designed for use in a legacy optical communication system with periodic dispersion compensation. The effects of noise and nonlinearity on the equalizer coefficients are investigated, and a suboptimal convergence algorithm to reduce such effects is proposed and verified. Our equalizer provides performance comparable to that obtained using digital backpropagation, while being computationally simpler, compensating linear and nonlinear physical impairment effects effectively even at high power levels where fiber nonlinearity is significant. Performance prediction of the designed DFE is also discussed, using a numerical method, with and without error propagation.

Demonstration of a 40 Gb/s Wavelength-Reused WDM-PON Using Coding and Equalization [Invited

The wavelength-division-multiplexed passive optical network (WDM-PON) has been generally regarded as a promising solution to the next-generation access network that will be required to deliver services over 40 Gb/s. However, fiber dispersion often limits the capacity and reach of WDM-PONs. Compared with dispersion compensation fiber, which is bulky and expensive with significant power loss, digital signal processing is a more suitable way to mitigate chromatic dispersion in PONs. Furthermore, expense is a critical concern in the WDM-PON, due to its need for a large number of lasers and a complex wavelength control mechanism. One practical solution is to reuse the downstream (DS) signal as the carrier for the upstream (US) modulation. In this case, the residual DS signal after remodulation can seriously degrade US transmission. In addition, system performance can be deteriorated by the unwanted reflection as uplinks and downlinks share one wavelength. In this paper, we propose using modified duobinary (MD) coding in the DS to improve its dispersion tolerance and reduce the crosstalk between DS and US induced by remodulation and reflection. MD is a correlative level code that can reduce signal bandwidth and achieve DC balance. We demonstrate a 15 km WDM-PON delivering a 40 Gb/s MD-coded signal in the downlink and a 10 Gb/s on-off keying signal in the uplink. Compared with no coding, the maximal allowable extinction ratio of the DS signal (ERd) is improved by 4 dB. Moreover, the reflection tolerance of the uplink and downlink is enhanced by 5 and 4 dB, respectively. In addition, investigations on the use of different equalizers in the DS to further suppress fiber dispersion confirm that the superior performance of nonlinear equalization in MD-coded transmission and that the network reach can be extended to 25 km by a nonlinear decision feedback equalizer.

Joint source and relay optimization for parallel MIMO relay networks

Abstract In this article, we study the optimal structure of the source precoding matrix and the relay amplifying matrices for multiple-input multiple-output (MIMO) relay communication systems with parallel relay nodes. Two types of receivers are considered at the destination node: (1) The linear minimal mean-squared error (MMSE) receiver; (2) The nonlinear decision feedback equalizer based on the minimal MSE criterion. We show that for both receiver schemes, the optimal source precoding matrix and the optimal relay amplifying matrices have a beamforming structure. Using such optimal structure, joint source and relay power loading algorithms are developed to minimize the MSE of the signal waveform estimation at the destination. Compared with existing algorithms for parallel MIMO relay networks, the proposed joint source and relay beamforming algorithms have significant improvement in the system bit-error-rate performance.

SC-FDMA 수신기를 위한 잡음 백색화 판정궤환 등화기

이 논문에서는 SC-FDMA 수신기를 위한 잡음 백색화 판정궤환 등화기를 제안하였다. SC-FDMA 방식은 다중경로의 영향을 제거할 수 있는 OFDMA 방식의 장점을 유지하면서 OFDMA의 단점인 높은 PAPR 문제를 해결할 수 있는 장점을 가지고 있다. 또 SCFDMA 방식은 기본적으로 단일 반송파 전송방식이지만, 주파수 영역에서 채널 등화기를 구현함으로써 OFDMA 수신기와 마찬가지로 등화기의 복잡도를 크게 감소시킬 수 있다. 뿐만 아니라 시간 영역 신호가 디지털 변조된 복소심볼이므로 시간 영역에서 추가적으로 비선형 등화인 판정궤환 등화를 함으로써 주파수 영역의 선형 등화에 의해 잔류해 있는 심볼간 간섭을 더 제거할 수 있다. 한편 지금까지 제시된 SC-FDMA용 판정궤환 등화기는 판정기에 입력되는 신호에 포함된 잡음이 백색화되어 있지 않기 때문에 최적판정을 수행하고 있지 않다. 이 논문에서는 이러한 문제를 해결하기 위해 선형 잡음 백색화 필터를 판정기 앞에 연결하여 판정궤환 등화기의 성능을 더 향상 시킬 수 있는 방법을 제시한다. 또 컴퓨터 모의실험을 통해 기존의 등화기와 제안된 등화기의 비트 오율 성능을 비교한다. In this paper, we propose a noise whitening decision feedback equalizer for single carrier frequency division multiple access (SC-FDMA) receivers. SC-FDMA has the same advantage as that of orthogonal frequency division multiple access (OFDMA) in which the multipath effect can be removed easily, and also solves the problem of high peak to average power ratio (PAPR) which is the main drawback of OFDMA. Although SC-FDMA is a single carrier transmission scheme, a simple frequency domain linear equalizer (FD-LE) can be implemented as in OFDMA, which can dramatically reduce the equalizer complexity. Moreover, some residual intersymbol interference in the output of the FD-LE can be further removed by an additional nonlinear decision feedback equalizer (DFE) in time domain, because the time domain signal is a digitally modulated symbol. In the conventional DFE, however, the noise is not white at the input of the decision device and correspondingly the decision is not optimum. In this paper, we propose an improved DFE scheme for SC-FDMA systems where a linear noise whitening filter is inserted before the decision device of the conventional DFE scheme. Through computer simulations, we compare the bit error rate performance of the proposed DFE scheme with the conventional equalizers.

Low-Complexity Iterative Frequency Domain Decision Feedback Equalization

Single-carrier transmission with frequency-domain equalization (SC-FDE) offers a viable design alternative to the classic orthogonal frequency-division multiplexing (OFDM) technique. However, SC-FDE using a linear equalizer may suffer from serious performance deterioration for transmission over severely frequency-selective fading channels. An effective method of solving this problem is to introduce nonlinear decision feedback equalization (DFE) to SC-FDE. In this paper, a low-complexity iterative DFE operating in the frequency domain of single-carrier systems is proposed. Based on the minimum-mean-square-error (MMSE) criterion, a simplified parameter estimation method is introduced to calculate the coefficients of the feedforward and feedback filters, which significantly reduces the implementation complexity of the equalizer. Simulation results show that the performance of the proposed simplified design is similar to the traditional iterative block DFE under various multipath fading channels, but it imposes a much lower complexity than the latter.

Multihop Nonregenerative MIMO Relays— QoS Considerations

For nonregenerative multihop multiple-input multiple-output (MIMO) relay communication systems, the optimal source precoding matrix and the optimal relay amplifying matrices have been recently established for a broad class of objective functions subjecting to the transmission power constraint at each node. However, existing works do not consider any quality-of-service (QoS) constraints, which are important in practical communication systems. In this paper, we derive the optimal source and relay matrices of a multihop MIMO relay system that guarantee the predetermined QoS criteria be attained with the minimal total transmission power. In particular, we consider two types of receivers at the destination node: the linear minimal mean-squared error (MMSE) receiver and the nonlinear decision feedback equalizer (DFE) based on the MMSE criterion. We show that for both types of receivers, the solution to the original optimization problem can be upper-bounded by using a successive geometric programming (GP) approach and lower-bounded by utilizing a dual decomposition technique. Simulation results show that both bounds are tight, and to obtain the same QoS, the MIMO relay system using the nonlinear MMSE-DFE receiver requires substantially less total transmission power than the linear MMSE receiver-based system.

Energy-Efficient Resource Allocation in Multipath CDMA Channels With Band-Limited Waveforms

This paper is focused on the cross-layer design problem of joint multiuser detection and power control for energy-efficiency optimization in wireless data networks through a game-theoretic approach. Unlike previous studies in this area, which have considered the application of game theory to achieve energy-efficiency in idealized synchronous code division multiple access systems, more realistic assumptions including system asynchronism, the use of band-limited chip-pulses, and the multipath distortion induced by the wireless channel are explicitly incorporated in the development of this paper. Several noncooperative games are proposed wherein each user may vary its transmit power and uplink receiver in order to maximize its utility, which is defined here as the ratio of data throughput to transmit power. In particular, the case in which a linear multiuser detector is adopted at the receiver is considered first, and then, the more challenging case in which a nonlinear decision feedback multiuser detector is employed is considered. Via large system analysis (LSA), a decentralized implementation of the power allocation game requiring very little prior information on the interference background is proposed. LSA is also used to compare the energy efficiency of several linear multiuser detectors, and to obtain the optimal (i.e., utility-maximizing) length of the training sequence of each data frame. Numerical results show the effectiveness of the proposed solutions, as well as a very satisfactory agreement of the LSA-based analysis with simulation results obtained for systems with finite (and not so large) numbers of users.

Adaptive multichannel decision feedback equalization for volterra type nonlinear communication channels

A model-based approach for the decision feedback equalization of Volterra type nonlinear communication channels is proposed such that the linear model-based decision feedback equalization can be considered as a special case of the proposed approach. In designing the decision feedback equalizer, the nonlinear decision feedback equalization problem is visualized as a linear, multichannel equalization problem. A complete modified Gram–Schmidt orthogonalization of the input vector is achieved by using modified sequential processing multichannel lattice stages. The elements of the multichannel desired signal vector are then estimated from the new orthogonal set by using only scalar operations. The probability of error performance of the proposed equalizer is improved by the estimation of the elements of the desired signal vector through a sigmoid activation function so that a polynomial perceptron equalizer is realized. The comparative computational complexity calculations and performance results of the proposed decision feedback equalizer are also provided.

Equalization with decision delay estimation using recurrent neural networks

In this paper, we propose a new recursive classifier based on a recurrent neural network. A supervised algorithm is employed to estimate the classifier parameters. The proposed classifier is used to form a non-linear Decision Feedback Equalizer (DFE) for communication channels. A new procedure allowing the estimation of the decision delay is also presented so that the classifier parameters and the decision delay are estimated at the same time. This new DFE leads to suitable equalization performances even in presence of non-linear and non–minimum phase channels.

Fast stochastic power control algorithms for nonlinear multiuser receivers

Uplink communication in a cellular radio network is considered where the base station in each cell employs linear or nonlinear (decision feedback) multiuser receivers. For any such receiver, the problem of interest is that of minimizing the total transmit power under the constraint that all the users of the network achieve their quality-of-service objective in terms of signal-to-interference ratio (SIR). When the solution is feasible for the desired SIR requirements, the optimum powers are computed with a distributed iterative power control strategy suitable for implementation at each base station. While the deterministic algorithm requires both in-cell and out-of-cell user information, the stochastic algorithm proposed in this paper can be implemented at the base stations in a truly distributed manner requiring knowledge of only in-cell parameters. Such an algorithm was proposed previously for the case where base stations use linear (single user) matched filter (MF) receivers. However, the feasibility region in terms of attainable SIRs for a well-designed multiuser receiver, particularly for a nonlinear receiver that employs decision feedback, is generally much larger than it is for the linear MF receiver. The stochastic power control algorithm in this paper, for linear or nonlinear multiuser receivers, converges in the mean-square sense to the minimal powers when the target SIRs are feasible. The second major focus of this paper is to improve the convergence properties of the conventional stochastic approximation based power control strategy by using the more recent results on averaging. Convergence issues of both the nonaveraged and averaged algorithms are investigated, and numerical examples are presented to demonstrate the performance improvement due to averaging.

Adaptive loading for OFDM/SDMA-based wireless networks

The two major obstacles toward high-capacity indoor wireless networks are distortion due to the indoor channel and the limited availability of bandwidth which necessitates a high spectral efficiency. A combined orthogonal-frequency division multiplexing/spatial-diversity multiple access (OFDM/SDMA) approach can effectively tackle both obstacles. The channel distortion due to multipath propagation is easily mitigated with OFDM while the bandwidth efficiency can be increased with the use of SDMA. In order to keep the network's cost acceptable, simplified SDMA processors are preferred over the exponentially complex optimal maximum-likelihood processors. However, these simplified processors perform significantly worse than the optimal ones in terms of average bit error rate (BER). In this paper, we show that by adapting the constellation sizes applied on the individual subcarriers to the channel conditions, the performance of OFDM/SDMA processors can be significantly enhanced. In the uplink, we derive simple closed-form equations for the optimal constellation sizes for both a simple linear minimum mean-square error (MMSE) detector and for a nonlinear MMSE decision feedback equalizer (DFE) detector. Furthermore, for each detector, we introduce a simplified loading algorithm which lowers the computational and signaling complexity substantially at a small performance penalty. In the downlink, we study the dual precoders of the uplink detectors, respectively, the linear MMSE precoder and the nonlinear Tomlinson-Harashima (TH) MMSE-based precoder. For both precoders, we derive expressions for the optimal and the simplified constellation sizes. Additionally, we show that in time-division duplexing systems, the constellation distribution of a set of dual detectors/precoders is identical for up- and downlink, which effectively halves the computational complexity of adaptive loading. In the fully loaded uplink, the proposed adaptive loading algorithm results in a gain of 9 dB for a BER=10/sup -3/ for the linear MMSE detector and a gain of 4.5 dB for the nonlinear MMSE-DFE detector. In the fully loaded downlink, a gain of 6.3 dB is achieved for the MMSE precoder and 5.5 dB for the TH-MMSE precoder.

Support vector machine techniques for nonlinear equalization

The emerging machine learning technique called support vector machines is proposed as a method for performing nonlinear equalization in communication systems. The support vector machine has the advantage that a smaller number of parameters for the model can be identified in a manner that does not require the extent of prior information or heuristic assumptions that some previous techniques require. Furthermore, the optimization method of a support vector machine is quadratic programming, which is a well-studied and understood mathematical programming technique. Support vector machine simulations are carried out on nonlinear problems previously studied by other researchers using neural networks. This allows initial comparison against other techniques to determine the feasibility of using the proposed method for nonlinear detection. Results show that support vector machines perform as well as neural networks on the nonlinear problems investigated. A method is then proposed to introduce decision feedback processing to support vector machines to address the fact that intersymbol interference (ISI) data generates input vectors having temporal correlation, whereas a standard support vector machine assumes independent input vectors. Presenting the problem from the viewpoint of the pattern space illustrates the utility of a bank of support vector machines. This approach yields a nonlinear processing method that is somewhat different than the nonlinear decision feedback method whereby the linear feedback filter of the decision feedback equalizer is replaced by a Volterra filter. A simulation using a linear system shows that the proposed method performs equally to a conventional decision feedback equalizer for this problem.

Adaptive nonlinear decision feedback equalization with channel estimation and timing recovery in digital magnetic recording systems

In high density digital magnetic recording systems, the nonlinear effects in the write process appear in the readback waveform as shifts in the peak positions and changes in the amplitude. The pulse shift causes a nonlinear intersymbol interference (ISI) on the readback signal. In this paper, a Volterra-DFE, in which a Volterra filter is used in the feedback section of decision feedback structure, is proposed to equalize the nonlinear ISI. By theoretical analysis, the minimum mean squared error (MSE) of the Volterra-DFE is found to be a function of sampling phase. This will affect the output signal-to-noise ratio (SNR) of the playback system. A baud-rate timing recovery system in conjunction with a channel estimator is used to operate the sampling clock on the optimum phase. By computer simulation, Volterra-DFE is found to outperform conventional DFE in both output SNR and BER in a high density magnetic recording system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Spatial diversity equalization applied to underwater communications

Underwater acoustic digital communication is difficult because of the nature of the fading multipath channels. Digital signal processing, such as adaptive equalization, is known to greatly improve the communication data rate by limiting intersymbol interference (ISI). However, existing underwater acoustic equalization studies are limited to single-channel techniques, and spatial diversity processing is limited to selection or combining. In this paper, we design minimum mean-square error (MMSE) equalizers jointly among all spatial diversity channels. We call this spatial diversity equalization (SDE). Results are based on a very sparse vertical array in a midrange underwater acoustic channel. We study the effect of element number and placement, the length of the equalization filters, and linear feedforward versus nonlinear decision feedback algorithms. A suboptimum equalizer combiner (EC) is studied to alleviate the computational intensity of JCE. We first design the system for a known acoustic channel; later, some results are verified using adaptive algorithms. Results are presented both in terms of the mean-square error (MSE) and the probability of a symbol error. The latter is important as it is the ultimate interest for a digital communication system. We found that system performance improves rapidly with an increase in the number of spatial channels.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Near-maximum-likelihood detectors for binary signals

The paper studies three developments of a class of near-maximum-likelihood detection processes derived from a conventional nonlinear (decision feedback) equaliser. The new detectors are suitable for binary signals transmitted over a linear baseband channel introducing severe amplitude distortion. The complexity of the processes is not excessive, and increases approximately linearly with the delay in detection. Thus, a sufficiently large delay in detection can be employed to achieve a near-optimum tolerance to noise when the received signal has been very severely distorted. The paper describes three novel detection processes, and presents the results of computer simulation tests, comparing the tolerances to additive white Gaussian noise of various arrangements of each detector with that of the optimum detector of the given class and that of a conventional nonlinear equaliser. Three different channels are used in the tests and binary signals are transmitted in every case.

Binary Signaling over Channels Containing Quadratic Nonlinearities

This paper examines the transmission of binary data signals over channels which contain quadratic nonlinearities and additive Gaussian noise. We consider the case where the channel is nonlinear with memory and where the signal is passed through an input receiver filter and sampled once every signaling interval. The samples are represented by a discrete Volterra series and a special case where the received sample contains a single quadratic distortion term is examined. The optimum (maximum-likelihood) receiver (processor) is derived and upper and lower performance bounds obtained. The performance of a practical, suboptimum receiver is examined by means of computer simulation and is shown to be very close to the lower bound of the optimum receiver. Next we examine the case where the received sample contains two quadratic distortion terms. Again, upper and lower performance bounds are obtained. The performance of a suboptimum receiver which uses nonlinear decision feedback is evaluated by computer simulation. Its performance is shown to be superior to an optimum linear receiver.