A nonlinear electrical equalizer with decision feedback for OOK optical communication systems

A model for a reduced complexity nonlinear electrical equalizer based on the Volterra theory is presented which can be utilized to mitigate dispersion and other distortions in optical communication systems. In recent years several electronic equalizers like the feed forward equalizer (FFE), the decision feedback equalizer (DFE) and the maximum likelihood sequence estimator (MLSE) were intensively investigated in optical communication systems. Also, nonlinear FFE/DFE structures based on the Volterra theory were proposed. These nonlinear equalizers can mitigate the effects of dispersion much better than the classical FFE/DFE but are more complicated to build. In a practical system the Volterra nonlinearity is therefore limited to second and third order. However, the number of filter coefficients for such a nonlinear FFE of appropriate order (e.g. 5 taps) is still very high for the nonlinear parts. This results in a very high effort in the equalizer control and optimization algorithm and makes a practical implementation questionable. In this Paper we present a reduced model for Volterra based nonlinear equalizers were the order of the nonlinear parts can be set separately from the linear order. This results in less complex filter structures as the number of coefficients is reduced drastically.

Radial basis function (RBF) network based channel equalisers have a close relationship with Bayesian schemes. Decision feedback is introduced in the design of the RBF equaliser in order to reduce its computational complexity. The RBF decision feedback equaliser (DFE) was found to give similar performance to the conventional mean square error (MSE) DFE over Gaussian channels using various quadrature amplitude modulation (QAM) schemes, while requiring a lower feedforward and feedback order. Over Rayleigh-fading channels similar findings were valid for binary modulation, while for higher order modems the RBF based DFE requires increased feedforward and feedback orders in order to outperform the conventional MSE DFE scheme.

Combining a channel memory-shortening filter with maximum likelihood sequence estimation (MLSE) effectively reduces MLSE complexity in low-bandwidth optical fiber communication systems. In this paper, we propose an enhanced decision feedback equalizer (DFE)-MLSE for high-speed fiber optic communication systems. This enhanced algorithm builds on our previous work by introducing a dispersion filter that adjusts channel memory length and by directly applying feedback filter coefficients in MLSE branch metric calculations. These advancements improve channel equalization performance, which we experimentally validate in a pulse-amplitude modulation level-4 (PAM-4) system. At a transmission rate of 112 GBd and a distance of 2 km, the enhanced DFE-MLSE achieves an approximate 0.5 dB improvement over the previous DFE-MLSE at a bit error rate of 3.8·10-3, demonstrating its potential for 200 Gbps transmission in short-reach optical networks.

By embedding a decision-feedback equalizer (DFE) into the structure of a maximum-likelihood sequence estimator (MLSE), an adaptive combined DFE/MLSE scheme is proposed. In this combined DFE/MLSE, the embedded DFE has three functions: (i) prefiltering the received signals and truncating the equivalent channel response into the desired one, (ii) compensating for channel distortions, and (iii) providing the MLSE detector with predicted values of input signals. Since the embedded MLSE detector operates on the predicted signals the detected symbols at the output of the DFE/MLSE do not suffer any delay and can be directly fed back into the embedded DFE so that the error propagation, which usually takes place in a conventional DFE, can be greatly reduced. Analytical and simulation results indicate that the performance is significantly improved by the DFE/MLSE compared to the conventional DFE while its computation complexity is much less than that of the conventional MLSE receiver. The combined DFE/MLSE can use different adaptive structures (block-updating, sliding window updating or symbol-by-symbol updating) to meet different performance objectives. Moreover, the proposed DFE/MLSE provides a trade-off between performance and complexity with a parameter m representing the MLSE detection depth as well as the number of predicting steps of the embedded DFE. For some particular values of m, this scheme is capable of emulating the conventional DFE, MLSE-VA, adaptive LE-MLSE equalizer, adaptive DDFSE, and adaptive BDFE without detection delay.

Three learning phases for radial-basis-function networks

In today's scenario there is a heavy demand of high speed data communication. Optical Communication systems can full fill this demand. Dispersion is one of the major limiting factors in such high data rate optical communication that degrades the performance of the optical system. Dispersion must be compensated to improve the performance at higher data rate. This paper presents a hybrid approach to compensate the dispersion in high speed 10 Gb/s optical system combining optical and electrical dispersion compensation schemes. In optical symmetrical compensation, dispersion compensating fiber is used in symmetrical configuration and in electrical compensation, feed forward - decision feedback equalizer is used. Performance of optical symmetrical compensation scheme and hybrid compensation scheme is analysed using eye diagram. Results show that the hybrid approach is the efficient way of compensating the dispersion in optical system at 10 Gb/s. Hybrid approach shows better performance enhancement compared to only optical compensation scheme.

Radial Basis Function (RBF) Network is popularly used for solving pattern recognition problems. The training of RBF Network is faster compared to multi layer perceptron using error backpropagation. However, the RBF Network uses the pseudo inverse matrix to calculate weights from the hidden layer to the output layer. Thus calculation cost increases when the number of data and the number of hidden units increase. In addition, in RBF Network the decision of optimum number of hidden units is difficult. It is also more prone to overtraining, needing repeated train and test cycles to ascertain a proper number of the Network hidden units, so that generalization performance is good. In this work, we propose a technique to set up RBF network parameters which is fast, as well as the number of hidden units are automatically determined. We start with training a Self-Organizing Maps (SOM), which is a unsupervised training, though our samples are labeled. SOM can find the distribution of data in multidimensional space, and map it on a two dimensional display. The results of SOM network is used to calculate the RBF parameters. It is shown by experiments that using the proposed method, RBF network parameters can be determined much faster compared to existing technique. Moreover, the recognition rate for the test data was higher, showing better generalization performance.

This article proposes a low-complexity maximum likelihood sequence estimation (MLSE) algorithm tailored for non-return-to-zero (NRZ) high-speed transceivers. In particle physics experiments, data transmission volumes are continually increasing, with transceivers assuming pivotal roles. MLSE has garnered significant attention due to its notable advantages in eliminating intersymbol interference (ISI) and its capability to replace decision feedback equalizers (DFEs). However, MLSE complexity exponentially escalates with the increment of traceback length and equalizer order. Hence, reducing MLSE complexity while preserving performance is imperative. This article simplifies MLSE transition metric calculations, obviating the necessity for intricate state computations and result storage. A configurable and highly adaptable transceiver simulation system is developed, utilizing a field-programmable gate array (FPGA), and the proposed algorithm is evaluated using this system. Synthesis results demonstrate that the proposed algorithm significantly reduces resource utilization while maintaining algorithm performance.

In order to forecast missile storage reliability better, the paper researched a forecasting method based on neural network which is with the ability of actualizing multi-nonlinear mapping from input to output, and discussed steps of forecasting based on back propagation (BP) network and radial basis function (RBF) network respectively. At last, the storage reliability of one type ship-to-ship missile is forecasted based on BP network and RBF network respectively. The results show that both of the BP and RBF are suitable for Missile storage reliability forecasting, and the precision of the train goal is better by using RBF network. RBF network is more suitable for dealing with this problem.

Radial basis function (RBF) network can be viewed as a fuzzy rule base with specified membership functions and fuzzy inference operations. However, there is a trade-off between the approximation performance of RBF network and the number of hidden neurons. To tackle this problem, this paper proposes a dynamic RBF (DRBF) network with a constructive learning. This DRBF network not only can create the new hidden neurons, but also can prune the insignificant hidden neurons. Then, an adaptive dynamic RBF fuzzy neural control (ADRFNC) system, including a neural controller and a saturation compensator, is developed. The neural controller uses a DRBF network to on-line mimic an ideal controller and the saturation compensator is designed to dispel the approximation error introduced by the neural controller. Finally, the proposed ADRFNC system is applied to a chaotic circuit and a DC motor control system. Simulation and experimental results show the proposed ADRFNC system can achieve a favorable tracking performance when the controller’s parameters have been learned and the network structure has been constructed by the proposed learning algorithm.

Generalized [formula omitted]-sparse algorithms for constructing fault tolerant RBF networks

A new learning method of radial basis function (RBF) network based on fuzzy C-means (FCM) clustering and ant colony optimization (ACO) is presented in the paper. Generally, the crucial problem of learning RBF network is the selection of the unit number, the centers and widths of the Gaussian radial basis function in hidden layer, and the weights between hidden layer and output layer. In this work, the centers are determined by FCM clustering, and the weights are determined by least mean squares (LMS) method. In addition, ACO is introduced to optimize two important parameters of FCM including the weighting exponent which impacts its performance, and the clustering number that is equal to the hidden unit number which impacts the generalization of RBF network, by minimizing an objective function integrated the generalization error with the hidden unit number of RBF network. Simulation results of identifying a nonlinear system illustrate the effectiveness of designing the RBF network with smaller structure but stronger generalization ability, comparing with K-means and orthogonal least squares (OLS) based learning methods.

We report a very efficient semianalytical approach for the performance evaluation of differential detection schemes for GMSK signals of the DECT standard. Precisely, for a given channel, the performance is determined by means of an analytical procedure which includes the saddlepoint approximation. We consider both static channels (with impulse response generated by the simulation program SIRCIM) and two-ray Rayleigh and log-normal fading channels. As a departure from previous works, our receiver includes an all-digital part after the analog differential detection scheme. The digital part includes: (1) a block for the estimation of both the optimum sampling phase and the nonlinear channel coefficients (by making use of the DECT training sequence), (2) a one-tap decision feedback (DF) equalizer, and (3) a block for the evaluation of the approximate optimum bias level (/spl gamma//sub e/) in the threshold detector. Both the DF equalizer coefficient and /spl gamma//sub e/ are based on the nonlinear channel coefficients estimate. For channels with a normalized delay spread up to 0.2, the use of the optimum threshold together with the DF equalizer permits a gain of about 2 dB at BER=10/sup -6/ with respect to a receiver without equalization and a zero-level decision threshold. In addition, we discover that, in indoor environments, the 2-bit GMSK detector performs roughly the same as the 1-bit detector. The threshold optimization is also effective in the presence of channels affected by fading. To support this statement, we report the performance of the 1-bit differential detection scheme combined with antenna selection diversity in the presence of a two-ray log-normal and Rayleigh fading channel.

In this paper we propose a multiple-input, multiple-output (MIMO) maximum-likelihood sequence estimation (MLSE) receiver for electronic dispersion compensation (EDC) of multimode optical fibers at 10 Gb/s data rate. As the primary example of the effectiveness of the techniques introduced here we present a receiver for the emergent 10 GBASE-LRM standard for 10 Gb/s Ethernet over multimode optical fibers [1]. We show that an MLSE receiver provides an advantage of at least 2 dB over other receivers, such as the decision-feedback equalizer (DFE), on 99% of the local area network (LAN) multimode fiber population, as modeled by a database proposed by the IEEE 802.3aq Task Force [2]. The paper deals with both theoretical and practical aspects of the architecture. To enable the complete integration of this receiver as a single chip in current 90 nm CMOS technology, we propose the parallel-processing digital implementation of a feedforward equalizer (FFE) and a Viterbi decoder together with an interleaved front-end analog to digital converter (ADC). The MIMO structure jointly compensates for fundamental channel impairments such as multimode dispersion, and implementation-related effects such as the limitations of the analog front end (AFE), particularly the one known as fixed-pattern noise (FPN) [3]. As a result of the high speed operation, FPN has a major impact on performance. We show that, without compensation, FPN could result in a degradation of 7.86 dB. With the compensation proposed here, the latter is reduced to 0.23 dB.

In the radial basis function (RBF) network, selection of width parameter of the basis functions is considered. The effect of the width parameter on multivariable discrete function approximation is analysed in the Fourier domain and based on this, an appropriate selection method for the width parameter is presented. The method basically takes the orthogonal multiresolutional decomposition by wavelet transform of the function subject to approximation and to each decomposed component, a separate RBF network having a suitable width parameter matching to the appropriate resolution level, is employed. Each outcome from these multiresolutional RBF networks is added to that from the others and a final approximation result is obtained. A marked enhancement of approximation is achieved which implies an enhancement of the generalisation capability of the network performing robust estimation at the same time.