Nonlinear Decision Feedback Equalizer Research Articles

Underwater wireless optical communication utilizing low-complexity sparse pruned-term-based nonlinear decision-feedback equalization.

The nonlinearity of the light-emitting diode (LED) in underwater wireless optical communication (UWOC) systems is considered the one major limiting factor that degrades the system's performance. Volterra series-based nonlinear equalization is widely employed to mitigate such nonlinearity in communication systems. However, the conventional Volterra series-based model is of high complexity, especially for the nonlinearity of higher-order terms or longer memory lengths. In this paper, by pruning away some negligible beating terms and adaptively picking out some of the dominant terms while discarding the trivial ones, we propose and experimentally demonstrate a sparse pruned-term-based nonlinear decision-feedback equalization (SPT-NDFE) scheme for the LED-based UWOC system with an inappreciable performance degradation as compared to systems without the pruning strategy. Meanwhile, by replacing the self/cross beating terms with the terms formed by the absolute operation of a sum of two input samples instead of the product operation terms, a sparse pruned-term-based absolute operation nonlinear decision-feedback equalization (SPT-ANDFE) scheme is also introduced to further reduce complexity. The experimental results show that the SPT-NDFE scheme exhibits comparable performance as compared to the conventional NDFE (nonlinear decision-feedback equalization) scheme with lower complexity (the nonlinear coefficients are reduced by 63.63% as compared to the conventional NDFE scheme). While the SPT-ANDFE scheme yields suboptimal performance with further reduced complexity at the expense of a slight performance degradation, the robustness of the proposed schemes in different turbidity waters is experimentally verified. The proposed channel equalization schemes with low complexity and high performance are promising for power/energy-sensitive UWOC systems.

Experimental Demonstration of 55-m / 2-Gbps Underwater Wireless Optical Communication Using SiPM Diversity Reception and Nonlinear Decision-Feedback Equalizer

Underwater wireless optical communication (UWOC) is considered as an enabling technology with a mass of potential applications. The silicon photomultiplier (SiPM) exhibits a bright prospect for UWOC thanks to the traits of low-light detection capability, low-voltage operation, and superior operability. However, the performance of the SiPM-based UWOC system is severely degraded by the dead-time caused nonlinear response. In this paper, to mitigate the dead-time induced nonlinear distortion and explore the achievable capacity of the newly developed SiPM, we propose and experimentally demonstrate a 55-m/2-Gbps UWOC system by virtue of SiPM diversity reception and nonlinear decision-feedback equalizer (NDFE). The performance of NDFE is superior to that of the conventional decision-feedback equalizer (DFE), and NDFE with a pruning factor of 5 declares similar performance as that without pruning strategy, while the number of the nonlinear equalizer can be reduced by ~31.8%. Significant performance improvement is also obtained by the proposed scheme under different turbidity waters. The measured data rate is pushed from 1 Gbps to 2 Gbps with a receiver sensitivity as low as −41.96 dBm, which to the best of our knowledge is the largest data rate ever achieved using the off-the-shelf SiPM among the reported UWOC works. In accordance with the receiver sensitivity and the model of optical propagation in the water channel, the maximum attainable distance/data rate is predicted to be 147 m/1 Gbps and 128 m/2 Gbps with the proposed scheme. The research results are promising for long-reach and high-speed UWOC.

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 $10^{-4}$ .

Design and Analysis of Sparsifying Dictionaries for FIR MIMO Equalizers

In this paper, we propose a general framework that transforms the problems of designing sparse finite-impulseresponse linear equalizers and non-linear decision-feedback equalizers, for multiple antenna systems, into the problem of sparsestapproximation of a vector in different dictionaries. In addition, we investigate several choices of the sparsifying dictionaries under this framework. Furthermore, the worst-case coherences of these dictionaries, which determine their sparsifying effectiveness, are analytically and/or numerically evaluated. Moreover, we show how to reduce the computational complexity of the designed sparse equalizer filters by exploiting the asymptotic equivalence of Toeplitz and circulant matrices. Finally, the superiority of our proposed framework over conventional methods is demonstrated through numerical experiments.

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.

Signal Shaping and Modulation for Optical Wireless Communication

In this paper, a signal shaping framework for optical wireless communication (OWC) is proposed. The framework is tailored to the single-carrier pulse modulation techniques, such as multi-level pulse position modulation (M-PPM) and multi-level pulse amplitude modulation (M-PAM), and to multi-carrier transmission realized through multi-level quadrature amplitude modulation (M-QAM) with orthogonal frequency division multiplexing (OFDM). Optical OFDM (O-OFDM) transmission is generally accomplished via direct-current-biased optical OFDM (DCO-OFDM) or asymmetrically clipped optical OFDM (ACO-OFDM). Through scaling and DC-biasing the transmitted signal is optimally conditioned in accord with the optical power constraints of the transmitter front-end, i.e., minimum, average and maximum radiated optical power. The OWC systems are compared in a novel fashion in terms of electrical signal-to-noise ratio (SNR) requirement and spectral efficiency as the signal band- width exceeds the coherence bandwidth of the optical wireless channel. In order to counter the channel effect at high data rates, computationally feasible equalization techniques such as linear feed-forward equalization (FFE) and nonlinear decision-feedback equalization (DFE) are employed for single-carrier transmission, while multi-carrier transmission combines bit and power loading with single-tap equalization. It is shown that DCO-OFDM has the highest spectral efficiency for a given electrical SNR at high data rates when the additional direct current (DC) bias power is neglected. When the DC bias power is counted towards the signal power, DCO-OFDM outperforms PAM with FFE, and it approaches the performance of the more computationally intensive PAM with DFE.

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.

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.

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.

Worst case equalizer for noncoherent HIPERLAN receivers

Coherent detection of HIPERLAN Gaussian minimum-shift keying signals calls for complex and expensive receivers. However, when the channel delay spread is limited to at the most 50% of the symbol time and a reliable line-of-sight component of the radiated signal exists (Rician fading model), noncoherent detectors are capable of achieving a good performance. Based on the above motivations, we compare four different demodulation techniques, namely the following: (1) one-bit differential detector; (2) discriminator detector; (3) limiter discriminator detector; and (4) limiter discriminator integrator detector (LDID). The intersymbol interference introduced by these demodulators is nonlinear (with respect to the data symbols) and a decision-feedback equalizer (DFE) based on a mean square-error criterion may not be appropriate. Moreover, at this high speed, a DFE may be very complex to implement. Hence, we propose a new DFE design method that increases the eye-diagram aperture by removing the worst case interference. Performance of the above demodulators in the presence of a simple nonlinear DFE (with feedback part only) is computed in terms of the bit-error rate (BER) by means of the saddle-point approximation. This procedure, for static channels, turns out to be a very general tool with a simple and robust implementation. The same method can be applied, for multipath fading channels, to the BER evaluation as part of a semianalytic approach. The main conclusion from this work is that for LDID demodulators and in the presence of Rician fading channels with an average normalized root mean square delay spread of 0.3 and dual antenna diversity, the new equalizer lowers the outage probability from 60% to 10% at a BER of 10/sup -4/.

NRZ timing recovery technique for band-limited channels

Numerous clock and data recovery techniques have been reported in recent years, but data rate has been limited by bandwidth. NRZ data such as used in Ethernet or Sonet, when transmitted over band-limited channels, suffer from dc wandering, where the received waveform is represented as a sum of individual symbol responses. The long tails of data symbols interfere with subsequent symbols, causing inter-symbol interference (ISI). The nonlinear decision-feedback equalizer (DFE) is well known to remove post-cursor ISI without amplifying high-frequency noise. This paper reports an NRZ timing recovery technique working with a DFE that enables data transmission at a rate five times higher than the standard rate. Furthermore, a timing recovery technique using a data-triggered phase detector is reported to sustain phase locking to NRZ data even with more than 600 consecutive missing transitions.

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>

Fast adaptive equalizers for narrow-band TDMA mobile radio

It is pointed out that the future European cellular digital mobile radio system in the 900 MHz band adopts a narrowband time division multiple access (TDMA) scheme with Gaussian minimum-shift keying (GMSK) modulation and burst type transmission. Consequently, very fast adaptation methods are necessary to cope with the time- and frequency-selective distortions produced by Rayleigh and multipath fading. The authors examine a few theoretical aspects of the application of recursive least squares (RLS) adaptation algorithms to the narrowband TDMA mobile radio system and give the relevant performance results for the fast Kalman algorithm, which turns out to be suitable for the considered application. In particular, signature curves, bit error rate, speed of convergence, steady-state behavior, numerical stability, required accuracy, and hardware complexity are discussed. Linear transversal and nonlinear decision-feedback equalizers are considered. >