Neural Network Equalizer Research Articles

Hidden-layers Extended Recurrent Neural Network Equalizer for Short Reach Optical Interconnects

Hidden-layers Extended Recurrent Neural Network Equalizer for Short Reach Optical Interconnects

An Adaptive Sigmoidal Activation Function for Training Feed Forward Neural Network Equalizer

Feed for word neural networks (FFNN) have attracted a great attention, in digital communication area. Especially they are investigated as nonlinear equalizers at the receiver, to mitigate channel distortions and additive noise. The major drawback of the FFNN is their extensive training. We present a new approach to enhance their training efficiency by adapting the activation function. Adapting procedure for activation function extensively increases the flexibility and the nonlinear approximation capability of FFNN. Consequently, the learning process presents better performances, offers more flexibility and enhances nonlinear capability of NN structure thus the final state kept away from undesired saturation regions. The effectiveness of the proposed method is demonstrated through different challenging channel models, it performs quite well for nonlinear channels which are severe and hard to equalize. The performance is measured throughout, convergence properties, minimum bit error achieved. The proposed algorithm was found to converge rapidly, and accomplish the minimum steady state value. All simulation shows that the proposed method improves significantly the training efficiency of FFNN based equalizer compared to the standard training one.

Comparison of Real- and Complex-Valued NN Equalizers for Photonics-Aided 90-Gbps D-band PAM-4 Coherent Detection

5G defines below 100 GHz as the millimeter-wave bands, whereas 100 GHz - 3 THz is categorized as THz band in 6G. Deep leraning (DL) is expected to enable a significant paradigm shift in 6G wireless networks. In this paper, D-band 90-Gbps single channel PAM-4 signal generation and transmission over 10-km SMF and 3-m wireless link at 140-GHz can be achieved. A novel complex-valued neural network (CVNN) equalizer using &#x2018;&Copf;ReLU&#x2019; activation function to directly recover PAM-4 signals from received noised signals is demonstrated. There are three DSP options in the experiment. In <i>Opt</i>.1, firstly conducted cascaded multi-modulus algorithm (CMMA) pre-equalization (pre-EQ) at transmitter, then processed via frequency offset estimation (FOE), carrier phase recovery (CPR) and finally real-valued neural network (RVNN) equalization at receiver. Here, the RVNN equalizers include DNN with a softmax output layer, two-step joint-DNN equalizer and LSTM. The experimental results show that LSTM-based equalizer outperforms the other real NN-based equalizers by average 0.5 to 1.5 dB at BER of 10^&#x2212;3 magnitude. Differently from <i>Opt</i>. 1, real-valued CMMA pre-EQ at transmitter is unexpected for CVNN in the other two options. In <i>Opt</i>. 2, we only combine down-conversion and CVNN regarded as &#x2018;pure data-driven&#x2019; training at receiver. This pure data-driven CVNN equalizer improves BER a lot and also has a larger computation burden, especially BER is as low as 1 &#x00D7; 10^&#x2212;4 with <i>n</i>₀ &#x003D; 571 and <i>n</i>₁ &#x003D; 200 training cells and the time complexity reaches 350000 in one iteration. Thanks to the aid of traditional mathematical-oriented models including FOE and CPR, the computation burden of CVNN in <i>Opt</i>. 3 is released significantly. Furthermore, we compare the performance of CVNN and RVNN in terms of BER decision accuracy, time complexity and receiver sensitivity. Followed by the same DSP with the same complexity, the comparison result between DNN and CVNN in the same structure of [371-260-1] with 11000 samples and 300 epochs shows that CVNN performs better due to its reservation of phase information. Therefore, we believe that the joint use of model-based, e.g., FOE, CPR steps and complex DL-based techniques has a potential for the future 6G wireless physical layer algorithms.

High-throughput hardware deployment of pruned neural network based nonlinear equalization for 100-Gbps short-reach optical interconnect.

Hardware implementation of neural network based nonlinear equalizers will encounter tremendous challenges due to a high-throughput data stream and high computational complexity for 100-Gbps short-reach optical interconnects. In this Letter, we propose a parallel pruned neural network equalizer for high-throughput signal processing and minimized hardware resources. The structure of a time-interleaved neural network equalizer with a delay module is deployed in a field programmable gate array with advanced pruned algorithms, demonstrating significant bit error rate reduction for 100-Gbps real-time throughput with 200 parallel channels. Moreover, the dependence of processing throughput, hardware resources, and equalization performance is investigated, showing that over 50% resource reduction without performance degradation can be achieved with the pruning strategy.

8.75 Gbps visible light communication link using an artificial neural network equalizer and a single-pixel blue micro-LED.

Visible light communication (VLC) beyond 10 Gbps is an important characteristic that can support the future 6 G high-capacity requirements. On the one hand, in order to break the electro-optics (E-O) bandwidth limitation of the light-emitting diodes (LEDs), we fabricated two high-bandwidth (>gigahertz) single wetting layer micro-LEDs with 50 and 75 µm active regions. On the other hand, for mitigating the nonlinear effects of the VLC system, an artificial neural network equalizer is designed and implemented in offline digital signal processing. Both efforts lead to a breakthrough of data rates at a single VLC link. Using quadrature phase shift keying orthogonal frequency division multiplexing, the data rate of a 1.025 GHz VLC link based on a 75 µm micro-LED can reach 8.75 Gbps with a bit-error-ratio (BER) of 2.73×10-3. In addition, the E-O characteristics and communication performances of micro-LED with two diameters are compared and discussed. To the best of our knowledge, the data rate of 8.75 Gbps is the highest record of the VLC link based on a single-pixel blue micro-LED with a BER within the forward error correction citation of 3.8×10-3.

Probabilistic shaping and neural network-based optimization for a nonlinear frequency division multiplexing system.

A joint scheme introducing probabilistic shaping (PS) at the transmitter and utilizing a neural network (NN) equalizer at the receiver is proposed to improve the performance of the b-modulated nonlinear frequency division multiplexing (NFDM) system. Through a numerical simulation, we demonstrate that PS plays a leading role for low launch power case, which improves the performance of the system effectively, while the NN equalizer's superiority appears in a high launch power region, whose main role is to weaken the correlation among subcarriers for improving system performance. The proposed scheme would enlighten the optimum modulation and detection schemes of the NFDM system.

The Utilization of Artificial Neural Network Equalizer in Optical Camera Communications.

In this paper, we propose and validate an artificial neural network-based equalizer for the constant power 4-level pulse amplitude modulation in an optical camera communications system. We introduce new terminology to measure the quality of the communications link in terms of the number of row pixels per symbol , which allows a fair comparison considering the progress made in the development of the current image sensors in terms of the frame rates and the resolutions of each frame. Using the proposed equalizer, we experimentally demonstrate a non-flickering system using a single light-emitting diode (LED) with of 20 and 30 pixels/symbol for the unequalized and equalized systems, respectively. Potential transmission rates of up to 18.6 and 24.4 kbps are achieved with and without the equalization, respectively. The quality of the received signal is assessed using the eye-diagram opening and its linearity and the bit error rate performance. An acceptable bit error rate (below the forward error correction limit) and an improvement of ~66% in the eye linearity are achieved using a single LED and a typical commercial camera with equalization.

Convolutional long short-term memory neural network equalizer for nonlinear Fourier transform-based optical transmission systems

We evaluate improvement in the performance of the optical transmission systems operating with the continuous nonlinear Fourier spectrum by the artificial neural network equalisers installed at the receiver end. We propose here a novel equaliser designs based on bidirectional long short-term memory (BLSTM) gated recurrent neural network and compare their performance with the equaliser based on several fully connected layers. The proposed approach accounts for the correlations between different nonlinear spectral components. The application of BLSTM equaliser leads to a 16x improvement in terms of bit-error rate (BER) compared to the non-equalised case. The proposed equaliser makes it possible to reach the data rate of 170 Gbit/s for one polarisation conventional nonlinear Fourier transform (NFT) based system at 1000 km distance. We show that our new BLSTM equalisers significantly outperform the previously proposed scheme based on a feed-forward fully connected neural network. Moreover, we demonstrate that by adding a 1D convolutional layer for the data pre-processing before BLSTM recurrent layers, we can further enhance the performance of the BLSTM equaliser, reaching 23x BER improvement for the 170 Gbit/s system over 1000 km, staying below the 7% forward error correction hard decision threshold (HD-FEC).

Using Least Squares Support Vector Machines for Adaptive Communication Channel Equalization

Adaptive equalizers are used in digital communication system receivers to mitigate the effects of non-ideal channel characteristics and to obtain reliable data transmission. In this paper, we adopt least squares support vector machines (LS-SVM) for adaptive communication channel equalization. The LS-SVM involves equality instead of inequality constraints and works with a least squares cost function. Since the complexity and computational time of a LS-SVM equalizer are less than an optimal equalizer, the LS-SVM equalizer is suitable for adaptive digital communication and signal processing applications. Computer simulation results show that the bit error rate of the LS-SVM equalizer is very close to that of the optimal equalizer and better than multilayer perceptron (MLP) and wavelet neural network (WNN) equalizers.

Deep Neural Network-Based Detection and Partial Response Equalization for Multilayer Magnetic Recording

To increase the storage capacity limit of magnetic recording channels, recent studies proposed multilayer magnetic recording (MLMR): the vertical stacking of magnetic media layers. MLMR readback waveforms consist of the superposition of signals from each layer recovered by a read head placed above the upper layer. This article considers the problem of equalization and detection for MLMR comprising two layers. To this end, we use MLMR waveforms generated using a grain switching probability (GSP) model that is trained on realistic micromagnetic simulations. We propose three systems for equalization and detection. The first is a convolutional neural network (CNN) equalizer followed by an MLMR Viterbi algorithm (VA) for detection. We show that this system outperforms the traditional 2-D linear minimum mean squared error (2-D-LMMSE) equalizer. The second system uses CNNs for equalization and separation of signals from each layer, which is followed by a regular VA. The third system contains CNNs trained to directly provide soft bit estimates. By interfacing the CNN detector with a channel decoder, we show that an areal density gain of 16.2% can be achieved by a two-layer MLMR system over a one-layer system.

Pulse shapings employed in an underwater visible-light communication system based on carrierless amplitude and phase modulation utilizing a complex deep neural network equalizer

We experimentally demonstrate the performance of a complex deep neural network (CDNN) equalizer in multi-band super-Nyquist carrier-less amplitude and phase (m-SCAP) modulation for underwater visible-light communications (UVLC). The in-phase and quadrature of the complex data after the match filter and down-sampling are combined as real number pairs and input to the CDNN, which outputs the real part and the imaginary part of the equalized complex data. We compare the different performances of three pulse shapings [better-than-Nyquist pulse shaping (BTN), square-root raised cosine (SRRC), and Xia] utilized in the m-SCAP UVLC system based on the CDNN. We demonstrate that the CDNN equalizer can outperform the traditional equalizer based on the Volterra series and least-mean-square algorithm. The experiments show that the low-roll-off BTN performs best, and the high-roll-off SRRC performs best in the m-SCAP system. In our experiment, the bit-error rate (BER) of the BTN system is 2.6 × 10 − 4, the BER of the SRRC is 3.6 × 10 − 4, and the BER of the Xia system is 7.3 × 10 − 4 when the spectral efficiency is 3.76 bit / s / Hz and the signal peak-to-peak voltage (Vpp) is 0.9 V.

Multitrack Detection With 2-D Iterative Soft Estimate Aided Neural Network Equalizer for Heat-Assisted Interlaced Magnetic Recording

Heat-assisted interlaced magnetic recording (HIMR) with interlaced track layout architecture enables the further increased areal density compared to the conventional heat-assisted magnetic recording. However, the severe transition curvatures of low temperature written tracks cause noticeable nonlinear distortions of readback signal, and the 2-D intersymbol interference (ISI), media noise, and thermal jitter also bring the challenges for data recovery. Correspondingly, a multitrack detection scheme with 2-D iterative soft estimate aided neural network equalizer (2D-ISA NNE) is proposed for the HIMR system, which iteratively feeds back the soft estimate of reliable sidetracks’ information (e.g., high temperature written tracks) during the neural network equalization (NNE) of middle track (e.g., low temperature written track). Here, the Bahl–Cocke–Jelinek–Raviv (BCJR) detector and low-density parity-check (LDPC) decoder are utilized for the following data detection and error corrections. Then, the similar ISA NNE is implemented to recover the sidetracks’ data. It is found that the proposed 2D-ISA NNE algorithm mitigates the 2-D ISI and nonlinear distortion more effectively compared to the conventional 2-D linear equalizer (LE) and neural network equalizer (NNE). For HIMR at the channel bit density of 3.51 Tb/in2 and overlapping ratio of 0.46, the proposed 2D-ISA NNE algorithm significantly decreases the bit error rate gap between the low temperature and high temperature written tracks. For the low temperature written track, it provides 3.1 and 4 dB signal-to-noise ratio (SNR) gains compared to the conventional 2-D NNE and 2-D LE, respectively.

A new training scheme for neural network based non-linear channel equalizers in wireless communication system using Cuckoo Search Algorithm

Widespread use of the internet has resulted in a massive rise in the data rate of a wireless communication system. Eventually, to mitigate the effect of inter-symbol interference (ISI) in multipath wireless channels, designing a channel equalizer is becoming more demanding. For severe non-linear distortion, the neural network (NN) based non-linear channel equalizers provide superior performance than the adaptive filter based linear equalizers. The NN equalizers are generally trained with back-propagation algorithm which has limitations of slower convergence, local minima stagnation and sensitivity to initial parameters. To overcome these limitations, this paper proposes a training scheme using Cuckoo Search Algorithm (CSA) for functional link artificial NN (FLANN) based channel equalizers. The proposed training scheme has a better ability to escape from local minima, higher exploitation and exploration capabilities. To choose the optimum values of the parameters, the sensitivity analysis of the CSA based approach is performed with its key parameters. Furthermore, three non-linear channels have been simulated to demonstrate the equalization performance of the CSA based training scheme and the results have been compared with recent and well-established algorithms. The simulations confirm that the proposed training scheme performs substantially better than existing metaheuristic algorithms in terms of BER and MSE performance. To show the robustness of the CSA based method, the burst error scenario has been considered and results proved that the method is more successful in handling such scenarios when compared to other methods. The performance of the proposed scheme has been validated for a wide range of signal-to-noise ratio through simulation studies and it is observed that the scheme outperforms the other algorithms in poor SNR conditions as well. Also, to examine the statistical significance of the results provided by the proposed scheme, the Wilcoxon test is performed and the test reveals that the obtained results are statistically significant.

Compressed Neural Network Equalization Based on Iterative Pruning Algorithm for 112-Gbps VCSEL-Enabled Optical Interconnects

Advanced nonlinear digital signal processing technologies, which bring significant performance gain for high-speed optical interconnects, are highly constrained by huge complexity in the actual deployment. Fully connected neural network-based equalizer has shown powerful efficacy to deal with the complex linear and nonlinear impairments for VCSEL-enabled multi-mode optical interconnects, but it also contains a number of redundancies with little impact on performance improvement. In this article, we experimentally demonstrate a compressed neural network equalization using the iterative pruning algorithm for 112-Gbps VCSEL-enabled PAM-4 and PAM-8 transmissions over 100-m MMF. We also study the impact of threshold and pruning span on the performance of proposed algorithms. The results show up to 71% connection compression by use of the iterative pruning algorithms and maximum 28.4% improvement compared with the one-shot pruning algorithm.

Demonstration of a low-complexity memory-polynomial-aided neural network equalizer for CAP visible-light communication with superluminescent diode

Visible-light communication (VLC) stands as a promising component of the future communication network by providing high-capacity, low-latency, and high-security wireless communication. Superluminescent diode (SLD) is proposed as a new light emitter in the VLC system due to its properties of droop-free emission, high optical power density, and low speckle-noise. In this paper, we analyze a VLC system based on SLD, demonstrating effective implementation of carrierless amplitude and phase modulation (CAP). We create a low-complexity memory-polynomial-aided neural network (MPANN) to replace the traditional finite impulse response (FIR) post-equalization filters of CAP, leading to significant mitigation of the linear and nonlinear distortion of the VLC channel. The MPANN shows a gain in Q factor of up to 2.7 dB higher than other equalizers, and more than four times lower complexity than a standard deep neural network (DNN), hence, the proposed MPANN opens a pathway for the next generation of robust and efficient neural network equalizers in VLC. We experimentally demonstrate a proof-of-concept 2.95-Gbit/s transmission using MPANN-aided CAP with 16-quadrature amplitude modulation (16-QAM) through a 30-cm channel based on the 442-nm blue SLD emitter.

Deep Neural Network Equalization for Optical Short Reach Communication

Nonlinear distortion has always been a challenge for optical communication due to the nonlinear transfer characteristics of the fiber itself. The next frontier for optical communication is a second type of nonlinearities, which results from optical and electrical components. They become the dominant nonlinearity for shorter reaches. The highest data rates cannot be achieved without effective compensation. A classical countermeasure is receiver-side equalization of nonlinear impairments and memory effects using Volterra series. However, such Volterra equalizers are architecturally complex and their parametrization can be numerical unstable. This contribution proposes an alternative nonlinear equalizer architecture based on machine learning. Its performance is evaluated experimentally on coherent 88 Gbaud dual polarization 16QAM 600 Gb/s back-to-back measurements. The proposed equalizers outperform Volterra and memory polynomial Volterra equalizers up to 6th orders at a target bit-error rate (BER) of 10 − 2 by 0.5 dB and 0.8 dB in optical signal-to-noise ratio (OSNR), respectively.

A Study on Block-Based Neural Network Equalization in TDMR System With LDPC Coding

To achieve a high track density, two-dimensional magnetic recording (TDMR) is combined with shingled magnetic recording (SMR). SMR makes it possible to record 1 bit on a few grains. However, the performance will be remarkably deteriorated by the increased media noise, the inter-track and inter-symbol interference (ITI and ISI). Therefore, the application of effective equalization and error control coding are required. In this paper, we investigate a simple block-based neural network equalizer (NNE) that mitigates the influence of ITI and ISI. We compare the equalization effects of the NNE and a conventional 2-D equalizer with low-density parity-check (LDPC) coding based on a random Voronoi grain media model. Simulation results show the proposed block-based NNE achieves better bit error rate performance than the conventional 2-D linear equalizer followed by the a posteriori probability (APP) detector and a sum-product (SP) decoder. In addition, we find the block-based NNE is sensitive to write errors.

Reduced-Complexity Artificial Neural Network Equalization for Ultra-High-Spectral-Efficient Optical Fast-OFDM Signals

Digital-based artificial neural network (ANN) machine learning is harnessed to reduce fiber nonlinearities, for the first time in ultra-spectrally-efficient optical fast orthogonal frequency division multiplexed (Fast-OFDM) signals. The proposed ANN design is of low computational load and is compared to the benchmark inverse Volterra-series transfer function (IVSTF)-based nonlinearity compensator. The two aforementioned schemes are compared for long-haul single-mode-fiber-based links at 9.69 Gb/s direct-detected optical Fast-OFDM signals. It is shown that an 80 km extension in transmission-reach is feasible when using ANN compared to IVSTF. This occurs because ANN can tackle stochastic nonlinear impairments, such as parametric noise amplification. Using ANN, the dynamic parameters requirements of the sub-ranging quantizers can also be relaxed compared to linear equalization, such as the reduction of the optimum clipping ratio and quantization bits by 2 dB and 2-bits, respectively, and by 2 dB and 2 bits when compared to the IVTSF equalizer.

FBMC-based dispersion compensation using artificial neural network equalization for long reach-passive optical network

This paper presents a Filter Bank Multicarrier (FBMC), a viable waveform candidate for fifth generation (5G) communications using Staggered-Modulated Multitone (SMT). FBMC is preferred in optical communication because of its ability to work without Cyclic Prefix (CP). In any case, the operation of FBMC in optical access systems with Artificial Neural Networks (ANNs) has not been broadly explored either downstream or upstream. This work presents an advanced Nonlinear Feed-Forward Equalizer (NFFE) that makes use of multilayer ANN for dispersion compensation. ANN is trained to act as a filter with an extensive equalizer training which has the ability to mitigate dispersion and increase the performance of the system. The simulation work is used to study the performance of intensity modulated FBMC system with direct detection in Long Reach-Passive Optical Networks (LR-PONs).The transmission data rate is varied between 8 and 10[Formula: see text]Gbps with the optical fiber length from 30 to 90[Formula: see text]km of Standard Single Mode Fiber (SSMF). The obtained result suggests that FBMC system with ANN-NFFE equalizer fundamentally builds the resilience to the Chromatic Dispersion (CD) distortion, and a CP-less transmission is possible upto 90[Formula: see text]km.

Blind Fuzzy Adaptation Step Control for a Concurrent Neural Network Equalizer

Mobile communications, not infrequently, are disrupted by multipath propagation in the wireless channel. In this context, this paper proposes a new blind concurrent equalization approach that combines a Phase Transmittance Radial Basis Function Neural Network (PTRBFNN) and the classic Constant Modulus Algorithm (CMA) in a concurrent architecture, with a Fuzzy Controller (FC) responsible for adapting the PTRBFNN and CMA step sizes. Differently from the Neural Network (NN) based equalizers present in literature, the proposed Fuzzy Controller Concurrent Neural Network Equalizer (FC-CNNE) is a completely self-taught concurrent architecture that does not need any training. The Fuzzy Controller inputs are based on the estimated mean squared error of the equalization process and on its variation in time. The proposed solution has been evaluated over standard multipath VHF/UHF channels defined by the International Telecommunication Union. Results show that the FC-CNNE is able to achieve lower residual steady-state MSE value and/or faster convergence rate and consequently lower Bit Error Rate (BER) when compared to Constant Modulus Algorithm-Phase Transmittance Radial Basis Function Neural Network (CMA-PTRBFNN) equalizer.