4-level Pulse Amplitude Modulation Research Articles

28 GBd PAM-8 transmission over a 100 nm range using an InP-Si3N4 based integrated dual tunable laser module.

This paper describes the detailed characterization of a novel InP-Si3N4 dual laser module with results revealing relative intensity noise (RIN) as low as -165 dB/Hz and wide wavelength tunability (100 nm). The hybrid coupled laser is deployed in an unamplified 28 GBd 8 level pulse amplitude modulation (PAM) short-reach data center (DC) transmission system. System performance, which is experimentally evaluated in terms of received signal bit error ratio (BER), demonstrates the ability of the proposed laser module to support PAM-8 transmission across a 100 nm tuning range with less than 1 dB variance in receiver sensitivity over the operating wavelength range. Comparative performance studies not only indicate that the proposed source can outperform a commercial external cavity laser (ECL) in an intensity modulation/direct detection (IM/DD) link but also highlight the critical impact of RIN in the design of advanced modulation short-reach systems.

Capacity Maximized Linear Precoder Design for Spatial-Multiplexing MIMO VLC Systems

This paper proposes a novel linear precoder design based on the singular value decomposition (SVD) for multi-input multi-output visible light communications (MIMO VLC). We provide an analytical expression on power allocation subject to the function of maximizing the lower bound of capacity according to the optical wireless communication channel model. The expression is rather different from the radio frequency (RF) communications due to the non-negativity of the transmitted signals in VLC. Furthermore, we design an adaptive bit loading scheme for sub-streams with consideration of the tremendous gain difference among subchannels. Performances of the proposed adaptive power and bits allocation strategy are evaluated in two traditional MIMO VLC scenarios, i.e., a practical $2\times 2$ indoor scenario and a classical $4\times 4$ system that is generated according to the MIMO model. In simulations, the techniques of unipolar M -level pulse amplitude modulation ( M -PAM) and spatial-multiplexing (SMP) are employed, and the performance comparison with other SVD-based linear precoders is also given. Simulation results show that the proposed approach can effectively improve the spectral efficiency and guarantee the bit error rate (BER) performance under the same constraints of aggregate optical power budget and non-negativity included by the intensity modulation. It indicates that the strategy of uneven bits and power allocation with full consideration of the ill-conditioned characteristics of subchannels performs better than that based on equal bits transmission in VLC systems.

137 Gb/s PAM-4 Transmissions at 850 nm over 40 cm Optical Backplane with 25 G Devices with Improved Neural Network-Based Equalization

An improved neural network-based equalization method is proposed and experimentally demonstrated. The up-to-137 Gb/s transmission of four level pulse amplitude modulation (PAM-4) signals with 25 G class 850 nm optical devices is achieved over an in-house fabricated 40 cm optical backplane. An in-depth investigation is conducted regarding the impact of delayed taps and spans on equalization performance. A performance comparison of the proposed method with the traditional maximum likelihood sequence estimation (MLSE) and decision feedback equalization (DFE) is also undertaken. For the bit rate from 80 to 100 Gb/s, the proposed method achieves an adopted hard-decision forward error correction (HD-FEC) requirement at a received optical power (RoP) of −9 and −8 dBm, while DFE and MLSE cannot meet the HD-FEC requirement. When the bit rate increases from 120 to 137 Gb/s, the proposed equalization method still successfully maintains the acceptable system performance at an RoP of −4 and −2.5 dBm. Furthermore, the specific bit error rate (BER) performances for varied maximum achievable bit rate under different RoPs by applying MLSE and the proposed method are also analyzed. This provides an important potential solution to realize the future data centers.

End-to-end optimized transmission over dispersive intensity-modulated channels using bidirectional recurrent neural networks.

We propose an autoencoding sequence-based transceiver for communication over dispersive channels with intensity modulation and direct detection (IM/DD), designed as a bidirectional deep recurrent neural network (BRNN). The receiver uses a sliding window technique to allow for efficient data stream estimation. We find that this sliding window BRNN (SBRNN), based on end-to-end deep learning of the communication system, achieves a significant bit-error-rate reduction at all examined distances in comparison to previous block-based autoencoders implemented as feed-forward neural networks (FFNNs), leading to an increase of the transmission distance. We also compare the end-to-end SBRNN with a state-of-the-art IM/DD solution based on two level pulse amplitude modulation with an FFNN receiver, simultaneously processing multiple received symbols and approximating nonlinear Volterra equalization. Our results show that the SBRNN outperforms such systems at both 42 and 84 Gb/s, while training fewer parameters. Our novel SBRNN design aims at tailoring the end-to-end deep learning-based systems for communication over nonlinear channels with memory, such as the optical IM/DD fiber channel.

Silicon Photonic Mach–Zehnder Modulator Architectures for on Chip PAM-4 Signal Generation

Four level pulse amplitude modulation (PAM-4) has become the modulation format of choice to replace on-off keying (OOK) for the 400 Gb/s short reach optical communications systems. In this paper, we investigate the possible modifications to conventional Mach-Zehnder modulator structures to improve the system performance. We present three different silicon photonic Mach-Zehnder modulator architectures for generating PAM-4 in the optical domain using OOK electrical driving signals. We investigate the transfer function and linearity of each modulator and experimentally compare their PAM-4 generation and transmission performance with and without use of digital signal processing (DSP). We achieve the highest reported PAM-4 generation and transmission without the use of DSP. The power consumption of each modulator is presented, and we experimentally show that multielectrode Mach-Zehnder modulators provide a clear advantage at higher symbol rates compared to conventional Mach-Zehnder modulators.

End-to-End Deep Learning of Optical Fiber Communications

In this paper, we implement an optical fiber communication system as an end-to-end deep neural network, including the complete chain of transmitter, channel model, and receiver. This approach enables the optimization of the transceiver in a single end-to-end process. We illustrate the benefits of this method by applying it to intensity modulation/direct detection (IM/DD) systems and show that we can achieve bit error rates below the 6.7\% hard-decision forward error correction (HD-FEC) threshold. We model all componentry of the transmitter and receiver, as well as the fiber channel, and apply deep learning to find transmitter and receiver configurations minimizing the symbol error rate. We propose and verify in simulations a training method that yields robust and flexible transceivers that allow---without reconfiguration---reliable transmission over a large range of link dispersions. The results from end-to-end deep learning are successfully verified for the first time in an experiment. In particular, we achieve information rates of 42\,Gb/s below the HD-FEC threshold at distances beyond 40\,km. We find that our results outperform conventional IM/DD solutions based on 2 and 4 level pulse amplitude modulation (PAM2/PAM4) with feedforward equalization (FFE) at the receiver. Our study is the first step towards end-to-end deep learning-based optimization of optical fiber communication systems.

60 Gbps 4-PAM VCSEL-based Raman assisted hyper-scale data centre: In context of spectral efficiency and reach extension

Abstract Cost effective large-scale installation of hyper-scale data centres has attracted extensive research recently, due to the exponential bandwidth demand over extended reach. Low cost, power and spectral efficient techniques for increasing network capacity, as well as extending the transmission reach while maintaining duplex connectivity are still key challenges facing current big data networks such as hyper-scale data centre networks. In this work, a low cost energy efficient technique for maximizing carrier spectral efficiency and extending transmission reach is experimentally demonstrated. This is achieved through combined adoption of vertical cavity surface emitting lasers (VCSELs), four level pulse amplitude modulation (4-PAM), dense wavelength division multiplexing (DWDM) and Raman amplification. Three class 10 G VCSEL channels are directly modulated with a 20 Gbps 4-PAM data signal therefore maximizing carrier spectral efficiency by doubling the data rate per channel. The channels are then converged to a single fibre link through DWDM technique at 0.4 nm spacing, achieving a total aggregated data rate of 60 (3 × 20) Gbps. By exploiting the 8.6 dB flat gain of a forward Raman pump, a 77.12 km of standard single mode fibre (SMF) transmission is experimentally achieved. To the best of our knowledge, this is the longest error free fibre transmission distance reported using VCSEL-based 60 Gbps 4-PAM, without any forward error correction (FEC), equalization and pre-emphasis mechanisms. Results show that a real time uncorrected BER

Spectral Efficiency Improved 2D-PAM8 Trellis Coded Modulation for Short Reach Optical System

This paper proposes and demonstrates a 31.25 Gbps two-dimensional eight level pulse amplitude modulation with trellis coded modulation (2D-PAM8-TCM) transmission in intensity modulation and direct detection based short reach system. In this system, the commercial directly modulated laser and photodiode with trans-impedance amplifier (PIN-TIA) with a combined modulation bandwidth of ∼16 GHz are used as transmitter and receiver, respectively. For 2D-PAM8-TCM signals, except for regular 8-state convolutional encoder, both 16-state and 32-state encoders are provided. Considering the coding gain and the complexity of convolutional encoder, the 16-state one is recommended. Moreover, instead of Viterbi decoder, the M-algorithm is utilized at the receiver side to reduce decoder complexity. It is experimentally demonstrated that 2D-PAM8-TCM scheme can achieve 2.5 b per symbol and ∼0.5 dB sensitivity improvement (bit error rate @ $3.8 \times {10^{ - 3}}$ ) over a 20 km standard single mode fiber in comparison with conventional PAM4. Thanks to no additional digital signal processing in receiver side except M-algorithm, this scheme is simple and effective, which can be considered as an attractive technique for future short reach system.

Performance evaluation of multilevel modulation formats using partial response for capacity upgrade in access network with limited electronic bandwidth

Abstract We present a successful experimental evaluation of 4 level Pulse Amplitude Modulation (4-PAM) and Duobinary modulation. An experimental performance evaluation is presented for Duobinary 4 PAM and other modulation formats. All modulation formants used, may be considered to be implemented in future Passive Optical Network (PON) class access networks with limited electrical bandwidth. We compared NRZ, Duobinary, 4-PAM and Duobinary 4-PAM operating at 9 Gbaud over 20 km single mode fiber. The results provides an insight and guidelines on the utilization of these advanced modulation formats.

IMDD-based bidirectional 20 Gb/s/λ WDM-PON with Nyquist 4 PAM employing Rayleigh backscattering noise detection-based self wavelength management

We experimentally demonstrate an optical intensity modulation transmitter with a Nyquist 4 level pulse amplitude modulation and direct detection (DD) receiver-based channel-reuse wavelength-division-multiplexing passive optical network (WDM-PON). A Rayleigh backscattering noise detection-based wavelength management method is employed for the tunable optical transmitter used in colorless optical network unit to achieve bidirectional 20 Gb/s/λ transmission over 45-km standard single-mode-fiber on a 100-GHz WDM grid. Chromatic dispersion induced power fading in the DD system is avoided with fiber Bragg grating filter-based vestigial-sideband filtering. The inter-symbol interference is cancelled with digital signal processing-based overlap frequency-domain equalizer. The transmission performance is also measured with different optical signal to Rayleigh backscattering noise ratio and different central wavelength shift between upstream and downstream in the channel-reuse system.

A reduced state variant of maximum likelihood sequence detection attaining optimum performance for high signal-to-noise ratios

In the detection of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</tex> -level pulse-amplitude modulation (PAM) signals transmitted over a noisy linear <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\nu</tex> -symbol memory channel, maximum likelihood sequence detection (MLSD) is asymptotically optimum in the sense that the exponent of the probability of symbol error in the limit of small noise is the largest that can be achieved by any detector. A reduced state detection (RSD) is developed with the aim of mitigating the computational complexity of MLSD while attaining the same error exponent as MLSD. In RSD, for each baud, the recent received signal levels delineate a certain list of the most probable of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m^{nu}</tex> possible states. Retention of only the paths threading through these most probable states is the key to success of RSD. Suppose it is required that the number of states retained at any time not exceed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\psi</tex> . When <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\psi</tex> is less than the number of states required for RSD, it is shown how to modify RSD so that no more than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\psi</tex> states are retained and how to assess the degradation of the error exponent.

Sequential M-ary PAM System

This paper examines the following M -level pulse-amplitude modulation (PAM) sequential communication system. Given that one of the M signals is repetitively sent over an additive Gaussian channel during successive intervals of time, what is the optimum sequential procedure to follow at the receiver in order to pick the correct signal with a probability of wrong selection no greater than \epsilon? The optimum procedure is defined to be one that minimizes the expected number of transmissions (sample size) before a decision is reached. The paper extends the results of Hecht for the test procedure (also obtained independently by the author). This paper shows the following. 1) The maximum a posteriori (MAP) test procedure is shown to be comparable in performance with the simultaneous test. 2) MAP test with a threshold 1 - e does not yield error probabilities equal to e if M \geq 3 . 3) Lower bounds on the expected sample sizes for any test procedure for the M -level PAM are obtained with the results from Hoeffding and Simons. 4) Both the simultaneous and the MAP tests are shown to achieve the lower bound when \epsilon \rightarrow 0 . 5) Approximations used by Hecht for the simultaneous test are made rigorous and slightly tighter expressions of error probability than the ones given by Hecht are obtained for some cases. 6) Energy savings of both the MAP and the simultaneous tests over the nonsequential scheme are presented for different values of M .