Achievable Information Rate Research Articles

Blind Carrier Phase Recovery Using Extended Kalman Filtering in Probabilistically Shaped Coherent Systems

In this paper, we propose an Extended Kalman Filtering with phase noise reconstruction (EKF-PC) scheme to enhance the carrier recovery capability for probabilistic shaping of coherent optical communication systems with various shaping factors. We first investigate the weights of the shaping factor and the noise rejection window length of EKF-PC for PS-64QAM at a fixed signal-to-noise ratio (SNR). After that, we jointly optimize the shaping factor and the noise rejection window length to obtain the maximum achievable information rate at a variety of SNRs. Then, we numerically analyze the carrier recovery performance of the EKF-PC for different linewidths and SF conditions. Finally, we conduct simulation experiments to compare EKF-PC, PCPE, and other currently available Kalman CPE algorithms with the SFs of 0.02, 0.025, 0.03, and 0.035 under back-to-back (B2B) scenarios. The experimental results show that EKF-PC obtains an average SNR improvement of 0.13–0.5 dB compared to PCPE and an average performance improvement of 0.5–1 dB compared to other Kalman algorithms.

Pace Time Modulation for Intra-Cardiac Communication

Although single-node leadless pacemakers eliminate several complications associated with subcutaneous pockets and leads, they have the significant limitation of only being able to perform single-chamber pacing. Multi-nodal pacing can outperform single-chamber pacing by providing a closer approximation of sinus rhythm but requires energy-efficient wireless communication to preserve synchrony. In this work, we propose a novel biocompatible communication concept wherein the pacemaker node located in the sinoatrial (SA) node stimulates the right atrium and simultaneously sends a synchronization message, encoded into the pacing time, to all other pacemaker nodes located at different sites in the heart. We refer to this concept as the Pace Time Modulation (PTM) method and assess its performance in terms of symbol error rate and achievable information rate. The analyses and numerical simulations indicate that PTM can be applicable in realistic scenarios, without deviating the heart rate from its normal range.

High-Cardinality Geometrical Constellation Shaping for the Nonlinear Fibre Channel

This paper presents design methods for highly efficient optimisation of geometrically shaped constellations to maximise data throughput in optical communications. It describes methods to analytically calculate the information-theoretical loss and the gradient of this loss as a function of the input constellation shape. The gradients of the mutual information (MI) and generalised mutual information (GMI) are critical to the optimisation of geometrically-shaped constellations. The analytically derived gradients of the achievable information rate metrics with respect to the input constellation are presented. The proposed method allows for improved design of higher cardinality and higher-dimensional constellations for optimising both linear and nonlinear fibre transmission throughput. Near-capacity achieving constellations with up to 8192 points for both 2 and 4 dimensions are presented. In the best case, a GMI value within 0.06 b/2Dsymbol of the additive white Gaussian noise channel (AWGN) capacity was achieved. Additionally, a design algorithm reducing the design computation time from days to minutes is introduced, allowing for the design of optimised constellations for both linear AWGN and nonlinear fibre channels over a wide range of signal-to-noise ratio values.

On Sparse Gain Flattening in Pump-Constrained Submarine Links

Having in mind the capacity optimization of power-constrained submarine links, by following the work in (Cho <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , 2020) we first compare the achievable information rate (AIR) of gain-flattened and un-flattened short links (called here blocks) of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{b}\leq 12$</tex-math></inline-formula> spans with span loss 16.5 dB and with end-span single-stage co-pumped erbium-doped fiber amplifiers (EDFA) when the transmitted wavelength division multiplexed (WDM) channels all have the same transmitted power. All EDFAs have the same pump power and the same physical parameters. In the flattened case, each EDFA is followed by an ideal gain-flattening filter (GFF) that chops off the EDFA gain exceeding the span loss. No GFFs are used in the un-flattended case. We show that, for block length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{b}&gt;7$</tex-math></inline-formula> , at large-enough input power the AIR of the GFF block exceeds that of the no-GFF block, while for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{b}\leq 7$</tex-math></inline-formula> at large input power the AIR is about the same. We next build a long submarine link by concatenating many <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{b}$</tex-math></inline-formula> -span no-GFF blocks, and placing a GFF at the last EDFA of each block in order to flatten the block gain down to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{b}$</tex-math></inline-formula> -span loss, and calculate the AIR of the resulting sparse-GFF submarine link, accounting also for nonlinear interference. For a 287-span case-study link with span loss 9.5 dB, we show that the best power efficiency is achieved by blocks of size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{b}=6$</tex-math></inline-formula> (i.e., one GFF every 6 spans) when the pump is around 11 mW. When the GFF excess loss is 0.3 dB the top-AIR gain over the standard all-GFF system is 9.5%, a value that decreases to 4% when the excess loss is zero. Considering that modern submarine-grade GFFs have almost zero excess loss, and that the most efficient pump power is likely too low to operate with, we conclude that sparse-GFF links offer little advantage in practice over the current design.

On Anomalous Diffusion of Devices in Molecular Communication Systems

A one-dimensional (1-D) anomalous-diffusive molecular communication channel is considered, wherein the devices (transmitter (TX) and receiver (RX)) can move in either direction along the axis. For modeling the anomalous diffusion of information carrying molecules (ICM) as well as that of the TX and RX, the concept of time-scaled Brownian motion is explored. In this context, a novel closed-form expression for the first hitting time density (FHTD) is derived. Further, the derived FHTD is validated through particle-based simulation. For the transmission of binary information, the timing modulation is exploited. Furthermore, the channel is assumed as a binary erasure channel (BEC) and analyzed in terms of achievable information rate (AIR).

Probabilistically shaped polar-coded MIMO-FSO communication systems with spatially correlated fading.

In this paper, the probabilistically shaped polar-coded multiple-input multiple-output free-space optical (MIMO-FSO) communication system with or without spatially correlated (SC) fading is investigated to improve transmission performance. The designed shaping-polar encoder can flexibly generate three typical shapes of distribution via shaping bits and be decoded in the conventional method. The achievable information rate (AIR) of MIMO-FSO systems with or without SC fading is evaluated to determine the number of shaping bits for the shaping-polar encoder. The non-pairwise distributions are demonstrated to be more suitable for turbulence channels than other distributions. The results show that the AIR of the shaped 4 × 4 systems even exceeds that of the uniform 4 × 5 systems in the low signal-to-noise ratio regions over strong turbulence channels. In terms of bit error rate performance, more than 15 dB shaping gains can be achieved by the shaped 4 × 4 systems compared to the uniform single-input single-output polar-coded systems. In addition, the shaped 4 × 4 systems outperform the uniform ones ranging from 1 dB to 1.9 dB over different atmospheric turbulence channels with or without SC fading, comparable to the uniform MIMO systems with one more physical receiver.

Outage Probability Due to PDL Using Threshold Exceedances: Implications of DD-LMS Equalization and Inter-Channel Fiber Nonlinearities

The outage probability due to polarization dependent loss (PDL) is estimated using the method of threshold exceedances for a multi-channel transmission model that includes i) decision-directed least-mean-square equalization to partially compensate PDL, ii) the dominant fiber nonlinear effects of cross-phase modulation and cross-polarization modulation, and iii) transceiver noise. The outage probability is defined in terms of the bit-wise achievable information rate (BW-AIR) being less than a threshold value for the generalized mutual information determined by the forward error correcting code rate. The root mean square error between the mean excess function and a theoretical fit to it is used for the critical step of determining the threshold below which the BW-AIR data is represented by the generalized Pareto distribution. The applicability of the method of threshold exceedances is demonstrated for 32 Gbaud, dual-polarization 64-ary quadrature amplitude modulation with a uniform constellation.

Successive Interference Cancellation on Frequency-Selective Channels With Mode-Dependent Gain

In ultra-long-haul optical communication systems, polarization-dependent gain from single-mode semiconductor optical amplifiers or mode-dependent gain from multi-mode erbium-doped fiber amplifiers causes a channel’s achievable information rate (AIR) using linear minimum-mean-square error (MMSE) detection to become substantially lower than the capacity of optimal maximum likelihood detection owing to loss of orthogonality between modes. However, such capacity loss can be mitigated using techniques that retain reasonable complexity, such as successive interference cancellation (SIC). In wireless systems, multicarrier transmission with many subcarriers transforms the frequency-selective channel into a set of uncoupled memoryless subchannels, and it is possible to obtain good performance using SIC on each subchannel independently. Multicarrier transmission in optical fibers, however, is susceptible to performance loss caused by Kerr nonlinearity. Therefore, we study methods for applying SIC on frequency-selective optical fiber channels using single-carrier transmission. We compare the theoretical performance of MMSE and SIC equalizers on frequency-selective optical fiber channels operating at 64 Gbaud with transmission distances up to 15,000 km and evaluate the penalties of SIC implementation. We consider single-mode fiber links with random artificial polarization-mode dispersion inserted along the link to enhance frequency diversity, as well as multi-core fiber links supporting 14 spatial and polarization modes. We show that SIC can increase outage capacity by 19%, but the AIR increase is reduced by almost half if error correction coding is not performed across modes. We confirm that SIC can adapt to fast channel perturbations with only a 3% decrease in AIR.

Waveform Learning for Next-Generation Wireless Communication Systems

We propose a learning-based method for the joint design of a transmit and receive filter, the constellation geometry and associated bit labeling, as well as a neural network (NN)-based detector. The method maximizes an achievable information rate, while simultaneously satisfying constraints on the adjacent channel leakage ratio (ACLR) and peak-to-average power ratio (PAPR). This allows control of the tradeoff between spectral containment, peak power, and communication rate. Evaluation on an additive white Gaussian noise (AWGN) channel shows significant reduction of ACLR and PAPR compared to a conventional baseline relying on quadrature amplitude modulation (QAM) and root-raised-cosine (RRC), without significant loss of information rate. When considering a 3rd Generation Partnership Project (3GPP) multipath channel, the learned waveform and neural receiver enable competitive or higher rates than an orthogonal frequency division multiplexing (OFDM) baseline, while reducing the ACLR by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {10~ \text {dB}}$ </tex-math></inline-formula> and the PAPR by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {2~ \text {dB}}$ </tex-math></inline-formula> . The proposed method incurs no additional complexity on the transmitter side and might be an attractive tool for waveform design of beyond-5G systems.

Higher-Order Modulation vs Faster-Than-Nyquist PAM-4 for Datacenter IM-DD Optics: An AIR Comparison Under Practical Bandwidth Limits

The 4-ary pulse amplitude modulation (PAM-4) has been widely deployed to both electrical and optical interfaces in datacenter applications. Based on 100-GBd PAM-4, the 200G per lane optical interface is being actively developed in both industrial interoperability groups and standard bodies. Going beyond 200G, it is questionable if PAM-4 could support an even faster interface with higher baud-rate, considering the bandwidth growth for both electronics and optical components has started lagging the ever-increasing capacity demand. Under limited bandwidth, one option is to improve the spectral efficiency by higher order formats like PAM-6 and PAM-8, but this induces backward incompatibility as well as potential modulation mismatch between electrical and optical interfaces that requires additional energy for gearboxing. This revives the study of faster than Nyquist (FTN) signaling to pursue higher PAM-4 baud-rate breaking the bandwidth limit. In ECOC 2021, we demonstrated a reduced-complexity maximum a posteriori probability (MAP) decoder in intensity-modulation (IM) direct-detection (DD) systems with superior FTN performance. In this paper, we extend our work by adding more algorithm details and experimental results. Moreover, we perform the achievable information rate (AIR) comparison between the FTN PAM-4 and the higher-order modulation within the Nyquist limit in different channel conditions. Remarkably, in a practical IM-DD channel with gradually decayed frequency response, FTN shows AIR gain over the Nyquist approach even at a low FTN decoding complexity. The finding suggests FTN PAM could be a promising candidate at post 200G era to offer both AIR and implementation advantages.

New Lower Bounds on the Capacity of Optical Fiber Channels via Optimized Shaping and Detection

Constellation shaping is a practical and effective technique to improve the performance and the rate adaptivity of optical communication systems. In principle, it could also be used to mitigate the impact of nonlinear effects, possibly increasing the information rate beyond the current limit dictated by fiber nonlinearity. However, this appealing idea is frustrated by the difficulty of designing an effective shaping strategy that takes into account the nonlinearity and long memory of the fiber channel, as well as the possible interplay with other nonlinearity mitigation strategies. As a result, only little progress has been made so far, while the optimal shaping distribution and the ultimate channel capacity remain unknown. In this work, we describe a novel technique to optimize the shaping distribution in a very general setting and high-dimensional space. For a simplified block-memoryless nonlinear optical channel, the capacity lower bound obtained by the proposed technique can be expressed analytically, establishing the conditions for an unbounded growth of capacity with power. In a more realistic scenario, the technique can be implemented by a rejection sampling algorithm driven by a suitable cost function, and the corresponding achievable information rate estimated numerically. The combination of the proposed technique with an improved (non-Gaussian) decoding metric yields a new capacity lower bound for the dual-polarization WDM channel.

Achievable Rate Maximization for Multi-Relay AF Cooperative SWIPT Systems with a Nonlinear EH Model.

In this paper, the maximization of the achievable information rate is proposed for the multi-relay amplify-and-forward cooperative simultaneous wireless information and power transfer communication systems, where the nonlinear characteristic of the energy harvesting (EH) circuits is taken into account for the receivers of the relay nodes. The time switching (TS) and power splitting (PS) schemes are considered for the EH receivers and the achievable rate maximization problems are formulated as convex and non-convex optimization problems, respectively. The optimal TS and PS ratios for the relay nodes along with the maximum achievable rates for the system are obtained, respectively, by solving the optimal problems with efficient algorithms. The asymptotic maximum achievable rates at low and high input signal-to-noise ratios (SNRs) for both the PS and TS schemes are also analyzed. It is demonstrated that the PS scheme is more susceptible to the variation of the relays’ location and the channel parameters than TS scheme, whereas the TS scheme is more susceptible to the mismatch of the resource allocation than PS scheme. Specifically, compared to the linear EH model, the nonlinear EH model achieves significant performance gain for the TS scheme, whereas inconspicuous performance improvement is achieved for the PS scheme.

Lower Bound on the Capacity of the Continuous-Space SSFM Model of Optical Fiber

The capacity of a discrete-time model of optical fiber described by the split-step Fourier method (SSFM) as a function of the signal-to-noise ratio SNR and the number of segments in distance K is considered. It is shown that if K ≥ SNR2/3 and SNR → ∞, the capacity of the resulting continuous-space lossless model is lower bounded by 1/2 log2(1 + SNR) - 1/2 + o(1), where o(1) tends to zero with SNR. As K → ∞, the inter-symbol interference (ISI) averages out to zero due to the law of large numbers and the SSFM model tends to a diagonal phase noise model. It follows that, in contrast to the discrete-space model where there is only one signal degree-of-freedom (DoF) at high powers, the number of DoFs in the continuous-space model is at least half of the input dimension n. Intensity-modulation and direct detection achieves this rate. The pre-log in the lower bound when K=δ√SNR is generally characterized in terms of δ. It is shown that if the nonlinearity parameter γ → ∞, the capacity of the continuous-space model is 1/2 log2(1 + SNR) + o(1). The SSFM model when the dispersion matrix does not depend on K is considered. It is shown that the capacity of this model when K=δ√SNR, δ > 3, and SNR → ∞ is 1/2n log2(1 + SNR) + O(1). Thus, there is only one DoF in this model. Finally, it is found that the maximum achievable information rates (AIRs) of the SSFM model with back-propagation equalization obtained using numerical simulation follows a double-ascent curve. The AIR characteristically increases with SNR, reaching a peak at a certain optimal power, and then decreases as SNR is further increased. The peak is attributed to a balance between noise and stochastic ISI. However, if the power is further increased, the AIR will increase again, approaching the lower bound 1/2 log(1 + SNR) - 1/2 + o(1). The second ascent is because the ISI averages out to zero with K → ∞ sufficiently fast.

DNN-assisted phase distance tuned PSK modulation for PAM4-to-QPSK format conversion gateway node.

This paper proposes an optical gateway that converts pulse amplitude modulation (PAM) format to phase shift keying (PSK) modulation format, enabling flexible intensity-to-phase mapping without relying on optical-electrical-optical data conversion at heterogenous network connections. A proof-of-principle experiment shows that optically converted PSK signals from regular PAM signals will induce non-uniform irregular phase noise distortion. The proposed optical gateway is designed to provide an optimized phase distance for PSK signals such that an achievable information rate is maximized by a deep learning-based decision on the receiver side. The phase distance-tuned PSK signals offer performance improvement of about 4 dB gain at a target generalized mutual information by making use of a digital neural network recovery.

Eigendecomposition-Precoded Faster-Than-Nyquist Signaling With Optimal Power Allocation in Frequency-Selective Fading Channels

In this paper, we propose eigenvalue decomposition (EVD)-precoded faster-than-Nyquist (FTN) signaling with power allocation in a frequency-selective fading channel. More specifically, we derive the mutual information associated with the proposed FTN signaling. Then, the optimal power coefficients are calculated such that the derived mutual information is maximized. Our analytical performance results show that the proposed FTN signaling scheme achieves a higher information rate than the conventional FTN signaling scheme without relying on power allocation and the classic Nyquist signaling scheme, under the assumption that all the schemes employ a root-raised cosine shaping filter. Moreover, we derive the proposed scheme&#x2019;s achievable information rate in the presence of channel estimation errors. Furthermore, our numerical simulation results for the bit error ratio performance and the power spectral density demonstrate that the proposed FTN scheme outperforms the conventional Nyquist signaling scheme without incurring any bandwidth broadening.

List-Encoding CCDM: A Nonlinearity-Tolerant Shaper Aided by Energy Dispersion Index

Recently, a metric called energy dispersion index (EDI) was proposed to qualitatively indicate the nonlinear interference (NLI) induced by correlated symbols during optical transmission. In this paper, we propose a new shaper architecture to decrease the EDI of transmitted symbols and thus, increase the signal-to-noise ratio (SNR). We call this shaper the list-encoding constant-composition distribution matcher (L-CCDM). L-CCDM consists of an additional EDI selecting module, which is compatible with standard probabilistic amplitude shaping (PAS) architecture. Numerical results obtained from a multi-span multi-channel system show that when compared to standard CCDM with 256-ary quadrature amplitude modulation (256QAM), the proposed architecture offers an effective SNR gain of 0.35 dB, an achievable information rate gain of 0.22 b/4D-symbol, or equivalently an 8% reach extension.

Joint Coordinated Beamforming and Power Splitting Ratio Optimization in MU-MISO SWIPT-Enabled HetNets: A Multi-Agent DDQN-Based Approach

This paper proposes a multi-agent double deep Q network (DDQN)-based approach to jointly optimize the beamforming vectors and power splitting (PS) ratio in multi-user multiple-input single-output (MU-MISO) simultaneous wireless information and power transfer (SWIPT)-enabled heterogeneous networks (HetNets), where a macro base station (MBS) and several femto base stations (FBSs) serve multiple macro user equipments (MUEs) and femto user equipments (FUEs). The PS receiver architecture is deployed at FUEs. An optimization problem is formulated to maximize the achievable sum information rate of FUEs under the constraints of the achievable information rate requirements of MUEs and FUEs and the energy harvesting (EH) requirements of FUEs. Since the optimization problem is challenging to handle due to the high dimension and time-varying environment, an efficient multi-agent DDQN-based algorithm is presented, which is trained in a centralized manner and runs in a distributed manner, where two sets of deep neural network parameters are jointly updated and trained to tackle the problem and avoid overestimation. To facilitate the presented multi-agent DDQN-based algorithm, the action space, the state space and the reward function are designed, where the codebook matrix is employed to deal with the complex transmit beamforming vectors. Simulation results validate the proposed algorithm. Notable performance gains are achieved by the proposed algorithm due to considering the beam directions in the action space and the adaptability to the Doppler frequency shifts. Besides, the proposed algorithm is shown to be superior to other benchmark ones numerically.

Maximizing Fiber Capacity in Flex-Grid Coherent Systems Through Symbol Rate Optimization

We demonstrate that, in an actual network, maximizing the transmission spectral efficiency requires not only to take into account transceiver impairments, but also to consider WSS filtering and flex-grid specifications. In a WDM transmission experiment over a 10-span link covering <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim 38$ </tex-math></inline-formula> nm, we study achievable rate, bitrate and spectral efficiency for different symbol rates of 62.5, 75, 87.5, 100 and 112.5Gbaud with corresponding channel spacings of 75, 87.5, 100, 112.5, 125GHz, therefore accounting for few GHz bandguard required for potential WSS filtering effect, as well as being compatible with flex-grid configuration. While maximum achievable information rate per transceiver (wavelength) is achieved for the lowest symbol rate, and operating at larger symbol rate maximizes the bitrate per wavelength, to maximize overall fiber spectral efficiency (and therefore, capacity), operation at intermediate symbol rates, from 75 to 100Gbaud in our study, is required as a trade-off between the penalties from transceiver impairments and WSS filtering.

Toward UAV-based communication: improving throughput by optimum trajectory and power allocation

It is predicted that the use of unmanned aerial vehicles (UAVs) in communication systems will be more extensive in future generations of wireless telecommunication networks, due to their facilitating advantages. In this paper, a UAV-based wireless communication system is considered in which a UAV is employed as a relay to connect two ground users. These two disconnected users make a communication pair. Our aim is to maximize the minimum achievable information rate for the communication link between the transmitter and receiver, by cooperatively optimizing UAV trajectory and transmitter and source power allocation. Motivated by the above, we formulate the optimization problem. The solving process is complicated because of the non-convexity of the formulated problem. To overcome this difficulty, we convert the main problem to some sub-problems by fixing some constraints and solving them with iterative algorithms such as successive convex optimization and reaching the solution for the main problem. Simulation results show the capability of the proposed algorithm.

Multistage Soliton Phase and Amplitude Estimation

A multistage signal estimation scheme is proposed for phase-and-amplitude modulated soliton communication systems. The estimator provides a significant mean-squared-error reduction in soliton amplitude estimation, which, in conjunction with detection of encoded phase information, results in spectral-efficiency improvements. A low-complexity version of the multistage estimation scheme is also proposed, whose performance is studied via numerical simulations under the distributed Raman amplification strategy. The achievable information rate is increased by about 1 bit/symbol for pulse bandwidth of 30 GHz, 40 GHz, and 50 GHz.