Stella Civelli, Enrico Forestieri, Alexey Lotsmanov, Dmitry Razdoburdin, Marco Secondini
A novel technique to optimize the input distribution and compute a lower bound for the capacity of the nonlinear optical fiber channel is proposed. The technique improves previous bounds obtained with the additive white Gaussian noise decoding metric.
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We study a nonlinear fiber optical channel impaired by cross-phase modulation and dispersion from the viewpoint of an interference channel. We characterize an outer bound on the capacity region of simultaneously achievable rate pairs, assuming a two-user perturbative channel model.
We consider the optical fiber channel modelled by the nonlinear Shrödinger equation with zero dispersion and additive Gaussian noise. Using Feynman path-integral approach for the model we find corrections to conditional probability density function, output signal distribution, conditional and output signal entropies, and the channel capacity at large signal-to-noise ratio. We demonstrate that the correction to the channel capacity is positive for large signal power. Therefore, this correction increases the earlier calculated capacity for a nondispersive nonlinear optical fiber channel in the i…
This paper focuses on delivering quantified results for the evaluation of the aggregated impact of stochastic antenna misalignment, multipath fading and hardware imperfections on the terahertz (THz) wireless fiber extenders. In this line, we present the appropriate signal model that accommodates the different technical and environmental parameters. In particular, it takes into consideration the antenna gains, the central frequency, the transmission range, the environmental conditions, i.e. temperature, humidity and pressure, the spatial jitter between the transmitter and receiver antennas, whi…
By taking advantage of the temporal correlations of the nonlinear phase noise in WDM systems we show that the capacity of a nonlinear fiber link is notably higher than what is currently assumed. This advantage is translated into the doubling of the link distance for a fixed transmission rate.
The per-sample zero-dispersion channel model of the optical fiber is considered. It is shown that capacity is uniquely achieved by an input probability distribution that has continuous uniform phase and discrete amplitude that takes on finitely many values. This result holds when the channel is subject to general input cost constraints, that include a peak amplitude constraint and a joint average and peak amplitude constraint.
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…
We consider multi-input multi-output (MIMO) communications over multi-mode fibers (MMFs). Current MMF standards, such as OM3 and OM4, use fibers with core radii of 50 μm, allowing hundreds of modes to propagate. Unfortunately, due to physical and computational complexity limitations, we cannot couple and detect hundreds of data streams into and out of the fiber. In order to circumvent this issue, we present input-output coupling schemes that allow the user to couple and extract a reasonable number of signals from a fiber with many modes. This approach is particularly attractive as it is scalab…
An upper bound to the information capacity of a wavelength-division multi- plexed optical fiber communication system is derived in a model incorporating the nonlinear propagation effects of cross-phase modulation (XPM). This work is based on the paper by Mitra et al., finding lower bounds to the channel capacity, in which physical models for propagation are used to calculate statistical properties of the conditional probability distribution relating input and output in a single WDM channel. In this paper we present a tractable channel model incorporating the effects of cross phase modulation. …
Regular perturbation is applied to the Manakov equation and motivates a generalized correlated phase-and-additive noise model for wavelength-division multiplexing over dual-polarization optical fiber channels. The model includes three hidden Gauss-Markov processes: phase noise, polarization rotation, and additive noise. Particle filtering is used to compute lower bounds on the capacity of multi-carrier communication with frequency-dependent powers and delays. A gain of 0.17 bits/s/Hz/pol in spectral efficiency or 0.8 dB in power efficiency is achieved with respect to existing models at their p…
Fiber Nonlinearity Mitigation in Coherent Optical Systems
该研究综述了相干光系统中光纤非线性抑制的两类主流方法及最新进展，提出星座整形、低复杂度DBP等未来方向，指出其兼具理论与实用价值。
The concept of a fiber aided wireless network architecture (FAWNA) is introduced in [Ray et al., Allerton Conference 2005], which allows high-speed mobile connectivity by leveraging the speed of optical networks. In this paper, we consider a single-input, multiple-output (SIMO) FAWNA, which consists of a SIMO wireless channel and an optical fiber channel, connected through wireless-optical interfaces. We propose a scheme where the received wireless signal at each interface is quantized and sent over the fiber. Though our architecture is similar to that of the classical CEO problem, our problem…
The optical fiber multiple-input multiple-output (MIMO) channel with intensity modulation and direct detection (IM/DD) per spatial path is treated. The spatial dimensions represent the multiple modes employed for transmission and the cross-talk between them originates in the multiplexers and demultiplexers, which are polarization dependent and thus timevarying. The upper bounds from free-space IM/DD MIMO channels are adapted to the fiber case, and the constellation constrained capacity is constructively estimated using the Blahut-Arimoto algorithm. An autoencoder is then proposed to optimize a…
A number of simplified models, based on perturbation theory, have been proposed for the fiber-optical channel and have been extensively used in the literature. Although these models are mainly developed for the low-power regime, they are used at moderate or high powers as well. It remains unclear to what extent the capacity of these models is affected by the simplifying assumptions under which they are derived. In this paper, we consider single channel data transmission based on three continuous-time optical models i) a regular perturbative channel, ii) a logarithmic perturbative channel, and …
A correlated phase-and-additive-noise (CPAN) mismatched model is developed for wavelength division multiplexing over optical fiber channels governed by the nonlinear Schrödinger equation. Both the phase and additive noise processes of the CPAN model are Gauss-Markov whereas previous work uses Wiener phase noise and white additive noise. Second order statistics are derived and lower bounds on the capacity are computed by simulations. The CPAN model characterizes nonlinearities better than existing models in the sense that it achieves better information rates. For example, the model gains 0.35 d…
The emerging cell-free massive multiple-input multiple-output (CF-mMIMO) is a promising scheme to tackle the capacity crunch in wireless networks. Designing the optimal fronthaul network in the CF-mMIMIO is of utmost importance to deploy a cost- and energy-efficient network. In this paper, we present a framework to optimally design the fronthaul network of CF-mMIMO utilizing optical fiber and free space optical (FSO) technologies. We study an uplink data transmission of the CF-mMIMO network wherein each of the distributed access points (APs) is connected to a central processing unit (CPU) thro…
The capacity of the channel defined by the stochastic nonlinear Schrödinger equation, which includes the effects of the Kerr nonlinearity and amplified spontaneous emission noise, is considered in the case of zero dispersion. In the absence of dispersion, this channel behaves as a collection of parallel per-sample channels. The conditional probability density function of the nonlinear per-sample channels is derived using both a sum-product and a Fokker-Planck differential equation approach. It is shown that, for a fixed noise power, the per-sample capacity grows unboundedly with input signal. …
In our previous paper [Phys. Rev. E 95, 062122 (2017)] we considered the optical channel modelled by the nonlinear Schrödinger equation with zero dispersion and additive Gaussian noise. We found per-sample channel capacity rof this model. In the present paper we extend per-sample model by introducing the initial signal dependence on time and the output signal detection procedure. The proposed model is a closer approximation of the realistic communication link than the per-sample model where there is no dependence of the initial signal on time. For the proposed model we found the correlators of…
Optical fiber signals with high power exhibit spectral broadening that seems to limit capacity. To study spectral broadening, the autocorrelation function of the output signal given the input signal is derived for a simplified fiber model that has zero dispersion, distributed optical amplification (OA), and idealized spatial noise processes. The autocorrelation function is used to upper bound the output power of bandlimited or time-resolution limited receivers, and thereby to bound spectral broadening and the capacity of receivers with thermal noise. The output power scales at most as the squa…
Antenna selection is capable of handling the cost and complexity issues in massive multiple-input multiple-output (MIMO) channels. The sum-rate capacity of a multiuser massive MIMO uplink channel is characterized under the Nakagami fading. A mathematically tractable sum-rate capacity upper bound is derived for the considered system. Moreover, for a sufficiently large base station (BS) antenna number, a deterministic equivalent (DE) of the sum-rate bound is derived. Based on this DE, the sum-rate capacity is shown to grow double logarithmically with the number of BS antennas. The validity of th…
Technology is moving towards space division multiplexing in optical fiber to keep up the trend in rate increase over time and to avoid an imminent capacity crunch. Thus, it is of paramount interest to estimate the potential gains of this approach. As more spatial channels are being packed into a single fiber, the increased crosstalk necessitates the use of MIMO to guarantee reliable operation. In this paper, we exploit the analogy between an optical fiber and a model from mesoscopic physics - a chaotic cavity - to obtain a novel channel model for the optical fiber. The model captures both rand…
It is shown that signal energy is the only available degree-of-freedom (DOF) for fiber-optic transmission as the input power tends to infinity. With $n$ signal DOFs at the input, $n-1$ DOFs are asymptotically lost to signal-noise interactions. The main observation is that, nonlinearity introduces a multiplicative noise in the channel, similar to fading in wireless channels. The channel is viewed in the spherical coordinate system, where signal vector $\underline{X}\in\mathbb{C}^n$ is represented in terms of its norm $|\underline{X}|$ and direction $\underline{\hat{X}}$. The multiplicative nois…
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 $\text{SNR}$ and the number of segments in distance $K$ is considered. It is shown that if $K\geq \text{SNR}^{2/3}$ and $\text{SNR} \rightarrow \infty$, the capacity of the resulting continuous-space lossless model is lower bounded by $\frac{1}{2}\log_2(1+\text{SNR}) - \frac{1}{2}+ o(1)$, where $o(1)$ tends to zero with $\text{SNR}$. As $K\rightarrow \infty$, the inter-symbol interference (ISI) averages out to zero due to the law of large numbers a…
Transmit and Receive Antenna Port Selection for Channel Capacity Maximization in Fluid-MIMO Systems
针对fluid-MIMO系统收发两端天线端口选择的离散容量最大化问题，提出JCR松弛，并构建JCR&RES与JCR&AO两种性能—复杂度权衡算法。
In this paper, we study the problem of best transmission link selection in a decode-and-forward (DF) cooperative system from capacity point of view. The transmission link can be a cooperative (via a relay) or direct link between the source and destination nodes. In a two-hop DF system with multiple relays and a direct link in between the source and destination, the transmission link selection can be performed based on full or partial channel state information (CSI) of all links involved in cooperation. We derive analytical ergodic capacity of full and partial CSI based path selection schemes i…
Probabilistic Amplitude Shaping and Nonlinearity Tolerance: Analysis and Sequence Selection Method
本文提出线性低通滤波器模型分析概率幅度整形的非线性效应，并基于该模型设计新的序列选择度量，以提升光纤通信系统的非线性容限。
We propose two novel techniques to implement sequence selection (SS) for fiber nonlinearity mitigation, demonstrating a nonlinear shaping gain of 0.24 bits/s/Hz, just 0.1 bits/s/Hz below the SS capacity lower bound.
MIMO processing techniques in fiber optical communications have been proposed as a promising approach to meet increasing demand for information throughput. In this context, the multiple channels correspond to the multiple modes and/or multiple cores in the fiber. In this paper we characterize the distribution of the mutual information with Gaussian input in a simple channel model for this system. Assuming significant cross talk between cores, negligible backscattering and near-lossless propagation in the fiber, we model the transmission channel as a random complex unitary matrix. The loss in t…
We demonstrate a high capacity IF-over-fiber mobile fronthaul solution for multi-user massive MIMO 5G RAN. Using this scheme, a record aggregated radio bandwidth of 25.6 GHz was transmitted on a single optical wavelength over 40 km without fiber chromatic dispersion compensation
In this paper, the symbol error rate (SER) and the bit error rate (BER) of orthogonal space-time block codes (OSTBCs) and their achievable capacity over an amplify-and-forward (AF) relay channel with multiple antennas at source and destination and single antenna at relay node are investigated. Considered are receive antenna selection, transmit antenna selection, and joint antenna selection at both the transmitter and the receiver. The exact SERs of OSTBCs for M-PSK and square M-QAM constellations are obtained using the moment generating functions (MGFs). Also, we analyze the achievable capacit…
In this letter, we analyze the ergodic capacity of bidirectional amplify-and-forward relay selection (RS) with imperfect channel state information (CSI), i.e., outdated CSI and imperfect channel estimation. Practically, the optimal RS scheme in maximizing the ergodic capacity cannot be achieved, due to the imperfect CSI. Therefore, two suboptimal RS schemes are discussed and analyzed, in which the first RS scheme is based on the imperfect channel coefficients, and the second RS scheme is based on the predicted channel coefficients. The lower bound of the ergodic capacity with imperfect CSI is …
Bounds on Covert Capacity with Sub-Exponential Random Slot Selection
本文研究随机时隙选择下的隐蔽通信，在时隙数随码长次指数增长时给出隐蔽容量的上下界，二者差距在√2倍以内且与信道无关，并证明隐蔽性度量选择不影响容量。
In this Paper, the effective capacity of a multiple-input multiple-output (MIMO) system in two different cases with receive antenna selection (RAS) and transmit antenna selection (TAS) schemes is investigated. A closed-form solution for the maximum constant arrival rate of this network with statistical delay quality of service (QoS) constraint is extracted in the quasi-static fading channel. This study is conducted in two different cases. When channel state information (CSI) is not available at the MIMO transmitter, implementation of TAS is difficult. Therefore, RAS scheme is employed and one …
Capacity-Maximizing Input Symbol Selection for Discrete Memoryless Channels
针对离散无记忆信道的输入符号选择问题，本文推导了基于转移矩阵的容量损失上界，并提出一种以该界为替代目标的聚类选择算法，通过数值实验验证其有效性。
This paper compares and evaluates a set of non-parametric mutual information estimators with the goal of providing a novel toolset to progress in the analysis of the capacity of the nonlinear optical channel, which is currently an open problem. In the first part of the paper, the methods of the study are presented. The second part details their application to several optically-related channels to highlight their features.
In this paper, delay constrained performance of a multiple-input multiple-output (MIMO) communication system in a dense environment with co-channel interference is investigated. We apply orthogonal space-time block coding (OSTBC) at the transmitter, and for alleviating the high complexity and cost of the MIMO system, receive antenna selection (RAS) scheme is employed in the downlink. Here, for simple and cheap mobile handsets, one antenna is chosen at the receiver in each utilization of the channel. Under these assumptions, a maximum constant arrival rate with the delay quality-of-service (QoS…
Perturbation-based Sequence Selection for Probabilistic Amplitude Shaping
本研究提出了一种用于概率幅度整形的符号依赖型序列选择度量及对应的信噪比增益预测方法，在单偏振256-QAM长距光纤传输场景下实现了0.5 dB的SNR增益。
We consider the problem of selecting $k_t \times k_r$ antennas from a Gaussian MIMO channel with $n_t \times n_r$ antennas, where $k_t \leq n_t$ and $k_r \leq n_r$. We prove the following two results that hold universally, in the sense that they do not depend on the channel coefficients: (i) The capacity of the best $k_t \times k_r$ subchannel is always lower bounded by a fraction $\frac{k_t k_r}{n_t n_r}$ of the full capacity (with $n_t \times n_r$ antennas). This bound is tight as the channel coefficients diminish in magnitude. (ii) There always exists a selection of $k_t \times k_r$ antenna…
Non-orthogonal multiple access (NOMA) has drawn tremendous attention, being a potential candidate for the spectrum access technology for the fifth-generation (5G) and beyond 5G (B5G) wireless communications standards. Most research related to NOMA focuses on the system performance from Shannon's capacity perspective, which, although a critical system design criterion, fails to quantify the effect of delay constraints imposed by future wireless applications. In this paper, we analyze the performance of a single-input multiple-output (SIMO) two-user downlink NOMA system, in terms of the link-lay…
A fiber optic channel is modeled in a variety of ways; from the simple additive white complex Gaussian noise model, to models that incorporate memory in the channel. Because of Kerr nonlinearity, a simple model is not a good approximation to an optical fiber. Hence we study a fiber optic channel with finite memory and provide an achievable bound on channel capacity that improves upon a previously known bound.
In this work, the achievable rate of three-node relay systems with selection relaying under statistical delay constraints, imposed on the limitations of the maximum end-to-end delay violation probabilities, is investigated. It is assumed that there are queues of infinite size at both the source and relay node, and the source can select the relay or destination for data reception. Given selection relaying policy, the effective bandwidth of the arrival processes of the queue at the relay is derived. Then, the maximum constant arrival rate can be identified as the maximum effective capacity as a …
The channel capacity of a nonlinear, dispersive fiber-optic link is revisited. To this end, the popular Gaussian noise (GN) model is extended with a parameter to account for the finite memory of realistic fiber channels. This finite-memory model is harder to analyze mathematically but, in contrast to previous models, it is valid also for nonstationary or heavy-tailed input signals. For uncoded transmission and standard modulation formats, the new model gives the same results as the regular GN model when the memory of the channel is about 10 symbols or more. These results confirm previous resul…
Capacity is the eternal pursuit for communication systems due to the overwhelming demand of bandwidth hungry applications. As the backbone infrastructure of modern communication networks, the optical fiber transmission system undergoes a significant capacity growth over decades by exploiting available physical dimensions (time, frequency, quadrature, polarization and space) of the optical carrier for multiplexing. For each dimension, stringent orthogonality must be guaranteed for perfect separation of independent multiplexed signals. To catch up with the ever-increasing capacity requirement, i…
This paper considers Gaussian half-duplex diamond $n$-relay networks, where a source communicates with a destination by hopping information through one layer of $n$ non-communicating relays that operate in half-duplex. The main focus consists of investigating the following question: What is the contribution of a single relay on the approximate capacity of the entire network? In particular, approximate capacity refers to a quantity that approximates the Shannon capacity within an additive gap which only depends on $n$, and is independent of the channel parameters. This paper answers the above q…
In this paper, the secrecy performance of a cooperative relay network with outdated relay selection is investigated where an eavesdropper intercepts the channels between the source and the destination. The best relay is chosen among N relays based on the opportunistic relay selection algorithm, which may not be the best relay at the time of transmission because of the outdated channel state information. We derive closed-form analytical expressions for the non-zero secrecy capacity, the secrecy outage probability, and the ergodic secrecy capacity. Finally, our theoretical analysis is validated …
In multi-(core/mode) optical fiber communication, the transmission channel can be modeled as a complex sub-matrix of the Haar-distributed unitary matrix (complex Jacobi unitary ensemble). In this letter, we present new analytical expressions of the upper and lower bounds for the ergodic capacity of multiple-input multiple-output Jacobi-fading channels. Recent results on the determinant of the Jacobi unitary ensemble are employed to derive a tight lower bound on the ergodic capacity. We use Jensen's inequality to provide an analytical closed-form upper bound to the ergodic capacity at any signa…
This paper presents an analysis of a multiple dual-hop relaying system, which is composed of km-class radio frequency (RF)-free-space optical (FSO) links. Partial relay selection based on outdated channel state information (CSI) is employed in order to select active relay for further transmission. Amplify-and-forward relaying protocol is utilized. The RF links are assumed to be subject to Rayleigh fading, and the FSO links are influenced by both Gamma-Gamma atmospheric turbulence and pointing errors. On the basis of our previously derived expression for cumulative distribution function of the …
This paper develops upper bounds on the end-to-end transmission capacity of multi-hop wireless networks. Potential source-destination paths are dynamically selected from a pool of randomly located relays, from which a closed-form lower bound on the outage probability is derived in terms of the expected number of potential paths. This is in turn used to provide an upper bound on the number of successful transmissions that can occur per unit area, which is known as the transmission capacity. The upper bound results from assuming independence among the potential paths, and can be viewed as the ma…
An upper bound on the capacity of a cascade of nonlinear and noisy channels is presented. The cascade mimics the split-step Fourier method for computing waveform propagation governed by the stochastic generalized nonlinear Schroedinger equation. It is shown that the spectral efficiency of the cascade is at most log(1+SNR), where SNR is the receiver signal-to-noise ratio. The results may be applied to optical fiber channels. However, the definition of bandwidth is subtle and leaves open interpretations of the bound. Some of these interpretations are discussed.
We consider a model nondispersive nonlinear optical fiber channel with additive white Gaussian noise at large $\mathrm{SNR}$ (signal-to-noise ratio) in the intermediate power region. Using Feynman path-integral technique we for the first time find the optimal input signal distribution maximizing the channel's per-sample mutual information. The finding of the optimal input signal distribution allows us to improve previously known estimates for the channel capacity. The output signal entropy, conditional entropy, and per-sample mutual information are calculated for Gaussian, half-Gaussian and mo…
The mutual information between a complex-valued channel input and its complex-valued output is decomposed into four parts based on polar coordinates: an amplitude term, a phase term, and two mixed terms. Numerical results for the additive white Gaussian noise (AWGN) channel with various inputs show that, at high signal-to-noise ratio (SNR), the amplitude and phase terms dominate the mixed terms. For the AWGN channel with a Gaussian input, analytical expressions are derived for high SNR. The decomposition method is applied to partially coherent channels and a property of such channels called "s…
RIS with Coupled Phase Shift and Amplitude: Capacity Maximization and Configuration Set Selection
本文针对RIS相移与幅度耦合的实际系统模型，提出线性复杂度的容量最大化反射系数优化方法，并解决最优配置集选择问题。
Storage capacity of perceptron with variable selection
本研究通过引入基于统计力学副本方法的变量选择技术，超越了Cover-Gardner理论的界限，揭示了感知机在高维数据中区分真实结构与偶然相关性的存储容量。
We consider the massive Multiple Input Multiple Output (MIMO) diversity channel affected by independent and identically distributed Rayleigh fading, with linear processing at both transmitter and receiver sides, and analyze the outage capacity for large number of antennas. We first discuss the classical Single Input Multiple Output (SIMO) diversity channel that uses Maximal Ratio Combining (MRC) or Selection Combining (SC). For MRC, a numerical computation and a Gaussian Approximation (GA) are considered, whereas for SC an exact evaluation is possible. The analysis is then straightforwardly ex…
Using a change of basis in the algebra of symmetric functions, we compute the moments of the Hermitian Jacobi process. After a careful arrangement of the terms and the evaluation of the determinant of an `almost upper-triangular' matrix, we end up with a moment formula which is considerably simpler than the one derived in \cite{Del-Dem}. As an application, we propose the Hermitian Jacobi process as a dynamical model for optical fibers MIMO channels and compute its Shannon capacity for small enough power at the transmitter. Moreover, when the size of the Hermitian Jacobi process is larger than …
A lower bound on the capacity of the split-step Fourier channel is derived. The channel under study is a concatenation of smaller segments, within which three operations are performed on the signal, namely, nonlinearity, linearity, and noise addition. Simulation results indicate that for a fixed number of segments, our lower bound saturates in the high-power regime and that the larger the number of segments is, the higher is the saturation point. We also obtain an alternative lower bound, which is less tight but has a simple closed-form expression. This bound allows us to conclude that the sat…
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