On the Robustness of Deep Learning-aided Symbol Detectors to Varying Conditions and Imperfect Channel Knowledge

Recently, a data-driven Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm tailored to channels with intersymbol interference has been introduced. This so-called BCJRNet algorithm utilizes neural networks to calculate channel likelihoods. BCJRNet has demonstrated resilience against inaccurate channel tap estimations when applied to a time-invariant channel with ideal exponential decay profiles. However, its generalization capabilities for practically-relevant time-varying channels, where the receiver can only access incorrect channel parameters, remain largely unexplored. The primary contribution of this paper is to expand upon the results from existing literature to encompass a variety of imperfect channel knowledge cases that appear in real-world transmissions. Our findings demonstrate that BCJRNet significantly outperforms the conventional BCJR algorithm for stationary transmission scenarios when learning from noisy channel data and with imperfect channel decay profiles. However, this advantage is shown to diminish when the operating channel is also rapidly time-varying. Our results also show the importance of memory assumptions for conventional BCJR and BCJRNet. An underestimation of the memory largely degrades the performance of both BCJR and BCJRNet, especially in a slow-decaying channel. To mimic a situation closer to a practical scenario, we also combined channel tap uncertainty with imperfect channel memory knowledge. Somewhat surprisingly, our results revealed improved performance when employing the conventional BCJR with an underestimated memory assumption. BCJRNet, on the other hand, showed a consistent performance improvement as the level of accurate memory knowledge increased.

On the Performance of Multidimensional Constellation Shaping for Linear and Nonlinear Optical Fiber Channel

Multidimensional constellation shaping of up to 32 dimensions with different spectral efficiencies are compared through AWGN and fiber-optic simulations. The results show that no constellation is universal and the balance of required and effective SNRs should be jointly considered for the specific optical transmission scenario.

Low-Complexity Soft Decision Detection for Combating DFE Burst Errors in IM/DD Links

The deployment of non-binary pulse amplitude modulation (PAM) and soft decision (SD)-forward error correction (FEC) in future intensity-modulation (IM)/direct-detection (DD) links is inevitable. However, high-speed IM/DD links suffer from inter-symbol interference (ISI) due to bandwidth-limited hardware. Traditional approaches to mitigate the effects of ISI are filters and trellis-based algorithms targeting symbol-wise maximum a posteriori (MAP) detection. The former approach includes decision-feedback equalizer (DFE), and the latter includes Max-Log-MAP (MLM) and soft-output Viterbi algorithm (SOVA). Although DFE is easy to implement, it introduces error propagation. Such burst errors distort the log-likelihood ratios (LLRs) required by SD-FEC, causing performance degradation. On the other hand, MLM and SOVA provide near-optimum performance, but their complexity is very high for high-order PAM. In this paper, we consider a one-tap partial response channel model, which is relevant for high-speed IM/DD links. We propose to combine DFE with either MLM or SOVA in a low-complexity architecture. The key idea is to allow MLM or SOVA to detect only 3 typical DFE symbol errors, and use the detected error information to generate LLRs in a modified demapper. The proposed structure enables a tradeoff between complexity and performance: (i) the complexity of MLM or SOVA is reduced and (ii) the decoding penalty due to error propagation is mitigated. Compared to SOVA detection, the proposed scheme can achieve a significant complexity reduction of up to 94% for PAM-$8$ transmission. Simulation and experimental results show that the resulting SNR loss is roughly 0.3 to 0.4 dB for PAM-4, and becomes marginal 0.18 dB for PAM-8.

Integrated Sensing and Communications with MIMO-OTFS

Orthogonal time frequency space (OTFS) is a promising alternative to orthogonal frequency division multiplexing (OFDM) for high-mobility communications. We propose a novel multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system based on OTFS modulation. We begin by deriving new sensing and communication signal models for the proposed MIMO-OTFS ISAC system that explicitly capture inter-symbol interference (ISI) and inter-carrier interference (ICI) effects. We then develop a generalized likelihood ratio test (GLRT) based multi-target detection and delay-Doppler-angle estimation algorithm for MIMO-OTFS radar sensing that can simultaneously mitigate and exploit ISI/ICI effects, to prevent target masking and surpass standard unambiguous detection limits in range/velocity. Moreover, considering two operational modes (search/track), we propose an adaptive MIMO-OTFS ISAC transmission strategy. For the search mode, we introduce the concept of delay-Doppler (DD) multiplexing, enabling omnidirectional probing of the environment and large virtual array at the OTFS radar receiver. For the track mode, we pursue a directional transmission approach and design an OTFS ISAC optimization algorithm in spatial and DD domains, seeking the optimal trade-off between radar signal-to-noise ratio (SNR) and achievable rate. Simulation results verify the effectiveness of the proposed sensing algorithm and reveal valuable insights into OTFS ISAC trade-offs under varying communication channel characteristics.

Analytical Model of Nonlinear Fiber Propagation for General Dual-Polarization Four-Dimensional Modulation Format

Coherent dual-polarization (DP) optical transmission systems encode information on the four available degrees of freedom of an optical field: the two polarization states, each with two quadrature components. Such systems naturally operate based on a four-dimensional (4D) signal space. Having a general analytical model to accurately estimate nonlinear interference (NLI) is key to analyze such transmission systems as well as to study how different DP-4D formats are affected by NLI. However, the available models in the literature are not completely general. They either do not apply to the entire DP-4D formats or do not consider all the NLI contributions. In this paper we develop a model that applies to the entire class of DP-4D modulation formats. Our model takes self-channel interference, cross-channel interference and multiple-channel interference effects into account. As an application of our model, we further study the effects of signal-noise interactions in long-haul transmission via the proposed model. When compared to previous results in the literature, our model is more accurate at predicting the contribution of NLI for both low and high dispersion fibers in single- and multi-channel transmission systems. For the NLI, we report an average gap from split step Fourier simulation results below 0.15dB. The simulation results further show that by considering signal-noise interactions, the proposed model in long-haul transmission improves the NLI power accuracy prediction by up to 8.5%.

Data-driven Enhancement of the Time-domain First-order Regular Perturbation Model

A normalized batch gradient descent optimizer is proposed to improve the first-order regular perturbation coefficients of the Manakov equation, often referred to as kernels. The optimization is based on the linear parameterization offered by the first-order regular perturbation and targets enhanced low-complexity models for the fiber channel. We demonstrate that the optimized model outperforms the analytical counterpart where the kernels are numerically evaluated via their integral form. The enhanced model provides the same accuracy with a reduced number of kernels while operating over an extended power range covering both the nonlinear and highly nonlinear regimes. A $6-7$~dB gain, depending on the metric used, is obtained with respect to the conventional first-order regular perturbation.

Band-ESS: Streaming Enumerative Coding with Applications to Probabilistic Shaping

Probabilistic amplitude shaping (PAS) is on track to become the de facto coded modulation standard for communication systems aiming to operate close to channel capacity at high transmission rates. The essential component of PAS that breeds this widespread interest is the amplitude shaping block, through which the channel input distribution is controlled. This block is responsible for converting bit strings into amplitude sequences with certain properties, e.g., fixed composition, limited energy, limited energy variation, etc. Recently, band-trellis enumerative sphere shaping (B-ESS) was introduced as an amplitude shaping technique that achieves limited energy variations which is useful in optical communication scenarios. B-ESS operates based on a trellis diagram in which sequences with high energy variations are pruned. In this work, we study the implementation of B-ESS. We first show that thanks to the trellis structure obtained by this pruning, B-ESS can be implemented with very low storage complexity. The trellis computation is shown to be reduced to a set of recursive multiplications with a scalar factor. Then we show that this scalar factor can be adjusted such that the trellis computation is further simplified and realized with only binary shifts. This shift-based B-ESS (1) can be implemented for arbitrarily long blocklengths without incurring an increase in complexity, and (2) can operate in a streaming mode similar to convolutional coding.

Temporal Properties of Enumerative Shaping: Autocorrelation and Energy Dispersion Index

We study the effective SNR behavior of various enumerative amplitude shaping algorithms. We show that their relative behavior can be explained via the temporal autocorrelation function or via the energy dispersion index.

On Optimum Enumerative Sphere Shaping Blocklength at Different Symbol Rates for the Nonlinear Fiber Channel

We show that a 0.9 dB SNR improvement can be obtained via short-blocklength enumerative sphere shaping for single-span transmission at 56 GBd. This gain vanishes for higher symbol rates and a larger number of spans.

Log-CCDM: Distribution Matching via Multiplication-free Arithmetic Coding

Recent years have seen renewed attention to arithmetic coding (AC). This is thanks to the use of AC for distribution matching (DM) to control the channel input distribution in probabilistic amplitude shaping. There are two main problems inherent to AC: (1) its required arithmetic precision grows linearly with the input length, and (2) high-precision multiplications and divisions are required. Here, we introduce a multiplication-free AC-based DM technique via three lookup tables (LUTs) which solves both problems above. These LUTs are used to approximate the high-precision multiplications and divisions by additions and subtractions. The required precision of our approach is shown to grow logarithmically with the input length. We prove that this approximate technique maintains the invertibility of DM. At an input length of 1024 symbols, the proposed technique achieves negligible rate loss ($<0.01$ bit/sym) against the full-precision DM, while requiring less than 4 kilobytes of storage.