We developed machine learning approaches for data-driven trellis-based soft
symbol detection in coded transmission over intersymbol interference (ISI)
channels in presence of bursty impulsive noise (IN), for example encountered in
wireless digital broadcasting systems and vehicular communications. This
enabled us to obtain optimized detectors based on the Bahl-Cocke-Jelinek-Raviv
(BCJR) algorithm while circumventing the use of full channel state information
(CSI) for computing likelihoods and trellis state transition probabilities.
First, we extended the application of the neural network (NN)-aided BCJR,
recently proposed for ISI channels with additive white Gaussian noise (AWGN).
Although suitable for estimating likelihoods via labeling of transmission
sequences, the BCJR-NN method does not provide a framework for learning the
trellis state transitions. In addition to detection over the joint ISI and IN
states we also focused on another scenario where trellis transitions are not
trivial: detection for the ISI channel with AWGN with inaccurate knowledge of
the channel memory at the receiver. Without access to the accurate state
transition matrix, the BCJR- NN performance significantly degrades in both
settings. To this end, we devised an alternative approach for data-driven BCJR
detection based on the unsupervised learning of a hidden Markov model (HMM).
The BCJR-HMM allowed us to optimize both the likelihood function and the state
transition matrix without labeling. Moreover, we demonstrated the viability of
a hybrid NN and HMM BCJR detection where NN is used for learning the
likelihoods, while the state transitions are optimized via HMM. While reducing
the required prior channel knowledge, the examined data-driven detectors with
learned trellis state transitions achieve bit error rates close to the optimal
full CSI-based BCJR, significantly outperforming detection with inaccurate CSI.

我们开发了机器学习方法，用于在存在突发脉冲噪声的信道中，通过状态转移矩阵的学习，实现数据驱动的栅格软符号检测，从而实现在无线数字广播系统和车载通信中的编码传输。

基于数据驱动的符号检测技术在突发冲击噪声下的互殴干扰信道中的应用

Data-Driven Symbol Detection for Intersymbol Interference Channels with  Bursty Impulsive Noise

In the presence of impulsive noise, and missing observations, accurate online
prediction of time-varying graph signals poses a crucial challenge in numerous
application domains. We propose the Adaptive Least Mean $p^{th}$ Power Graph
Neural Networks (LMP-GNN), a universal framework combining adaptive filter and
graph neural network for online graph signal estimation. LMP-GNN retains the
advantage of adaptive filtering in handling noise and missing observations as
well as the online update capability. The incorporated graph neural network
within the LMP-GNN can train and update filter parameters online instead of
predefined filter parameters in previous methods, outputting more accurate
prediction results. The adaptive update scheme of the LMP-GNN follows the
solution of a $l_p$-norm optimization, rooting to the minimum dispersion
criterion, and yields robust estimation results for time-varying graph signals
under impulsive noise. A special case of LMP-GNN named the Sign-GNN is also
provided and analyzed, Experiment results on two real-world datasets of
temperature graph and traffic graph under four different noise distributions
prove the effectiveness and robustness of our proposed LMP-GNN.

提出了自适应最小均值 $p^{th}$ 功率图神经网络 (LMP-GNN)，结合了自适应滤波和图神经网络的通用框架，用于在线图信号估计。LMP-GNN 在处理噪声和缺失观测方面保持自适应滤波的优势，并具有在线更新能力。在噪声冲击下，通过 $l_p$ 范数优化的自适应更新方案，LMP-GNN 实现了时间变化图信号的鲁棒估计结果。两个真实世界数据集（温度图和交通图）上的实验证明了提出的 LMP-GNN 方法的有效性和稳健性。

自适应最小均值 p 次幂图神经网络

Adaptive Least Mean pth Power Graph Neural Networks

Compressed sensing (CS) is an important theory for sub-Nyquist sampling and
recovery of compressible data. Recently, it has been extended by Pham and
Venkatesh to cope with the case where corruption to the CS data is modeled as
impulsive noise. The new formulation, termed as robust CS, combines robust
statistics and CS into a single framework to suppress outliers in the CS
recovery. To solve the newly formulated robust CS problem, Pham and Venkatesh
suggested a scheme that iteratively solves a number of CS problems, the
solutions from which converge to the true robust compressed sensing solution.
However, this scheme is rather inefficient as it has to use existing CS solvers
as a proxy. To overcome limitation with the original robust CS algorithm, we
propose to solve the robust CS problem directly in this paper and drive more
computationally efficient algorithms by following latest advances in
large-scale convex optimization for non-smooth regularization. Furthermore, we
also extend the robust CS formulation to various settings, including additional
affine constraints, $\ell_1$-norm loss function, mixed-norm regularization, and
multi-tasking, so as to further improve robust CS. We also derive simple but
effective algorithms to solve these extensions. We demonstrate that the new
algorithms provide much better computational advantage over the original robust
CS formulation, and effectively solve more sophisticated extensions where the
original methods simply cannot. We demonstrate the usefulness of the extensions
on several CS imaging tasks.

本研究提出了一种基于大规模凸优化的非光滑正则化算法，直接解决了压缩感知 (corrupted compressive sensing) 问题，同时提出了针对各种情况的鲁棒压缩感知算法和简单有效的求解扩展问题的算法，在计算效率和求解难度等方面得到了显著提高，同时在几个压缩感知成像任务上取得了良好的效果。