Turbo Receiver Design with Joint Detection and Demapping for Coded Differential BPSK in Bursty Impulsive Noise Channels

It has been recognized that the impulsive noise (IN) generated by power devices poses significant challenges to wireless receivers in practice. In this paper, we assess the achievable information rate (AIR) and the performance of practical turbo receiver designs for a well-established Markov-Middleton IN model. We utilize a commonly used commercial transmission setup consisting of a convolutional encoder, bit-level interleaver, and a differential binary phase-shift keying (DBPSK) symbol mapper. Firstly, we conduct a comprehensive assessment of the AIRs of the underlying channel model using DBPSK transmitted symbols across various channel conditions. Additionally, we introduce two robust turbo-like receiver designs. The first design features a separate IN detector and a turbo-demapper-decoder. The second design employs a joint approach, where the extrinsic information of both the detector and demapper is simultaneously updated, forming a turbo-detector-demapper-decoder structure. We show that the joint design consistently outperforms the separate design across all channel conditions, particularly in low AIR situations. However, the maximum performance gain for the channel conditions considered in this paper is merely 0.2 dB, and the joint system incurs significantly greater computational complexity, especially for a high number of turbo iterations. The performance of the two proposed turbo receiver designs is demonstrated to be close to the estimated AIR, with a performance gap dependent on the channel parameters.

Modified Baum-Welch Algorithm for Joint Blind Channel Estimation and Turbo Equalization

Blind estimation of intersymbol interference channels based on the Baum-Welch (BW) algorithm, a specific implementation of the expectation-maximization (EM) algorithm for training hidden Markov models, is robust and does not require labeled data. However, it is known for its extensive computation cost, slow convergence, and frequently converges to a local maximum. In this paper, we modified the trellis structure of the BW algorithm by associating the channel parameters with two consecutive states. This modification enables us to reduce the number of required states by half while maintaining the same performance. Moreover, to improve the convergence rate and the estimation performance, we construct a joint turbo-BW-equalization system by exploiting the extrinsic information produced by the turbo decoder to refine the BW-based estimator at each EM iteration. Our experiments demonstrate that the joint system achieves convergence in just 4 EM iterations, which is 8 iterations less than a separate system design for a signal-to-noise ratio (SNR) of 6 dB. Additionally, the joint system provides improved estimation accuracy with a mean square error (MSE) of $10^{-4}$. We also identify scenarios where a joint design is not preferable, especially when the channel is noisy (e.g., SNR=2 dB) and the turbo decoder is unable to provide reliable extrinsic information for a BW-based estimator.

Analysis of Impulsive Interference in Digital Audio Broadcasting Systems in Electric Vehicles

Recently, new types of interference in electric vehicles (EVs), such as converters switching and/or battery chargers, have been found to degrade the performance of wireless digital transmission systems. Measurements show that such an interference is characterized by impulsive behavior and is widely varying in time. This paper uses recorded data from our EV testbed to analyze the impulsive interference in the digital audio broadcasting band. Moreover, we use our analysis to obtain a corresponding interference model. In particular, we studied the temporal characteristics of the interference and confirmed that its amplitude indeed exhibits an impulsive behavior. Our results show that impulsive events span successive received signal samples and thus indicate a bursty nature. To this end, we performed a data-driven modification of a well-established model for bursty impulsive interference, the Markov-Middleton model, to produce synthetic noise realization. We investigate the optimal symbol detector design based on the proposed model and show significant performance gains compared to the conventional detector based on the additive white Gaussian noise assumption.

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

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.

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.