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

TL;DR

This work assesses how a neural-network–assisted MAP detector, BCJRNet, generalizes beyond ideal CSI in finite-memory ISI AWGN channels. By comparing BCJRNet to conventional BCJR across six imperfect CSI scenarios and both stationary and rapidly time-varying channels, it shows BCJRNet often outperforms in stationary settings but its gains diminish under fast channel variation; memory accuracy emerges as a key factor for both detectors. The data-driven approach reliably learns likelihoods from noisy training data and can handle tap uncertainties, yet sharp temporal changes challenge its generalization. Practically, BCJRNet offers a robust option for channels with stable memory and imperfect CSI, while traditional BCJR remains competitive when channel dynamics invalidate learned likelihoods; the study highlights the importance of memory modeling in detector design for real-world ISI channels.

Abstract

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.

Figures (3)

• Figure 1: Schematic diagrams (10 realizations) for the six different scenarios listed in Table \ref{['tab:exp']}. The top row shows the channel taps for the simulation of the transmission channels, while the bottom row shows the estimated/training channels.
• Figure 2: Symbol error rate (for channels operated with an ideal exponential decay profile) as a function of four different exponential decay constants $\gamma=\{0.5, 1, 1.5, 2\}$ for the conventional BCJR and BCJRNet detectors. Case 1 -- inaccurate knowledge ($\hat{L}$) of the channel memory ($L$). Case 2 -- inaccurate knowledge ($\hat{\gamma}$) of the channel parameter ($\gamma$). Case 3 -- uncertainty/deviation in the estimation/training, in terms of error variance $\sigma_l^2=\{0.01, 0.05, 0.10\}$, of the channel taps ($h_l$).
• Figure 3: Symbol error rate (for channels operated with rapidly time-varying channel taps with variances $\sigma_l^2=\{0.01, 0.05, 0.10\}$ for Case 4 and 5, and $\sigma_l^2=\{0.05\}$ for Case 6) as a function of four different exponential decay constants $\gamma=\{0.5, 1, 1.5, 2\}$ for the conventional BCJR and BCJRNet detectors. Case 4 -- ideal exponential decay estimated/training channel. Case 5 -- rapidly time-varying estimated/training channel (with identical variances as in the transmission channel). Case 6 -- rapidly time-varying estimated/training channel ($\sigma_l^2=0.05$) as well as inaccurate knowledge ($\hat{L}$) of the channel memory ($L$).