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X-RACE: XAI-assisted Recurrent neural network Attribution for Channel Estimation

Abdul Karim Gizzini, Yahia Medjahdi

arXiv:2609.11211v1eess.SPcs.AI

TL;DR

LSTMs capture temporal dependencies useful for channel estimation in high-mobility vehicular environments, but their hidden-unit allocation is opaque. X-RACE jointly attributes inputs and internal units and adds temporal metrics; simulations report at least 44.1% lower inference complexity while improving BER.

  • Problem

    In doubly-selective channels, LSTMs model temporal dependencies for channel estimation, but their hidden-unit allocation is opaque.

    Source: §I · p. 1, 4) Hidden State and Output Generation · p. 2

  • Method

    X-RACE jointly attributes input subcarriers and internal hidden units with a one-shot strategy and uses temporal metrics to assess LSTM learning dynamics and memory convergence.

    Source: §I · p. 1

  • Results

    At least 44.1% lower inference complexity accompanies improved BER performance with X-RACE.

    Source: §V · p. 5

  • Takeaways & Limitations

    X-RACE offers a superior performance-complexity-interpretability trade-off over classical XAI for LSTM channel estimation in doubly-selective channels.

    Source: §V · p. 5

Abstract

from arXiv · show

Deep learning models, notably Long Short-Term Memory (LSTM), have demonstrated promising performance in channel estimation for high-mobility vehicular environments. However, their black-box nature and architectural overhead limit trustworthiness and efficiency. Classical explainable AI (XAI) methods rely on costly iterative processes, offering only input-level filtering without addressing architectural fine-tuning. To overcome these limitations, this paper proposes the XAI-assisted Recurrent neural network Attribution for Channel Estimation (X-RACE) framework. X-RACE uses a low-complexity, one-shot dual-optimization strategy to simultaneously evaluate and prune irrelevant input subcarriers and internal hidden units. Furthermore, we propose novel temporal XAI metrics: Saturation Time, Importance Drift, and Relevance Contrast to characterize the LSTM's learning dynamics and memory convergence. Extensive simulations demonstrate that X-RACE reduces inference complexity by at least 44.1% while improving or preserving Bit Error Rate (BER) performance, outperforming classical XAI schemes.

I. INTRODUCTION

X-RACE jointly attributes subcarriers and hidden units in recurrent channel estimators, addressing LSTM opacity and overhead alongside limitations of classical XAI. The paper introduces temporal metrics to characterize LSTM learning dynamics and memory convergence.

I. INTRODUCTION

  • LSTMs track long-term temporal dependencies for high-mobility channel estimation, but opacity and excessive hidden units create trustworthiness and computational-overhead concerns.Classical XAI methods offer input-level filtering but are iterative and do not prune the LSTM architecture.Source: §I · p. 1
  • X-RACE uses one-shot dual optimization to identify relevant subcarriers and hidden units by perturbing a pre-trained LSTM’s inputs and internal memory state.The framework also introduces temporal XAI metrics to evaluate convergence and relevance stability.Source: §I · p. 1
  • Sliding-window XAI metrics measure the LSTM’s learning dynamics and memory convergence.The paper names Saturation Time, Importance Drift, and Relevance Contrast as its temporal metrics.Source: §I · p. 1
  • X-RACE substantially reduces computational complexity while preserving BER performance and outperforming classical XAI schemes, according to the reported simulations.The introduction reports no specific reduction value.Source: §I · p. 1

II. LSTM-BASED CHANNEL ESTIMATION

  • In OFDM channel estimation, LSTM recurrent states track Doppler impact over time while the input feature vector captures spectral snapshots.The received-symbol model includes additive white Gaussian noise and Doppler-induced inter-carrier interference.Source: §II · pp. 1–2

1) Long-Term Memory Gating:

The LSTM’s forget gate scales historical memory, while its input gate controls updates from the current channel estimate and candidate cell state.

1) Long-Term Memory Gating:

  • The forget gate uses a sigmoid scaling vector to selectively discard irrelevant historical components from long-term memory.Its input weights, recurrent weights, and bias are Wf, Uf, and bf, respectively.Source: 1) Long-Term Memory Gating · p. 2

2) Current Input Gating and Candidate Generation:

  • The input gate sets the update magnitude for each memory coordinate, while a tanh candidate cell state models potential adjustments.The input and candidate gates have separate input weights, recurrent weights, and biases.Source: 2) Current Input Gating and Candidate… · p. 2

3) Long-Term Cell State Synchronization:

The LSTM synchronizes past and present information in its cell state, then generates a hidden state for channel tracking and a final channel estimate.

3) Long-Term Cell State Synchronization:

4) Hidden State and Output Generation:

  • The output gate filters synchronized memory into an updated hidden state for instantaneous tracking, and an FNN then produces the channel estimate despite opacity in the dense parameter interactions.The opacity motivates joint filtering of inputs and hidden units without altering pre-trained model performance.Source: 4) Hidden State and Output Generation · p. 2

III. PROPOSED X-RACE FRAMEWORK

X-RACE evaluates a pre-trained LSTM channel estimator using an interpretability LSTM that generates time-varying perturbation masks for inputs and internal memory.

III. PROPOSED X-RACE FRAMEWORK

  • X-RACE evaluates the time-varying sensitivity of a pre-trained LSTM channel estimator U, parameterized by hidden-state dimension S.Source: §III · p. 2

1) Joint Noise Mask Generation:

  • An interpretability LSTM N tracks sequential channel inputs and generates time-varying, subcarrier-specific perturbation masks for inputs and internal memory.The mask elements are bounded to [0, 1] by a sigmoid activation.Source: 1) Joint Noise Mask Generation · p. 2
  • Standard-normal weight-noise vectors are added to the conventionally estimated channel and cell state after mask generation.Source: 1) Joint Noise Mask Generation · p. 2

2) Utility Model Tracking with Perturbed States:

X-RACE perturbs a pretrained LSTM’s inputs and cell memory together to assess their relevance for channel tracking. Its joint objective balances tracking accuracy with attribution, while selecting pruning settings subject to a BER constraint.

2) Utility Model Tracking with Perturbed States:

3) Customized Joint Optimization Loss Function:

  • The customized objective balances the pretrained estimator’s tracking loss with an attribution objective that pushes noise toward unity for irrelevant components.The objective uses weighting hyperparameters λ1 and λ2.Source: 3) Customized Joint Optimization Loss… · pp. 2–3
  • The optimization minimizes channel-estimation MSE while selecting input-relevance and pruning thresholds under a constraint that pruned-model average BER does not exceed the full baseline’s.The threshold and pruning-percentile choices are searched over defined sets.Source: 3) Customized Joint Optimization Loss… · p. 3

4) Proposed XAI-Assisted Temporal Metrics:

The proposed temporal metrics characterize LSTM memory adaptation through convergence timing, the magnitude of adaptation, and the steady-state difference between pilot and data relevance.

4) Proposed XAI-Assisted Temporal Metrics:

  • Saturation Time is the earliest index at which noise updates stabilize over a window; a moving average smooths the noise sequence before detection.The local sensitivity is dynamically scaled by each subcarrier’s temporal range to improve identification robustness.Source: 4) Proposed XAI-Assisted Temporal… · p. 3
  • Importance Drift measures the mean absolute displacement in induced noise from the initial time index to Saturation Time for data and pilot subcarriers.Source: 4) Proposed XAI-Assisted Temporal… · p. 3
  • Relevance Contrast measures the steady-state discriminative trust gap between data and pilot subcarriers.Figure 2 presents pilot and data averaged noise-weight trajectories annotated with the proposed metrics.Source: 4) Proposed XAI-Assisted Temporal… · p. 3, Figure 2 · p. 4

IV. SIMULATION RESULTS

The simulations evaluate X-RACE with a DPA-LSTM-NN estimator against input downsampling, SHAP, and LIME across specified vehicular channel conditions and analysis criteria.

IV. SIMULATION RESULTS

  • The DPA-LSTM-NN estimator is evaluated against uniform input downsampling, SHAP, and LIME.Source: §IV · p. 4
  • The setup uses IEEE 802.11p parameters and high-mobility VTV-EX low-frequency-selective and VTV-SDWW high-frequency-selective channel scenarios at Fd = 1000 Hz.Source: §IV · p. 4
  • Training uses 105 frames with an 80%/20% train-test split; the analysis covers learning dynamics, frequency selectivity, modulation order, and computational complexity.The Adam optimizer runs for 500 epochs with batch size 128; the temporal metrics use L = 3 and W = 5 symbols.Source: §IV · p. 4

A. LSTM Learning Dynamics: Time Selectivity Analysis

The temporal metrics show that LSTM pilot-versus-data behavior varies with Doppler and modulation: high Doppler increases pilot reliance and adaptation, while low-Doppler QPSK shows similar convergence.

A. LSTM Learning Dynamics: Time Selectivity Analysis

  • In the LF scenario, Figure 2 evaluates Tsat, ¯DΦ, and ∆¯R across Doppler frequencies and modulations; under low Doppler and QPSK, data and pilot subcarriers show similar convergence (Tsat = 5TOFDM).Source: A. LSTM Learning Dynamics: Time… · p. 4
  • Under 64QAM, the relevance contrast widens as the LSTM prioritizes pilots, with Tsat = 6TOFDM and ˜zi ≈ 0.19, while increasingly masking data subcarriers.Source: A. LSTM Learning Dynamics: Time… · p. 4
  • A direct BER comparison with XAI-CHEST is omitted because differing dataset shaping causes FNNs and LSTMs to undergo unequal gradient updates per epoch.Source: A. LSTM Learning Dynamics: Time… · p. 4
  • At high Doppler, channel decorrelation drives heavier pilot reliance, aggressive data filtering, increased Saturation Time, and higher Importance Drift and Relevance Contrast.The authors interpret these metrics as illustrating context-dependent LSTM adaptation.Source: A. LSTM Learning Dynamics: Time… · p. 4

B. Impact of Frequency Selectivity

Under QPSK at Fd = 1000 Hz, X-RACE’s relevance selection and BER performance adapt to frequency selectivity: it uses fewer inputs in LF and more inputs and hidden units in HF.

B. Impact of Frequency Selectivity

  • In LF, X-RACE achieves BER superiority using 5 inputs at threshold 0.3 and 37 hidden units, outperforming SHAP, LIME, and uniform downsampling.Those alternatives use larger relevant subsets without BER gains.Source: B. Impact of Frequency Selectivity · p. 4
  • X-RACE assigns pilots a relevance score of 0.9 in both LF and HF, while HF leaves fewer data subcarriers at a neutral zero score.The passage attributes the latter pattern to HF requiring more informative data subcarriers.Source: B. Impact of Frequency Selectivity · p. 4
  • In HF, X-RACE scales to 33 relevant inputs at threshold 0.1 and 42 hidden units, reflecting the greater input and model capacity needed under severe frequency selectivity.Source: B. Impact of Frequency Selectivity · p. 4

C. Impact of Modulation Order

Across modulation orders and computational-complexity analysis, X-RACE combines input and architectural attribution with BER-preserving complexity reductions in reported settings. The conclusion reports at least 44.1% lower inference complexity while improving BER.

C. Impact of Modulation Order

  • Under 64QAM, pilot-only inputs with the full LSTM architecture match the unpruned baseline, whereas architecture or double optimization degrades BER, mainly in HF.All XAI methods select pilots as the only relevant inputs; X-RACE maintains uniform, stable relevance scores while LIME and SHAP show score variance.Source: C. Impact of Modulation Order · p. 4
  • The 64QAM findings support aggressive input pruning only when the original LSTM capacity is preserved to maintain BER.Source: C. Impact of Modulation Order · p. 4

D. Computational Complexity Analysis

  • 78.5% fewer FLOPs for LF-QPSK while improving BER, and 61.5% fewer FLOPs for 64QAM while preserving BER, are reported for X-RACE versus the full baseline.The passage describes its input and memory relevance masks as derived in one pass with O(Kon + S) complexity.Source: D. Computational Complexity Analysis · p. 4, Table I · p. 5

V. CONCLUSION

  • At least 44.1% lower inference complexity while improving BER is reported for X-RACE in the conclusion.The conclusion also identifies gradient-based XAI and other RNN-based channel estimators as future work.Source: §V · p. 5
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