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Telling Neural Network What We Know: Weight Configuration for RNN and Its Application to NextG Real-Time Neural Receiver

Ummay Sumaya Khan, Lizhong Zheng, Lingjia Liu

arXiv:2610.31210v1eess.SP

TL;DR

Reliable MIMO-OFDM detection is challenged by multipath fading and imperfect channel knowledge, while principled configuration of skip-augmented reservoirs for estimated-statistics NLoS channels remains unexplored. The paper introduces skip-RNN, configuring its fixed IIR–FIR basis from channel statistics and adapting a linear readout online. Across both channel models and modulation orders, the configured receiver achieves the lowest BER among evaluated receivers.

  • Problem

    Reliable symbol detection is challenging under multipath fading and imperfect channel knowledge, and principled configuration for skip-augmented reservoirs on estimated-statistics NLoS channels remains unexplored.

    Source: §I · p. 1

  • Method

    Skip-RNN configures fixed recurrent and skip branches as IIR and FIR bases using channel statistics, then adapts a linear readout online with a statistical FIR prior.

    Source: §I · pp. 1–2

  • Results

    Across both channel models and modulation orders, configured skip-RNN achieves the lowest BER among evaluated receivers, followed by Random WESN.

    Source: C. BER Performance Comparison · p. 11

  • Takeaways & Limitations

    The consistent improvement over randomly configured reservoirs demonstrates the benefit of adapting recurrent structure to channel characteristics.

    Source: C. BER Performance Comparison · p. 11

Abstract

from arXiv · show

AI-enabled receivers offer a promising approach to adaptive physical-layer processing, but conventional neural receivers often require extensive offline training and computationally expensive backpropagation, limiting their suitability for low-latency cellular systems. Moreover, classical MIMO-OFDM receivers rely on accurate channel estimation, leading to substantial pilot overhead. This paper introduces skip-RNN, a lightweight skip-augmented recurrent neural receiver that performs online time-domain receive processing using fixed recurrent and skip branches with an adaptive linear readout. We show that the skip-RNN can be interpreted as a structured deconvolution filter whose recurrent and skip branches realize IIR and FIR basis functions, respectively. We develop a domain-knowledge informed weight-configuration framework for the skip-RNN by exploiting its structural correspondence with the target stable and causal inverse filter of mixed-phase channels. The dominant IIR structure extracted from estimated channel statistics is used to configure the recurrent dynamics, while the non-minimum-phase component is addressed through the skip branch and a statistical FIR readout prior incorporated into prior-centered regularized online readout adaptation. We further derive an approximation-error bound that characterizes the resulting configured neural-receiver representation. Simulations over standardized 3GPP channels demonstrate the effectiveness of the configured neural receiver under extremely low pilot overhead.

I. INTRODUCTION

The introduction presents skip-RNN as a channel-informed, interpretable receiver for MIMO-OFDM over mixed-phase channels, where conventional detection is challenged by imperfect channel knowledge and recurrent training is costly. It relates this design to the causal inverse-filtering problem and reports improved BER in standardized 3GPP NLoS evaluations.

I. INTRODUCTION

  • Imperfect CSI can degrade LMMSE detection, while backpropagation costs, millisecond-scale channel changes, and pilot overhead motivate efficient online adaptation and principled reservoir configuration.The stated research gap is configuration for skip-augmented reservoirs over realistic non-minimum-phase NLoS channels using estimated channel information.Source: §I · p. 1
  • Skip-RNN combines fixed recurrent dynamics and a finite received-sample window with a trainable linear readout, matching IIR and FIR components of the causal inverse filter.The recurrent branch supplies stable IIR basis functions; the skip branch supplies a finite causal FIR delay basis.Source: §I · pp. 1–2
  • Wiener–Hopf factorization and finite decision delay yield a parallel IIR–FIR representation of the stable causal inverse filter for mixed-phase channels.Its stable rational IIR modes and finite causal FIR component motivate the receiver architecture and weight configuration.Source: §I · p. 2
  • The weight-configuration framework uses estimated channel statistics to configure recurrent poles and input weights, set skip-window length, and form a statistical FIR readout prior for per-TTI adaptation.The readout uses prior-centered regularized least-squares adaptation; the paper also derives an approximation-error bound.Source: §I · p. 2
  • The configured skip-RNN improves BER over model-based LMMSE and sphere-decoding receivers using estimated CSI, and learning-based SDNet and randomly initialized WESN baselines.The evaluation uses standardized 3GPP NLoS MIMO-OFDM channel models.Source: §I · p. 2

A. General Framework for MIMO-OFDM Receive Processing

  • CP-OFDM converts within-symbol linear convolution into circular convolution after cyclic-prefix removal, while time-domain neural and frequency-domain conventional receivers address the same inverse-filtering problem.The cyclic prefix prevents inter-symbol interference in retained samples when the channel is approximately invariant over an OFDM symbol.Source: §II · p. 2, A. General Framework for MIMO-OFDM… · p. 3

B. Time-Domain Stable and Causal Equalization of Mixed-Phase Channels

The section derives a stable, causal finite-delay LMMSE inverse for mixed-phase channels and shows it has a parallel IIR–FIR form. This structure provides a target for configuring the skip-RNN branches.

Generalization and receiver configuration

  • The parallel IIR–FIR interpretation also applies beyond a particular receiver design criterion; different filters induce different poles, residues, and FIR coefficients.The skip-RNN branches are configured to approximate the target filter’s dominant IIR and FIR components.Source: B. Time-Domain Stable and Causal… · p. 3

Mixed-phase inversion

  • For mixed-phase channels, the exact stable inverse is generally noncausal, while enforcing causality on the exact inverse leads to instability.The section therefore treats a realizable receiver as an approximation or regularization of the two-sided inverse.Source: B. Time-Domain Stable and Causal… · p. 4

LMMSE target

  • The LMMSE filter is used as a noise-regularized inverse that limits amplification along weak channel modes.Its unconstrained solution is generally two-sided for a mixed-phase channel and cannot be directly implemented as a causal receiver.Source: B. Time-Domain Stable and Causal… · pp. 3–4

Causal projection and decision delay

  • Finite decision delay retains the first Δ + 1 coefficients of the stable left-sided component as a causal FIR polynomial, with increased delay preserving more of the unconstrained solution.Increasing Δ therefore trades increased detection latency for retaining more of that solution.Source: B. Time-Domain Stable and Causal… · p. 4

Finite-delay IIR–FIR representation

  • The causal LMMSE inverse admits a stable IIR component in parallel with a finite causal FIR component.The IIR component is a stable rational factor; the FIR component arises from the finite-delay causal projection.Source: B. Time-Domain Stable and Causal… · pp. 4–5

III. ONLINE REAL-TIME NEURAL RECEIVER FOR MIXED-PHASE CHANNELS

This section develops the online skip-RNN receiver for mixed-phase channels and explains how its branches realize stable causal IIR–FIR filtering.

III. ONLINE REAL-TIME NEURAL RECEIVER FOR MIXED-PHASE CHANNELS

  • The section develops an online skip-RNN receiver for stable causal processing over mixed-phase channels.It proceeds step by step through how the recurrent and skip branches realize the established mixed IIR–FIR structure.Source: §III · p. 5
  • The section connects the skip-RNN branches to the mixed IIR–FIR structure established for stable causal processing.The stated scope is mixed-phase channels.Source: §III · p. 5
  • The receiver architecture is presented as the Skip-RNN Neural Receiver.Fig. 2 is identified as its architecture.Source: Figure 2 · p. 5

A. Skip-Augmented Recurrent Receiver

The skip-RNN combines a recurrent state with a finite received-sample window and an online-adapted linear readout. Its two branches yield a causal MIMO deconvolution response with infinite and finite duration components.

A. Skip-Augmented Recurrent Receiver

  • The skip window stacks the current received sample with its Nw − 1 predecessors alongside the recurrent state.The receiver processes time-domain samples within a TTI.Source: A. Skip-Augmented Recurrent Receiver · p. 5
  • The recurrent and skip features are concatenated for a linear readout, with recurrent and input weights fixed and the readout adapted online from pilot observations.Setting Nw = 0 removes the skip branch and recovers a conventional recurrent receiver.Source: A. Skip-Augmented Recurrent Receiver · p. 5

B. Time-Domain Deconvolution Realized by the Skip-RNN

  • The skip-RNN is equivalent to a causal MIMO deconvolution filter: the recurrent branch contributes an infinite-duration response and the skip branch a finite response over the first Nw delays.Both branches operate directly on delayed received samples.Source: B. Time-Domain Deconvolution Realized… · p. 6

C. IIR–FIR Filter Representation in the z-Domain

In the z-domain, the skip-RNN exposes recurrent IIR modes and a finite skip FIR delay basis. Together, these branches realize the parallel IIR–FIR structure of the causal stable inverse for mixed-phase channels.

C. IIR–FIR Filter Representation in the z-Domain

  • The z-domain representation makes the recurrent branch’s pole structure and the skip branch’s finite-delay structure explicit.The section introduces this representation after establishing the receiver’s time-domain relation.Source: C. IIR–FIR Filter Representation in… · p. 6

1) Recurrent IIR basis:

  • In modal coordinates, the recurrent branch consists of Nn independent first-order IIR modes with poles λj.The modal transformation reveals these basis functions while leaving the input–output transfer function unchanged.Source: 1) Recurrent IIR basis · p. 6

2) Skip FIR basis:

3) Combined IIR–FIR representation:

  • The combined skip-RNN spans a structured IIR function space through its recurrent branch and a finite-dimensional FIR delay space through its skip branch.This matches the parallel IIR–FIR structure of the causal stable inversion for mixed-phase channels.Source: 3) Combined IIR–FIR representation · p. 7

D. Geometric Interpretation and Weight Configuration Problem Formulation

The skip-RNN’s fixed recurrent and skip features span an IIR–FIR function space, and readout training projects the target causal LMMSE filter onto that space. Weight configuration is therefore a function-space design problem: choose a basis aligned with the channel-inverse ensemble.

D. Geometric Interpretation and Weight Configuration Problem Formulation

  • Wres and Win determine the recurrent IIR basis, while Nw sets the dimension of the FIR basis.The fixed configuration determines the function space available to online readout adaptation.Source: D. Geometric Interpretation and Weight… · p. 7
  • The readout projects the LMMSE inverse filter onto the joint IIR–FIR space spanned by the recurrent and skip features.Under the received-signal metric over the pilot block, output-weight training selects the linear combination that best approximates the target.Source: Figure 4 · p. 7, D. Geometric Interpretation and Weight… · p. 7
  • Even an optimal readout cannot represent target-filter components outside the fixed skip-RNN space, leaving a configuration-dependent representation error.The readout changes only the linear combination of basis functions, not the space itself.Source: D. Geometric Interpretation and Weight… · p. 7
  • Random reservoir poles lack channel-inverse knowledge, so the resulting representation error varies across initializations and channels.Readout training cannot compensate for a poor draw because it cannot leave the fixed subspace.Source: D. Geometric Interpretation and Weight… · p. 7
  • Because the offline configuration must serve different channel realizations, it targets expected representation error over the channel ensemble.Estimated channel realizations are used to infer the dominant target-function structure because the true channel distribution is unavailable.Source: D. Geometric Interpretation and Weight… · pp. 7–8

IV. CHANNEL-INFORMED WEIGHT CONFIGURATION OF SKIP-RNN

The configuration method aligns a fixed skip-RNN basis with channel-informed causal LMMSE inverse-filter structure. Its empirical approximation bound separates recurrent-basis error from finite skip-window error.

IV. CHANNEL-INFORMED WEIGHT CONFIGURATION OF SKIP-RNN

  • The configured basis combines a channel-informed recurrent IIR structure and an FIR skip window, while a statistical FIR prior improves readout estimation with limited pilots without changing the function space.The prior is incorporated through prior-centered regularized online adaptation.Source: §IV · p. 8

A. Low-Dimensional Approximation of the IIR Component

  • The recurrent basis approximates dominant low-dimensional IIR modes with stable rational functions, assigning K first-order terms to each of M retained modes for Nn = MK configured recurrent weights.The skip branch supplies the finite causal delay basis, while the recurrent branch captures the realization-dependent IIR component.Source: A. Low-Dimensional Approximation of… · p. 8

B. Approximation Error Bound

  • The empirical approximation bound separates finite configured recurrent-basis error from skip-window truncation error, distinct from finite-pilot readout estimation error.The skip branch represents the first Nw FIR coefficients exactly; if Nw ≥ D∆, the FIR component lies entirely in the skip space.Source: B. Approximation Error Bound · p. 9

C. Online Readout Adaptation with Prior FIR weights

After offline configuration, recurrent weights remain fixed, and each TTI adapts only the readout using available reference symbols. The FIR prior centers regularization on the ensemble-expected correction for non-minimum-phase channels.

C. Online Readout Adaptation with Prior FIR weights

  • The FIR prior centers regularization on the statistically expected FIR correction for non-minimum-phase channels, while current pilots drive the per-TTI readout fit.The prior does not change the FIR basis itself; it supplies an informed initialization and regularization center.Source: C. Online Readout Adaptation with… · p. 9
  • After offline configuration, Wres and Win remain fixed, and each TTI adapts only the readout from available reference symbols.The readout combines recurrent and FIR skip features.Source: C. Online Readout Adaptation with… · p. 9

D. Complexity Analysis

Weight configuration has an offline cost dominated in the worst case by eigen decomposition, which can be amortized across runtime iterations. After configuration, training and inference complexity match those of a randomly initialized model.

D. Complexity Analysis

  • The offline configuration cost is dominated in the worst case by eigen decomposition and is amortized across runtime iterations when reused.The per-iteration overhead is FLOPscfg/Nrun and becomes negligible for long runs.Source: D. Complexity Analysis · p. 10
  • After configuration, training and inference complexity remain identical to those of a randomly initialized model.Training comprises reservoir-state generation and readout estimation; testing comprises state updates and output computation.Source: D. Complexity Analysis · p. 10

V. PERFORMANCE EVALUATION

The configured skip-RNN achieves the lowest BER across the evaluated 3GPP NLoS channels and modulation orders, with the strongest advantage over a randomly initialized reservoir. The evaluation compares it with model-based and learning-based receivers under a pilot-scarce setup.

A. Simulation Setup

  • The evaluation uses standardized CDL-B and CDL-C NLoS channels, 16 RBs, and a 4-by-4 MIMO-OFDM system at 30 km/h.The neural receiver uses a nonorthogonal pilot pattern; its configuration draws on 20 estimated channel slots, with 32 recurrent neurons and a window length of 32.Source: A. Simulation Setup · p. 10

B. Baseline Receive Processing Approach

  • The configured receiver is compared with LMMSE and sphere decoding using estimated CSI, SDNet, and a randomly initialized WESN.SDNet uses offline neural-network optimization and explicit channel estimates, whereas Random WESN performs direct time-domain detection without explicit channel estimation.Source: B. Baseline Receive Processing Approach · p. 11

C. BER Performance Comparison

  • Across CDL-B and CDL-C and both modulation orders, configured skip-RNN achieves the lowest BER, followed by Random WESN.The advantage over Random WESN narrows at low Eb/N0, where noisy channel information makes weight configuration less reliable; at sufficiently high SNR, SD can outperform skip-RNN.Source: C. BER Performance Comparison · pp. 11–12, Figure 6 · p. 11, Figure 7 · p. 11

VI. CONCLUSION

  • The conclusion characterizes skip-RNN as a causal deconvolution filter whose recurrent and skip branches provide complementary IIR and FIR basis functions.Historical estimated channel statistics configure the recurrent dynamics, FIR memory, and statistical readout prior for regularized online adaptation.Source: §VI · p. 12

APPENDIX A PROOF OF PROPOSITION 1

The proof establishes that the causal LMMSE inverse is stable and rational, then separates it into finite and strictly proper components. Under a distinct-pole assumption, the latter admits a stable partial-fraction form.

APPENDIX A PROOF OF PROPOSITION 1

  • The causal LMMSE inverse is a causal, stable, rational transfer function under the stated factorization and rationality assumptions.Its finite poles are those of the inverse spectral factor that are not cancelled by zeros of the finite-delay factor.Source: Appendix A · p. 12
  • The inverse transfer function is split into a finite polynomial part and a strictly proper rational part.The polynomial part is finite-degree in z^-1.Source: Appendix A · p. 12
  • With distinct poles, the strictly proper component has a partial-fraction expansion using stable modes with |p_m| < 1.The proof then identifies the resulting component as an FIR transfer function.Source: Appendix A · p. 12

APPENDIX B PROOF OF PROPOSITION 2

The proof treats the causal LMMSE inverse as a parallel decomposition and the skip-RNN as corresponding recurrent and skip branches. It combines branchwise approximation errors to obtain an averaged bound over observed channel realizations.

APPENDIX B PROOF OF PROPOSITION 2

  • For each channel realization, the causal LMMSE inverse admits a parallel decomposition.The proof compares this target with the skip-RNN realization.Source: Appendix B · p. 12
  • The recurrent and skip readout blocks control separate branch components, allowing their coefficients to be selected independently.The proof uses the branchwise minimizers together as a feasible joint readout.Source: Appendix B · p. 12
  • The proof squares the joint error, averages over observed channel realizations, and bounds the cross term using Cauchy–Schwarz.This combines with the preceding branchwise approximation result to establish the bound.Source: Appendix B · pp. 12–13
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