In-Context Learning for MIMO Turbo Receivers

Zihang Song; Matteo Zecchin; Bipin Rajendran; Petar Popovski; Osvaldo Simeone

eess.SPMay 9, 2025

In-Context Learning for MIMO Turbo Receivers

Authors: Zihang Song, Matteo Zecchin, Bipin Rajendran, Petar Popovski, Osvaldo Simeone

Organizations: The authors are with the Centre for Intelligent Information Processing Systems (CIIPS), Department of Engineering, King’s College London, London WC2R 2LS, U.K.

Abstract

Multiple-input multiple-output (MIMO) turbo receivers iteratively exchange information between a soft-input soft-output detector and a decoder. Traditional implementations rely on pilot-based channel estimates, which can be poor in the case of short pilot sequences or mismatched channel models, resulting in significant performance degradation. To address this limitation, we introduce the EXTrinsic In-Context Learning Network (EXT-ICLNet), a Transformer-based detector that takes the pilots as in-context examples and is trained to approximate the symbol extrinsic posterior distribution given the pilots, without explicit channel estimation. EXT-ICLNet is thus compatible with existing turbo receivers, as it implements a log-domain prior skip connection, ensuring that the network learns only the extrinsic information. Numerical results for a $4\times4$ MIMO system with 16-QAM and a quantized front end show that EXT-ICLNet outperforms baselines based on explicit channel state information (CSI) estimation at low-to-medium signal-to-noise ratios (SNRs), as well as expectation-propagation (EP) baselines with perfect CSI at high SNRs. The results are further validated by comparing the extrinsic information transfer (EXIT) charts of EXT-ICLNet, a neural EP baseline, and EXT-ICLNet without skip connection, demonstrating how EXT-ICLNet provides a more favorable transfer of a priori and extrinsic information.

Figures & tables

Panel of Figure 1 — Fig. 1: Block diagram of coded MIMO transmission with a quantized front end.

Panel of Figure 2 — Fig. 2: Block diagrams of a turbo receiver: (a) with a conventional soft detector assisted by estimated CSI, and (b) with an ICL-based soft detector that takes the pilots directly as input.

Panel of Figure 3 — Fig. 3: EXT-ICLNet architecture: (a) the prompt $\mathcal{P}_{i}$ and the per-stream posterior estimates $\hat{\bm{q}}_{i}^{(n)}$ ; (b) the shared Transformer backbone, stream-specific output heads, and log-domain prior skip.

Panel of Figure 4 — Fig. 4: Training data generation. For each training prompt, the task $\tau$ and the prior PMFs $\bm{p}_{t}$ are sampled independently. The symbols $\bm{x}_{t}$ are drawn from the priors, the received signals $\bm{y}_{t}$ are generated under the sampled task, and the resulting query-label pairs form the training sequence $\mathcal{P}_{\text{train}}$ .

Panel of Figure 5 — Fig. 5: Training and inference pipelines. Gray lines indicate the attention connections permitted by the corresponding attention mask.

Panel of Figure 6 — Fig. 6: Post-decoding BER at SNR $=$ 10 dB under 16-QAM, one-shot detection: (a) impact of quantization resolution $B$ at $T_{P}=32$ with all baselines using perfect CSI; (b) impact of pilot length $T_{P}$ at $B=8$ , with baselines using LS-estimated CSI (solid) and perfect CSI (dashed).

Panel of Figure 7 — Fig. 7: Post-decoding BER vs. SNR under 16-QAM, rate $1/2$ , $B{=}8$ , $T_{P}{=}32$ . Top row: baselines with perfect CSI; bottom row: baselines with estimated CSI. Black dashed and dash-dotted curves show MAP and pilot-aided MAP, respectively.

Panel of Figure 8 — Fig. 8: Extrinsic information quality at $B=8$ , $T_{P}=32$ , 16-QAM, $4\times 4$ . (a)–(b) EXIT charts comparing EXT-ICLNet against baselines with LS-estimated CSI, with the rate- $1/2$ and rate- $3/4$ decoder characteristics, respectively; the LDPC decoder characteristic is plotted with swapped axes. (c) EXIT curves at SNR $=$ 10 dB; inset zooms the high- $I_{A}$ region. (d) Post-decoding BER after the 5th turbo iteration vs. prior scale $\gamma$ at SNR $=$ 6 dB.

Panel of Figure 9 — Fig. 9: Turbo gain $10\log_{10}(\mathrm{BER}_{1}/\mathrm{BER}_{5})$ versus LDPC code rate (16-QAM, $4\times 4$ , $B=8$ , $T_{P}=32$ , $N_{c}=1024$ ). All baselines use estimated CSI.

Panel of Figure 10 — Fig. 10: Post-decoding BER versus SNR under the Kronecker correlated channel model with $\rho=0.5$ (16-QAM, $4\times 4$ , $B=8$ , $T_{P}=32$ , rate $1/2$ ). Baselines use estimated CSI.

Panel of Figure 11 — Fig. 11: EXT-ICLNet versus the number of distinct training channel realizations $N_{\text{train}}$ at SNR $=$ 10 dB (16-QAM, $4\times 4$ , $B=8$ , $T_{P}=32$ , rate- $1/2$ LDPC). (a) Post-decoding BER after the fifth turbo iteration, together with perfect-CSI baselines. (b) EXIT mutual information at the uniform ( $I_{A}=0$ ) and one-hot ( $I_{A}=1$ ) prior endpoints on a held-out probe set.

Detector	Complexity
BLMMSE-PIC	$\mathcal{O}\big(T(N^{4}+NM)\big)$
P-BEP	$\mathcal{O}\big(S_{\mathrm{EP}}T(N^{3}+NM)\big)$
OAMP-Net2	$\mathcal{O}\big(N_{\mathrm{iter}}T(N^{3}+NM)\big)$
EXT-GEPNet	$\mathcal{O}\big(T_{G}T(N^{3}+L_{G}N^{2}N_{h}^{2}+NM)\big)$
STS-SD	$\mathcal{O}\big(T(\bar{\nu}N+NM)\big)$ , $\bar{\nu}\leq M^{N}$
MAP	$\mathcal{O}\big(TM^{N}N\big)$

TABLE I: Computational complexity per turbo iteration, with

N\coloneqq\max(N_{t},N_{r})

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Wireless communications studies how information is sent over radio links and how networks manage signals, spectrum, and resources reliably.

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