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.
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 4×4 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
Fig. 1: Block diagram of coded MIMO transmission with a quantized front end.
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.
Fig. 3: EXT-ICLNet architecture: (a) the prompt Pi and the per-stream posterior estimates q^i(n) ; (b) the shared Transformer backbone, stream-specific output heads, and log-domain prior skip.
Fig. 4: Training data generation. For each training prompt, the task τ and the prior PMFs pt are sampled independently. The symbols xt are drawn from the priors, the received signals yt are generated under the sampled task, and the resulting query-label pairs form the training sequence Ptrain .
Fig. 5: Training and inference pipelines. Gray lines indicate the attention connections permitted by the corresponding attention mask.
Fig. 6: Post-decoding BER at SNR = 10 dB under 16-QAM, one-shot detection: (a) impact of quantization resolution B at TP=32 with all baselines using perfect CSI; (b) impact of pilot length TP at B=8 , with baselines using LS-estimated CSI (solid) and perfect CSI (dashed).
Fig. 7: Post-decoding BER vs. SNR under 16-QAM, rate 1/2 , B=8 , TP=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.
Fig. 8: Extrinsic information quality at B=8 , TP=32 , 16-QAM, 4×4 . (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- IA region. (d) Post-decoding BER after the 5th turbo iteration vs. prior scale γ at SNR = 6 dB.
Fig. 9: Turbo gain 10log10(BER1/BER5) versus LDPC code rate (16-QAM, 4×4 , B=8 , TP=32 , Nc=1024 ). All baselines use estimated CSI.
Fig. 10: Post-decoding BER versus SNR under the Kronecker correlated channel model with ρ=0.5 (16-QAM, 4×4 , B=8 , TP=32 , rate 1/2 ). Baselines use estimated CSI.
Fig. 11: EXT-ICLNet versus the number of distinct training channel realizations Ntrain at SNR = 10 dB (16-QAM, 4×4 , B=8 , TP=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 ( IA=0 ) and one-hot ( IA=1 ) prior endpoints on a held-out probe set.
Detector
Complexity
BLMMSE-PIC
O(T(N4+NM))
P-BEP
O(SEPT(N3+NM))
OAMP-Net2
O(NiterT(N3+NM))
EXT-GEPNet
O(TGT(N3+LGN2Nh2+NM))
STS-SD
O(T(νˉN+NM)) , νˉ≤MN
MAP
O(TMNN)
TABLE I: Computational complexity per turbo iteration, with N:=max(Nt,Nr) .
We develop an enhanced in-context learning (ICL) framework to improve the performance of pilot-based beamforming in multi-user multiple-input single-output (MU-MISO) systems. The proposed scheme integrates the ICL-Transformer backbone with the pilot encoder-decoder network (EDN) and the beamformer EDN. A crucial feature of our ICL network is that it can handle multiple channel models without retraining, enabled by the construction of model-specific context datasets. To improve convergence and robustness, we introduce three key innovations: (a) a curriculum learning (CL) strategy that smoothly transitions from supervised LMMSE-labeled imitation to unsupervised sum-rate maximization, (b) a self-evolving mechanism that dynamically expands and refines the context datasets for all channel models during CL-based training, and (c) a mismatch-aware extension that incorporates several mismatches into the general ICL framework and bypasses explicit channel calibrations. Ablation studies validate the effectiveness of the in-context architecture and enhanced training strategies. Simulation results over diverse communication environments show that the proposed scheme is able to rapidly adapt to both seen and unseen channel models without gradient-based parameter updates, and can mitigate the mismatch issues via intelligent context constructions. Furthermore, our scheme consistently outperforms the existing beamforming schemes under pilot-based settings, including the WMMSE benchmark and the recent Transformer-based methods.
Yubo Zhang, Xiaodong Wang
Department of Electrical Engineering, Columbia University, New York, NY 10027
High-order multiple-input multiple-output (MIMO) detection requires efficient search over a large discrete symbol space while producing reliable soft information for channel decoding. This paper develops a learning-to-transition (L2T) framework that formulates MIMO detection as a stochastic sequence of complete-vector transitions. At each transition, a channel-coupled Transformer updates both the instance embedding and the sampling policy, while a blockwise autoregressive factorization captures inter-stream dependence with moderate sequential complexity. For hard-output detection, a transition network is applied recursively and trained through a residual-to-BER curriculum, which first learns the MIMO search geometry from the exact residual metric and then aligns the policy with transmitted-bit accuracy. For soft-output reception, the well-trained hard policy is cloned at the parameter level into every layer of an untied soft-input soft-output iterative detection and decoding (IDD) receiver. This tied-to-untied transfer preserves the learned zero-prior search dynamics while enabling layer- and round-specific specialization under decoder feedback. Within each IDD round, decoder priors tilt candidate generation according to Bayes' rule, and likelihood-weighted terminal hypotheses produce posterior and extrinsic log-likelihood ratios for LDPC decoding. A multi-stage training strategy further stabilizes the hard-to-soft transfer by progressively exposing the receiver to synthetic and in-loop decoder-generated priors.
Learning-based MIMO detection has shown strong empirical performance, yet existing methods typically rely on fixed-depth architectures without explicitly modeling the progressive refinement of symbol estimates. In this paper, we revisit MIMO detection from a flow matching perspective and propose the Soft Graph Diffusion Transformer (SGDiT), which reformulates detection as a noise-level-conditioned denoising process that progressively transforms a Gaussian initialization toward the posterior conditioned on channel observations. An adaptive layer normalization (AdaLN)-conditioned soft graph transformer is employed to parameterize the denoising dynamics, enabling stage-aware information integration between observation and symbol domains. To better align with the discrete nature of symbol detection, we further adopt a cross-entropy-based training objective that directly models bit-wise posterior probabilities, providing a more suitable inductive bias than conventional regression-based formulations. Experimental results across various MIMO system configurations demonstrate that SGDiT achieves competitive bit error rate (BER) performance compared with representative baselines. Furthermore, the proposed model exhibits good generalization capability across different channel conditions. Overall, the SGDiT framework provides an effective and practical approach for neural MIMO detection.
Nan Jiang, Jiadong Hong, Lei Liu +3
College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China · Theory Lab, Central Research Institute, 2012 Labs, Huawei Technologies Co., Ltd., Hong Kong, China