DeepSIC: Deep Soft Interference Cancellation for Multiuser MIMO Detection

I. INTRODUCTION

• Joint MAP detection, which recovers all symbols simultaneously, becomes infeasible as the number of symbols grows, whereas separate detection recovers each symbol individually, treats the rest as noise, and is strictly sub-optimal [4, Ch. 6].Source: §I · p. 2
• Model-based detectors require channel models and parameters, and their linear-Gaussian assumptions exclude channels that are unknown, complex, or unlike the assumed physical model.The introduction notes that many communication scenarios do not obey the linear-Gaussian model, limiting interference-cancellation methods.Source: §I · p. 2
• Even for known linear channels, CSI uncertainty can significantly degrade model-based detection, motivating model-agnostic data-driven methods.Previously proposed unfolded MIMO receivers assume linear channels with Gaussian noise and available or pilot-estimated CSI.Source: §I · pp. 2, 4
• Black-box DNN receivers can operate across channel setups when trained for them, but their many parameters require large training sets; unfolded networks encode algorithm iterations [31].Despite their interpretability and smaller parameter counts, previously proposed unfolded MIMO receivers remain tied to specific channel assumptions.Source: §I · p. 3
• ViterbiNet learns detection from small training sets, but its complexity grows rapidly with input cardinality, making it unsuitable in its current form for MIMO detection.This motivates integrating machine learning into an established detection algorithm for a data-driven, model-agnostic MIMO detector.Source: §I · p. 4
• DeepSIC replaces iterative soft interference cancellation building blocks with dedicated DNNs to learn MAP-comparable symbol detection from limited training data without a channel model.Its learned cancellation of interference is part of this data-driven implementation.Source: §I · p. 4

• DeepSIC can be trained end-to-end or sequentially by training subsets of its iterative-SIC blocks, with sequential training learning symbol detection from fewer samples.Source: §I · p. 5
• DeepSIC approaches model-based iterative SIC on standard linear Gaussian-noise MIMO, improves error-rate performance over prior data-driven receivers, and remains reliable when CSI uncertainty degrades SIC and MAP detection.Source: §I · p. 5
• On nonlinear channels, DeepSIC achieves MAP-comparable performance and substantially outperforms iterative SIC, whose additive-interference cancellation assumption does not apply.Source: §I · pp. 4–5
• Small-training-set capability can facilitate self-supervised online tracking of dynamic channels.Source: §I · p. 5
• The results support integrating machine-learning methods into model-based algorithms to realize efficient and robust communication systems.Source: §I · p. 5

A. System Model

• The receiver seeks to recover transmitted symbols from channel outputs using a learned mapping, without assuming a linear channel or known channel distribution.The setup assumes a stationary, memoryless channel and a training set of paired channel outputs and transmitted symbols.Source: A. System Model · pp. 6–7
• The MAP detector jointly searches M^K channel-input combinations, becoming infeasible as the number of users K grows.For binary constellations, the search space exceeds 10^6 inputs at K = 20.Source: A. System Model · pp. 6–7

B. Iterative Soft Interference Cancellation

• The reviewed SIC algorithm assumes a linear channel with known channel matrix and additive white Gaussian noise.Its soft-detection step approximates the canceled output's conditional distribution as Gaussian and refines estimates across iterations.Source: B. Iterative Soft Interference… · pp. 7–9
• Iterative SIC starts with symbol-distribution estimates and repeatedly performs interference cancellation and soft detection for each user.Each iteration uses estimated interference statistics to form a canceled output, then estimates conditional symbol probabilities; the final decision selects the most probable symbol.Source: B. Iterative Soft Interference… · pp. 7–9

C. Advantages and Challenges of Iterative SIC

• Iterative SIC replaces exhaustive joint search with computations whose complexity grows linearly with the number of users, and can approach MAP-detector performance.Sequential refinement and soft values mitigate error propagation.Source: C. Advantages and Challenges of… · p. 10
• With Q = 5 iterations, SIC can achieve substantial gains over separate detection with only a small additional detection delay.The passage reports this as a numerical observation from.Source: C. Advantages and Challenges of… · p. 10
• Iterative SIC is designed for linear channels because its interference-cancellation step requires additive interference contributions.The Gaussian approximation may also degrade performance when channels do not follow the linear Gaussian model.Source: C. Advantages and Challenges of… · pp. 10–11
• Even for linear channels, iterative SIC requires full, accurate CSI and its performance degrades heavily when CSI is erroneous.Obtaining the required channel matrix and noise variance may entail substantial overhead.Source: C. Advantages and Challenges of… · p. 11
• DeepSIC integrates machine learning into iterative SIC so it can operate in arbitrary memoryless stationary channels without a priori channel-model knowledge.The authors select iterative SIC for its MAP-comparable performance and structure that can be converted to a data-driven approach.Source: C. Advantages and Challenges of… · p. 11

A. Data-Driven Receiver Architecture

• DeepSIC replaces the channel-model-based conditional-distribution computations in iterative SIC with classification DNNs.The receiver retains the iterative SIC structure while using learned blocks to estimate conditional distributions.Source: A. Data-Driven Receiver Architecture · pp. 11–12
• Each DNN takes the channel output and prior interference-distribution estimates as inputs and outputs probabilities over the M possible constellation classes.The network is trained as a classifier, with softmax outputs estimating conditional probabilities.Source: A. Data-Driven Receiver Architecture · p. 12
• The initial conditional-distribution estimates are set to a uniform distribution.Source: A. Data-Driven Receiver Architecture · p. 12
• The authors state that properly trained classification DNNs can estimate conditional distributions in complex nonlinear setups without prior channel-model knowledge.They characterize DeepSIC as implementing iterative soft interference cancellation for arbitrary channel models in a data-driven fashion.Source: A. Data-Driven Receiver Architecture · pp. 12, 14

B. Training the DNNs

• End-to-end training jointly updates the parameters of all K·Q building-block DNNs, a large parameter set that may require many input-output pairs.The authors propose sequential training to address this expected sample demand.Source: B. Training the DNNs · p. 14
• Sequential training fits each DNN individually and uses outputs from previously trained iterations to generate the soft estimates needed as inputs.Those soft estimates are not supplied in the training set, so the blocks are trained in sequence.Source: B. Training the DNNs · p. 15
• Sequential training uses the same input-output pairs while reducing the number of parameters by a factor of K·Q.The authors expect this to require fewer training samples, at the cost of a longer learning procedure for a given training set.Source: B. Training the DNNs · p. 15
• Sequential training may degrade performance because the building blocks are not jointly trained, but simulations show a relatively minor gap from end-to-end training.Source: B. Training the DNNs · p. 15

C. Discussion

• For linear channels where iterative SIC applies, DeepSIC is expected to approach MAP-comparable performance, as observed numerically.The authors attribute this expectation to DeepSIC implementing an established detection algorithm rather than using arbitrary network layers.Source: C. Discussion · pp. 16–17
• DeepSIC’s inference complexity grows linearly with the number of users, making it applicable where conventional MAP detection is infeasible.The authors note that explicitly characterizing DeepSIC’s complexity is difficult because DNN complexity depends on parameter count and learning algorithm.Source: C. Discussion · p. 16
• Sequential training adapts only P parameters at a time and can learn iterative SIC from relatively few samples, supporting quick retraining in dynamic channels.The discussion connects small-data training with self-supervised online adaptation using communication-protocol structure.Source: C. Discussion · p. 16
• Unlike subtraction-based iterative SIC, DeepSIC learns interference cancellation without assuming additive interference, extending its use to non-linear channels.The discussion reports that iterative SIC can increase errors in non-linear channels and is highly sensitive to inaccurate CSI even in linear settings.Source: C. Discussion · p. 16
• DeepSIC learns the model-based computations of iterative SIC using dedicated DNN blocks, yielding an interpretable architecture with fewer parameters than black-box deep receivers.The authors say this can support training with smaller datasets and faster retraining in dynamic environments.Source: C. Discussion · p. 17
• Unlike unfolding-based receivers that assume a linear channel and typically require CSI, DeepSIC is channel-model independent and was evaluated from linear Gaussian to non-linear Poisson channels.The discussion relates DeepSIC’s component structure to mutual learning and plug-and-play methods, while distinguishing its origin and MIMO-detection target.Source: C. Discussion · p. 17

IV. NUMERICAL STUDY

• The study covers linear Gaussian channels, quantized Gaussian and Poisson channels, training-method comparisons, and block-fading channels.The sections compare DeepSIC with model-based and data-driven detectors where applicable.Source: §IV · p. 18
• DeepSIC is trained on 5,000 training samples and tested over 20,000 symbols; the small training set demonstrates its ability to train with a sample set on the order of a preamble sequence.Source: §IV · p. 18
• Sequential training adapts subsets of building blocks and can tune more parameters than end-to-end training on the same training set.End-to-end training jointly trains all blocks; the study uses different fully connected DNN structures for the two strategies.Source: §IV · p. 18
• End-to-end blocks use a compact one-hidden-layer network, while sequential-training blocks use three fully connected layers.Figure 5 depicts the two architectures used as DeepSIC building blocks.Source: §IV · p. 18, Figure 5 · p. 19

A. Linear Gaussian Channels

• The comparison evaluates SER versus SNR for 6 × 6 and 32 × 32 AWGN channels, including perfect-CSI and CSI-uncertain conditions.For DeepSIC and DetNet, perfect CSI uses training and test samples from the same channel; under uncertainty, training samples come from different channels.Source: A. Linear Gaussian Channels · pp. 19–20, Figure 6 · p. 20, Figure 7 · p. 21
• At SER 10^-3 in the 6 × 6 channel, MAP requires approximately 10 dB SNR, iterative SIC and E2E DeepSIC require 11 dB, and Seq. DeepSIC requires at least 12 dB.With perfect CSI, E2E DeepSIC approaches iterative SIC, which is within a small gap of optimal MAP performance.Source: A. Linear Gaussian Channels · pp. 20–21, Figure 6 · p. 20
• In the 32 × 32 channel, E2E DeepSIC also approaches iterative SIC, while sequential training trails end-to-end training by approximately 1.5 dB at SER 10^-3.The result indicates applicability in a setting where MAP-based joint detection is computationally infeasible.Source: A. Linear Gaussian Channels · p. 21, Figure 7 · p. 21
• With nt = 5000 training samples, DetNet has very poor SER; only with 100 times more samples does it reach SER within a small gap of Seq, trained with 1% of the training set.Source: A. Linear Gaussian Channels · p. 21
• Under CSI uncertainty, DeepSIC substantially outperforms iterative SIC and MAP receivers, and DetNet using noisy H even when trained with a hundred times more inaccurate training samples.Source: A. Linear Gaussian Channels · p. 22

B. Non-Linear Channels

• The non-linear evaluations use a 4 × 4 quantized Gaussian channel and a 4-user, 4-antenna Poisson channel with on-off keying.Figure 8 compares MAP and iterative SIC in the quantized Gaussian setup; Figure 9 compares them in the Poisson setup.Source: B. Non-Linear Channels · pp. 22–23, Figure 8 · p. 24, Figure 9 · p. 25
• With perfect CSI, DeepSIC effectively coincides with optimal MAP; under the same CSI uncertainty, it hardly degrades, unlike model-based receivers, whose error does not monotonically decrease with SNR.Source: B. Non-Linear Channels · p. 23
• In the Poisson channel, DeepSIC remains within a small gap of perfect-CSI MAP and is more robust to CSI uncertainty than model-based MAP.Sequentially trained DeepSIC outperforms end-to-end training in this non-Gaussian setting, where the authors conclude that more complex DNN models are required for accurate interference cancellation and soft detection.Source: B. Non-Linear Channels · p. 24
• Iterative SIC performs very poorly in the Poisson channel even with accurate H, so the study omits its CSI-uncertainty performance there.The authors describe this channel input-output relationship as substantially different from the linear Gaussian model for which iterative SIC was designed.Source: B. Non-Linear Channels · p. 24

C. Training Methods Comparison

• End-to-end DeepSIC often achieves improved performance over sequential DeepSIC despite using smaller networks.The authors attribute the difference to joint training producing improved configurations.Source: C. Training Methods Comparison · p. 25
• With 100 samples, sequential training operates reliably; end-to-end accuracy degrades as labels shrink, though end-to-end training can improve configurations with sufficient data.Sequential training adapts parameter subsets in sequence, whereas end-to-end training jointly adapts the complete architecture.Source: C. Training Methods Comparison · p. 26

D. Online Tracking of Channel Variations

• FEC-decoded messages are re-encoded and re-modulated to retrain DeepSIC online, allowing channel tracking without additional pilots or communication overhead.The decoder can recover messages even when symbol errors are present.Source: D. Online Tracking of Channel Variations · pp. 27–28
• Online self-supervised DeepSIC tracked channel variation with low per-codeword errors and zero errors across considered linear AWGN blocks, while nontracking receivers began erring around codeword ten.Nontracking includes DeepSIC without retraining and MAP detection using initial CSI.Source: D. Online Tracking of Channel Variations · p. 28
• Joint training across channel conditions reduced errors versus initial-CSI MAP and initial-channel DeepSIC, particularly for the Poisson channel.The paper identifies this pattern as potential robustness improvement.Source: D. Online Tracking of Channel Variations · p. 28

V. CONCLUSION

• DeepSIC replaces iterative SIC's model-based building blocks with dedicated DNNs, producing a channel-model-independent receiver.The paper describes iterative SIC as computationally feasible and naturally extendable to machine-learning methods.Source: §V · pp. 28, 30
• Sequential training is more suitable for small training sets and supports rapid adaptation in dynamic environments.The conclusion contrasts it with end-to-end training.Source: §V · p. 30
• For conventional linear channels, DeepSIC approaches MAP performance, outperforms previously proposed DNN-based receivers, and improves robustness to CSI uncertainty.These conclusions are reported for the evaluated settings.Source: §V · p. 30
• DeepSIC's comparable performance and resilience to uncertainty extend to nonlinear channels, where iterative SIC and previously proposed machine-learning receivers have limited applicability.Source: §V · p. 30