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Selective Interference Suppression of Siamese-Net in Heterogeneous Interference Channels
Arkadeep Sinha, Shubham Paul, R. Manivasakan, Nambi Seshadri, R. David Koilpillai
TL;DR
The paper studies whether Siamese-coupled short-block coding can handle heterogeneous interference without imposing uniform orthogonality. It models interference-weighted encoder coupling and finds selective suppression: dominant links become near-orthogonal while weak links retain coding structure, with corresponding BLER robustness.
Problem
The paper addresses whether learned multi-user codes can balance interference suppression and coding gain when only a few user pairs are strongly coupled.
Method
It analyzes Siamese-coupled short-block autoencoders with single-user decoding using gradient coupling and an interference-weighted frame-potential formulation.
Results
The learned codebooks become near-orthogonal for dominant interference links while weakly coupled pairs remain correlated, producing BLER robustness under unequal interference.
Takeaways & Limitations
Siamese training adapts codebook geometry to the interference topology rather than enforcing uniform separation across users.
Abstract
from arXiv · showhide
We study an end-to-end learnt short-block codes for a $N$-user real Gaussian interference channel with heterogeneous pairwise interference strengths, while keeping single-user decoding at every receiver. In this paper, we study the case wherein only a few dominant interferers exist and investigate whether Siamese-style coupled training can adapt selectively to encode (\& decode) to ensure optimal performance corresponding to best tradeoff between orthogonality and coding gain or it enforces unnecessary global orthogonality oblivious of the reality. Our work focuses on a 4-user unequal-interference configuration with one dominant pair $(1,2)$ (of strength $Λ$) and a weak pair (with weak background coupling ($λ$)), through which we demonstrate a selective interference suppression phenomenon where the learned codebooks become near-orthogonal primarily for the dominant pair, while weakly coupled pairs retain alignment needed for coding gain. We quantify this behaviour using latent-space cross-user similarity statistics (worst-case coherence measure, average similarity measure, etc) and connect these geometric signatures to the observed BLER robustness under unequal interference. It seems that the SiameseNet selectively suppresses the interferences from various interferring user pairs to yield optimal tradeoff between coding gain and BLER dictated by orthogonality.
I. INTRODUCTION
The paper asks whether Siamese-coupled training adapts to sparse heterogeneous interference or imposes unnecessary uniform orthogonality. It proposes selective suppression guided by interference topology and coding-gain trade-offs.
- Motivation: Dense interference-limited wireless systems motivate coding and signalling schemes beyond strict orthogonalization while retaining simple decoding.Advanced receivers such as SIC can be complex and mismatch-sensitive as user counts grow.
- Prior SiameseNet framework: SiameseNet jointly trains encoders to reduce own decoding errors and interference induced at other users, while decoders remain non-joint.Earlier work primarily studied structurally symmetric two-user channels.
- Research gap: Heterogeneous channels often contain a few strongly coupled pairs and many weakly coupled pairs, making uniform orthogonality potentially wasteful.Over-separating weak pairs can sacrifice coding gain without requiring strong mutual suppression.
- Contribution: Siamese-coupled training yields near-orthogonal codebooks for strong interferers while retaining correlation among weakly coupled pairs.This selective geometry is presented as an optimal coherence structure balancing suppression and coding gain.
- Contribution: The paper interprets this behavior through gradient coupling and an interference-weighted Grassmannian design perspective.Pairwise correlations are penalized according to interference strengths, linking learned coding to frame theory and code design.
II. SYSTEM MODEL AND TRAINING
The system uses one SiameseNet-driven encoder and single-user decoder per user over a real Gaussian interference channel. Encoders learn jointly through all users’ losses, whereas each decoder is trained independently.
- System model: Each of N users has its own encoder and decoder operating over a real interference channel with potentially asymmetric pairwise interference.The model is designed to study how asymmetric interference affects wireless-system performance.
- Encoding: Each message is encoded into a real codeword zi(Mi) ∈ R^n by an encoder parameterized by θi.The supplied model specifies short real codewords for the users.
- Interference model: Interference from user j to user i is represented by αij, with αij = αji unless stated otherwise.Homogeneous interference uses equal coefficients, whereas heterogeneous interference permits pair-dependent values.
- Decoding: Each receiver adds white noise and uses a single-user decoder Di to produce an estimate of Mi from yi.The decoding architecture avoids joint decoding across users.
- Training: SiameseNet minimizes the net cross-entropy loss using steepest descent, with joint encoder updates but independent decoder learning.Each user’s loss updates its own decoder and encoder, while also contributing to other users’ encoder updates.
A. Gradient Coupling and Interference-Weighted Repulsion
Selective suppression arises because each encoder receives its own loss gradient plus interference-scaled gradients from other users. Strong links therefore encourage separation, while weak links preserve alignment and coding gain.
- Gradient derivation: The analysis computes each codebook’s loss gradient through the received signal Jacobian and the chain rule.The Jacobian depends on the interference coefficients αij.
- Gradient Coupling: Other users’ loss gradients propagate back to encoder j scaled by their interference coefficients αij.Thus, the encoder update reflects both self-gradient and cross-user interference effects.
- Interference-Weighted Repulsion: When codewords overlap, cross-coupled gradients push them apart in Grassmannian space; otherwise, they retain alignment that supports coding gain.The mechanism links geometric separation directly to the interaction among users’ losses.
- Interference-Weighted Repulsion: Moderate-to-high αij drives near-orthogonal codebooks for strongly connected users, whereas small αij preserves coding-gain alignment.For αij ≈ 0, the cross-user gradient term vanishes and encoder j trains effectively on its own loss.
- Weighted Frame Potential: Proper Jacobian scaling makes gradient descent approximately minimize a Weighted Frame Potential whose pairwise penalties reflect interference strengths.This provides the mathematical objective underlying selective interference suppression.
B. Implicit Weighted Frame Potential (WFP) Objective Function
The paper interprets SiameseNet training as approximately minimizing a weighted frame potential, where interference strengths weight cross-user codeword correlations. This yields selective geometric separation: strong links are pushed toward near-orthogonality, while weak links can retain coding-gain-preserving alignment.
- Implicit WFP objective: The WFP is a weighted sum of squared cross-user coherences, with weights encoding the physical interference topology.The squared inner product |⟨z_i, z_j⟩|^2 is the codebook-dependent quantity linked to interference cost.
- Geometric consequence: The resulting design is not necessarily globally equiangular; it is selectively orthogonal according to the weighted interference structure.This connects Siamese multi-user coding to weighted Grassmannian design and classical frame-theoretic code design.
- Gradient mechanism: Gradient coupling makes each encoder update depend on its own loss and other users’ losses, producing cross-user codeword interactions.The encoder codeword z_j leaks into other users’ cross-entropy losses, so interference-dependent gradients jointly shape the codebooks.
- Optimization interpretation: At stationarity, encoder dynamics are consistent with minimizing the WFP subject to the power constraint ∥z_i∥^2 = n.The derivation retains cross-user inner products as the codebook-dependent terms in the expected summed loss.
- Topology-dependent weighting: Weights w_ij = α_ij^2 make stronger interference links exert greater pressure toward geometric separation.Moderate-to-high α_ij supports near-orthogonal codebooks for strongly connected users, whereas small α_ij permits alignment for coding gain.
C. Coherence Metrics
The paper quantifies selective interference suppression through pairwise codebook similarity and coherence statistics. These metrics distinguish dominant-link orthogonalization from retained correlation on weak links.
- Strong-link metric: β_strong is the worst-case cross-user coherence for the strongest interference link identified from the interference matrix.A small β_strong indicates that dominant interferers’ codebooks have been pushed close to orthogonality.
- Pairwise similarity: Pairwise cosine similarity ρ_mn is the inner product of normalized codewords and equals cos(θ_mn).The angle θ_mn therefore measures each pair’s deviation from orthogonality.
- Coherence statistics: Worst-case coherence μ is the maximum absolute pairwise similarity across distinct codewords.It corresponds to the largest cross-user correlation and is especially relevant to error floors.
- Angular interpretation: The worst-case angular deviation satisfies Δϕ_max = arcsin(μ), with μ ≈ Δϕ_max in the near-orthogonal regime.The approximation applies for small angular deviations measured in radians.
IV. RESULTS:
The results evaluate trained SiameseNet encoders and decoders in short-block heterogeneous interference settings, using topology diagrams and angular deviations between latent codewords.
- The trained model is evaluated by applying test data to optimized encoder and decoder parameters, then computing BLER from Eq. (5).
- Case 3 contains all links to node 1 strong, whereas Case 4 contains all links from node 1 strong.
- Table I reports minimum and maximum angular deviation from 90° orthogonality between user latent codewords across four heterogeneous topologies.
A. Unequal-Interferences
Across unequal-interference topologies, SiameseNet reduces correlation primarily for strongly coupled pairs while allowing weakly coupled pairs to retain coding structure and coding gain.
- k = 4 bits and n = 8 real symbols per user define the short-block setup, with rate r = 0.5 and evaluation over Eb/N0 from 0 to 8 dB.Training samples SNR uniformly over a range.
- Single-Dominant Pair of Interferer: 0.6 dB better than purely orthogonal TDMA is achieved by User 1 under strong interference, while User 4 gains 2.8 dB because only the dominant pair is orthogonalized.The strong pair is (1,2); weak pairs retain coding gain because orthogonalization constraints are not imposed on them.
- Single-Dominant Pair of Interferer: Strong pair (1, 2) exhibits markedly lower correlation than weak pairs (1, 3) and (1, 4) in Case 1.
- Single-Dominant Pair of Interferer: βstrong ≈ 0.01 and βweak ≈ 0.17 produce S ≈ 0.06 ≪ 1 when Λ = 1 and λ = 0.1.The learned representations reduce cross-user correlation predominantly for the strong pair, while weak pairs are not over-orthogonalised.
- Dominant-Neighbour and Multiple-Interferer Cases: User 1 is suppressed more strongly than other users when it participates in many strong interference links in Case 3.Case 4 probes the transition toward broader orthogonalisation when multiple users strongly interfere into receiver 1.
- Two-Dominant-Pairs of Interferers: Strong pair (3, 4) exhibits markedly lower correlation than weak pairs (3, 2) and (3, 1) in Case 2.
- Red-bordered strongly coupled pairs are the lightest cells in every case, while weakly coupled pairs retain coding structure.The shading encodes correlation: lighter cells indicate tighter near-orthogonality.
V. CONCLUSION
The paper concludes that Siamese-coupled training adapts codeword geometry to heterogeneous interference rather than enforcing uniform separation. This selective geometry is associated with coding gain for weakly coupled users and BLER robustness under unequal interference.
- Dominant interference links become near-orthogonal while weakly coupled pairs remain aligned, with residual coherence allocated to the weakest links.
- Receiver 3 orthogonalizes only with User 1 and not with other users in Case 3.
- Strong pairs (1, 2), (1, 3), and (1, 4) show markedly lower correlation in Case 4, indicating broader orthogonalisation.
- The learned representation adapts its geometry to the interference graph, offering a route to interference-aware coding that scales with interference sparsity rather than user count.