💻 computer science

A Lightweight Complex-Valued CNN with Complex Squeeze-and-Excitation Attention for Single-Channel Blind Source Separation of Co-Frequency Communication Signals

This paper proposes a lightweight, 235K-parameter complex-valued CNN with a novel Complex Squeeze-and-Excitation block that achieves competitive single-channel blind source separation performance for co-frequency communication signals while significantly reducing model size and preserving phase information.

Original authors: Bin Nong, Weihong Fu, Zhuoyun Jiang

Published 2026-10-22

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Bin Nong, Weihong Fu, Zhuoyun Jiang

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the invisible air around us, radio waves carry our conversations, data, and commands. Often, these signals travel on the same frequency, overlapping like voices in a crowded room. For decades, engineers have struggled to untangle these mixed signals when they can only listen through a single antenna. This is a particularly stubborn puzzle because the signals are not just random noise; they are structured messages encoded with specific patterns, and when they arrive at nearly the exact same pitch, traditional methods of sorting them out often fail. The challenge is to take this single, jumbled stream of information and separate it back into its original, distinct sources without knowing what those sources sounded like to begin with.

A team of researchers has approached this problem by teaching a computer to listen to the signals in a new way. Instead of treating the radio waves as simple up-and-down lines, they designed a system that understands the signals as complex pairs of values, capturing both the timing and the phase of the wave. They built a compact, efficient neural network—a type of artificial intelligence that learns by example—to perform this separation. The key innovation in their design is a mechanism that acts like a smart volume knob for different parts of the signal. This "attention" block looks at the entire mixture, decides which parts of the signal are important, and amplifies them while keeping the delicate timing relationships intact. The result is a system that is remarkably small, requiring only a fraction of the computing power usually needed for such tasks, yet it manages to separate the signals with a level of clarity that rivals much larger, more complex systems.

The researchers tested their creation on a difficult scenario where two communication signals overlap almost perfectly, differing by only a tiny fraction of a hertz. They simulated mixtures of four different types of digital signals, ranging from simple to highly complex, and fed them into their model. The system, which contains roughly 235,000 adjustable settings, successfully untangled the signals in most attempts. When measured by how well the original message could be recovered, the new model achieved a score of about 2.31 decibels. While this might sound like a small number, it is a significant achievement for a system of this size. It performed nearly as well as a much larger, more established model that uses over three times as many settings, and it was far more consistent than other smaller models that tended to give up and output silence when faced with the difficult mixtures.

One of the most striking findings was how the system behaved when the signals were almost identical. In many cases, similar systems fail completely, collapsing into a state where they produce nothing but noise. The new design, however, proved more resilient. By using a specific method to weigh the importance of different signal features, it avoided this failure mode in most of its training runs. The researchers also discovered that the system could generalize well; even when they trained it on signals with very small frequency differences, it could still separate signals that were slightly further apart, and it even held its own when tested on signals that were exactly the same frequency, a scenario it had never seen during training.

The study also addressed a common question in this field: does the system need to treat the signal's real and imaginary parts as separate entities, or can it handle them together? The researchers tested different ways of combining these parts and found that the simplest approach—using a single real-valued weight to adjust the signal strength—was just as effective as more complicated methods. This suggests that for this specific task, the most important factor is knowing how loud a signal should be, rather than trying to rotate its phase in complex ways. The system achieved this performance while running quickly on standard hardware, making it a viable candidate for use in portable devices or software-defined radios where space and power are limited.

Ultimately, the work demonstrates that a small, carefully designed neural network can solve a problem that usually requires massive computational resources. The researchers did not claim to have solved the problem perfectly for every possible situation, nor did they suggest their method is statistically superior in every single test. Instead, they showed that a lightweight, phase-preserving approach offers a practical and efficient path forward. By keeping the system small and focused, they created a tool that is robust enough to handle the messy reality of overlapping radio signals, proving that sometimes the most effective solution is not the biggest one, but the one that listens most carefully.

Problem Definition

The paper addresses Single-Channel Blind Source Separation (SC-BSS) for co-frequency communication signals. This is an ill-posed problem where multiple unknown source signals, overlapping at nearly identical carrier frequencies, must be recovered from a single observed mixture.

Context: Applications include spectrum surveillance, cognitive radio, electronic warfare, and Non-Orthogonal Multiple Access (NOMA).
Challenges: Unlike speech separation, communication signals are complex-valued (I/Q representations), structured (finite modulation alphabets), and often share the same spectral band, rendering classical time-frequency masking or Independent Component Analysis (ICA) ineffective.
Gap: Existing deep learning approaches either treat I/Q as independent real channels (losing phase coupling) or apply complex-agnostic attention mechanisms that fail to exploit real-imaginary correlations. There is a lack of lightweight, complex-native attention mechanisms specifically designed for this domain.

Methodology

1. Signal Model

The system models a received baseband mixture $y(t)$ containing two sources $s_1$ and $s_2$ with random amplitudes, multipath fading (3-tap complex Gaussian), and additive white Gaussian noise (AWGN). The sources use standard modulations (BPSK, QPSK, 8PSK, 16QAM) with carrier frequency offsets $\Delta f$ within $\pm 5$ Hz of a reference. The task is to estimate $\hat{s}_1$ and $\hat{s}_2$ given only $y$ .

2. Proposed Architecture: ComplexLightweightSepNet

The authors propose a lightweight encoder-decoder network with 235,525 parameters, designed to run on resource-constrained edge devices (e.g., 8 GB GPUs).

Complex-Valued Building Blocks: The network uses complex convolutions, ComplexBatchNorm (split real/imaginary), and ComplexReLU/PReLU. These preserve the algebraic structure of complex numbers ( $C \cong R^2$ ) without the overhead of true complex whitening.
Core Innovation: Complex Squeeze-and-Excitation (C-SE) Block:
- Squeeze: Performs global average pooling separately on the real and imaginary parts of each complex channel, concatenating them into a descriptor vector $z \in R^{2C}$ .
- Excitation: Passes $z$ through a shared Multi-Layer Perceptron (MLP) with a reduction ratio ( $r=4$ ) and sigmoid gating to produce a weight vector $s \in R^{2C}$ .
- Scale: The output is split into real and imaginary halves, averaged to form a single real-valued weight $w \in R^C$ per channel. This weight scales the magnitude of the complex feature map while preserving its phase.
- Rationale: This design allows the network to learn channel importance based on I/Q correlations while maintaining the phase information critical for demodulation.

3. Training

The model is trained end-to-end using a combined loss function: $L = 0.5 L_{MSE} + 0.5 L_{SI-SDR}$ . It is optimized with Adam and cosine annealing over 25 epochs on synthetic data.

Key Contributions

C-SE Block: A novel channel-attention mechanism native to complex-valued feature maps that jointly pools real/imaginary statistics and applies a real-valued scaling factor to preserve phase.
Lightweight Architecture: A 235K-parameter model (ComplexLightweightSepNet) that is roughly 3.5 $\times$ smaller than a comparable Complex Conv-TasNet, enabling deployment on edge devices.
Comprehensive Evaluation: Experiments across four modulation types, multiple baselines, and rigorous statistical analysis (5 random seeds) to assess performance, stability, and parameter efficiency.

Experimental Results

Performance Metrics

Evaluated at 10 dB SNR on 5 Hz co-frequency mixtures:

Proposed C-SE: Achieves a mean SDR of 2.31 dB (std 0.62 dB) across 5 seeds.
Baselines:
- Complex Conv-TasNet (817K params): 3.23 dB SDR (3 seeds).
- CNSE (scaled, 6.69M params): 2.38 dB SDR (3 seeds, high variance).
- S4-UNET (scaled, 1.57M params): 3.05 dB SDR (3 seeds, highly stable).
- Parameter-Matched No-SE (242K params): 1.81 dB SDR.
- Parameter-Matched Real-Valued CNN (237K params): 2.20 dB SDR.

Key Findings

Collapse Resistance: The C-SE block significantly reduces the "output collapse" failure mode (where the network suppresses all output). In parameter-matched tests, the No-SE baseline collapsed in 4/5 seeds, whereas C-SE collapsed in only 2/5 seeds.
Modulation Robustness: The performance gap between C-SE and Conv-TasNet narrows as modulation complexity increases. For the hardest case (16QAM–16QAM), C-SE achieves 2.52 dB vs. Conv-TasNet's 2.69 dB.
Frequency Generalization: A model retrained on carrier gaps drawn from $U(0, 5)$ Hz generalizes to a flat SDR of $\approx 3.3$ dB across the entire $[0, 500]$ Hz range, including the unseen co-frequency limit ( $\Delta f = 0$ Hz).
Ablation Studies:
- Scale Mode: The proposed real-valued scaling mode performs nearly identically to complex-mean or separate scaling modes, suggesting magnitude scaling is the primary driver of performance in this setting.
- Pooling: Simple mean pooling is sufficient; combining mean and power statistics causes instability.
- Length: The model generalizes well to signal lengths half and double the training length (2048 and 8192 samples) without retraining.

Significance and Claims

The paper adopts a modest and rigorous stance regarding its claims:

No Statistical Superiority: The authors explicitly state they do not claim statistical superiority or equivalence. Paired Wilcoxon signed-rank tests on common seeds yield p-values $> 0.05$ (e.g., $p=0.125$ vs. No-SE, $p=0.25$ vs. Conv-TasNet). The small sample size (5 seeds) makes it structurally impossible to reject the null hypothesis at $\alpha=0.05$ unless all differences align perfectly.
Value Proposition: The significance of C-SE lies in its operating point:
1. Partial Collapse-Resistance: It offers better stability than parameter-matched complex CNNs without attention.
2. Per-Parameter Efficiency: It delivers performance comparable to real-valued baselines and within $\sim 1$ dB of larger complex baselines (like S4-UNET) at a fraction of the parameter cost (235K vs. 1.57M+).
3. Predictable Runtime: It is suitable for edge deployment where memory and compute are constrained.

The authors conclude that phase-preserving complex attention at the 235K-parameter scale is a viable design point for communication-signal BSS, offering a balance between efficiency, stability, and performance, while acknowledging that further research is needed to relax symbol-alignment assumptions and validate on over-the-air data.