FlowSep-RF: Rectified Flow Matching for Single-Channel Radio-Frequency Signal Separation

We study a problem of signal separation: estimating a signal of interest (SOI) contaminated by an unknown non-Gaussian background/interference. Given the training data consisting of examples of SOI and interference, we show how to build a fully data-driven signal separator. To that end we learn a good discrete tokenizer for SOI and then train an end-to-end transformer on a cross-entropy loss. Training with a cross-entropy shows substantial improvements over the conventional mean-squared error (MSE). Our tokenizer is a modification of Google's SoundStream, which incorporates additional transformer layers and switches from VQVAE to finite-scalar quantization (FSQ). Across real and synthetic mixtures from the MIT RF Challenge dataset, our method achieves competitive performance, including a 122x reduction in bit-error rate (BER) over prior state-of-the-art techniques for separating a QPSK signal from 5G interference. The learned representation adapts to the interference type without side information and shows zero-shot generalization to unseen mixtures at inference time, underscoring its potential beyond RF. Although we instantiate our approach on radio-frequency mixtures, we expect the same architecture to apply to gravitational-wave data (e.g., LIGO strain) and other scientific sensing problems that require data-driven modeling of background and noise.

The goal of single-channel source separation is to reconstruct $K$ sources given their mixture. In supervised settings where vast amounts of clean source data are available, this challenging, ill-posed problem has been addressed successfully by generative diffusion and flow-based prior models. However, access to such clean source samples is often limited, and even when available, supervised models are vulnerable to domain shifts. To bridge this gap, we present Separation via Unsupervised Remixing Flow (SURF), an unsupervised flow matching approach for source separation that learns directly from observed mixtures. This method relies on a novel combination of state-of-the-art supervised flow matching and regression-based self-supervised techniques. At a high level, starting from a teacher model, we utilize a "remixing" step to bootstrap the learning of a student flow model from the teacher's estimates. We provide insights into the objectives optimized by this approach and draw a novel connection to the Wake-Sleep algorithm. Empirical evaluations on image and audio benchmarks demonstrate that SURF establishes a new state-of-the-art, significantly outperforming existing unsupervised methods. See our demo page for examples. https://google.github.io/df-conformer/surf/

In multiple-input multiple-output (MIMO) semantic communication, imperfect channel state information (CSI) and equalization mismatch can seriously degrade semantic reconstruction quality. To address this issue, we propose a unified restoration flow matching (RFM)-based framework for channel refinement and equalization correction. Specifically, the channel RFM (CRFM) module is developed to refine the coarse channel, thereby improving channel estimation accuracy. Based on the refined channel, the developed semantic RFM (SRFM) module is employed to correct the residual distortions in the post-equalization latent space. The key idea is to formulate the two cascaded inverse problems of channel estimation and equalization as the unified conditional restoration task, in which the learned conditional velocity field guides the perturbed distribution towards the target distribution. To enhance the robustness of these two modules under various distortion conditions, we develop a dual-anchor perturbation training strategy that jointly learns near-manifold refinement and large-error correction, and implement inference through a few-step deterministic ordinary differential equation (ODE) solver. Extensive experiments on MIMO channels and visual semantic transmission tasks demonstrate that the proposed scheme improves key metrics for channel estimation and semantic reconstruction quality. Moreover, compared with representative diffusion-based generative baselines, the proposed method requires fewer sampling steps.