Fast Geometric Learning of MIMO Signal Detection over Grassmannian Manifolds

TL;DR

The paper tackles rapid domain shifts in dynamic MIMO channels by learning on Grassmannian subspaces and using a geodesic flow kernel (GFK) to integrate over intermediate subspaces between training and unseen test domains. The GFK is computed in closed form using principal angles between subspaces and is employed within a geometric SVM (G-SVM) for unsupervised symbol detection, enabling robust detection with only about $1{,}200$ labeled training samples and no online retraining. The approach yields competitive symbol error rates against baselines like OAMPNet, MMNet, and HyperMIMO, while avoiding large training datasets and online fine-tuning. Practically, it offers a geometry-aware, data-efficient solution for mobility-rich wireless networks, reducing adaptation delay and computational burden in dynamic environments.

Abstract

Domain or statistical distribution shifts are a key staple of the wireless communication channel, because of the dynamics of the environment. Deep learning (DL) models for detecting multiple-input multiple-output (MIMO) signals in dynamic communication require large training samples (in the order of hundreds of thousands to millions) and online retraining to adapt to domain shift. Some dynamic networks, such as vehicular networks, cannot tolerate the waiting time associated with gathering a large number of training samples or online fine-tuning which incurs significant end-to-end delay. In this paper, a novel classification technique based on the concept of geodesic flow kernel (GFK) is proposed for MIMO signal detection. In particular, received MIMO signals are first represented as points on Grassmannian manifolds by formulating basis of subspaces spanned by the rows vectors of the received signal. Then, the domain shift is modeled using a geodesic flow kernel integrating the subspaces that lie on the geodesic to characterize changes in geometric and statistical properties of the received signals. The kernel derives low-dimensional representations of the received signals over the Grassman manifolds that are invariant to domain shift and is used in a geometric support vector machine (G-SVM) algorithm for MIMO signal detection in an unsupervised manner. Simulation results reveal that the proposed method achieves promising performance against the existing baselines like OAMPnet and MMNet with only 1,200 training samples and without online retraining.

Figures (4)

• Figure 1: An example of the transformation of coordinate system through the representation of data on Grassmannian manifolds. Here, $[b_1,b_2]$ is the basis of $\Omega_{\boldsymbol{X}}$, $r_1, r_2$ are the row vector of $\boldsymbol{X}$. $\boldsymbol{U}_{\boldsymbol{X}}=[u_{i,j}]$ where $u_{i,j}$ is the length of the component of $r_i$ in the direction of $b_j$.
• Figure 2: The training overhead for obtaining CSI and online training versus node velocities for the target SER of ${10}^{-3}$.
• Figure 3: Average SER performance for different Doppler shift with the average transmit SNR equal to 15 dB.
• Figure 4: Average SER performance for different average transmit SNR with the normalized Doppler shift fixed at $6\times {10}^{-3}$.